Exponentiell Gewichtet Gleitender Durchschnitt Filter C Code

OxMetrics-Referenzteil: 1 OxMetrics-Referenzhandbuch Kapitel 10 OxMetrics-Statistik OxMetrics bietet viele praktische grafische Optionen für die vorherige Datenanalyse. Der Einfachheit halber bezeichnen wir die ausgewählte Variable mit xt. T1. T. In diesem Kapitel werden die zugrundeliegenden Formeln zusammengefasst. 10.1 Tatsächliche Serien - und Streudiagramme Die aktuelle Reihe gibt für jede ausgewählte Variable einen Graphen, der die Variable über die Zeit zeigt. Die Option Alle Streudiagramme gibt Streudiagramme zwischen allen ausgewählten Variablen (ohne redundante Streudiagramme). 10.2 Durchschnittliche Standardabweichung und Varianz Diese sind für die nachfolgend beschriebenen Statistiken relevant. Für eine Folge xt. T. T: Hier ist x 0 1T-j sum tj1 T x t der Stichprobenmittelwert von x t. Tj1. T und x j 1T-j Summe tj1 T x t-j ist der Stichprobenmittelwert von x t-j. So daß r x302 j einem korrekten Korrelationskoeffizienten entspricht. Man beachte den Unterschied zur Definition der Stichprobenautokorrelationen j in (eq: 10.4) oben. Dieser Unterschied ist tendenziell klein und verschwindet asymptotisch, wenn die Reihe stationär ist. Aber, wie in Nielsen (2006). Bietet das Korrelogramm eine bessere Unterscheidung zwischen stationären und nicht-stationären Variablen: Bei einem autoregressiven Wert von einem (oder höher) sinkt das Korrelogramm langsamer als das ACF. Wenn das Korrelogramm zum Plotten ausgewählt wird, basiert die PACF nicht auf dem ACF, sondern auf den Korrekturwerten. Die Handhabung der fehlenden Werte ist die gleiche wie beim ACF. 10.6 Kreuzkorrelationsfunktion (CCF) Die Beispiel-Kreuzkorrelationsfunktion (CCF) zeigt die Korrelation zwischen einer Reihe x t und den Verzögerungen einer anderen Reihe y t. Unter Verwendung der Vollprobe bedeutet x und y. Der CCF zwischen x t und y t unterscheidet sich von dem zwischen y t und x t. R x302 xy j ne r x302 yx j. Beide sind in demselben Graphen aufgetragen. 10.7 Periodogramm Das Periodogramm ist definiert als: für omega 0, 2piT, 4piT. (Int (T2) 2pi) T. Wenn das Periodogramm aufgetragen wird, werden nur Frequenzen größer als null und bis zu pi verwendet. Darüber hinaus ist die x-Achse mit den Werten 0. pi als 0 dargestellt. 1. Wenn T4 die x-Koordinaten 0,5,1 sind, die pi2, pi entsprechen. Wenn T5, sind die x-Koordinaten 0.4,0.8 entsprechend 2pi5, 4pi5. Allerdings, wenn das Periodogramm mit dem Algebra-Funktion Periodogramm ausgewertet wird. Sie wird bei allen Frequenzen bis zu 2pi ausgewertet, was zu T Periodogrammwerten führt. Für T4 werden diese mit 0, pi2, pi, 3pi2 ausgewertet. Für T5: 0, 2pi5, 4pi5, 6pi5, 8pi5. Die Frequenzen werden im letzten Argument des Periodogramms zurückgegeben. 10.8 Spektraldichte Die geschätzte Spektraldichte ist eine geglättete Funktion der Probenautokorrelationen j, definiert wie in (Gl. 10.4). Die Probenspektraldichte ist dann definiert als: wobei. Nimmt den Absolutwert an, so dass z. B. r x302 -1 r x302 1. Die Funktion K (.) Wird als Verzögerungsfenster bezeichnet. OxMetrics verwendet das Parzen-Fenster: 1-6 (jm) 2 6 jm 3. Wir haben K (-j) K (j), so dass das Vorzeichen von j keine Rolle spielt (cos (x) cos (-x)) . Die r x302 j s basieren auf weniger Beobachtungen, wenn j zunimmt. Die Fensterfunktion fügt abnehmende Gewichte zu den Autokorrelationen bei Nullgewicht für jgtm hinzu. Der Parameter m wird als Verzögerungskorrekturparameter bezeichnet. In OxMetrics gilt dies als die gewählte Länge des Korrelogramms. Wenn Sie z. B. s12 (die Länge mit der Länge im Dialog) auswählen, ergibt sich m12. Je größer m, desto weniger Glatt wird das Spektrum, aber je niedriger die Vorspannung. Das Spektrum wird bei 128 Punkten zwischen 0 und pi ausgewertet. Für weitere Informationen siehe Priestley (1981) und Granger und Newbold (1986). 10.9 Histogramm, geschätzte Dichte und Verteilung Gegeben sei ein Datensatz t (x 1. x T), der Beobachtungen einer Zufallsvariablen X ist. Der Bereich von t wird in N Intervalle der Länge h mit h definiert, die unten definiert sind. Dann stellt der Anteil von x t in jedem Intervall das Histogramm dar, wobei die Summe der Proportionen einheitlich auf der Skalierung in OxMetrics ist. Die Dichte kann als eine geglättete Funktion des Histogramms unter Verwendung eines normalen oder Gaußschen Kerns geschätzt werden. Dies kann dann summiert (integriert) werden, um die geschätzte kumulative Verteilungsfunktion (CDF) zu erhalten. Bezeichnet die tatsächliche Dichte von X bei x durch f x (x). Eine nichtparametrische Schätzung der Dichte wird aus der Probe erhalten durch: wobei h die Fensterbreite oder der Glättungsparameter ist und K (.) Ein Kern ist, so daß: als Standardwert die Standardnormaldichte für K (. ). Die Standardfensterbreite wird verwendet, wenn die Dialogoption auf Standardleisten gesetzt ist. Alternativ ist es möglich, direkt die Anzahl von Stäben auszuwählen, wobei in diesem Fall die Dichteabschätzung umso weniger gleich ist, je mehr Stäbe. Das Histogramm verwendet das gesamte Sample und überspringt fehlende Werte. F x (x) x302 wird üblicherweise für 128 Werte von x berechnet, aber da die direkte Auswertung in der Computerzeit etwas teuer sein kann, wird eine schnelle Fourier-Transformation verwendet (wir sind Dr. Silverman für die Berechtigung zur Verwendung seines Algorithmus dankbar). Das geschätzte CDF von X kann von f x (x) x302 abgeleitet werden, was mit einem normalen normalen CDF zum Vergleich gezeigt ist. Ein hervorragender Hinweis auf die Dichtefunktionsschätzung ist Silverman (1986). 10.10 Regressionslinien und Glättungen Mit der Option Streudiagramme können verschiedene Arten von Regressionslinien gezeichnet werden. Eine einzelne Regressionslinie zeichnet die eingefügten Werte aus den OLS-Schätzungen alphax302 und betax302 unter der Annahme, dass y t und x t die ausgewählten Variablen sind. Die Unterscheidung zwischen sequentiellen und rekursiven Regressionsgeraden lässt sich leicht anhand von drei Zeilen erklären. Teilen Sie die Probe in drei Teile: 1. T3, T31. 2T3 und 2T31. T, dann: was in einem gewissen Sinne optimal ist. Die optimale Bandbreite, die der für die nichtparametrische Dichteabschätzung gewählten Standard entspricht, lautet: Die Funktion yx302 h (.) Wird mit 128 Punkten berechnet. Als hrarr0, yx302 h (.) Rarr y. Das Stichprobenmittel ist der passende Wert für jedes x. Auf der anderen Seite, wenn hrarrinfin das Intervall auf Null geht, und wir passen den nächsten entsprechenden y-Wert, so dass jeder Datenpunkt genau aufgenommen wird. Man beachte jedoch, daß die yx302 (.) - Funktion an den T-Datenpunkten xt (die Zeit in Abwesenheit von x) ausgewertet wird. Hax308rdle (1990) ist ein allgemeiner Hinweis auf die nichtparametrische Regression. Es gibt drei Möglichkeiten, die Bandbreite zu bestimmen: Anzahl der Parameter Hier wird die äquivalente Anzahl von Parametern angegeben (ungefähr vergleichbar mit der Anzahl der bei einer linearen Regression verwendeten Regressoren). Die Standardeinstellung ist Setzt die Bandbreite direkt. Wählt die Bandbreite durch verallgemeinerte Kreuzvalidierung (GCV). Wir finden, dass die Wahl Bandbreite mit GCV oder Cross-Validierung (CV) tendenziell untermooth. Die Gleichung (eq: 10.14) unten zeigt an, wie GCV berechnet wird. Der Kernel glatt ist nicht mit einer Fourier-Transformation berechnet, sondern direkt, so kann für große T langsam sein. Die glatte wird über die gesamte Probe überspringen über fehlende Werte innerhalb der Probe, die durch die Passung von den glatten geschätzt werden. Ein Nachteil dieser glatten ist, dass für Trending-Linien, es verhält sich intuitiv an den Rändern. Betrachten wir z. B. die linke Kante der Kernel-Glättung einer Variablen, die nach oben tendiert. Da die Glattheit als ein gleitender Durchschnitt von Punkten beginnt, die nur nach rechts und damit hauptsächlich höher sind, hat die linke Kante eine J-Form, die über dem, was mit dem Auge angebracht wäre, beginnt. 10.10.2 Spline glatt Eine Spline ist eine weitere Methode zur Glättung eines Streudiagramms. Man betrachte eine Darstellung von yt. Gegen x t. Und sortieren Sie die Daten nach x: altx 1 lt. Ltx T ltb. In einem Spline-Modell wird die Summe der quadratischen Abweichungen von einer Funktion g minimiert, vorbehaltlich einer Rauhigkeitsstrafe: OxMetrics verwendet einen natürlichen kubischen Spline. Die kubisch ist, weil die Funktion g als Polynom dritten Grades gewählt wird und natürlich, weil die Glattheit eine Gerade zwischen a und x 1 und zwischen x T und b ist. Dadurch wird das Endpunktproblem des Kernel-Glattes des vorherigen Abschnitts vermieden. Zwei gute Referenzen auf Splines und nichtparametrische Regression sind Green und Silverman (1994) und Hastie und Tibshirani (1994). Der Alpha-Parameter ist die Bandbreite: Je kleiner alpha, desto geringer ist die Rauhigkeitsstrafe, und je näher der reibungslose Verlauf der tatsächlichen Daten ist. Der Spline wird an allen Datenpunkten ausgewertet, wobei fehlende y-Werte durch die Passung von dem glatten geschätzt werden. Die Spline-Prozedur behandelt Bindungen in der x-Variablen. Der zur Berechnung des Splines verwendete Algorithmus ist von der Ordnung T, und ausführlich diskutiert in Green und Silverman (1994, Chs.2, 3). Für gleichmäßig beabstandete Daten (z. B. Streudiagramm gegen Zeit) beinhaltet der Algorithmus eine Toeplitz-Matrix. Dies illustriert die Nähe einer natürlichen kubischen Spline zum Hodrick - Prescott - Filter, der in der Makroökonomie populär ist: Der einzige Unterschied besteht in dieser Toeplitz - Matrix. Da der Hodrick - Prescott - Filter alpha1600 (für vierteljährliche Daten) verwendet, sind die Glättungsmittel beider Methoden nahezu identisch. Anmerkung: Einige Artikel beschreiben die Berechnung des Hodrick - Prescott - Filters mit Invertierung einer TtimesT - Matrix. Das ist eindeutig nicht der Fall. Es wird in dem Reinsch-Algorithmus vermieden, der für das allgemeine Scatter-Plot glatt verwendet wird, und offensichtlicher in dem gleichmäßig beabstandeten Fall, wo alles, was erforderlich ist, die Lösung eines linearen Systems ist, das eine bandförmige Toeplitz-Matrix einschließt. Alternativ kann das Kalman-Filter verwendet werden, wie in Koopman, Harvey, Doornik und Shephard (2013). Es gibt drei Möglichkeiten, die Bandbreite festzulegen: Anzahl der Parameter Hier wird die äquivalente Anzahl von Parametern angegeben, k e. (Etwa vergleichbar mit der Anzahl der bei einer linearen Regression verwendeten Regressoren). Der Standardwert ist Setzt die Bandbreite direkt, mit dem Standardwert von 1600 entsprechend dem Hodrick - Prescott - Filter für vierteljährliche Daten (siehe Abschnitt 11.5.4.1 für andere Frequenzen). Wählt die Bandbreite durch verallgemeinerte Kreuzvalidierung (GCV). Wir finden, dass die Wahl Bandbreite mit GCV oder Cross-Validierung (CV) tendenziell untermooth. Das GCV-Kriterium wird berechnet als: Wir haben GCV statt CV angenommen, weil eine sehr gute Passform an einem Punkt das CV-Kriterium dominieren könnte. 10.11 QQ-Diagramm Zeichnet ein QQ-Diagramm. Die Variable enthält normalerweise kritische Werte, die von einer bestimmten Verteilung ausgehen. Diese Funktion zeichnet dann eine Querdarstellung dieser beobachteten Werte (sortiert) gegen die theoretischen Quantile (die horizontale Achse). Die 45 o-Linie wird als Referenz gezeichnet (je näher das Kreuz-Diagramm zu dieser Linie ist, desto besser das Spiel). Die QQ-Diagrammlinie wird über die gesamte Probe gezeichnet und überspringt fehlende Werte. Folgende Verteilungen werden unterstützt: Das normale QQ-Diagramm enthält die punktweise asymptotischen 95 Standardfehlerbanden, wie sie in Engler und Nielsen (2009) für Reste von Regressionsmodellen (ggf. autoregressiv) mit einem Intercept abgeleitet werden. Hier wird das normale QQ-Diagramm für die standardisierten Daten erzeugt, jedoch auf der ursprünglichen Skala gezeichnet. Die Standardfehler werden durch die Quadratwurzel von gegeben: wobei z die Koordinaten der Referenzverteilung (die Standardnormale), Phi die Standardnormale cdf und phi die Dichte sind. 10.12 Schachteldiagramm Ein Schachteldiagramm zeigt die Verteilung einer Variable in Form ihrer Quartile mit der Bezeichnung Q 1. Q & sub2; Q 3 (die 25, 50 und 75 quartiles). Definieren Sie den Interquartilbereich als IQR 1.5 (Q 3 - Q 1). Das Kastenplot besteht aus den folgenden Elementen: einem Kasten mit horizontalen Linien bei Q 1. Q 2 (der Median) und Q 3 eine vertikale Linie von Q 1 - IQR zu Q 3 IQR (ausgelassen in der Box) einzelne Beobachtungen: alle Beobachtungen außerhalb des Bereichs (Q 1 - IQR, Q 3 IQR) sowie die beiden Beobachtungen An beiden Enden, die nur in diesen Bereich fallen. Das Box-Plot verwendet das gesamte Sample und überspringt fehlende Werte. 10.13 Exponential gewichteter gleitender Durchschnitt (EWMA) Ein einfacher exponentiell gewichteter gleitender Durchschnitt einer Folge yt. T1. T ist definiert als: mit m 1 y 1. Die resultierende Folge z t ist z t m t. Außer wenn ein y th für hge1 fehlt, in welchem ​​Fall es durch Prognosen z th m t ersetzt wird. Eine erweiterte Version führt einen Steigungskoeffizienten beta ein und heißt auch Holts-Methode: und r 1, r 2 werden auf fehlende Werte gesetzt. Wenn irgendein y th oder x th fehlt, wird r th auf r t gesetzt. Wenn man den Zähler und den Nenner von rt um 1-lambda multipliziert, zeigt dies, dass mt (1-lambda) pt (x, y) der EWMA des Kreuzprodukts mit alpha1-lambda und m1 0 ist. Kapitel 11 Algebra-Sprache 11.1 Einführung OxMetrics ist zumeist menügesteuert für eine einfache Bedienung. Um die Flexibilität zu erhöhen, können bestimmte Funktionen durch Eingabe von Befehlen aufgerufen werden. Die Syntax dieser Befehle, die als kleine Computersprachen zu sehen sind, wird in diesem und im nächsten Kapitel beschrieben. Darüber hinaus gibt es die Ox-Sprache, die eine ernstere Computersprache ist und in einem separaten Buch beschrieben. 11.2 Algebra-Code ausführen Algebra ist eine einfache Vektorsprache, die nur mit einem Objekttyp arbeitet: den Variablen in der Datenbank. Dieses Objekt wird als Ganzes manipuliert, obwohl es möglich ist, den Zugriff auf eine Teilprobe zu beschränken. Die einzigen gültigen Aussagen sind Zuordnungen und bedingte Zuordnungen. Statements müssen mit einem Semikolon beendet werden. Wenn während der Ausführung des Algebra-Codes ein Fehler auftritt, wird die Verarbeitung abgebrochen und die Kontrolle an OxMetrics zurückgegeben. Alle erfolgreichen Aussagen bis zu diesem Zeitpunkt werden mit entsprechenden Änderungen an der Datenbank ausgeführt. Berücksichtigen Sie dies, wenn Sie den korrigierten Code erneut ausführen. Es gibt drei Möglichkeiten, Algebra-Code auszuführen, wie in den nächsten drei Abschnitten beschrieben. 11.2.1 Rechner (Altc) Der Taschenrechner ermöglicht eine einfache Manipulation der Variablen in der Datenbank und ist eine bequeme Möglichkeit, Algebra-Ausdrücke zu schreiben. Ziel ist es, einen gültigen Algebra-Ausdruck im Ausdrucksfenster (ohne Zuweisungsteil und abschließenden Semikolon) zu erstellen. Alle erfolgreichen Transformationen werden im Ergebnisfenster als Algebra-Code protokolliert. 11.2.2 Algebra Editor (Alta) Mit dem ToolsAlgebra Editor können Sie die Datenbankvariablen durch Eingabe mathematischer Formeln in einen Editor umwandeln. Der Algebra-Code kann gespeichert und neu geladen werden. Der Algebra-Editor erlaubt auch die Auswahl der Datenbank, auf die der Code angewendet wird. 11.2.3 Algebra aus den Ergebnisfenstern (Ctrla) Eine Textauswahl mit Algebra-Code kann direkt aus diesem Fenster mit dem Befehl EditRun als Algebra (oder Ctrla als Kurzbefehl) ausgeführt werden. Der Code wird auf die aktuell aktive Datenbank angewendet. Die aktuelle Datenbank wird geändert, indem Sie den Fokus auf diese Datenbank setzen oder eine der Dropdown-Felder (Rechner, Algebra-Editor, Grafiken) verwenden oder den Befehl usedata () verwenden. 11.2.4 Algebra aus einer Batch-Datei Algebra-Code kann in einem Batch-Programm angegeben werden, siehe Kap. 12. und spezifisch sect12.5.1. Eine Algebra-Datei kann auch in eine Batchdatei geladen werden (sect12.5.14). 11.3 Syntax der Algebra-Sprache 11.3.1 Variablen und Variablennamen Die Namen bestehen aus Buchstaben und Ziffern. Das erste Zeichen muss ein Buchstabe sein. Unterstriche () zählen als Buchstabe. Gültige Namen sind CONS, cons, cons1, a1b usw. Beispiele für ungültige Namen sind DeltaCONS, 1-CONS, log (X) usw. Ungültige Namen können in der Algebra verwendet werden, wenn sie in doppelte Anführungszeichen eingeschlossen werden Die Variable X existiert. Bei der Algebra wird zwischen Groß - und Kleinschreibung unterschieden: CONS und Cons beziehen sich auf verschiedene Variablen. Wenn Sie eine neue Variable über eine Zuweisungsoperation erstellen, wird sie sofort der Datenbank hinzugefügt und auf fehlende Werte initialisiert. Bei Bedarf wird der Datenbankname gekürzt (längere Namen sind in der Algebra erlaubt als in der Datenbank). 11.3.2 Kommentar Alles zwischen und gilt als Kommentar. Beachten Sie, dass dieser Kommentar nicht verschachtelt werden kann. So führt zu einem Syntaxfehler. Alles, was bis zum Ende der Zeile folgt, ist auch Kommentar. 11.3.3 Konstanten Eine Konstante ist eine Zahl, die in einem Ausdruck verwendet wird. Beispiele sind 1. 1.2. .5. -77000. -5e-10 und 2,1E-12. 11.3.4 Algebra-Operatoren 11.3.4.1 Arithmetische Operatoren Die binären arithmetischen Operatoren sind 4.,,, -. Die 4 ist der Power Operator CONS 4 2 hebt die Variable CONS auf die Macht zwei. Alle Berechnungen sind Gleitpunktarithmetik mit doppelter Genauigkeit. Die Rangfolge ist: 4. Deutsch - Übersetzung - Linguee als Übersetzung von. Dann. . und schlussendlich . Aufrechtzuerhalten. Ein Beispiel für unären Minus ist: x -1. Jede arithmetische Operation mit fehlenden Werten gibt einen fehlenden Wert zurück. 11.3.4.2 Relationale und logische Operatoren Die relationalen Operatoren sind lt, lt, gt, gt, stehen für weniger, weniger oder gleich, größer, größer oder gleich. Die Gleichstellungsoperatoren sind und. Gleich ist und nicht gleich ist. Diese werden unterhalb der relationalen Operatoren als Rangfolge eingestuft. Noch niedriger sind logische AND (ampamp) und logische OR (). Der unäre Negationsoperator hat die höchste Priorität. Ein Beispiel für eine unäre Negation ist: new hat eine 0, wobei die Saisonfunktion eine 1 zurückgibt und umgekehrt. Boolesche Arithmetik wird auch in Gleitkomma durchgeführt. Das numerische Ergebnis ist 1. für einen Ausdruck, der auf true und 0 für einen Wert false auswertet. Ein Ausdruck mit dem Wert 0 ist false, während ein Wert, der nicht 0 ist, wahr ist. Fehlende Werte werden wie folgt behandelt: Ergebnis, wenn ein andor b ein fehlender Wert ist 11.3.5 Zuweisungsanweisungen Der Zuweisungsoperator ist das Symbol. Zuweisungsanweisungen müssen mit einem Semikolon () beendet werden. Wenn die Variable, zu der ein Ergebnis zugeordnet ist, noch nicht existiert, wird sie erstellt und der Datenbank hinzugefügt. Andernfalls wird die vorhandene Variable überschrieben. Beachten Sie, dass Zuweisungsausdrücke Vektorausdrücke sind: Alle Beobachtungen werden überschrieben (es ist möglich, die Zuordnung zu einer Teilmenge mit der Beispielfunktion zu beschränken). Einige gültige Zuweisungsanweisungen sind: Die letzte Anweisung konstruiert eine Variable namens Seasonal, die 1 in Periode 1 und 0 sonst 0 ist. Diese Variable wird in weiteren Beispielen in diesem Kapitel verwendet. Achten Sie darauf, die Symbole und Symbole nicht zu verwechseln: vergibt, vergleicht. Klammern können in Ausdrücken in der üblichen Weise im obigen Beispiel verwendet werden (cons2 5) 1,55 bewertet nach cons2 1,55 5 1,55. 11.3.6 Bedingte Zuweisungsanweisungen Der Bedingungsausdruck hat die folgende Form: TestExpression. TrueExpression. FalseExpression Zuerst wird die TestExpression ausgewertet, wenn sie wahr ist (nicht 0.), dann wird TrueExpression ausgewertet, sonst FalseExpression. Betrachten wir ein Beispiel, das die oben erzeugte saisonale Variable einschließt, die 1 im ersten Quartal und 0 in den anderen Quartalen ist. Die Anweisung kann folgendermaßen gelesen werden: Die Variable new erhält den Wert von CONS, wenn Seasonal wahr ist (dh, wenn Seasonal nicht 0 ist, also im ersten Quartal eines jeden Jahres), sonst erhält er den Wert 0 In diesem Fall hätte das gleiche Ergebnis erreicht werden können: Wenn wir jedoch eine Saison mit dem Wert 2 im ersten Quartal und den restlichen Nullen verwendet hätten, hätte nur die bedingte Zuweisung das gewünschte Ergebnis gegeben (da 2 nicht Falsch, und daher wahr). Beachten Sie, dass das: FalseExpression-Teil optional ist. Beispiel: ist eine gültige Zuweisungsanweisung. Nun wird die Variable den Wert CONS für das erste Quartal haben, aber die anderen Beobachtungen von new werden nicht berührt (wenn also durch diesen Ausdruck neu erzeugt wird, enthält er fehlende Werte für Quartale 2, 3 und 4, wodurch die Variable unbrauchbar wird Für Modellierungszwecke). Ein weiteres Beispiel: Diese neue Variable nimmt die Werte von CONS an. Wobei fehlende Werte durch Nullen ersetzt werden. 11.3.7 Indexierung Es ist möglich, eine bestimmte Beobachtung in einer Variablen mit rechteckigen Klammern zu indizieren. Zum Beispiel: Es gibt drei Methoden der Indexierung: Relativ zur aktuellen Beobachtung. Jede Algebra-Anweisung kann als Laufen innerhalb einer Schleife über alle Beobachtungen gesehen werden. Der relative Index wird auf die aktuelle Beobachtung in der Schleife versetzt. Man kann also folgendes interpretieren: Folglich hat diese Aussage dieselbe Wirkung wie By absolute date. In diesem Fall hat der Index das Formular Jahr (Periode). Zum Beispiel nach absolutem Index In diesem Fall hat der Index den Formindex (0). Die den Beobachtungsindex (mit der ersten Beobachtung mit dem Index 0) verweist. Beispiel: 11.3.8 Schlüsselwörter Die Algebra-Schlüsselwörter werden durch Algebra reserviert: Tabelle: 11.2 Algebra-Algebra-Schlüsselwörter 11.4 Algebra-Implementierung Jede Algebra-Anweisung hat eine implizite Schleife über die Stichprobengröße. Z. B. Entspricht dem folgenden Pseudocode: So bedeutet meanLCONS für jede Beobachtung denselben Wert. Standardmäßig ist die Schleife über alle Beobachtungen der Datenbank. Die Beispielfunktion kann die Schleife jedoch auf eine Teilprobe beschränken. Implementierung von Transformationen in Ox ist anders: Dort werden Variablen aus der Datenbank extrahiert, da Spaltenvektoren und Operationen auf den Vektor als Ganzes arbeiten. Implementierung der gleichen Code in Ox: Beachten Sie, dass der Mittelwert eines Vektors ist nur eine einzige Zahl, so dass ein Vektor, der diesen Wert für jede Beobachtung wird mit der konstanten Funktion in Ox implementiert (und das Hinzufügen dieser Datenbank ist nicht sehr nützlich ). 11.5 Algebra-Funktionen Eine große Menge von Funktionen wird durch Algebra bereitgestellt. Die meisten von ihnen nehmen sowohl Variablen als auch Konstanten als Argumente. Ein Funktionsname muss von Klammern gefolgt werden, auch wenn es keine Argumente enthält. Siehe Algebra-Funktionsliste der Tabelle: 11.3 für Funktionsdefinitionen. Einige Beispiele für Anweisungen mit Funktionen sind: 11.5.1 Differencing - und Lag-Funktionen Eine Variable wird mit der Lag-Funktion verzögert. Hinweis: In den meisten Fällen ist es besser, keine Lags in der Datenbank zu speichern. Die meisten Schätzmodule behandeln Lags explizit Analyse des Modells. Und differenziert mit der diff-Funktion. Zum Beispiel für erste Verzögerung und Differenz sowie zweite Verzögerung und Differenz: Dieser Code übernimmt die Namenskonvention, die von OxMetrics verwendet wird: anhängen einen Unterstrich gefolgt von Verzögerungslänge für eine verzögerte Variable und ein Präfix D für differenzierte Variablen. Bei einer ersten Differenz oder Verzögerung fehlt die erste Beobachtung für eine zweite Differenz oder Verzögerung, die ersten beiden Beobachtungen fehlen usw. Keine Funktion kann einen Ausdruck als Argument für die Differenzierung haben. Sie können also nicht diff (diff (Y, 1), 1) schreiben, sondern müssen schreiben: Beachten Sie, dass dieses DDY nicht das gleiche wie D2Y ist. Schließlich nimmt die Funktion dlog (.) Die erste Differenz des (natürlichen) Logarithmus der Variablen ein. 11.5.2 Funktionen des ACF und des Periodensystems Die Beispiel-Autokorrelationsfunktion lässt sich leicht abbilden. Um die exakten Werte des ACF zu berechnen, verwenden Sie den folgenden Algebra-Code: Die ersten beiden Zeilen sind erforderlich, um die Ausgangsvariablen für die ACF-Funktion zu erzeugen. Die Ausgabe von acf ist die tatsächlichen ACF-Werte (hier in ACFDCONS gespeichert) und die Verzögerungslänge (in ACFLAG). Die Periodogrammfunktion hat eine ähnliche Syntax, die das Periodogramm des Beispiels im zweiten Argument zurückgibt, und die Frequenzen, mit denen es im dritten berechnet wurde. 11.5.3 Sortierfunktionen Die Sortierfunktionen ändern die Reihenfolge der Beobachtungen in der Datenbank und müssen sorgfältig gehandhabt werden. Beachten Sie, dass die Funktion trend () verwendet werden kann, um eine Variable zu erstellen, die dem ursprünglichen Beobachtungsindex der Daten entspricht. Wenn also diese Variable zusammen mit der zu sortierenden Variablen sortiert wird, kann sie verwendet werden, um die Variable aufzuheben. Sortiert die Variable arg1 in aufsteigender Reihenfolge (arg1 muss eine Variable sein und darf kein Ausdruck sein). Gibt den Wert von arg1 nach der Sortierung zurück. Angenommen, die Residuen einer Regression wurden in der Variablen Residual gespeichert. Dann wird eine sortierte Kopie wie folgt erzeugt: Sortiert die Variable arg1 in aufsteigender Reihenfolge und sortiert arg2 entsprechend. Gibt den Wert von arg1 nach der Sortierung zurück. Arg1 und arg2 müssen Variablen sein. Angenommen, die Residuen einer Regression wurden in der Variablen Residual gespeichert. Dann wird ein sortierter Rest wie folgt erstellt: Mit der folgenden Anweisung wird die alte Sortierung zurückgesetzt (die Anweisung index trend () wird nicht mehr ausgeführt, da der Index überschrieben wird und die Informationen über die ursprüngliche Bestellung verloren gehen): Sortiert die Variable arg1 Sortiert und sortiert die gesamte Datenbank entsprechend. Gibt den Wert von arg1 nach der Sortierung zurück. Diese Funktion eignet sich besonders bei Querschnittsdaten, um zB fehlende Werte ans Ende zu schieben: 11.5.4 Glättungsfunktionen Auch die Glättungsfunktionen, die in Streudiagrammen zur Verfügung stehen, können aus der Algebra aufgerufen werden. 11.5.4.1 Hodrick - Prescott-Filter Der Hodrick-Prescott ist ein Filter, der in der Makroökonomie populär ist und nahezu identisch mit einem natürlichen kubischen Spline ist (Sect.10.10.2). Die Syntax lautet: wobei var die zu glättende Variable ist, alpha die Bandbreite (0 für die Voreinstellung von 1600) und vardest die Zielvariable (muss von var verschieden sein). Zum Beispiel: das durch die Zuweisungsanweisung hpCONS erzeugt und als Ziel für die angepassten Werte aus dem Filter verwendet. Wenn es fehlende Werte in der Datenreihe gibt, verwendet smoothhp Daten ab der ersten gültigen Beobachtung und stoppt danach mit dem ersten fehlenden Wert (dies ist im Gegensatz zu den Glättungsfunktionen des nächsten Abschnitts, die über fehlende Werte mit dem Maximum überspringen) Sample). Die verwendete Probe kann mit der Beispielfunktion eingeschränkt werden. Der mit dem Hodrick - Prescott - Filter assoziierte Bandbreitenparameter ist 100 (freq) 2. gibt die äquivalente Anzahl der zu verwendenden Parameter an. Diese Funktionen verwenden alle verfügbaren Beobachtungen (sofern sie nicht durch die Beispielfunktion eingeschränkt sind) und füllen die fehlenden Werte unter Verwendung der Passung von der glatteren. 11.5.4.3 Exponential gewichteter gleitender Durchschnitt und Korrelation Ein einfacher exponentiell gewichteter gleitender Durchschnitt (siehe Sekt.10.13) einer Reihe y kann erstellt werden durch: Hier wird alpha0.5. Eine erweiterte Version führt einen Steigungskoeffizienten beta ein und wird auch als Holts-Methode bezeichnet, z. B. Mit beta0.1: In beiden Fällen werden fehlende Werte durch Prognosen ersetzt. Die exponentiell gewichtete Bewe - gungsprobekorrelation (siehe Sekt 10.14) von zwei Serien y und x (beide angenommen, dass sie Erwartungsnull haben) können erzeugt werden durch: Hier wird Lambda auf 0,5 gesetzt. 11.5.4.4 Datums - und Uhrzeitfunktionen Wenn eine Datenbank datiert wird, gibt es Funktionen, um Komponenten des aktuellen Datums und der Uhrzeit für jede Beobachtung: Tag zurückzugeben. Monat. Woche. Std . Protokoll . Sekunden. Die Makedate - und Maketime-Funktionen übersetzen Jahr, Monat, Tag und Stunden, Minuten, Sekunden bis Datum und Uhrzeit jeweils. Diese können zusammen addiert werden, um ein Datum mit einer Zeit zu erstellen. Der Tag der Woche. Isdayofmonth und iseaster-Funktionen sind bei der Urlaubsbestimmung erforderlich, zum Beispiel um alle Feiertage und Wochenenden aus einer Datenbank zu löschen. Der folgende Code, der als holidayus. alg im Algebra-Ordner angegeben wird, bestimmt alle offiziellen US-Feiertage: UK-Feiertage erfordern auch die Iseaster-Funktion: 11.6 Algebra-Funktionszusammenfassung Verfügbare Funktionen sind in Tabelle tabelliert: 11.3. Jede Funktion, die auf fehlenden Werten arbeitet, gibt einen fehlenden Wert zurück. Jede Funktion, die fehlschlägt, gibt ebenfalls einen fehlenden Wert zurück. Wenn das Argument var. Es muss nur ein Variablenname sein, z. B. Ein 1 cum (eins) ist erlaubt, aber cum (1) nicht. Ähnlich: lag (CONS1,1) ist nicht erlaubt, während lag (CONS, 1) 1 ist. Mehrere Beispiele für Algebra-Code wurden oben zur Vereinfachung angegeben, die hier zusammengefasst sind: Tabelle: 11.3 Algebra-Funktionen Kapitel 12 Batch-Sprache 12.1 Einführung Die Batch-Sprache gibt Ihnen die Kontrolle über OxMetrics über eine Befehlssprache. Dies ermöglicht die Automatisierung wiederkehrender Aufgaben oder als schnelle Möglichkeit, an einen bestimmten Punkt in Ihrer Analyse zu gelangen. Andere Programme (wie PcGive, STAMP und X12arima) erweitern diese Batch-Sprache mit eigenen modulspezifischen Befehlen. Mit OxMetrics können Sie das aktuellste Modell aus dem aktuellen Modul als Batchdatei speichern (sofern vom Modul unterstützt). Wenn ein Modell interaktiv erstellt wurde, kann es als Batch-Datei für eine weitere Bearbeitung oder einen einfachen Rückruf in einer späteren Sitzung gespeichert werden. Dies ist auch der bequemste Weg, um eine Batchdatei zu erstellen. 12.2 Ausführen von Batch-Befehlen Wenn während der Ausführung der Batch-Befehle ein Fehler auftritt, wird die Verarbeitung abgebrochen und die Kontrolle an OxMetrics zurückgegeben. Alle erfolgreichen Aussagen bis zu diesem Zeitpunkt werden ausgeführt. Es gibt fünf Möglichkeiten, Batch-Befehle auszuführen, wie in den nächsten vier Abschnitten beschrieben. 12.2.1 Batch-Editor (Altb) Der Befehl ToolsBatch-Editor aktiviert das Edit-Fenster, in dem Sie einen Satz von Batch-Befehlen laden können. Die Dateierweiterung für Batchdateien ist. FL. 12.2.2 Batch aus Ergebnisfenster (Ctrlb) Mit dem EditRun als Batch-Befehl (oder Ctrlb als Short Cut) kann eine Textauswahl mit Batch-Befehlen direkt aus diesem Fenster ausgeführt werden. 12.2.3 Batch aus dem FileOpen-Befehl Wenn Sie FileOpen verwenden. Und legen Sie den Dateityp auf Run Batch-Datei (.fl). Dann wird die Batchdatei sofort ausgeführt. 12.2.4 Batch aus dem Windows Explorer Sie können auf eine. FL Datei im Windows Explorer doppelklicken, um die Datei direkt auszuführen. Wenn OxMetrics noch nicht aktiv ist, wird es automatisch gestartet. 12.2.5 Batchdatei aus einer Batchdatei Eine Batchdatei kann aus einer anderen Batchdatei aufgerufen werden, siehe sect12.5.15. 12.3 Batchdateien und Standardordner Wenn eine Batchdatei ausgeführt wird, wird der Arbeitsordner auf die der Batchdatei gesetzt. Dadurch können Daten - und Algebra-Dateien, die sich im Ordner der Batchdatei befinden, gefunden werden, auch wenn die Batchdatei von einem anderen Ort aus ausgeführt wird. Zusätzlich erlaubt der Befehl chdir die Angabe eines neuen Standardverzeichnisses. Schließlich können Pfade zu Datendateien fest codiert werden, aber das sollte vermieden werden, wenn möglich. Wenn eine Batchdatei in den Batch-Editor geladen und dann ausgeführt wird, wird kein zugehöriger Standardordner vorhanden sein. Der Vorgang des Öffnens der Batchdatei würde jedoch den Standardordner zu dem der Batchdatei setzen. 12.4 Allgemeine Batch-Befehlsübersicht Tabelle Tabelle: 12.1 gibt eine alphabetische Liste der OxMetrics-Batch-Sprach-Anweisungen an. Tabelle: 12.1 Batch-Befehl Zusammenfassung 12.4.1 Kommentar Alles zwischen und gilt als Kommentar. Beachten Sie, dass dieser Kommentar nicht verschachtelt werden kann. Alles, was bis zum Ende der Zeile folgt, ist auch Kommentar. 12.4.2 Befehlstypen Es gibt zwei Arten von Batch-Befehlen: Funktionsaufrufe (mit oder ohne Argumente), die durch ein Semikolon beendet werden. Ein Beispiel ist der Befehl loaddata. Block-Befehle, gefolgt von Anweisungen zwischen geschweiften Klammern. Ein Beispiel ist der Algebra-Befehl. 12.4.3 Standard-Argumente Tabelle 12.1 zeigt zwei Instanzen von Default-Argumenten im Befehl appenddata und im Befehl setdraw. Wenn beispielsweise das letzte Argument wie in dem Befehl ausgelassen wird, wird es tatsächlich interpretiert als: 12.5 Batch-Befehle In der folgenden Liste werden Funktionsargumente durch Worte angezeigt. Während die Bereiche, in denen Anweisungsblöcke erwartet werden, durch angezeigt werden. Beispiele folgen der Liste der Beschreibungen. Für Terme in doppelten Anführungszeichen muss der gewünschte Term ersetzt und zusammen mit den Anführungszeichen gesetzt werden. In der Tabellendarstellung ist eine Befehlsübersicht aufgeführt: 12.1. Modulspezifische Befehle sind mit jedem Modul dokumentiert (also für PcGive Batchbefehle siehe Band I der PcGive-Bücher). 12.5.1 algebra Enthält den auszuführenden Algebra-Code. Der Block der Algebra sollte in geschweifte Klammern eingeschlossen werden, zum Beispiel: 12.5.2 appenddata (quot filename quot quote quote quotquot) Fügt die Daten aus der benannten Datendatei in die vorhandene In-Memory-Datenbank ein. Wenn noch keine Datenbank existiert, wird die angegebene Datendatei wie im Befehl loaddata () geöffnet. If the second argument is omitted, or equal to quotquot (that is, no group name is specified) the whole file will be appended, otherwise only the named group. 12.5.3 appresults(quot filename quot ) Append the contents of the Results window to the named file and clear the Results window . 12.5.4 break Stop the batch file, return to OxMetrics menus. While a batch file is running, there is no way of stopping it other than this batch command. 12.5.5 chdir(quot path quot ) Sets the current working folder to the specified path. There are three special forms of this command: chdir(quotbatchquot) sets the working folder to that of the batch file chdir(quothomequot) sets the working folder to that of the OxMetrics. exe executable file (but if it ends in bin that will be deleted). If OxMetrics. exe is in its default folder Program FilesOxMetricsbin . then this command will set the working folder to Program FilesOxMetrics . chdir(quotquot) prints the current working folder. 12.5.6 closedata(quot databasename quot ) Closes the database, which is currently loaded in OxMetrics. The database is closed without saving, so any changes which have been made since the last save are lost. 12.5.7 command(quot commandline quot ) Sends the line of text directly to the active module. The module must be able to accept commands (either via batch, or as an input console module). 12.5.8 database(quot name quot . year1 . period1 . year2 . period2 . freq ) Creates a database with the specified name and frequency, and sample period year1 ( period1 ) to year2 ( period2 ). 12.5.9 draw( area . quot y quot . quot mode quotquotquot ) Graphs variable y from the current database in the requested area (the first area has number 0). If the second argument is missing, the graph is a standard time-series plot. For other types of graphs, mode can be one of: 12.5.13 exit Stops the batch file and exits OxMetrics . 12.5.14 loadalgebra(quot filename quot ) Loads and executes the algebra code from the named. ALG file. The extension must be provided. See sect12.3 on the default folder. 12.5.15 loadbatch(quot filename quot ) Loads and executes the batch code from the named. FL file. The extension must be provided. See sect12.3 on the default folder. 12.5.16 loadcommand(quot filename quot ) Sends the contents of the named file to the active module. The module must be able to accept commands (either via batch, or as an input console module). 12.5.17 loaddata(quot filename quot ) Load the data from the named. IN7 file. To load, a full pathname would sometimes have to be specified, e. g. quotc:mydatadata. in7quot . The extension indicates the data type and must be provided. Inside OxMetrics, the database will then be known as data. in7, and will be the current default database. See sect12.3 on the default folder. If the database is already opened, the command works as usedata() . 12.5.18 loadgraph(quot filename quot ) Load the graph from the named file. To load, a full pathname would sometimes have to be specified, e. g. quotc:mydatadata. in7quot . The extension indicates the file type and must be provided (but OxMetrics will always require the. gwg file for loading, so when using loadgraph(quotfig1.epsquot), OxMetrics will look for fig1.gwg. 12.5.19 module(quot name quot ) Starts the specified module. When the module is already active, it becomes the focus for subsequent module-specific batch commands. Otherwise the module is started first. 12.5.20 package(quot packagename quot . quot modeltype quotquotquot) Used to specify the package and model type for modelling: 12.5.21 print(quot text quot) 12.5.22 println(quot text quot) Prints the specified text in the Results window. This can be useful to introduce explanatory notes. The println commands adds a new line after printing the text. 12.5.23 printdate Prints the current date and time in the Results window. The date and time are pasted into the text in ISO format yyyy-mm-dd hh:mm:ss, so putting the year first and using a 24-hour clock. 12.5.24 savedata(quot filename quot) Save the current database to the named. IN7 file. The. BN7 file will get the same base name. If files with these names already exist, they will be overwritten 12.5.25 savedrawwindow(quot filename quot . quot window quotquotquot) If no window is specified, the command saves the current Batch Graphics window to the named file (or gives an error message Cannot save to if there is no Batch Graphics window or the file cannot be saved). Otherwise it saves the named graphics window. 12.5.26 saveresults(quot filename quot ) Save the contents of the results to the named file and clear the Results window . If a file with that name already exists, it will be overwritten 12.5.27 setdraw(quot option quot . i1 0 . i2 0 . i3 0 . i4 0 . i5 0 ) This command changes the default settings used in graphics. The easiest way to use this command is to design the layout using the interactive dialogs ( Graphics Setup and Postscript Setup ). Then use the Write as batch command on both pages of the Graphics Setup dialog to record the batch code in the results window. This can then be pasted to the batch editor, and saved to a file. Or edited, and run directly from the results window. 12.5.28 setdrawwindow(quot name quot ) Sets the name of the graphics window in which the graphs appear. The default is quotBatch Graphicsquot . 12.5.29 show Shows the graph created in batch. Note that graphs from draw drawf drawx drawz commands are not displayed until the show command is issued. 12.5.30 usedata(quot databasename quot . i1 0 ) Sets the default database to databasename . The database must already be loaded into OxMetrics. Normally, only the one-argument function would be used, e. g, usedata(quotukm1.in7quot) . If the second argument is 1 . the database is marked clean: when it is closed there is no prompt for saving it. This can be useful after a section of algebra, which implements basic transformation for a dataset. This can be used as follows: 12.6 Examples We finish with two example batch files. The first uses most non-graphics Batch commands, as well as some commands from the PcGive module. The final example uses many graphics batch commands, and is supplied as plots. fl with OxMetrics: Chapter 13 OxMetrics Graphics 13.1 Graphics paper Graphs in OxMetrics are drawn on a graphics worksheet, consisting of 10000 by 15000 pixels, with (0,0) in the bottom left corner: These pixels are virtual and different from screen pixels: the paper is always 10000 times15000, regardless of the screen resolution or the size on screen. Positions can be specified in pixel coordinates, as for example (p x, p y ) (700,3200). More often it is convenient to use real-world coordinates to map the pixel coordinates into real data values. This is done by specifying an area on the graphics worksheet, and attaching real-world coordinates to it. These areas are allowed to overlap, but need not: The areas are numbered from left to right and top to bottom, counting starts at zero . Suppose we have set up all areas as being from (x, y)(0.0,0.0) to (x, y)(1.0,1.0) (again within each area the origin is the lower left corner). Then we can draw a line through area 2 in two ways: in real coordinates within an area step 1: select area 2 step 2: move to (0.0, 0.0) step 3: draw a line to (1.0,1.0). using pixel coordinates on the worksheet step 1: move to pixel coordinates (600,600) step 2: draw a line to pixel coordinates (3600, 3600). where we assume that (600,600) to (3600,3600) are the pixel coordinates chosen for area 2. Drawing in real-world coordinates has the advantage that it corresponds more closely to our data. 13.2 Creating graphs A graph is created from data in a database using the Graphics toolbar button, or Model Graphics. These graphs appear in the window labelled OxMetrics Graphics. Subsequent graphs are added to this window. To start from scratch, close the window, or select and delete each area. To keep the existing OxMetrics graphics window and open a new one for subsequent graphs, use File New Data Plot Window (note that the menu contents change according to the type of window which is active). Modules such as PcGive will put their graphs in a window with a different name. 13.2.1 Actual series with optional transformations plots the actual values of all selected variables against time (or the observation index for undated series), together or each in a separate graph. If there are missing values, these show up as gaps in the line. Create separate Plots This creates as many graphs as there are series. Style Lines Symbols Lines and symbols Index line: plot first series as index Index line and symbols: plot first series as index Bars: plot all series as bars Shading: use shading where this variable is 1, no shading otherwise First as bar: plot only the first as bar chart Transformation: Logarithms: natural logs of the series: log (y t ) Growth rates: log (y t - y t-1 ) First differences: Deltay t y t - y t-1 Seasonal growth rates: log (y t - y t-s ), s4 for quarterly data, s12 for monthly data, Seasonal differences: Delta s y t y t - y t-s Use log scale: assumes the data are in logs and powers up the axis to reflect the log scale. 13.2.2 Multiple series with optional transformations Match series by None: no matching is done Mean amprange matched to first series Second series on right scale Start 100 Style: as above Transformation: as above Use log scale 13.2.3 Scatter plots The available scatter-plot types are: Y against X Y against X, labels along the axes Scatter plot with regression line With cubic spline smooth, automatic bandwidth All scatter plots The Style. Regression and Smoothing sections allow additional options and combinations. If there are missing values, these are omitted from the graphs. 13.2.4 Distribution Estimated density and histogram, optionally with normal reference The histogram is a simple graph: the range of x t is divided into intervals, and the number of observations in each interval is counted. The height of each bar records the number of entries in that interval. In OxMetrics, these are divided by the total number of observations to show the relative frequency (use bar to keep the count). OxMetrics sets a default number of intervals dependent on the sample size, but this can be changed by the user by clicking on Smoothing and Use custom bar count to set a different value. Estimated distribution against normal: a QQ plot Frequencies andor cumulative frequencies QQ plot against Uniform, normal, t. F. or chi 2 distribution Box plot 13.2.5 Time-series: ACF etc. The sample autocorrelation function (ACF), or correlogram, plots the correlations r x302 j between x t and successive x t-j . Also see sect10.3. The length of the ACF can be set by the user. Since the correlation between x t and x t is always unity, it is not drawn in the graphs. Partial autocorrelation function The partial autocorrelation coefficients correct the autocorrelation for the effects of previous lags. So the first partial autocorrelation coefficient equals the first normal autocorrelation coefficient. The sample cross-correlation function (CCF) graphs the correlation between a series and the lags of another series. The periodogram and the spectrum (or more accurately here: spectral density) graph the series in the frequency domain. The sample periodogram is based on the coefficients of the Fourier decomposition of the sample autocorrelations (that is, the correlations j between x t and x t-j ). The sample spectral density is a smoothed (and scaled) function of the periodogram. It is symmetric between - pi and pi, and so is only graphed for 0,pi 1 on the horizontal axis stands for pi, 0.5 for 0.5pi, etc. Peaks at certain frequencies can indicate regular (cyclical or seasonal) behaviour in the series. In a seasonal sub-plot, the data are displayed by season. For example, for quarterly data, first the quarter 1 data are graphed, then quarter 2, etc. This helps detecting changing seasonal patterns. 13.2.6 QQ plots QQ (quantile-quantile), or cross-probability, plots: Quantile plot: against uniform QQ plot against normal (same mean, variance) QQ plot with choice of distribution As discussed in the companion book on PcGive, statisticians view variables as being described by probability distributions. If X is the variable, and x a value it could take, then is the probability that the value is in fact greater than x. For example, if the variable is the height of a child, when x is one metre, P x ( Xgt1) is the probability that the child is taller than a metre. The values of x can be any number, but P x (. ) cannot be negative or exceed unity. Plotting P x ( Xgtx) against x generates an int-shaped curve (but more stretched out horizontally), which is hard to interpret. When X has a uniform distribution over ( 0,1). if P x (. ) is plotted against x in a unit square, the result is a straight line. A similar idea applies to all distributions and QQ plots can be selected so some reference distribution is a straight line with the empirical distribution compared to it. The QQ plot options page on the Graphics dialog allows for a choice of reference distributions. For the t. F and chi 2 distribution it is necessary to also supply the degrees of freedom arguments. Drawing a variable against a uniform results in a so-called quantile plot. 13.2.7 Two series by a third Error bars Error bands Error fans High-low Show Z values As symbol size: Bubble chart A bubble chart consists of a scatter plot, where the symbols are circles, and the size of the circle indicates a third dimension (e. g. market share). 13.2.8 3-dimensional plots Surface from scatter: X, Y,Z are vectors Triangulation from scatter: X, Y,Z are vectors Surface from table: Z, Y columns match Surface from table: Z, X columns match 3D points 2D contour from 3D scatter surface With 3-dimensional plots there are two ways of presenting the data: as a scatter of points in three-dimensional space, or as a table with the X and Y values along the side, and the Z values in the cells. The tabular format specifies the 3D surface directly, whereas for the scatter it is left to OxMetrics to work out the surface. Although the tabular format leads to better results, the scatter is easier to use, as it requires only three variables. To create a surface from a scatter, OxMetrics derives a triangulation, and from the triangulation a smooth surface. This method works best when the surface is smooth. There are a few additional edit actions available for 3-dimensional graphs: Rotation The Edit menu has an entry for rotation: leftright (azimuth, key short-cut is lt and gt), updown (elevation, key short-cut is and -) and side ways (twist). This can be done for the currently selected 3-d area, or for all graphs. The Style entry for the 3D graph on Edit Graphs allows for a choice of palette. The same page allows for the addition of contour lines to a surface (but not a triangulation). 13.3 Printing graphs Select File Print to print to an attached printer and File Print Preview to first view the results. The following control of headers and footers is available for printing from File Print Page Setup. Orientation: portrait or landscape Column and scale are ignored, as the graph will fill the page Draw a box The size of margin to use Draw a header for the graph. This is controlled via the Header and Footer boxes. There are five specials: ampdate prints the date, amptime prints the time, amppage prints the page number, amppages prints the total number of pages, ampfile prints the file name. Other text in the edit field is printed directly. Other print setup options are printer specific. Use File Print Preview to view the result before printing. Note that colours are shown in the preview, but will come out in grey levels (unless you have a colour printer of course). 13.4 Graphics formats Graphs can be saved to disk in various formats: Enhanced metafile (.emf ) These can easily be inserted into Microsoft Word 2003 or newer using Insert Picture From File. Encapsulated PostScript (.eps ), which is the format used to produce all the graphs in this book OxMetrics Graphics File (.gwg ) PDF (.pdf ), this is a popular binary document storage format. PostScript (.ps ), this is like EPS, but defaulting to a full page print. Portable Network Graphics (.png ), which is a bitmap format that may be useful for insertion in web pages The GWG format is particular to OxMetrics no other program can read it and no printer can handle it. OxMetrics requires the GWG format, because it needs to be able to allow re-editing of the graph when it is reloaded the other formats do not store sufficient information. When you save a graph in any format, the GWG file is automatically saved alongside it. Then, when loading a previously saved EPS file (say), OxMetrics can use the GWG file to reload the graph. 13.5 Saving and loading graphs Use File Save As or the diskette toolbar button to save the graph to a file. At the bottom of the dialog is a dropdown listbox in which you select the type of file. When you save a graph in any format, the GWG file is automatically saved alongside it. Then, when loading a previously saved EPS file (say), OxMetrics can use the GWG file to reload the graph. Choose File Open. to open a previously saved graphics file type. 13.6 Editing graphs Each graph consists of a collection of objects, which in most cases can be manipulated, moved or deleted. The main one, the area, was introduced in sect13.1. 13.6.1 Graph layout An area defines a rectangle on the paper which has world coordinates attached to it. The concept of areas enables multiple graphs on the paper, up to 36. Areas are allowed to overlap. The Graph Layout page of the Edit Graphics dialog allows for making adjustments that are relevant for the whole graph. Activate this through Edit Edit Graph. or by double clicking in an area. You can: Change the Areas layout, e. g. for example from 2 times1 to 1 times2. Box all areas in the current graphics window. Change the aspect ratio. for example to half-height graphs as used occasionally in this book. The aspect ratio of the graph paper defaults to 1.5 (15000 along the x-axis and 10000 along the y-axis). This usually works very well, but occasionally it may need changing, for example to make the graphs square on paper. Half-size graphs can also look good in publications. Change margins. Adjust all styles to make all lines in all the areas thicker or thinner, or to Increase all font sizes. Set the PostScript mode. usually plots on screen are colour, but required in gray levels for publication purposes. Display mode can be changed from colour to black ampwhite. Occasionally, this can be useful when pasting to another application for printing. OxMetrics always starts in colour mode. Paper colour allows the colour to be set for the (normally) white space around the graphics areas, e. g. to a light grey. 13.6.2 Area layout By default, an area has automatic pixel coordinates, which means that, when an area is added, the pre-existing area will automatically shrink to make space. An area can be selected with the mouse, and moved around the paper. This changes the automatic paper positioning into a fixed position. Real world coordinates are also selected automatically, but can be set to fixed values. The Area Layout page of the Edit Graphics dialog contains the settings that relate to positioning and layout of each individual area. You can: change world coordinates: select the desired area and select the Set checkbox for the X or Y coordinates, then adjust the settings. Press All to apply this to all areas. reset pixel coordinates to automatic or set specific pixel coordinates. change layout, e. g. for example from 2 times1 to 1 times2. Box the current area, or all areas in the current graphics window. The Edit menu allows you to rotate 3-dimensional graphs. This applies to the currently selected 3D area, or all 3D areas if none is selected: Rotate left or right (from the keyboard use Altlt or Altgt this does not require the shift key, so just hold Alt pressed while typing the lt or gt key). This canges the azimuth . Rotate up or down (from the keyboard use Alt - or Alt ). This canges the elevation . Twist left or right. Reset the rotation and twist back to the original values. 13.6.3 Variable against time, scatter, or 3D The title of this section is derived from the variables being plotted, such as CONS x (time) x z or INC x (time). The variable (or vector) is the main graphics object: it consists of a sequence of observations, graphed against time or another variable. A variable cannot be moved, nor can observations be moved on screen. There are essentially four types of vectors: variable against time variable against another variable variable against another variable by a third variable. The third variable can indicate symbol size, have its value printed, or specify error bars. 3D graphs: surface, contour or scatter. The Lines page of the Graphics Property dialog controls how the vector is displayed. The line type joining the observations can be: Line. linked, Symbols. not linked, but showing symbols, Line and symbols. Index. this draws a line from the point to the zero axis (if part of the area), or the edge of the area (towards zero). A non zero base can be specified in the Base for indexbars edit field. Index and symbols. Bars. this draws a bar to the zero axis (if part of the area), or the edge of the area (towards zero), with the bar centred on the current point. A non zero base can be specified in the Base for indexbars edit field. Style allows a choice of the colour or pattern for the currently selected entry the type choice is repeated in the drop-down box. The colour with which lines and symbols are drawn is set in the first column the line width and pattern is set in the second combo box. In both cases an entry is selected from one of the 16 defined line types. These can be changed in Model Preferences Graphics Setup The observations can be marked by a symbol, and the style and size of that symbol can be set in the third column. For 3D graphs it is possible to change the colour palette, or add contour lines (but not for a triangulation). The global palette definition is set in Model Graphics Setup The entries used in the legend can be changed by renaming the labels of the variables in the X, Y, Z label boxes. If there is no name, that component will be omitted from the legend label for the vector: if all labels are empty, the legend entry will be omitted alltogether. 13.6.3.1 Error bars Error bar options are only shown if the line object has error bars. Then you can switch between bars, bands and fans, choose a color for the barsbands. A multiplication factor may also be set for error bars and bands. For example, if the data in the Z variable are standard errors, then a factor 2 will show the data plusminus 2 standard errors (which would be a 95confidence interval if the data come from a normal distribution). To rename a label for the selected vector, click on Rename. or double-click on the vector in the list box. 13.6.3.2 Regression, Scale The Regression, Scale page of the Edit Graphics dialog allows adding regression lines to variables, and adjustment of the scaling (relative to the selected variable): None removes all scaling. Means matches the means of all variables to that of the selected variable: the shift factor will be set to make the means of the variables equal. Ranges. the scale factor will be set to give all the variables the same range. Maximum -- minimum will now be the same for every variable. Adjustment is made relative to the selected variable. Means and Ranges matches means and ranges. Both the shift and scale factors are set. The scale and shift factor can also be set directly. The regression options in this page are: Number of least squares lines. By default no least squares lines are drawn you can select up to 40 lines. Sequential versus Recursive regression lines. The default is sequential regression: the X-axis is divided in s sections (where s is the number of regression lines). Each section gets its own regression line. Recursive regression lines will lead to each subsequent section added on to the previous. With or without Projections projections shows the deviation between the variable and the regression line. Style sets the line colour and pattern. 13.6.4 Axes An X and Y axis (and Z for 3D graphs) is added automatically to each graph. Usually the default suffices, but a large number of adjustments can be made in the Axis entries of the Edit Graphics dialog. 13.6.4.1 Settings for non-default labelling Each axis consists of (values are in world coordinates): Minimum and Maximum First large tick. the value at which the first large tick mark appears Intervals for large ticks. the gap between large tick marks Intervals for small ticks. the gap between small tick marks These values are all set to a default, but can be changed when Default labelling is unchecked. 13.6.4.2 Location and transformation The location and transformation settings further position and define the axis: Anchor. determines where the axis is anchored, e. g. for an X-axis this is a Y value (changing the anchor would move the X-axis up or down). Minimum anchors at the left (bottom) of an area, Maximum at the right (top). Use specified anchor allows anchoring anywhere in the graph. For 3D graphs, the X axis is anchored at an Y and Z value, Y at X, Z and Z at X, Y. The Axis type: Normal the default axis without transformation Log (data is in logs) when the data is in natural logarithms, use this to show the original values on the axis Log10 (data is in log10) when the data is in logarithms of base 10, use this to show the original values on the axis Use specified shift and scale allows the shift and scale factors to be set Dates when the values on the axis are to be interpreted as date values. 13.6.4.3 Style The following adjustments can be made to an axis (all adjustments apply to the current axis only): hide an axis by checking Hide. (Axes can also be deleted, but when an area has no X or Y axis and is redrawn, that axis will be added.) No base line removes the line, leaving only tick marks. No small ticks removes the small tick marks. Line at y0 is only for X-axes, and uses the same line colour and type as the grid. By default a line showing zero is added when both negative and positive data occur. Grid attaches a grid, perpendicular to the selected axis. The grid is at the large tick marks. The grid colour and type is set in Graphics Setup. the default is that of line colour and type 14. The Tick Size. This sets the small tick size, the large tick size is twice the small tick size. The Font Size sets the size of the axis labels. 13.6.4.4 Label style Labels other side puts the labels on the other side of the axis. Rotate labels writes text of labels along the Y-axis (Y axis), or at a right angle (X-axis). Centre dates puts the labels in between the tick marks. For example for annual data, the label 1960 is centred at 1960 by default. With Centre dates it is set half way between 1960 and 1961. This option is for X axes only. This does not work when the axis is dated. Note that you may have as many axes as you wish. Axes can be selected on screen with the mouse. 13.6.5 Legend style Legends are added automatically in an appropriate size, unless the legend font gets too small. In that case (normally with more than sixteen areas), the legend will be omitted. In addition, a legend can be hidden, and subsequently unhidden. Legends can be selected with the mouse, and moved around. Deleting the legend results in it being hidden. The available options in the Legend style page of the Edit Graphics dialog are: Hide. legends are never completely deleted. Auto resize. by default, legends are reduced when the area gets smaller. When the text gets too small, the legend is hidden. Boxed draws a box around the legends. Default box size will be unchecked if the box is resized with the mouse. When it is checked, the box size is left to OxMetrics. Columns sets the number of columns for the labels the default is two. Font size determines the size of the label. This is reduced further when Auto resize is set. Transparent is the default. In that case, legends are drawn below data plots, with the exception of shading and separately drawn symbols. Opaque legends, on the other hand, are drawn on top of everything else. 13.6.6 Histogram The only available options for histograms is to select a line colorpattern for the outside line and for the area inside the boxes. 13.6.7 Copy properties to other areas Some aspects of one area can be copied to all other areas in the graph: Pixel coordinates. width and height or reset the default World coordinates. X or Y Axes. labelling, scale tyle or label style Legend style Histogram style. 13.6.8 Text Text can be added from the Edit menu using Add Text. Text belongs to an area, in which case it is deleted if the area is deleted (or copied when the area is copied). Text entered outside any area will be part of area 0. More than one line of text can be entered at a time. Text can also be rotated, by specifying the angle in degrees. This does not work so well for multiple line text blocks. Text entered immediately above the graph will have the title property, which means that it is moved with the area when the area is moved. Text uses a LaTeX-style of formatting, see sect13.9. 13.6.9 Lines and symbols Lines can be added from the Edit menu using Draw. Line coordinates may be specified in world coordinates (the default when the line is drawn inside an area), in which case the line is deleted if the area is deleted (or copied when the area is copied). Alternatively, lines may be specified in pixel coordinates. The appearance of a line can be changed to a box or a solid box. 13.6.10 Adding, moving and deleting objects Objects are added from the Edit menu. Most objects can be selected with the mouse, and moved and deleted subsequently. 13.6.11 Pointing The status bar shows the graphics coordinates of the the mouse. 13.6.12 Graphics setup Persistent setup for graphics is set through the Model Preferences Graphics Setup dialog. 13.7 Copy and paste There is a distinction between use of the clipboard inside OxMetrics, and that for external use. There are three copy commands: Copy is for internal use. When no area is selected, the whole graphics window is copied. When an area is selected, only that is copied to the clipboard. These clipboard items are not recognized by other programs. When a OxMetrics graphics format is on the clipboard, it can be added to an existing graph (no area selected) or to an existing area (which must be selected). Copying in the internal format is delayed, which means that the full copying is not actually performed until a paste is requested. This implies that when a graphics window is closed it is not available for pasting anymore. Copy Bitmap to Clipboard copies the whole graphics window in bitmap format. This can be pasted into other programs that recognize bitmaps. Copy Metafile to Clipboard copies the whole graphics window in EMF format, from which is a vector format that can be pasted into other programs. It is not possible to paste from other programs into OxMetrics graphs, with the exception of text. 13.8 Graphs and sample selection All types of graphs will use all valid observations, just skipping over missing values. 13.9 Text formatting Text uses a LaTeX-style of formatting, which allows for complex mathematics be used to annotate graphs. OxMetrics implements a subset of the normal LaTeX commands, and mathematics is typeset using the Symbol font. Mathematics is enclosed in . superscripts and subscripts are only allowed in math mode. A superscript is written as . a subscript as . For example, hat epsilon gives epsilonx302 i-1 k1. Tables Table:13.1 to Table:13.6 list the mathematics symbols which are available in OxMetrics. The entries in Tables Table:13.7 to Table:13.8 do not require math mode. Note that, to write you must enter respectively ( for a backslash is not standard in LaTeX, where it denotes a line break). Table:13.1 Greek symbols Chapter 14 OxMetrics Data Management 14.1 Creating data File New allows for the creation of a new database. All variables in a database have the same frequency. A sample period is required, but can be extended or changed later. 14.2 Database font View Increase Text Size and View Decrease Text Size are useful to select a smaller or larger font size for displaying the database on screen. 14.3 Database description A database can have a description for documentation purposes, and separate from the variable description. Only. in7.bn7 data files can preserve the description. 14.4 Printing data Use File Print when a database has the focus to print the database. File Print Preview is available to view the result before printing. Select File Print to print to an attached printer and File Print Preview to first view the results. The following control of headers and footers is available for printing from File Print Page Setup. Orientation: portrait or landscape Number of columns on the printed page Scale for printing: 100 is full scale, 90 smaller, etc. Draw a box The size of margin to use Write a header and footer. This is controlled via the Header and Footer boxes. There are five specials: ampdate prints the date, amptime prints the time, amppage prints the page number, amppages prints the total number of pages, ampfile prints the file name. Other text in the edit field is printed directly. 14.5 Data formats The data format specific to OxMetrics consists of a pair of files with extensions . in7 and . bn7 . The latter is a binary file containing the actual data, whereas the . in7 file holds the information on the contents of the binary file such as variable names, sample periods, frequencies etc. The information file is a human-readable file, the. bn7 is binary and is not human-readable. In addition, OxMetrics can read and write human-readable files, Excel spreadsheet files, comma-separated files, and GAUSS and Stata files. 14.6 Summary statistics This command prints the name of the database, the sample period and number of variables to the Results window. For each variable in the database the name is printed as well as: leading sample -- the first valid sample period without missing values, obs -- number of valid observations, miss -- number of observations with missing values, minimum -- minimum value, mean -- mean of valid observations, see (eq:10.1 ), maximum -- maximum value, std. dev -- standard deviation of valid observations, see (eq:10.1 ). 14.7 Saving data Use File Save As or the diskette toolbar button to save the data to a disk file. At the bottom of the dialog is a dropdown listbox in which you select the type of file. 14.8 Navigation and editing A database cursor indicates which is the current observation. The cursor can be moved from the keyboard or using the mouse. A block of observations can be selected (highlighted) for: copying to the clipboard as a destination for a block from the clipboard to set to a single value: press Enter to specify the value, whence you will be prompted whether the value should be applied to the whole selection. Press Enter or double click on an observation to edit the value. Single click on a cell with the cursor will give access to the inline editor. Algebra and the Calculator allows manipulation of variables through mathematical expressions. 14.9 Renaming variables Press Enter or double click on the variable name in the database to change the name or documentation. When in the Calculator or the Algebra Editor. click Ren when a variable is selected in the list box to rename. 14.10 Deleting variables Click on the variable name in the database to select the variable (or a group of variables), then press the Del key to delete (confirmation of the deletion will be required). When in the Calculator. press the Del buttonwhen a variable is selected in the list box to delete, confirmation will be required again. 14.11 Reordering variables The variables listbox in the Calculator and Algebra Editor allows variables to be picked up with the mouse and moved down or up in the listbox. 14.12 Adding variables Double click on an empty field in the database next to an existing variable to create a new variable. Alternatively use Edit New Variable. 14.13 Extending or reducing the sample period Double click on an empty field in the database below an existing variable to activate the Extend Database sample dialog. Alternatively use Edit Extend sample. Enter a negative value to reduce the sample size. The Change Sample option on the Edit menu allows the following actions: Add observations at the start Add observations at the end Delete observations at the start Delete observations at the end. 14.13.1 Changing the sample period The Change Sample option on the Edit menu allows changing the start year and period, as well as the frequency. The number of observations remains unchanged, and no data will be lost. 14.14 Copy and paste The standard copy and paste facilities are available, also see sect14.8. 14.15 Appending data A database can be appended from disk to an open database, using Append Data File when right clicking on a database in the workspace. This requires the frequencies to match. OxMetrics will make additional adjustments when these are required: the sample of the open database will be extended to encompass that of the appended database if a variable from the appended database already exists in the open database, then the existing variable is updated, except where the appended variable has missing values (for those observations the existing variable is not changed). 14.16 Daily, weekly and timed data Note: The calendar is Gregorian from 15 October 1582 onwards, and Julian before (so there is no year 0: year -1 precedes year 1 day 0 is on Julian date 1 January -4713). index used by OxMetrics is the Julian day number. For example, Julian day 2453402 corresponds to 2005-01-31. An optional fractional part specifies the fraction of the day: 2453402.75 corresponds to 2005-01-01T18:00. If the day number is zero, it is interpreted as a time only, so 0.75 is just 18:00 (6 PM). Note: This is similar to how Excel stores dates and times. OxMetrics uses the ISO representation yyyy-mm-dd, and the 24 hour clock for time, hh:mm:ss:.hhh. A date with a time are joined by the letter T, as shown above. In many fields it is possible to enter a date or time, which is then automatically translated to the internal representation. Years with week number are then also recognised, e. g. 1976-W3 returns the calendar index for the Monday of week 3 in 1976. (Week 1 is the first week that contains the first Thursday or equivalently, the week that contains 4 January.) OxMetrics uses two methods for dating a database: Fixed frequency Denoted by a start year, start period and frequency. From this, the date of any subsequent observation can be worked out. For example, if the start year is 2005, the start period 1, and the frequency 4 (quarterly), then the sixth observations is for 2006(2), the second quarter. This works well for monthly, quarterly and annual data. For undated data we simply set the start year and period to one, and the frequency as well. Dated The fixed frequency method does not work for weekly or daily data: not every year has the same numbers of observations. The solution adopted in OxMetrics is as follows: an integer value represents a date. A database variable can be classified as of type date, in which case the date is displayed, rather than the underlying value. The following criteria must be satisfied for a database to be dated: the first column must be of type Date. the first column holds date values, the optional fractional part of this indicates time as a fraction of 24 hours e. g. 2453372.75 is 18:00 on 2005-1-1 (2005-1-1T18:00 in ISO notation), the first and last observation must be valid, i. e. cannot be missing. Note that the fixed sample period is still available for a dated database, but this is usually set as for an undated database (start year, start period, frequency all set to one). Also note that the first variable in a dated database (which defines the calendar dates of the observations) is a variable as any other: it can be renamed, transformed, moved, deleted, etc. But some of these will make the database undated again. References Davidson, J. E. H. D. F. Hendry, F. Srba, and J. S. Yeo (1978). Econometric modelling of the aggregate time-series relationship between consumers expenditure and income in the United Kingdom. Economic Journal 88 . 661--692. Reprinted in Hendry, D. F. Econometrics: Alchemy or Science Oxford: Blackwell Publishers, 1993, and Oxford University Press, 2000 and in Campos, J. Ericsson, N. R. and Hendry, D. F. (eds.), General to Specific Modelling . Edward Elgar, 2005. Doornik, J. A. (2006). The role of simulation in econometrics. In T. Mills and K. Patterson (Eds.), Palgrave Handbook of Econometrics . pp. 787--811. Basingstoke: Palgrave MacMillan. Doornik, J. A. (2013). Object-Oriented Matrix Programming using Ox (7th ed.). London: Timberlake Consultants Press. Doornik, J. A. and D. F. Hendry (2013). Interactive Monte Carlo Experimentation in Econometrics Using PcNaive (3rd ed.). London: Timberlake Consultants Press. Doornik, J. A. and M. Ooms (2005). Outlier detection in GARCH models. Discussion paper 2005-w24, Nuffield College. Doornik, J. A. and M. Ooms (2008). Multimodality in the GARCH regression model. International Journal of Forecasting 24 . 432--448. Engler, E. and B. Nielsen (2009). The empirical process of autoregressive residuals. Econometrics Journal 12 . 367--381. Golub, G. H. and C. F. Van Loan (1989). Matrix Computations . Baltimore: The Johns Hopkins University Press. Granger, C. W. J. (1966). The typical spectral shape of an economic variable. Econometrica 34 . 150--161. Granger, C. W. J. and P. Newbold (1986). Forecasting Economic Time Series, (2nd ed.). New York: Academic Press. Green, P. J. and B. W. Silverman (1994). Nonparametric Regression and Generalized Linear Models. A Roughness Penalty Approach . London: Chapman and Hall. Hall, B. H. and C. Cummins (2005). Time Series Processor 5.0 Users Guide . Palo Alto, CA: TSP International. Hax308rdle, W. (1990). Applied Nonparametric Regression . Cambridge: Cambridge University Press. Harvey, A. C. (1993). Time Series Models, (2nd ed.). Hemel Hempstead: Harvester Wheatsheaf. Hastie, T. J. and R. J. Tibshirani (1994). Generalized Additive Models . London: Chapman and Hall. Hendry, D. F. and J. A. Doornik (2013). Empirical Econometric Modelling using PcGive: Volume I (7th ed.). London: Timberlake Consultants Press. Koopman, S. J. A. C. Harvey, J. A. Doornik, and N. Shephard (2013). Structural Time Series Analysis, Modelling, and Prediction using STAMP (5th ed.). London: Timberlake Consultants Press. Laurent, S. (2013). GRCH Professional 7 (5th ed.). London: Timberlake Consultants Press. Makridakis, S. S. C. Wheelwright, and R. C. Hyndman (1998). Forecasting: Methods and Applications (3rd ed.). New York: John Wiley and Sons. Nielsen, B. (2006). Correlograms for non-stationary autoregressions. Journal of the Royal Statistical Society B 68 . 707--720. Priestley, M. B. (1981). Spectral Analysis and Time Series . London: Academic Press. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis . London: Chapman and Hall. PHYSIOLOGY amp RELATED SCIENCES - A SHORT GLOSSARY A. R. Gardner-Medwin (UCL), N. A. Curtin, (Imperial), P. Tatham (UCL) copy 1990-2001 Words in science are often used in different ways from ordinary English. Completely different meanings even occur in different branches of physiology, e. g. for the word accommodation. As a student, it is easy to despair But the meanings of words are very precise in science: if you dont understand them, or if you use them casually, you wont be able to study efficiently, and you wont get good marks. This glossary is for browsing in, testing yourself, and learning about words that catch your eye. Stop and read wherever you may have doubts or interest. Also of course it is a place to look up words you come across and dont understand. But it is very selective. You need both an English dictionary and a scientific or medical dictionary too. Many words that you think you understand OK, you may find arent used quite how you thought This glossary concentrates on words that often cause confusion, especially in the basic sciences (physics, chemistry and mathematics) that are the foundation of physiology. You dont need to understand everything, but the more you understand, the easier it will be to learn more. You are often expected in exams to explain the meanings of words: practise doing it A short glossary of Medical Terms - Dissected, Defined and Explained is also available. Suggestions, corrections, additions: Click or email to a. gardner-medwin ltagt ucl. ac. uk a - Prefix, usually equivalent to ab-, ad-, or an-. abscissa RELATED: X, Y axes CONVERSE: ordinate 9830 X-axis, horizontal axis. It is usually simpler and clearer to say horizontal axis, since most people have to stop to think which axis abscissa means. As an aid to memory: Abscissa-Ordinate, X-Y, Horizontal-Vertical are all in alphabetical order. absolute refractory period The time within a refractory period during which no stimulus, however big, can elicit a second action potential from an excitable tissue. absorption Transfer of substances into the body or into the blood, usually across an epithelial surface. Z. B. absorption through the skin or from the gut, or re-absorption of substances from the lumen of tubules in the kidney. absorption spectrum Graph of the proportion of incident light (or other radiation) absorbed by a substance as a function of wavelength, frequency or energy. acceleration Rate of change of velocity. Note that all parts of a rotating object are accelerating (except on the axis), even if the rotation is steady: the acceleration is 4960 2 f 2 r where f is the frequency of rotation and r is the radius from the axis. Accelerations are sometimes expressed relative to the free acceleration due to gravity (1g9.81 m. s -2 ). Acceleration is detected in man largely by the labyrinths. acclimatization, acclimation The process of adaptation to a new environment, for example with altered ambient temperature, pressure or (with aquatic animals) salinity. Acclimation is sometimes used specifically to mean adaptation to a single changed factor (as under laboratory conditions). accommodation RELATED: adaptation 9830 A process of adjustment to new conditions. Used in several senses: 1. Attenuation or absence of a response when a stimulus is applied slowly (e. g. failure to detect a smell when it builds up slowly, or failure of a slow depolarisation to give an action potential). NB this is distinct from adaptation, but is often seen in the same systems. 2. Adjustment of focus of the eye. accumulation Progressive build-up of a substance, etc. Cumulative toxins are ones that are absorbed but not excreted, for which it is the total dose over a prolonged period that matters rather than the level of exposure at any one time. accuracy of measurement RELATED: resolution 9830 The limits of confidence in a parameter, based on its measurement. Accuracy is limited firstly by the ability of a measuring system to distinguish different conditions (resolution) and secondly by its ability to relate the conditions correctly to a standard (calibration). The two considerations must not be confused. A high resolution instrument giving stable readings and sensitive to small changes may nevertheless be completely inaccurate if not adequately calibrated. Accuracy cannot usually be greater than the resolution of a measurement, except in special circumstances(e. g. where a digital reading flicks between adjacent values and it may be possible to conclude that the value is close to an incremental step). acid CONVERSE: base 9830 An aqueous solution with a pH less than 7.0. A molecule or ion that can dissociate to release a proton (H ). For example, H 2 CO 3 and H 2 PO 4 - are both acids. acidosis CONVERSE: alkalosis 9830 Abnormally low pH of the blood. An acidotic condition may be capable of being restored to normal acid-base balance by increasing respiratory ventilation to reduce the CO 2 content of the body (respiratory acidosis), or it may require retention or injection of HCO 3 - (metabolic acidosis). acid-base balance Control of the factors influencing the pH of the blood. The main factors under homeostatic control are the excretion of CO 2 . HCO 3 - and NH 4 . Disturbances are lessened in the short term by numerous pH buffer systems. Influences affecting blood pH are altered absorption, metabolism and respiration, and disturbances affecting the control systems. acoustic RELATED: auditory 9830 Related to sound or sound waves. action potential ABBREV: spike 9830 A transient voltage change recorded inside or close to a nerve, skeletal muscle or other excitable cell, due to a characteristic change of membrane potential. Action potentials occur spontaneously or as all-or-none or frequency coded reactions to stimulation. The rising (depolarizing) phase is due to voltage dependent membrane channels allowing passive influx of Na or Ca . The falling phase is due to passive K efflux. Sodium spikes are brief (ca. 1-2 ms long) calcium spikes are more prolonged. Extracellularly recorded action potentials may be small (lt1mV), while the voltage changes across the membrane may be gt100mV. A compound action potential is an extracellular recording of the combined effect of action potentials in many cells. activation The process of initiating or increasing activity of some sort. In muscle physiology, activation usually means the induction of action potentials in the cell membrane ( excitation) rather than the initiation of tension (NB the link between the two is excitation-contraction coupling). activation energy RELATED: Arrhenius plot 9830 The energy required to achieve an intermediate state in a chemical reaction. A high activation energy lowers the rate of a reaction in proportion to e - EaRT according to Arrhenius equation. A catalyst reduces the activation energy. active CONVERSE: passive, inactive 9830 1. Requiring energy: e. g. active transport vs. passive transport. 2. Doing something: e. g. an active nerve fibre, undergoing action potentials. 3. (Rather vague amp confusing, best avoided) vigorous, important: e. g. carbon dioxide plays an active role in respiration. 4. Effective: E. g. an active ingredient. active site The part of a cell or of a receptor that binds to a substrate. active transport RELATED: carrier mediated transport 9830 Net movement of a substance across a membrane from a lower to a higher concentration or (in the case of ions) against an electrochemical gradient. This requires energy, and can occur by linkage of carrier mediated transport to a process providing energy, such as the hydrolysis of ATP or the downhill movement of another substance. activity RELATED: concentration 9830 1. The state of doing something: E. g. action potentials, secretion, movement according to tissue. 2. (In chemistry) a parameter similar to concentration, that determines the rate at which reactions take place. The ratio of activity to concentration is the activity coefficient, usually less than 1 because of molecular interactions in the solution that interfere with reactions. acuity Ability to identify fine detail in a sensory pattern. Visual acuity depends on light level, and is highest at the fovea. It is usually measured clinically by the ability to discriminate letters on a Snellen Chart: an acuity of 624 means that an individual can just read letters at 6m distance that a person with nominally normal acuity could just read at 24m. Somatosensory acuity varies markedly over the body surface and may be measured by the separation required to identify that the skin is being touched at two points. acute CONVERSE: dull, chronic 9830 Sharp, severe, short-lived, or of sudden onset. Rather ambiguous. Z. B. acute pain, acute phase of a response (usually a part of a response that is large and short-lived). An acute experiment is one in which an animal is anaesthetised at the start and eventually killed before recovering consciousness. AC-coupled RELATED: DC-coupled, filter, off-scale 9830 A recording that is sensitive to changes in the measured parameter, but not to its steady level. Useful if the changes are of interest, and a large or variable background level means that the record would otherwise go off-scale. The transition between what is and is not recorded is characterised by a cut-off frequency, below which signals are severely attenuated (by more than a factor of 2 in energy). Some AC-coupled circuits are characterised by a time constant, where the return to baseline following a step change of input level is exponential. AC-coupling introduces distortion of signals that have frequency components around or below the cut-off frequency. ad - Towards, beside. adaptation Decline of a response while a stimulus is maintained constant after onset. Distinguish carefully from both accommodation and habituation. Light and dark adaptation are the processes of adjustment of the eye to different light levels (whether fast or slowly changing). adequate stimulus The form of stimulation that normally elicits a specific reaction, such as an action potential or a reflex response. adrenaline, epinephrine (USA) A hormone released together with noradrenaline from the adrenal medulla, especially in conditions of stress. Acts at both alpha and beta adrenergic receptors, and mimics some of the effects of sympathetic nerve activation. adrenergic Related to adrenaline or noradrenaline. Adrenergic fibres release noradrenaline, while alpha and beta adrenergic receptors bind adrenaline, noradrenaline and other adrenergic agonists. adult Sexually andor emotionally mature. aequorin A natural protein extracted from jellyfish (Aequorea aequorea) that emits light in the presence of ATP and Ca ions. Used experimentally to measure Ca concentrations within cells. aerobic CONVERSE: anaerobic 9830 Involving the use of oxygen. Aerobic conditions are ones in which O 2 is present. aetiology, etiology (USA) The cause of a disease. affect RELATED: effect 9830 Affect and effect often cause trouble. Affect is a verb meaning to alter, e. g. salt affects the taste of food. Effect is a noun meaning consequence, e. g. salt has many physiological effects. The simplest plan is to learn amp stick to these meanings. However, effect can be a verb too, meaning to produce, e. g. salt effects a reduction in urine flow. Note that it is true to say salt affects urine production but untrue to say salt effects urine production (it does exactly the opposite). Be careful A last complication is that affect is a technical noun in psychology, meaning mood. It is even true that lithium salts have effects that affect affect: clinical depression is an affective disorder for which lithium can provide effective treatment, though unfortunately it seldom effects a permanent cure. affective Relating to emotion or mood. afferent CONVERSE: efferent 9830 Travelling or conveying something towards a structure, or relating to its inputs. Afferent nerves or action potentials are usually those travelling towards the central nervous system. Afferent vessels carry fluids towards a specified organ or tissue. afferent arteriole Arterioles carrying blood towards a structure organ, such as the kidney glomeruli, in which there is arteriolar control of both afferent and efferent vessels. affinity The strength of binding of two chemicals, or a chemical or ion to a receptor or enzyme. Affinity of a receptor for an agonist may be expressed by the agonist concentration at which half of the receptors are bound to agonist molecules (the dissociation constant for the complex: KD), or by - log 10 of this quantity, or by its reciprocal. afterdischarge Action potentials occurring after cessation of a stimulus or a voluntary action. agonist CONVERSE: antagonist 9830 Something that assists or mimics an action. For example, agonist muscles pull parts of the skeleton in the same direction. Agonist drugs or chemicals bind to the same receptors, producing the same effects. algorithm A set of rules for solving a problem. These are often expressed in a computer program. alimentary Relating to food, or the gastro-intestinal tract. all-or-none RELATED: threshold, positive feedback CONVERSE: graded 9830 A response that appears only if the strength of a stimulus exceeds some threshold level, but whose amplitude and characteristics do not depend on the stimulus, e. g. an action potential, or a sneeze. The sneeze is more familiar: pepper either does or doesnt lead to a sneeze. A little pepper doesnt lead to a small sneeze, though it may lead to fewer sneezes. This isnt to say that sneezes are always identical: you can stifle a sneeze and, for example, reduce the noise it makes. These alterations are nothing to do with the stimulus that caused the sneeze, however. Exactly parallel things are true for action potentials. All-or-none responses usually involve some form of positive feedback. alpha radiation ABBREV: 945-rays 9830 Helium nuclei emitted during disintegration of some radioactive elements. altitude Height above sea level. This affects physiological processes largely through the reduced atmospheric pressure, which falls exponentially by ca. 12 per 1000m rise (18 per 5000ft). Oxygen percentage in inspired air remains constant (ca. 21). Effects of altitude are often studied by simulation in a chamber with reduced pressure. Respiration is affected noticeably at 4000m (13,000ft) and severely at 6000m (20,000ft). Reduced PO 2 leads to hyperventilation, which partially maintains arterial PO 2 but lowers arterial PCO 2 . alveolar air Air that is or has been in the alveoli. Samples of alveolar air can be taken at the end of expiration after dead-space air has been expelled (end-tidal samples). Alveolar air is normally approximately in equilibrium with arterial blood, and therefore has approximately the same partial pressures of O 2 and CO 2 as arterial blood. alveolus The terminal air sacs in the lungs, where gas exchange takes place with the blood. Typically 150-300microm in diameter in man (ca. 5nl volume). ambient Relating to the environment of an animal. Z. B. ambient temperature, pressure. Note that the conditions for a particular tissue may be different from the ambient conditions. ampere ABBREV: A, amp 9830 Unit of electrical current flow. amplification RELATED: gain CONVERSE: attenuation 9830 Increase in the size of a signal. This may be active (requiring energy, as in an electrical amplifier) or passive, as in the amplification of movement that may be achieved where a muscle pulls on a lever. Quantitatively, amplification is the ratio of the two signals. amplitude Magnitude how big something is. It can often be defined in several different ways, and it is important to specify what your definition is. For example, the amplitude of a sinusoidal waveform ya. sin(wt) may mean the coefficient a in this expression, or it may mean the peak-to-peak amplitude (i. e. difference in height between the maxima and minima in the waveform (2a), or it may mean the root mean square (r. m.s.) amplitude (0.71a). The same thing goes for measurements you make of a response amplitude, for example an action potential: always say how you are measuring it (e. g. from the resting potential to the positive peak). an - Without, lacking. ana - Up, increased. anaesthesia RELATED: paraesthesia, analgesia 9830 The absence of sensation. This may be general anaesthesia, in which case the subject is unconscious, or local anaesthesia affecting sensation from just a part of the body. Local anaesthesia may be due to influence of an anaesthetic drug or to nerve trauma, etc.. analgesia Absence of pain sensation. analogue RELATED: graded 9830 1. Continuously variable. An analogue parameter can have any value within a range, e. g. body temperature. This is as opposed to a digital parameter, which can only have certain (perhaps integer) values, e. g. the number of limbs an animal has. Analogue numbers are approximated in computers by digital numbers. 2. A drug similar to another drug or to a hormone, etc. analytical RELATED: numerical 9830 Analytical methods for solving mathematical problems employ mathematical techniques to arrive at explicit solutions, which can then be used in more or less general instances. Numerical methods, by contrast, use computers to solve problems in specific cases. aneurysm An abnormally bulging part of a vessel, usually an artery. NB nothing to do with nerves: derives from ana up eurys wide. Aringngstrom ABBREV: Aring 9830 An old-fashioned unit of length: 10 -10 m or 0.1nm. angular velocity Rate of change of orientation of a rotating body, usually measured in radians. s -1 (in which case the angular velocity is 2960 9830 frequency of rotation. anion CONVERSE: cation 9830 Negative ion. NB negative ions move towards an anode (positive electrode) in solution: hence the seemingly confusing nomenclature. anisotropy Having different properties in different directions. annulus Ring shaped. The zone between two concentric circles. anodal block Prevention of propagation of action potentials in a region close to an anode, due to hyperpolarization. anode CONVERSE: cathode 9830 A positive electrode. In solution, cations move away from and anions towards an anode, both contributing to current flow away from the anode. anode break stimulation Initiation of action potentials close to an anode (where the cell is hyperpolarised during current flow), occurring after cessation of the current flow. anomalous Unexpected, different from the main trend of the results or from theoretical expectation. anoxia A condition without oxygen. antagonist CONVERSE: agonist 9830 Something having the opposite effect. Z. B. a chemical opposing the action of another chemical, or a muscle pulling in the opposite direction. ante - CONVERSE: post - 9830 Before. Z. B. antenatal before birth. anterior CONVERSE: posterior 9830 Near or nearer to the front. anti - RELATED: contra - CONVERSE: ortho - 9830 Opposite, against. Z. B. antidromic opposite direction to normal. antilog RELATED: logarithm 9830 The inverse function of a logarithm. It is nearly always used for the inverse of logarithms to the base 10. In this case antilog(x)10 x . antrum Cavity. Narrow duodenal end of the stomach (pylorus). aqueous Associated with water. arc 1. Part of the circumference of a circle. 2. A reflex arc. Arrhenius plot A plot of a reaction rate against 1T, where T is the absolute temperature. This is usually linear, according to Arrhenius equation, with a slope of - EaR where Ea is the activation energy and R the gas constant. artefact, artifact Something arising incidentally from the way an experiment is carried out, and not related to the main aim of the experiment. Control experiments are often helpful in trying to identify artefacts. arterial pressure The pressure within an artery, relative to ambient atmospheric pressure. This varies during the pulse between systolic pressure (maximum) and diastolic pressure (minimum). It also varies along the length of arteries due to the effects of hydrostatic pressure and (especially in small or obstructed arteries) the resistance of the arteries to flow. Standard clinical measurements are normally made in a large artery at the same height as the heart. arteriole Narrow terminal portion of an artery, leading to the capillaries. Resistance vessel. Major site of control of blood flow to tissues, via innervation, chemosensitivity and thermal sensitivity of the smooth muscle of the arteriole walls. Constriction increases the resistance to flow in the arterioles. Note that it does not directly increase the pressure within the arterioles (a common misapprehension), since they are open at both ends. Indeed, constriction generally reduces pressure at the distal (capillary) end of the arterioles, because blood flow through the capillaries is reduced and the capillary pressure therefore becomes closer to venous pressure. arteriosclerosis Loss of elasticity of arteries, usually due to ageing and atherosclerosis. arteriovenous Relating arteries and veins. The arteriovenous pressure difference is the net driving force that causes blood to flow through a tissue. artery Elastic, thick walled vessels carrying blood at relatively high pressure away from the heart. Small arteries are contractile, due to smooth muscle present in the tunica media. The elasticity is important in accommodating the blood ejected from the heart during systole without excessive rise in pressure. - ase Enzyme that breaks down a substance. asymptote A straight line that is approached but never quite reached by a graph, usually as you go far along one or other axis. Not all functions give asymptotes. For example, the graph of y1x approaches both axes asymptotically the graph of yx1x approaches the y axis and the line yx. Neither yx 2 nor ysin(x) have asymptotes. Try sketching these graphs, with their asymptotes where applicable. asynchronous Out of synchrony, or not occurring in relation to an ongoing rhythm, such as the cardiac cycle. atmospheric air Composition of fresh air varies little, apart from water content (0-7). Oxygen is 21, N 2 78 and CO 2 0.03 of dried air. The CO 2 content can be regarded as zero for all practical purposes in animal physiology. The total pressure (ca. 10.1kPa, 760mmHg at sea level) is the sum of the partial pressures of constituent gases, including water vapour pressure ( relative humidity 9830 saturated water vapour pressure). atomic weight Average mass of the naturally occurring isotopes of an element, relative to H as 1 or O as 16. The atomic weights of the commonest biologically important elements are: H 1.0, C 12.0, N 14.0, O 16.0, Na 23.0, Mg 24.3, P 31.0, S 32.1, Cl 35.5 K 39.1, Ca 40.0 attenuation RELATED: amplification, gain CONVERSE: amplification 9830 Reduction in size or effect. Sounds are attenuated with distance. The changes in blood pressure during the pulse are attenuated in small arteries. A recording device may have an attenuator to allow you to vary the gain (or overall amplification). atto - ABBREV: a RELATED: SI units 9830 One million million millionth, 10 -18 . autonomic RELATED: parasympathetic, sympathetic 9830 Relating to the autonomic nervous system. This innervates smooth muscle, glands and visceral organs, which are not normally under voluntary control. Subdivided principally into the sympathetic and parasympathetic efferent systems. Autonomic reflexes are reflexes that act through these efferent systems their afferent pathways may be either the same as pathways that subserve conscious perceptions (as with salivation) or they may be different (as with baroreceptor reflexes). The afferent pathways are not distinctive in any anatomical way, and are not usually described as autonomic except by association with particular reflex actions. autoradiography Localization of radioactive material in tissue by the apposition of film or incorporation of photographic emulsion in the histological processing of tissue. autoregulation A process by which an organ directly regulates changes in its vascular resistance so as to control its blood flow, without involving the central nervous system or systemic hormonal influences. This can produce a relatively flat portion of the graph of flow against arterial pressure. Avogadros number 6.0times10 23 g -1. The number of atoms or molecules having a mass, in grams, equal to their atomic or molecular weight. Avogadros principle Equal volumes of different gases contain, under the same conditions of temperature and pressure, the same number of molecules. A corollary of more direct physiological relevance is that the percentage breakdown of a gas mixture by volume (e. g. 21 O 2 in normal air) is the same as its percentage breakdown by the number of moles or molecules of the constituent gases. One mole of gas at 1atm pressure occupies 24 litres at 20 o C (22.4 litres at 0 o C). Thus 1 litre of air contains 42mmol of combined constituents at 20 o C, including ca. 9mmol of O 2 . axon A nerve fibre. May be myelinated or unmyelinated. A nerve is made up of many axons, Schwann cells (supporting cells) and a sheath. balance A balance control on a measuring instrument (e. g. an oscilloscope amplifier) allows you to adjust the internal circuitry of the instrument for ideal operation. To adjust the balance control of an oscilloscope, connect the input of the amplifier to earth and gradually increase the sensitivity from minimum. With no input (zero volts) you should expect the recording (i. e. spot or trace height) not to change with increasing sensitivity. If it does change, adjust the balance and try again from minimum sensitivity. Once you have done this, you should not use the balance control to make adjustments if a recording goes off-scale: you can usually use a shift or offset control. band pass RELATED: filter, high pass, low pass 9830 A type of filter that lets through a range of frequencies and cuts both higher and lower frequencies. A high pass and a low pass filter acting in series will achieve this, though it may also be achieved in a single circuit. A band pass filter with a narrow pass band is equivalent to a resonant filter. bandwidth RELATED: frequency response 9830 The range of frequencies that a system will respond to, or that is passed by a filter. bar graph RELATED: X-Y graph, histogram 9830 A graph in which the observations (normally along the vertical axis) are shown as bars rather than as points. This is preferred if the horizontal axis, separating different experimental conditions, is qualitative rather than quantitative. For example, measurements may be made with and without a drug or a lesion, or in patients and control subjects. A histogram is a special kind of bar graph, where the horizontal axis is quantitative. - baric SUF Relating to pressure. Z. B. hyperbaric above atmospheric pressure. base In an expression of the form ya b. a is the base and b is the exponent. Correspondingly, logarithms are defined in relation to a specific base. In the expression ya b. b is the logarithm to the base a of y. In chemistry a base is a molecule or ion that will bind hydrogen ions. baseline RELATED: control 9830 Period of recording before a stimulus is given. Recordings in an experiment are usually useless unless there is some baseline recording, showing reasonably stable measurements. A response is only worth considering if it is larger than, or at least different from, baseline fluctuations. Sometimes it is impossible to get baseline measurements: for example, you usually cannot make baseline measurements on patients before they get sick. Then you have to rely on control subjects (e. g. people who arent sick) to check that they dont show the same changes when you start to make measurements on them. basic science Research carried out without the immediate aim of applying the results in a technological or clinical context. Discoveries that lead on to enormously important applications are often made purely as a result of the scientific curiosity of a researcher (e. g. Faradays discovery of the principles of electric power generation, or Flemings discovery of penicillin). Much debate takes place over the question of whether progress in the useful application of science is best encouraged by putting money into applied or basic research. billion A number best avoided It usually means 1012 or 10 12 in the UK and 109 or 10 9 in the USA and in financial circles. Call it a thousand million or a million million. binary RELATED: digital, decimal, octal, hexadecimal 9830 Having only 2 possible values. Numbers are represented in computers as sequences of binary elements: e. g. 2511001, corresponding to the fact that 25 1times16 1times8 0times4 0times2 1times1. This is essentially similar to the familiar decimal convention in which 25 means 2times10 5times1. Fractions can also be represented in binary, e. g. 0.625(decimal) 0.101 (binary), i. e. 1times0.5 0times0.25 1times0.125. birefringence Optical anisotropy of a material leading to a different refractive index for light polarized in different directions. blind RELATED: double blind 9830 An experiment in which either the experimenter or the subject is not aware of some aspect of the experimental conditions. For example, an assay might be done blind, with the person carrying it out not aware of the source of individual samples. This helps to eliminate bias, i. e. the possibility of preconceived ideas of the experimenter affecting the results. block 1. In physiology and pharmacology, block usually means to stop something happening (e. g. a local anaesthetic blocks action potentials in nerve fibres), or to diminish (by any of a number of ways) the effectiveness of a drug, e. g. curare blocks the action of acetylcholine at the nerve-muscle junction. 2. An experiment with trials carried out in a block means the trials are close in time, or not interspersed with other trials under different conditions. boundary conditions RELATED: differential equations 9830 The conditions that determine the particular form of solution that a differential equation will have. Sometimes these are conditions at a physical boundary, e. g. the edge of a piece of tissue. Sometimes they are conditions at a particular time or place, as when there is a sudden local disturbance. For example, the diffusion equation applied to a region of tissue has different solutions depending on whether the surface is permeable and washed by a solution free of the diffusing substance (c0 at the surface), or is impermeable to the substance (implying zero flux and concentration gradient perpendicular to the surface). buffer RELATED: pH 9830 A buffer mechanism makes the effects of a disturbance less than they would otherwise be. Particular mixtures of chemicals can buffer the concentration of an ion, for example H or Ca . A buffer for pH is a mixture of the protonated and unprotonated forms of a weak acid (e. g. H 2 PO 4 - and HPO 4 --. Addition of acid or base causes conversion between these two forms, binding (or releasing) hydrogen ions. This keeps the pH relatively constant. Buffers are most effective, for a given total concentration, when the pH is approximately equal to the pK of the reaction: the two forms of the buffer are then in equal (and therefore quite high) concentration. bug A mistake or problem, usually in a computer program. To debug is to remove such mistakes, while a debugger is a program that helps you to do this. bulk flow Flux of a solution as a whole, carrying all its solutes. cable equation The partial differential equation governing the spread of current and voltage along electric cables and cell membranes. If V is disturbance of membrane potential from rest, T the membrane time constant and 923 the electrotonic length constant for the cell, then dVdt(923 2 d 2 Vdx 2 - V)T (away from the site of a disturbance). Solutions of this equation are set out in Jack, Noble amp Tsien (1975), for various boundary conditions and for cells coupled together to form syncytia. One important situation is where there is a local but relatively long lasting disturbance (e. g. at a synapse): the resulting shift of membrane potential falls off exponentially with an exponential length constant of 923. cable theory Mathematical description of the purely passive spread of electrical current in a cell. Similar to the theory necessary for understanding the properties of very long telephone cables. calci - Relating to calcium, E. g. hypercalcaemia calculus In mathematics, the methods for handling gradients, derivatives and integrals. Anatomically, a stone or hard deposit in tissue. calibration RELATED: accuracy 9830 Comparison of a measurement with a known standard. A set of standards are often required to construct a calibration curve: a graph of the output of a measuring system against the known values. An accurately linear measuring system permits interpolation between just two standards. calorie Unit of energy, particularly heat. 1 calorie 4.18 Joules. The Calorie of nutrition, in a non-scientific context, is unfortunately usually 10 3 calories. However, kcal on a food packet will correctly mean 10 3 cal, not 10 6 cal. Best to avoid this unit (not strictly part of S-I units) when possible, and use Joules. cannula RELATED: catheter 9830 A tube inserted into a vessel (usually a blood vessel) through its wall, so that solution can be put into or withdrawn from the vessel. capacitance Physiological capacitance vessels in the circulation are ones that can contain an extra volume of blood with little or no increase in pressure (mainly the veins, which are like floppy tubes). Electrical capacitance is related: electrical charge is like an amount of electrical substance, and voltage is like pressure. The capacitance between places A and B is the amount of charge you can shift from A to B per unit of voltage change between A and B. A large capacitance (measured in farads: CoulombsVolt) means you need a lot of charge to get much of a voltage shift. Myelinated nerve fibres conduct faster, largely because the myelin reduces the capacitance of the axon. cardiac Relating to the heart, or (as in cardiac sphincter) to the top end of the stomach. carrier RELATED: channel 9830 In the context of membrane transport, a protein that binds a specific substance and by changing conformation transports the substance to the other side of the membrane. A carrier is very much like an enzyme. Carriers are involved in facilitated diffusion, in which the net flux is always down an electrochemical gradient, and also in active transport. Some carriers move two substrates at once. catabolism Metabolism involving the destruction or disappearance of tissue. Fat stores, and ultimately muscle tissue, are catabolised in starvation. catheter RELATED: cannula 9830 Tube inserted into a narrow opening so that fluid can be removed or introduced. You might sometimes insert a catheter through a cannula. cation CONVERSE: anion 9830 Positive ion. caudal CONVERSE: rostral 9830 Toward the tail end of the animal. causal factor Something that contributes to the probability of occurrence of something else, but does not always cause it. centi - ABBREV: c RELATED: SI units 9830 One hundredth 10 -2. Seldom used, except in the unit cm (10mm). cerebral Relating to the brain. cervical Relating to the neck, or the neck of the uterus (womb). cgs RELATED: mks 9830 A system of units based on the centimetre, gram and second. This used to be the commonest standard in the UK, but was replaced some years ago by the SI system, which uses mks units. channel RELATED: permeability, carrier 9830 In membrane transport, a protein that spans the cell membrane and allows substances (usually ions) to move across the membrane. A conformational change in the protein is not involved for each ion that moves, unlike with a carrier. Much higher fluxes can occur than with carriers, and channels are mainly responsible for the permeability of most membranes. Many channels are gated, i. e. can be opened or closed, e. g. as a result of binding of transmitters, hormones or intracellular messengers, or as a result of changes of membrane potential. Different channels also have different selectivities for the ions they let through. Single isolated ion channels can be studied with patch techniques. chaos RELATED: turbulence 9830 A recently developed branch of mathematics, dealing with systems that obey well defined equations, but that are nevertheless intrinsically unpredictable in some respects. The solutions of the equations are very sensitive to the initial starting conditions, so that conditions that are very similar (perhaps within the resolution of any measuring system) can lead, after a short time, to completely different behaviour. It may be possible to predict the behaviour in statistical terms (e. g. the mean velocity of turbulent fluid flow), but not in detail. There are potential applications of chaos theory to the physiological understanding of irregular cardiac rhythms and neural networks. chronic RELATED: tonic CONVERSE: acute 9830 Continuous, or existing for a long time. circa ABBREV: ca.) 9830 Approximately. circadian rhythms RELATED: nocturnal, diurnal 9830 Cyclic patterns of behaviour or of tissue activity (e. g. hormone secretion) that repeat with a period of approximately 24 hours, even when organisms are isolated from the normal daily environmental changes. clamp To keep a parameter constant, or change it in a controlled way to a required value during an experiment. Usually the process involves a control system with negative feedback, which automatically adjusts the parameter if there is a discrepancy from its set value. A voltage clamp circuit is used to control the membrane voltage of a cell in order to study the effects of changes in membrane voltage. It usually requires two microelectrodes in the cell: one to measure the membrane potential, and the second to pass current into the cell to alter the membrane voltage (though sophisticated circuits can sometimes use a single electrode for both purposes). coefficient This is usually a number by which something is multiplied in an equation. For example, the area of a circle is proportional to the square of the radius, with a coefficient 960 (i. e. A960timesr 2 ). In much the same way, it is often used for a quotient (or ratio) of two things, expressing some characteristic property of a substance or an observation. For example the coefficient of variation of a measurement is its standard deviation divided by its mean value. cofactor A chemical in addition to the substrates (reactants) that must bind to an enzyme for a reaction to take place. compartment A definable part of the total volume of a tissue or organism. Z. B. blood plasma, intracellular or interstitial fluid compartments. competitive In considering the binding of substrates to receptors, enzymes or carriers, this means that two or more related substances are similar enough to bind to the same site. Consequently, the extent of binding of one will be reduced if the other is also present and binding to some of the sites. This can lead to competitive inhibition of a reaction or of the normal physiological effects produced by substrate-receptor binding. Many drugs (competitive antagonists) act in this way. compiler RELATED: interpreter 9830 A computer program that translates instructions written in a high level computer language into a form that can be used directly by a specific type of computer. Once a program has been written, the compiler only has to be used once to generate the machine code, usually in the form of an executable file that can then be used without the compiler. The translation process may take quite a long time, and must be repeated when mistakes are corrected in the original program or when changes are required. In these respects, the translation process is quite different from the use of an interpreter. complex A complex is a combination of several things, for example anatomical structures that occur together, or signs and symptoms that occur together in a disease. complex numbers ABBREV: xiy RELATED: vector 9830 A way of thinking about vectors (i. e. arrows) on a 2-dimensional plane as if they were represented by single (but complex) numbers. In an ordinary sense it takes 2 numbers to characterise an arrow: either its length (r) and orientation (952), or the displacements it produces in the x amp y directions. It turns out that the complex expressions xiy and rtimese i952 ), where i is an imaginary number that gives -1 when squared, follow exactly the same rules as vectors when added and multiplied. In handling vectors and sine waves (which correspond to the height of a rotating vector) it is often convenient to use these complex formulae and avoid the need to think in geometrical terms. compliance ABBREV: RELATED: stiffness 9830 A measure of how easily something complies with a force applied to it. For muscles tendons, etc. it is the increase in length divided by the increase of force applied to the structure (i. e. the gradient of the graph of length plotted against force). For the lungs, compliance is the increase of volume divided by the increase of pressure applied at the mouth to inflate the lungs. Stiffness is the reciprocal of compliance. concentration ABBREV: RELATED: activity 9830 The quantity of a solute per unit volume. It may be measured in gl, molsl, kgm 3. g100ml, etc. always with dimensions massvolume. Physiological concentrations are most often expressed in molsl (i. e. the molar concentration or molarity). The unit of molar concentration is 1moll, also written as 1M. Note that it is quite wrong to express a concentration either as 1mol, or 1Ml. These are NOT units of concentration Occasionally concentrations are expressed as , or parts per million (ppm), or gkg. These ratios usually mean the weight of solute per unit weight of solution, or (for a gas) the volume fraction within a mixture. may also mean g100ml. condenser In electricity: old-fashioned word for a capacitor. conductance The reciprocal of resistance. The unit of electrical conductance, the reciprocal ohm, is also called a mho or a Siemens (S). It is often more convenient to think about conductance than resistance. For example, the conductance of a membrane is proportional to its area and is characterised by a specific membrane conductance in S. m -2 . conductivity The reciprocal of resistivity. Units: 937 -1 m -1 or S. m -1 . confidence limits RELATED: significance 9830 The range of values within which you are confident that the true result lies, after doing an experiment. The mean result that you obtained will normally be around the middle of the range. Depending on how variable your individual results were, and how many results you obtained, you may need to assign a large or small range of uncertainty around this mean. 95 confidence limits indicate that if the true mean is outside these limits, the probability that your result would have come out as far away as it did from the true mean is less than 5. constant RELATED: variable 9830 A parameter that is always, and everywhere, the same within the experimental conditions under consideration, but whose value may be relevant to the results. For example the temperature of the Ringer solution might be a constant throughout a series of experiments on isolated muscle: when you describe the results you should state what it is, since it very likely might be relevant. In order to establish whether and how it is relevant, you would have to treat it as a variable in another set of experiments. Physical constants (e. g. the charge on an electron or the speed of light) cannot be treated as variables since so far as we know they always have the same values. constriction CONVERSE: dilation 9830 Narrowing of a vessel. Z. B. vasoconstriction narrowing of blood vessels, usually due to contraction of smooth muscle. contra - RELATED: anti - 9830 Against, opposite contraction CONVERSE: relaxation 9830 State of activity of a muscle in which it may produce force andor shorten, depending on the mechanical constraints on it. Note that contraction in ordinary English means getting smaller. In muscle physiology the word shortening is reserved for this, and contraction may occur even while a muscle is lengthening. Note also that activation in muscle physiology is also different from contraction, referring specifically to the electrical activation of the membrane. control RELATED: control system, control experiment 9830 Many physiological systems are control systems, maintaining homeostasis of some tissue parameters. Control here means regulation, just as you might control the temperature in your room. A control experiment, or control for short, has a different meaning. Control here means check. It doesnt take this meaning in ordinary English, unlike in some other languages (where the gasman might control your meter). A control experiment is one designed to check that a result is not due to an incidental aspect of your protocol. For example, if you dissolve a drug in oil to administer it, you should do some controls to check that oil alone does not have some effect. cooperative A process in which different individual elements do not act independently, but produce a bigger effect in combination than the sum of their effects on their own. Chemical reactions exhibiting cooperativity give a sigmoid (S-shaped) curve when product concentration is plotted against reactant concentration. correlation RELATED: regression 9830 A systematic relationship between two variables. If A tends to be high when B is high, it is a positive correlation, while if A is high when B is low it is a negative (or inverse) correlation. A correlation need not be perfect. Thus in the adult population there is a positive correlation between height and weight, even though the taller of two people is not invariably the heavier. A correlation coefficient indicates the degree of consistency of the correlation. Uncertainty and misunderstanding sometimes surround the issue whether a correlation indicates a causal relationship. If stress is correlated with early mortality, is it perhaps because stress is also correlated with smoking cortex The skin, or outer part of an organ (e. g. the cerebral cortex or adrenal cortex). coulomb The unit of electrical charge. 1 Amp 1 Coulomb flowing per second countercurrent A mechanism in which fluids flowing in opposite directions interact by transport between them of heat or solutes, etc. Such mechanisms are important in many animals for the conservation of heat in limbs exposed to extreme cold (where the transfer is purely passive), and in the kidney for the concentration of solutes in excreted fluids (where the transport of solutes involves active transport). cranial Relating to the skull (cranium). critical experiment RELATED: crucial experiment 9830 An experiment in which the outcome disproves a hypothesis, or in principle could disprove a hypothesis. It is of course true that science advances through experiments that support hypotheses. However, experiments that merely support a hypothesis and that do not disprove a different hypothesis that was otherwise plausible, are of less value: they are not critical. crucial experiment RELATED: critical experiment 9830 An experiment for which two plausible hypotheses give clearly distinct predictions. It may be better than a critical experiment, because it may separate the two hypotheses. If you think that muscle fatigue (i. e. a drop in maximum voluntary tension) might be due to either a failure of the nerve-muscle junctions or a failure in the muscle cells, then a crucial experiment would be to measure the tension due to direct muscle stimulation, before and during the fatigue. If you stimulated instead the nerve to the muscle, this would be a critical but not a crucial experiment (i. e. it could prove both hypotheses wrong, but it couldnt tell them apart). CT scan RELATED: CAT 9830 Computed tomography, or computed axial tomography. An X-ray technique in which an image of the internal structure of tissue is reconstructed, not just a shadow picture as in an ordinary X-ray. current RELATED: charge 9830 An electric current is the rate of flow of charge in a circuit. Its units are Amps (A). Moving charges may be positive (e. g. in tissue, Na . K ions) or negative (e. g. Cl - ions or (in metals) electrons). The DIRECTION of current flow is the direction that positive charges are moving, if there are any present (as there always are in an ionised solution). Negative charges move in the opposite direction. The DIRECTION of current in a resistor or in tissue is always from ve to - ve (unless the current is coupled to a chemical reaction, as in a battery, or a form of ACTIVE TRANSPORT providing energy, when charge may be moved uphill towards places with a more positive voltage. curvilinear A non-linear relation, i. e. one for which the graph is curved in at least part of its range. E. g. a sigmoid relation. data The results of an experiment or investigation. Strictly, it is the plural of datum, and you should say for example These data show. . In practice, the word datum is hardly ever used and it is probably more common to say This data shows. . database RELATED: keyword 9830 A computer program for keeping track of large numbers of related records, allowing them to be sorted, ordered, and selected on the basis of information contained in them. deca - ABBREV: da RELATED: SI units 9830 Prefix meaning ten times, as opposed to deci - meaning one tenth. Very easily confused and very seldom used in physiology. deci - ABBREV: d RELATED: SI units 9830 One tenth 10 -1. Seldom used. The SI system of units encourages units based on multiples of 10 3. A litre is 1dm 3. Old-fashioned rulers sometimes mark a decimetre (100mm). Dont talk about it decibel ABBREV: dB) 9830 A unit of intensity of sound, or other forms of energy. It is a logarithmic unit, which compresses the huge range of audible sound intensities into a range from 0-100dB or thereabouts. 10dB corresponds to an increment of 1 in the log of the sound energy, or a factor of 10 in the energy itself. The sound intensity corresponding to 0dB is nominally the threshold of hearing. This is one of the few units where the prefix deci - is used. The primary unit (1bel10dB) is seldom used at all. default What is to be understood if you dont specify something different. This word has become common through computer usage, where software will often use its own (default) values for parameters unless you take steps to change them. Some scientific words like percentage or amplitude have default meanings in particular contexts, that can nevertheless be altered. It is usually good practice not to assume a default meaning, since it may not be universally accepted. definition The precise meaning of a word or phrase. The meaning may depend on context: see e. g. steuern. Scientific and physiological meanings often differ from those in an ordinary dictionary. Where there is ambiguity, the context should make the meaning clear. Ambiguities are a plague in science, as in everything except the subtler arts If you are asked for a definition, give (a) one or more paraphrases of what the word or phrase can mean, (b) brief accounts of the contexts in which it might be used, with examples, (c) if appropriate, an equation relating it to other concepts (e. g. for peripheral resistance). Dont write an essay on Everything you need to know about X, except what it is. degrees of freedom ABBREV: d. f. RELATED: statistical test 9830 The number of things that can be varied independently. These may be anatomical (e. g. the shoulder has 3 d. f. of movement), or physiological (e. g. the properties of the eye mean that you have just 3d. f. in mixing colours that can be distinguished in high light levels and only 1d. f. in low light levels). In mathematics, a linear relation has 2d. f. (e. g. slope and height, or 2 points it must pass through). In statistics, the no. of d. f. is usually 1 or 2 less than the no. of variables that go into your calculation, often because the result (e. g. a standard deviation) would be unaffected if you were to use the (n-1) differences from the first sample, instead of the (n) individual measurements. delta ABBREV: 916X, 948X, dX RELATED: differential 9830 The Greek letter delta is often used to indicate a change in a parameter. dendrite A branching, tree-like structure. Most commonly, the part of a neuron that receives synaptic contacts. denominator RELATED: numerator 9830 The bottom line of a quotient. B in the expression AB. It is seldom necessary to use the word: certainly avoid it if you might confuse it with numerator. You could call it the bottom line of the expression to avoid ambiguity. dependence CONVERSE: independence 9830 Dependence of A on B means either simply that A affects B (e. g. skin temperature depends on environmental temperature) or, in some contexts, that B cannot exist without A (e. g. consciousness depends on adequate cerebral blood flow). Note that either relationship is a dependence, not a dependency (which is usually a small island off the coast somewhere - i. e. something that is dependent). dependent Dependent and independent variables are tricky concepts. In many experiments you vary something (an independent variable) and measure another (dependent) variable. When you draw a graph (e. g. say, cell volume against osmolarity of your solution), you always plot the independent variable horizontally and the dependent variable vertically. In some experiments, both variables may be strictly dependent: you might measure red cell volume and blood osmolarity in a lot of different subjects. You could plot this relation either way. You would need extra experiments, or a clear argument in discussion, to establish whether a correlation reflected a dependence of one variable on the other. depression RELATED: inhibition CONVERSE: potentiation, facilitation 9830 A decrease in the activity of tissue or the amplitude of a response. If the decrease is due to the involvement of structures (e. g. particular synapses) that appear to have the specific function of causing the depression, then it is usually called inhibition. Spreading depression is a disturbance that causes a profound but transient depression of the excitability of nerve cells in local regions of the central nervous system. Clinical depression is a mental condition characterized by extreme sadness, a component of several clinical syndromes. derivative ABBREV: dydx RELATED: partial derivative CONVERSE: integral 9830 The gradient of the graph of a function: dydx is the gradient of y plotted against x. The second derivative (d 2 ydx 2 ) is the gradient of the graph that you get if you plot dydx (the first derivative) against x. If you know the equation for a graph, you can usually write down an equation for its derivative (i. e. differentiate the equation). If you know the shape of a graph, you should always be able to sketch the graph of the derivative. In chemistry, a derivative is a compound of similar structure that can be made from another compound. derivatives (simple functions) RELATED: differentiate 9830 If you need to differentiate an equation, then you need to know the rules for differentiation, plus the derivatives of some simple functions. The most important examples are: If yx, then dydx1. If yx 2. then dydx2x. If y1x, then dydx-1x 2. NB these are really all special cases of a single rule: if yx n. then dydxnx n-1 ). If ye x. then dydxe x. If yln(x), then dydx1x. For functions of angles, the derivatives are simplest if the angles are measured in radians: if ysin(x), then ycos(x) if ycos(x), then dydx-sin(x). describe RELATED: results, discussion 9830 Describe the results is a common beginning to an exam question. You should understand how this is quite different from Discuss the results. The same distinction holds between the RESULTS and DISCUSSION in a scientific paper. Describe means give a clear account of just the facts in front of you (which may include graphs or tables). Indicate how the data were obtained, and draw attention to the amplitude and time course of any effects or correlations that are demonstrated (identifying dependent and independent variables), and try to assess which features look likely to be reproducible (either by eye or with the help of statistical tests). Try to lay a constructive base for a discussion. determine Two distinct, but straightforward, meanings: (1) To measure. (e. g. Determine the pH of the blood. means Take blood and use a pH meter. (2) To influence and control. What determines the pH of the blood asks for an account of the role of respiration and the kidney in acid-base physiology it does not invite the one line answer a pH meter. diastole RELATED: relaxation, filling CONVERSE: systole 9830 The part of the cardiac cycle during which the ventricular myocardium relaxes, pressure falls and the chamber fills with blood. Diastolic pressure is the arterial pressure at the end of diastole, i. e. the lowest arterial pressure during the cycle. differential ABBREV: 948X or dX RELATED: delta 9830 A change in a parameter. In mathematics it is a very small (actually infinitesimal) change. Gradients (rates of change, derivatives) are the ratios of differentials for two parameters plotted against each other, hence the terminology dydx. The word differential is sometimes used incorrectly for derivative. A differential diagnosis is, more straightforwardly, the process of distinguishing two clinical conditions that have similar symptoms. differential equation RELATED: boundary conditions 9830 An equation involving a derivative, or rate of change, of a function. For example, in many situations following a disturbance from a normal steady state the rate of return towards the steady state is proportional, at each instant, to the size of the disturbance: dydt-ay. This gives rise to an exponential solution: yAe - at. with a time constant 1a. A partial differential equation relates partial derivatives with respect to two or more parameters (e. g. time and position). Important examples of partial differential equations in physiology are the diffusion equation (Ficks second law) and the cable equation. differentiate RELATED: derivative CONVERSE: integrate 9830 To find the derivative of a graph, e. g. by making a sketch, by calculation with a computer, or (if you know the equation of the graph) by using the rules of differentiation. There are 3 rules: (1) If functions add, then their derivatives add: i. e. if yf(x)g(x) then dydxdfdxdgdx. (2) If two functions are multiplied, yf(x)timesg(x) then dydxftimesdgdxgtimesdfdx. (3) If y is a function of a function, i. e. yf(u) where ug(x), then dydx(dfdu)times(dgdx). Rule 3 is best understood by example: if y(1x 2 ) 3. then this can be written yu 3 where u1x 2. Therefore dydx(3u 2 )times(2x) 6x(1x 2 ) 2. These rules, plus knowledge of the simple derivatives, enable you to differentiate any function. differentiation The process of finding the derivative (gradient) of a mathematical function. The process by which cells acquire different properties during development. diffusion The process by which molecules get from one place to another (or across a membrane) by random thermal motion. Facilitated diffusion is where a special molecular mechanism in a membrane (a carrier) allows diffusion of certain molecules that would not otherwise get through: rather like a parent who lifts children over a fence. diffusion coefficient The constant that appears in either of Ficks two laws of diffusion. It has dimensions L 2 T -1. Typical values for small molecules and ions in free solution are of order 10 -9 m 2 s -1. Typical values for diffusion of gaseous molecules are roughly 10 4 times larger hence diffusion can be an important physiological mechanism in the gas phase (for example for fluxes of O 2 and CO 2 ) over much larger distances than in solution. diffusion equation The partial differential equation governing the diffusion of substances. Ficks second law of diffusion. It states that dcdtD(d 2 cdx 2 d 2 cdy 2 d 2 zdz 2 ), where c is concentration and D is the diffusion coefficient. In vector notation it is dcdtD8711 2 c. It has the same form as the equation for conduction of heat, so solutions of the diffusion equation with particular boundary conditions (see e. g. Crank: Diffusion) can often be obtained by reference to the equivalent solutions in a textbook of heat theory (Carslaw amp Jaeger: Conduction of Heat in Solids). Solutions are often gaussian or error functions. digital RELATED: binary CONVERSE: analogue 9830 A system (e. g. a computer or measuring system) that uses numbers that can only have discrete values (i. e. a limited number of specific values). A digital oscilloscope is convenient because it can store and manipulate data, but in some ways it is less satisfactory than an analogue oscilloscope, because it makes measurements at discrete time intervals and may therefore miss a signal of interest. dilatation, dilation CONVERSE: constriction 9830 Opening up of a hollow or tubular structure, such as a blood vessel or the pupil of the eye. The form dilation is apparently incorrectly formed from Latin, but seems to be rising in popularity (there is no distinction in meaning). dimension RELATED: unit 9830 The relation between the fundamental physical quantities that correspond to a parameter. Z. B. velocity has dimension lengthtime pressure has dimension forcearea, or mass(length x time 2 ). Quantities with particular dimensions may be measured in different units (e. g. velocity in ms or kmhr). The units must themselves have the correct dimensions however. In order to compare the size of two parameters, they must have both the same dimensions and the same units. discrete Separate, unmixed (e. g. discrete compartments in the body). Taking one of certain specific values (e. g. discrete frequencies at which a piano string will resonate: the fundamental and its harmonics). discuss RELATED: describe 9830 Read first about describe. You may be asked to discuss something specific, but in general a discussion sets out firstly what you think you can conclude from the results. This may not be anything very definite, but you should at least be able to generate some ideas (hypotheses) that could explain the data. You may also see that some ideas you might have had are ruled out by the data: this is the often the most constructive kind of conclusion in science. Put this all down. Discuss how you might distinguish the different hypotheses with extra experiments or with more information. In general, try to clarify the implications and limitations of the data, and relate it to what you already know. dissect RELATED: isolate 9830 To cut. To remove a piece of tissue or a cell from some larger structure. To separate or cut through part of a structure to expose some element of it. distal CONVERSE: proximal 9830 Far (or farther) from some implied point. The distal parts of a limb are those far from the body. Distal parts of a neuron are those far from either the central nervous system (when talking about peripheral nerves) or from the cell body of the neuron. (NB occasionally this can cause confusion: for example, the term should not be used without clarification when talking about the dorsal roots, where the two directions are opposite.) distortion RELATED: filter 9830 A change from normal, usually in relation to physical shape or the time course of a signal. A tissue may be distorted by pushing on it. A waveform may be distorted by passing it through a filter. A filter may be useful for cutting out noise or interference even if it does distort signals somewhat. distribution In mathematics, this is the way a set of points are scattered along one axis or throughout the plane of a graph. A probability distribution is the way they would be scattered if you took very many samples. It can be expressed by a histogram, showing how many points lie in each interval, or by a probability density function (essentially the same thing, for very many points and very small intervals). Data for analogue variables often has a normal or gaussian (bell-shaped) distribution, which can be characterised by a single parameter: its standard deviation. In physiology, distribution also means the range of places in a tissue where you will find a particular substance. dorsal CONVERSE: ventral 9830 Relating to the back. dose-response curve A graph of the response to an applied drug, plotted against drug concentration or dosage. double blind RELATED: blind 9830 An experimenter in which both subject and experimenter are unaware of the conditions relating to each individual subjects. For example, neither patient nor doctor may know whether the patient is taking a drug being tested or a placebo. Information about which condition relates to each subject is kept separately and used eventually at the end of the study to analyse the results. drift RELATED: trend 9830 A gradual, continuous change in a parameter. Often this is an unwanted change due to an instability in a physiological system or a gradual change in the properties of a measuring instrument (e. g. baseline drift). drive RELATED: trigger 9830 A structure is said to drive another if events in the first trigger events in the second. For example, the pacemaker region drives the cardiac cycle in other parts of the heart. Drive, as a noun, usually relates to a state of an animal in which its behaviour is directed to satisfying a particular need, such as hunger, sex, etc.. - dromic SUF Relating to direction. Z. B. antidromic. drug A chemical that affects biological tissues. Often the usage is restricted to chemicals that are used clinically or for research purposes, or ones that are abused socially. Nutrients, toxins, and chemicals one is particularly fond of, tend not to be called drugs. dyne The cgs unit of force: 10 -5 newtons. dys - Abnormal, painful. Z. B. dyspneabreathless. earth RELATED: ground (esp. in USA) 9830 An electrical concept. You cant measure a voltage at one place. You can only measure voltage differences. It is convenient therefore to have a constant reference, relative to which you measure all voltages in a circuit or a tissue. This is called earth. It is usually connected to the chassis of equipment and to the outer part (the screen) of screened cables. For safety reasons, and also to reduce interference, the reference points are usually connected to the ground and to metal parts of the building if not, the reference is said to be floating. - ectomy SUF RELATED: - tomy 9830 Cutting and removing. Z. B. lobectomy removing a lobe of an organ. effect RELATED: affect 9830 See affect for a clarification of the difference in meaning of these two words. efficiency The ratio of how effective something is to the maximum effectiveness it could possibly have. The thermodynamic definition is the ratio: work done by a system available free energy. z. B. RELATED: i. e. 9830 Distinguish carefully between e. g. and i. e.. It can give quite the wrong meaning if you muddle them. z. B. means example given (strictly, exempli gratia in Latin). D. h. means that is ( id est in Latin). If you mean to say You can get drinks (e. g. beer) from the bar. and you actually say You can get drinks (i. e. beer) from the bar. then it would imply that the bar only provides beer. Einthovens triangle A standard way of analyzing the electrocardiogram, in which the electrodes are assumed for simplicity to be at the corners of an equilateral triangle. The axis of the heart is taken as the vector that would give the observed signals when projected onto the sides of this triangle. electrical axis See axis of the heart. electrocardiogram ABBREV: EKG or ECG) 9830 Voltage changes recorded with electrodes on the skin, due to the electrical events of the cardiac cycle. Standard electrodes are placed on the left (L) and right (R) arms and on the left leg or foot (L). The right leg is earthed. Additional (precordial) electrodes may be used on the front of the chest. Three standard connections of leads are usually made, to record the differences in voltages: IL-R, IIF-R, IIIF-L. Alternative augmented configurations are also sometimes used (aVR, aVL, aVR). The principal components of the EKG signal are the P wave (due to atrial depolarization), the QRS complex (ventricular depolarization) and T wave (ventricular repolarization). electroencephalogram ABBREV: EEG) 9830 Voltage changes due to the brain, recorded from electrodes on the scalp. electrolyte A salt that dissociates into ions especially when dissolved in water. An electrolyte may be strong e. g. NaCl or weak e. g. an amino acid. Any electrolyte in solution will conduct electricity. All tissue fluids contain electrolytes. Strong solutions of strong electrolytes (e. g. 3M NaCl) have a high conductivity (i. e. low resistivity). electromyogram ABBREV: EMG) 9830 Voltage changes due to muscle, recorded from electrodes on the skin over the muscle. electroneutrality The principle of electroneutrality states that the total charges on positive and negative ions in a solution must be equal and opposite. This leads to a great paradox in physiology and physical chemistry: how can this be true if at the same time we talk about fluxes of just one kind of ion (e. g. sodium ions) between the solutions on two sides of a membrane The answer is that electroneutrality is not always exact. However, unbalanced fluxes (even big enough to produce large shifts of membrane potential, say 100mV) are so small that the violation of electroneutrality would be quite unmeasurable with chemical techniques (corresponding typically to a concentration ratio of 1.0001:1). electro-oculogram ABBREV: EOG) 9830 Voltage changes due to movements of the eyes, recorded from electrodes above and below, or on either side of, the eyes. embarrass Physiologically, an organ or a function is embarrassed if it is prevented from operating normally. For example, putting your shoulder over the back of a chair can embarrass the circulation to your arm. embolism RELATED: air embolism 9830 Blockage of an artery by an embolus. Emboli in the venous circulation generally lodge in the lungs (pulmonary embolism). Arterial (systemic) emboli can be more serious, sometimes producing stroke, myocardial infarction or gangrene depending on the site of obstruction. embolus Abnormal fragments of material carried in the circulation, e. g. a blood clot (thrombus), fat, air (as a bubble) or foreign bodies. e. m.f. The potential difference between the terminals of an electrochemical cell or battery when no current is drawn from it. Units are Volts. endo - CONVERSE: epi-, exo - 9830 Within. Z. B. endogenous arising within a tissue. enzyme A protein that catalyses (enhances the rate of) a chemical reaction. Its action involves binding of the substrate or substrates (reactants) and a conformational change in the enzyme itself. epi - RELATED: peri - CONVERSE: endo - 9830 Above, surrounding. Z. B. epicardium layer of tissue immediately surrounding the heart (part of the pericardium), epidermis outer parts of the skin. epinephrine See adrenaline. equilibrium RELATED: partial pressure 9830 A condition in which there is no tendency for a substance to move spontaneously in either direction across a boundary. A solution in contact with a gas mixture will be in equilibrium when there is no net flux of gas molecules across the interface, and the partial pressures of the gases in solution are then the same as in the gas phase. An ion is at equilibrium across a membrane if there is no passive flux of the ion (though NB there might be active transport of the ion species, requiring energy, even at equilibrium. A third example is osmotic pressure: absence of passive water flux across a semi-permeable membrane (selectively allowing water across) requires that any tendency for water to diffuse (due to an osmolarity difference) is balanced by a pressure difference: this equilibrium defines the osmotic pressure difference across the membrane. equilibrium potential ABBREV: Veq(x) RELATED: Nernst equation, resting potential 9830 The value of the membrane potential of a cell at which there would be electrochemical equilibrium for a specified ion. In general in a particular cell the equilibrium potential is different for different ions. If the membrane potential is made equal to Veq for a particular ion, then there is no net passive flux of that ion even if there are open channels that are permeable to it. In nerve cells, Veq(K) is close to the negative resting potential, while Veq(Na) is positive). The equilibrium potential can be calculated from the Nernst Equation. error bars RELATED: standard error, confidence limits 9830 Graphs are often drawn with bars at each point, as well as the mean measurement. These indicate a measure of the variability of the data that has contributed to the mean. Usually the bars extend 1 standard error above and below the mean, though it should always be stated exactly what the bars are, since they may be standard deviations or confidence limits. If they are standard error bars, then a useful rule of thumb is that if the error bars overlap for 2 sets of measurements, then the means for these measurements are certainly not significantly different. If they are separate, but not far apart, you would need to do a statistical test to see if the difference was significant error function RELATED: gaussian 9830 Error functions are integrals of the gaussian and closely related functions, i. e. the area under a part of the bell-shaped curve. You cant write down an exact expression for calculating these, but you can look them up in tables: e. g. tables of the areas under the graph of a standard normal distribution, also known as the cumulative normal distribution. eu - RELATED: ortho - 9830 Normal. Z. B. eupnea normal breathing. evoked An evoked response is a response following a brief applied stimulus. In neurophysiology it is often a voltage change, also called an evoked potential or an event related potential. excise RELATED: dissect 9830 To cut out and remove. excitability RELATED: threshold 9830 The ease with which a cell can be made to respond to a stimulus, for example by giving an action potential. The term is usually used loosely for comparison (e. g. low extracellular calcium concentration increases the excitability of neurons). It is not usually defined as a quantitative parameter, though it is inversely related to threshold. excitation RELATED: stimulation 9830 Stimulation above a threshold level for producing a response, particularly an action potential response of nerve or muscle cells (excitable cells). exo - RELATED: epi - CONVERSE: endo - 9830 Outside. Z. B. exoskeleton structural support on the outside, rather than the inside of tissue, as in many invertebrates exogenous something not normally found in the tissue. expectation RELATED: mean, average 9830 In an ordinary sense this is what you expect in a situation, given your assumptions and theories. In a mathematical sense, the expectation of a parameter is the mean value that it would have if you repeated a large number of observations (more strictly, the limit for an infinite number of observations). This can sometimes be calculated as the sum of products of all possible values of the parameter with the probability of obtaining each value. The expectation for the outcome of throwing a dice is 3.5 (16 26. 66). The expectation for the height of a subject selected at random is the mean for the population from which he is selected. experiment RELATED: critical, crucial, exploratory experiments 9830 A procedure for finding out something new or for demonstrating a known fact. In physiology, an experiment sometimes refers to a procedure carried out on a single animal or sample of tissue, sometimes to a set of procedures including control observations, etc. carried out on many animals or samples. explicit CONVERSE: explicit 9830 An equation involving a parameter (x) is explicit for x if it is written in the form x equals some expression not involving x. For example, if you have a quadratic equation: ax 2 bxc0, the quadratic formula for solution of such an equation enables you to solve the equation explicitly. exploratory experiment RELATED: critical experiment 9830 An experiment carried out to find out what happens in a particular situation, without any clearly formulated hypothesis at the start. For example, if you discovered a new type of cell in the body, but had no idea about its function, you might study the effects on it of several known hormones. Much research is of this general type. It provides information that may generate hypotheses and eventually support or disprove ideas. exponent RELATED: logarithm 9830 The power to which a number is raised: if yx a. then a is the exponent. If a1,2,3, etc. the meaning is simple: x is multiplied by itself a times. Note that x a times x b is x ab. This rule allows us to generalise to negative and fractional exponents. Firstly, x 0 must be 1, since the rule requires that x 0 times x a x a. Secondly, x - a times x a x 0 (1), so x - a is the reciprocal of x a. Third, x 1a is the ath root of x, since if you multiply it by itself a times, you get x 1. Lastly, x ba is the ath root of x b. by the same argument. You should become completely familiar with the first 2 or 3 of these rules exponential constant RELATED: time constant (964), space constant(923), rate constant, half-life 9830 This is a common way to express how fast an exponential function falls or rises. In graphical terms, if you draw a tangent to an exponential curve at any point, it crosses its baseline exactly one exponential constant to left or right. It is the reciprocal of a rate constant ( rate of change displacement from steady value . For a declining exponential, the time constant is the time it would take to reach the final steady value if the rate of decline didnt slow down. An exponential curve actually falls (or rises) to 1e (times0.368) or timese (times2.718) in this time, so an equivalent definition is the time for the value (relative to its steady value) to change to 37 or 272 of its current value (1.44 times half-life or doubling time). exponential function ABBREV: e x. exp(x) RELATED: natural logarithm 9830 The function ye x. where e is a specific number (approx. 2.718) always called just e. The exact value of e cannot (like 960) be written down. You can get as good an approximation as you like by calculating the value of (11n) n with n large enough. Try this on a calculator This definition of e (as the limit of the expression as n 8594 8734) arises naturally from the way e is introduced in the entry on the exponential constant. The function ex is especially important because its gradient is always exactly equal to its value. In other words, it is a solution of the differential equation dydxy. This makes it the simplest exponential relation to handle mathematically. exponential relation A relation is exponential if one parameter changes by a constant factor every time another changes by a constant amount. It has the form yatimesbx. This means that for 1 unit shift along the x axis, y gets multiplied by a constant factor b. The graph is increasing or decreasing, depending on whether bgt1 or blt1. NB, note the important difference from a power law (yatimesx b ). In an exponential relation the variable parameter x appears in the exponent. There is really only one shape of exponential curve, since all graphs of the form yatimesbx can be made equivalent by changes of scale or reversing the axes. An exponential relation gives a straight line if you plot log(y) against x, for example on log-linear graph paper. exponentials: examples Rising exponentials are seen in unrestricted population growth (e. g. bacteria, which might double their population each hour) or growth of capital in a bank account (8 interest per annum corresponds to a rate constant for increase of 0.077ann, a doubling time of 9 years, or a time constant of 13 years). Decreasing exponentials are common in physiology: disturbances often decline by an approximately constant factor per unit time, for example membrane potential disturbances with a time constant of a few ms after stimulation, or heart rate over minutes after exercise. The size of a synaptic potential declines with distance from the synapse along a dendrite approximately exponentially, with a space constant that might typically be 0.5mm. exsanguinate To let out much or all of the blood from an animal. extra - CONVERSE: intra - 9830 Outside. Z. B. extravasation something getting out of blood vessels. z. B. Example given. Beispielsweise. Dont muddle this with i. e., which implies that what follows is always true, not just an example of what might be true. If you do muddle these, the reader may be led to think you have quite the wrong idea. facilitation RELATED: potentiation CONVERSE: embarrassment, inhibition 9830 A process that makes something easier or increases its effectiveness. For example, a bronchodilator can facilitate breathing. An influence is said to facilitate a response if the response to a constant stimulus is increased while the influence is applied. For example, clenching of the fists often facilitates the knee-jerk tendon reflex (the Jendrassik manoeuvre). Potentiation, on the other hand, is an increase that outlasts the influence that causes it. factor Something that influences or induces the response of a tissue. The term factor is often used when very little is known about an influence: for example, vasodilation might in some situation be caused by a neural or hormonal factor, or by a physical factor such as a change of temperature. Factor analysis is a statistical technique for identifying the combinations of known variables that are the best predictors of a measured parameter (e. g. of IQ). factorial ABBREV: n) 9830 Product of all the integers from 1 to n. 11, 22, 36, 424, etc. For large numbers, a reasonable approximation is (ne)n. farad ABBREV: F) 9830 Unit of electrical capacitance. The capacitance of a membrane is proportional to its area, and is typically about 1uF. cm -2 . faraday ABBREV: F) 9830 The amount of electrical charge per mol of univalent positive ions: 96,500 coulombsmol, i. e. about 10 5 coulombsmol. You need to know this whenever you are thinking about how much of a concentration change is associated with electrical changes, as with current flowing across cell membranes. This is the F of the quantity RTF that comes into the Nernst equation. Note that the abbreviation F is the same as for a farad. This should not lead to confusion, since a faraday is a quantity, while a farad is a unit, but you do need to be careful. fatigue A reduction in a response as a result of repeated or prolonged stimulation or activity. In the context of muscle function, it usually means a reduction in the amount of force that the muscle can produce. feedback RELATED: control 9830 Information sent to an earlier stage in a multistep process. Negative feedback has effects that reduce the subsequent feedback signal, or reduce its rate of increase. This usually has a control function, keeping a parameter in the system constant. For example, the activity of the heart raises the arterial blood pressure. If the pressure rises above a controlled level, signals are sent via baroreceptors and the brain back to the heart, leading to a decrease in heart rate. Positive feedback produces changes that lead to a further increase in the feedback signal. This can lead to runaway changes in the system, and usually to an all-or-none response (e. g. an action potential). femto - ABBREV: f RELATED: SI units 9830 One thousand million millionth. 10 -15. The smallest fraction of a unit you normally come across in physiology. For example, the small magnetic fields produced by brain activity are measured in femto-Tesla (fT). fibrillation RELATED: atrial flutter 9830 Repetitive high frequency spontaneous activation or contraction of a muscle, particularly cardiac muscle. Quivering. Atrial fibrillation is faster than atrial flutter (gt300min) and more irregular. Ventricular fibrillation is similar, and arises frequently from electrocution or a myocardial infarct: it is normally lethal within a few minutes if not arrested (e. g. by electric shock from a defibrillator) or unless blood flow is sustained by cardiac massage. filter RELATED: low, high, band pass notch filter 9830 An electrical circuit or structure that passes some things and prevents passage of others. Electrical filters usually pass and cut particular frequency components of a signal. They may be passive (not requiring a power source) or active (requiring a power source). Physiological systems, such as the kidney glomeruli, sometimes act as physical filters, passing water and some solutes to produce a filtrate or ultrafiltrate (the latter including only small molecules). A substance is freely filtered if (as with inulin in the kidney) it is in about the same concentration in the filtrate as in the filtered solution. fixation Chemical treatment of a tissue to precipitate proteins and ensure that cell structures will not change subsequently. This is the first procedure in the preparation of specimens for microscopy. Fixatives (e. g. formaldehyde, glutaraldehyde) kill cells and may introduce artefacts (distortions of normal structure). fluorescent Capable of emitting light at one wavelength when light of another wavelength is absorbed. The wavelength of the emission is always longer (more towards the red end of the spectrum) than the wavelength of the exciting light. Fluorescent dyes are useful for marking cells into which they are injected, or for labelling receptors to which they bind. Some dyes exhibit fluorescence that changes with pH or pCa, and these can be used as indicators to measure H or Ca 2 concentrations. flux RELATED: net flux 9830 Rate of movement of a substance or solute. Movement may be in both directions at once, as with molecules diffusing within solution or across a membrane, in which case the net flux is the difference between the rates in each direction separately (the unidirectional fluxes). Unidirectional fluxes are often measured with the help of radioactive tracers, labelling the solute on one side. In an equilibrium situation there is no net flux, unless active transport is involved. Flux is sometimes measured as the total amount moving per second (e. g. into a cell), sometimes as the amount moving through unit area per second. The units should make it clear which is used (e. g. mol. m -2.s -1 ). form RELATED: time course, profile 9830 The shape of a graph, for example of the time course of a parameter. The form of a relationship is considered to be independent of the scale on which the graph is drawn, on either axis. Thus the time courses for the recovery from tachycardia (high heart rate) and hyperthermia (high temperature) after exercise have the same form (both roughly exponential), even though the restoration of normal heart rate may be much faster. fractional change RELATED: proportional, percentage 9830 The fraction by which a parameter has changed, i. e. (new value - old value)(old value). Fractional changes are often multiplied by 100 to give percentage changes. frequency components RELATED: sinusoidal 9830 The waveform of any signal can be broken down into a combination of frequency components: individual sinusoidal waves, each with its own frequency. The signal is the sum of these frequency components. This is called Fourier analysis. The reason for choosing this particular breakdown of a signal is that any linear system produces a very simple response to a sinusoidal signal: an output that is sinusoidal at the same frequency, with just an amplitude and a phase to be determined. The response to an arbitrary signal can then be predicted from a simple description of its response to different frequencies. Signals may be broken down into spatial as well as temporal frequency components. frequency response RELATED: transient response 9830 The range of frequencies to which an instrument will respond. All instruments have an upper limit to their frequency response. For example, pens can follow signals up to ca. 100Hz, while oscilloscopes may follow up to 1MHz or more. The lower limit is 0Hz in a DC-coupled instrument or a higher frequency in an AC-coupled instrument. Physiological systems may also have a frequency response: e. g. the response of the human auditory system is ca. 30Hz-20kHz. Since the response of any system falls off gradually with frequency, in instrument assessment the frequency for a 3dB cut is usually specified (i. e. when the energy in the signal falls to 50, or the amplitude to 71 of normal). function In mathematics, this is merely a relationship between 2 or more variables, usually expressible as an equation. In physiology, the statement A is a function of B (where A and B are two parameters) implies not only that you could sketch a graph of A against B, but that there is a specific causal relationship: changes in B cause changes in A (NB changes in A may or may not cause changes in B). For example, urine production is a function of alcohol concentration in the blood (but not vice versa). Ventilation rate is a function of arterial CO 2 concentration, and also vice versa but note that the graphs of these two functional relations would be completely different (with opposite slopes). gain RELATED: amplifier 9830 Amplification. gate The verb to gate means to switch something on or to allow something through under controlled circumstances. A stimulator may be gated, i. e. generate pulses only when a voltage is applied at a specific (gate) input. Ion channels may be voltage-gated (i. e. open only if the membrane voltage falls within a specific range) or receptor-gated (i. e. opened or closed by the binding of a substrate to a receptor associated with the channel molecule). gaussian RELATED: normal distribution, error functions 9830 The function corresponding to the normal distribution, giving a bell-shaped curve. The equation is y a exp(-0.5x 2 ), where x is the actual deviation from the mean divided by the standard deviation. The same function arises in the mathematics of diffusion: if something spreads from an initially highly concentrated point source, the subsequent bell-shaped distributions are gaussian or closely related functions, depending on the exact geometry involved (e. g. whether it can spread in one or more directions). - genic SUF Giving rise to. Z. B. anxiogenic leading to anxiety. - genous SUF Arising from. Z. B. exogenous something that comes from outside the body or tissue. giga - ABBREV: G RELATED: SI units 9830 One thousand million. 10 9. For example, a patch electrode that is well sealed to a biological membrane may have a resistance (between the inside of the electrode to the bath solution) of several giga-ohms. glyc - Relating to glucose or glycogen. Goldman equation RELATED: Nernst equation 9830 If a membrane is only permeable to one type of ion that is present on either side, that ion will move across the membrane carrying charge, until the membrane potential adopts the Nernst equilibrium potential for that ion. If it is permeable to several ions, perhaps present in different concentrations and with different permeabilities, then the membrane potential will adopt a value intermediate between the different equilibrium potentials: a weighted average, biassed towards the values for ions with high permeability and high concentration. It is more important to understand the concepts in these terms than to remember the Goldman equation, which gives a reasonable approximation to the results. For Na, K and Cl - it can be written, with permeabilities P Na . etc. and concentrations Na i . Na o . etc. V m - RTF log e ( (P Na Na i P K K i P Cl - Cl o ) (P Na Na o P K K o P Cl - Cl i ) ) To gain some insight into the equation, see what happens to V m when any one of the 3 permeabilities becomes much bigger than all the others (as P Na does in an action potential). It should of course (and does) reduce to the appropriate Nernst Equation. graded CONVERSE: all-or-none 9830 Capable of having any one of a continuous range of values. A physiological response is graded if variations in the strength of a stimulus produce variations in the amplitude of a response: a graph of response against stimulus strength is a smooth curve, unlike the graphs for all-or-none or stepped responses. Instruments often have both graded and stepped (click-position) controls for varying their settings, for example the amplitude or frequency controls on a stimulator. gradient ABBREV: dydx RELATED: slope 9830 The ratio of changes in one parameter to changes in another. The gradient (or slope) of y plotted against x corresponds to the steepness of the graph, i. e. the amount it moves up in a small segment, divided by the amount it moves horizontally. The dimensions and units of the gradient are those of y divided by those of y. A linear relation has a constant gradient. A curvilinear relation has a varying gradient. ground RELATED: earth 9830 USA term for earth in an electric circuit. gustatory Relating to taste. g-i tract Gastrointestinal tract, from the mouth to the anus. Reduction of a reflex response on successive repetitions of a stimulus. haemostasis Blood clotting. half life ABBREV: t 12 RELATED: time constant 9830 The length of time for something (most commonly a rate of radioactive decay) to fall to 50 of its current value. If the half life is constant whatever the current value, then the decline is exponential. The half life is then ln(2) (0.69) times the exponential time constant for the decline. hardware RELATED: software 9830 The actual equipment (particularly a computer) that you use. These days, the usefulness of computer-based equipment often depends more on the quality of the software than on the hardware. The modern equivalent of A bad workman always blames his tools is perhaps A frustrated user should blame the software, not the hardware. Hebb synapse A synapse or hypothetical synapse in which strengthening of excitatory action occurs following conditions in which presynaptic firing contributes to the successful firing of the postsynaptic cell (following a hypothesis for a learning mechanism put forward by DO Hebb, 1949). hecto - ABBREV: h RELATED: SI units 9830 One hundred, 10 2. Hardly ever used. hepato - Related to the liver. hertz ABBREV: Hz) 9830 Unit of frequency. 1Hz 1 cycle or repetition per second. Z. B. Mains frequency is 50Hz (60Hz in the USA). A filter might pass only frequency components above 2kHz. A nerve might be stimulated at 10Hz. SI recommendations say that you should only use Hz for sinusoidal components of a signal. People seem usually to ignore this, however. Strictly according to this rule you should say you are stimulating at 10 pulses per sec, or 10s -1. unless you are using a sinusoidal stimulus current (which would be rather unusual). hetero - CONVERSE: homo - 9830 Different, varied. high pass RELATED: low pass, filter 9830 A type of filter that lets through high frequency components and removes (or cuts) low frequencies. histogram RELATED: bar graph 9830 A bar graph in which the area of each bar shows the number of observations within a particular range on the horizontal axis. The range is indicated by the bar width. This is a good way of showing the distribution of values obtained for a parameter. Values within a range (sometimes called a bin or a cell) are pooled and counted together, so that the detailed information about precise values is lost and doesnt confuse the overall picture of the distribution. homeo - RELATED: homo-, iso - 9830 Same. Z. B. homeostasis. homo - RELATED: homeo-, iso - CONVERSE: hetero - 9830 Same. Equivalent to homeo-, in words that come from Latin instead of Greek. Z. B. homogeneous (homogenous in USA) having a constant property everywhere. homogeneous RELATED: isotropic 9830 Having the same properties at every place. Distinguish carefully from isotropic. For example, the structure of contractile proteins within a skeletal muscle cell is homogeneous, but not isotropic. Any place in the cell has similar characteristics to any other, but these characteristics are very different in different directions. hormone RELATED: endocrine 9830 A chemical that is released from cells and transported to its target organ in the blood. humoral Relating to body fluids. hyper - RELATED: iso-, normo-, ortho - CONVERSE: hypo - 9830 Above normal. Z. B. hypertonic more concentrated than normal, tending to make cells shrink hyperventilate breathing more then normal). hyperbolic A relation for which the graph is a hyperbola, most commonly one of the form yax (i. e. an inverse proportional relation) or ya(xb)c (which is the same curve shifted on both axes, as in Hills equation for the relation between force and velocity in muscle tissue). hypo - RELATED: iso-, normo-, ortho - (all meaning roughly normal or equal CONVERSE: hyper - 9830 Below, less than normal. Used as a prefix, e. g. hypotonic less concentrated than isotonic. Hypoxic less oxygenated than normal. Hypodermic below the skin. hypothesis RELATED: null hypothesis, theory 9830 A suggestion part of a theory a postulate. Many of the explanations in physiological textbooks for how things work are really hypotheses. They may be widely accepted, or sometimes rather uncertain and controversial. It is seldom possible in science to prove that a hypothesis is correct. You should always treat scientific explanations with a healthy scepticism, regarding them as in principle capable of being proved wrong or requiring some modification in the light of new experiments. If you are asked for a hypothesis to explain some data, it is always a good idea to think of 2 hypotheses: you may then be able to devise a crucial experiment to distinguish them. i. e. RELATED: e. g. 9830 i. e. means That is. (Latin: id est). This introduces either a rephrasing of what has gone before, or something that is strictly implied by it. Distinguish it carefully from e. g.. Examples: Salt can cause natriuresis (i. e. sodium excretion in the urine). Hypothermia can stop respiration, i. e. ultimately cause death. impedance RELATED: resistance, reactance 9830 Equivalent to the resistance of a circuit, but under more general conditions where the ratio of voltage and current depends on the frequency of the signals. Often it is used more or less interchangeably with resistance: e. g. you might read that the input impedance of an amplifier is 10M937. Strictly, though, impedance should be quoted for a particular frequency: e. g. gt10M937 at lt50kHz. If the impedance varies with frequency (as it will do if capacitative effects are significant) then there will be a phase difference between the voltage and the current changes. Impedance is often then expressed as a complex number (q. v.). The symbol Z is often used for impedance: ZRiX where R is the resistance and X the effective reactance in series. implicit CONVERSE: explicit 9830 An equation involving a parameter x may imply that x has a particular value, but not enable you to calculate it by direct (explicit) application of any formula. The value of x is then implicit. For example, the equation xe - x clearly has a solution (as a sketch will show), but cannot be solved explicitly. The solution (x ca. 0.675) can be found by iteration, for example by using the Newton-Rhapson method to derive the iterative formula x2(1e x ) to get a new estimate x from an existing estimate x. impulse Action potential. in parallel CONVERSE: in series 9830 Two things that happen at the same time, or are arranged side by side. The brain can often do several tasks at once, in parallel. Muscle fibres produce more force if they are arranged in parallel. in series RELATED: serial CONVERSE: in parallel 9830 Two things that happen one after the other, or that are arranged physically in a row. Resistors in series are connected end to end, giving a total resistance that is the sum of the individual values. in situ RELATED: in vivo, in vitro 9830 In the normal position in the body, or tissue. in vitro RELATED: culture CONVERSE: in vivo 9830 Literally, in glass. Often refers to a procedure carried out on cells or tissue isolated from the body and maintained in a tissue bath. inch Approximately 25.4mm. independent RELATED: dependent 9830 See dependent for a discussion of dependent and independent variables. The concepts of independent measurements and independent samples are also important. If you carry out 15 blood counts, but 5 of them were on blood from the same subject, then you do not have 15 independent measurements. The 5 are more likely to be similar to each other than to the counts from other subjects. The samples were not independent. It would be incorrect to calculate a standard deviation and to treat it as a measure of the variation of blood counts between individuals. The validity of statistical tests often depends on your samples or measurements being independent. indication A sign, hint, or suggestion. In clinical terminology: a circumstance that suggests that a particular therapeutic regime or diagnostic test is merited (as opposed to a contra-indication: a circumstance that suggests that a course of action might be unwise). indifferent An indifferent electrode is one used as a reference for measuring voltages at one or more different places, or one used when stimulating with a different electrode to pass the return current from the tissue. infarct A non-functioning, or totally dead, region of tissue (often resulting from ischaemia). infinitesimal RELATED: differential 9830 The limit of very small quantities, analogous to the reciprocal of infinity. In one sense, an infinitesimal quantity is simply zero. However, you may be interested in the ratio of two things as they become infinitesimal, when it is not helpful to think of them as zero. infinity ABBREV: 8734 RELATED: limit CONVERSE: infinitesimal 9830 The limit of very large values. Infinity is not a number, and it can be confusing to think of it as such. You can usually rephrase any statement about infinity in the form As x tends to infinity (i. e. gets larger and larger), y increases without limit, or As x tends to infinity, y tends to a particular value (i. e. gets closer and closer to this value). infra - RELATED: sub-, hypo - CONVERSE: supra - 9830 Below. Z. B. infra-orbital below the orbit (eye socket). infusion A continuous slow injection over a long period. Sometimes referred to colloquially as a drip, because a drip chamber is often used to check that the infusion is proceeding normally. inhibition RELATED: depression CONVERSE: excitation, facilitation 9830 An influence that reduces activity in a tissue or reduces the response produced by a stimulus. Synaptic inhibition can operate either by hyperpolarizing a cell (subtracting from the effects of excitation) or by reducing the amount of depolarization caused by excitation (diminishing the excitatory influence, with no effect unless excitation is taking place). The second situation can arise with presynaptic inhibition, and also as a result of a postsynaptic conductance increase that opens channels that tend to keep the membrane potential close to the resting potential. If the decrease of a response outlasts the influence that brings it about, it is usually called depression. innervate One tissue is innervated by another if it contains terminals of axons arising from cell bodies in the second tissue. These might be synaptic terminals or sensory terminals (as in the sensory innervation of the skin from cells in the dorsal column nuclei). The term is essentially anatomical, and does not relate to the processes of activation or synaptic transmission. input CONVERSE: output 9830 An influence or a physical route into a structure, that is capable of affecting it. The influence may be the physical entry of something (e. g. the input of food into the stomach) or the passage of information (e. g. action potentials in the innervation of the stomach). Cables connecting pieces of equipment usually have clearly defined input and output ends: signals or electric power are usually conveyed in one specific direction, which you should identify to make sense of the wiring. input impedance, input resistance The impedance (or resistance) between the input terminals of an amplifier. Amplifiers for measuring voltages without disturbing the conditions they are measuring should have a very high input impedance, so that whatever voltage the source generates, very little current is drawn by the amplifier. Input resistances of 10 12 937 are easily achieved with modern components, though at frequencies of physiological interest (e. g. 10kHz) the input impedance will be much less because the input behaves like a capacitor in parallel with a resistor. integral ABBREV: 8747 y dx) 9830 The area under a curve. A definite integral of a function f(x) is the area under the curve yf(x) between two specified values of x, in some cases plusmn infinity. An indefinite integral is itself a function of (x): the area under the curve to the left of (x). An indefinite integral includes an arbitrary constant, since the left hand limit of the area is not stated in the definition. An indefinite integral is in a sense the opposite of a derivative. If I(x)8747f(x)dx, then f(x)dI(x)dx. Thus the integrals of functions can sometimes (not always) be written down by using backwards the rules for derivatives. Integration can always be carried out numerically on a computer. inter - RELATED: intra - 9830 Between. Be careful to distinguish inter - from intra-. For example, intercellular means between cells. It may therefore refer to the extracellular space, or to junctions between cells. interpolate RELATED: extrapolate 9830 Estimate the value of a function between two or more known points, either by assuming a linear relationship between the two nearest points (linear interpolation) or by fitting a more complex function. interpreter RELATED: compiler 9830 A program that translates instructions written in a high level computer language into a form that can be executed by the computer, at the time the program is being used. The interpreter must be used every time the high level program is used (unlike a compiler). An interpreter is slow in execution compared with a compiler, because it repeats the translation process every time an instruction is used. Computers are often so fast that this is not important. Interpreters can save time if a program needs to be changed frequently, because no compiling is needed after each change. The commonest interpreted language is BASIC. interstitial RELATED: extracellular 9830 Relating to the interstices, or spaces in between things (usually cells). The interstitial space is the extracellular compartment. intra - RELATED: inter - CONVERSE: extra - 9830 Inside. Intracellular means inside cells, quite different from intercellular. invasive CONVERSE: non-invasive 9830 An invasive procedure involves putting something into the tissue under study, removing a sample of it (biopsy), or performing some surgery. Radiation, X-rays, etc. are usually regarded as invasive because the invisible penetration by particles or waves is capable of doing damage. inverse Two things are inversely related if one goes up when the other goes down. For example, pH and hydrogen ion concentration are inversely related. If the relation is not strict (as it is in this case, where there is an equation that always relates the two things exactly), then it is more usual to talk about a negative correlation than an inverse relationship. inverse function ABBREV: INV) 9830 This is in a sense the opposite of a function. If yf(x), then xINVf(y). For example, the inverse of x 2 is x 0.5 or sqrt(x), while INVlog(x)10x. Sometimes (e. g. on calculators) the shorthand terminology f -1 (x) is used, but this is potentially very confusing since it could also mean 1f(x): avoid this terminology. In trigonometry, the expressions arcsin(x), arccos(x) are used for the inverse functions of sin(x) and cos(x). The inverse of x is sometimes used to mean 1x, but this is best avoided since the word reciprocal means this and is unambiguous (e. g. conductance is the reciprocal of resistance, rather than the inverse of resistance). ipsi - RELATED: auto - CONVERSE: contra - 9830 Same, self. Ipsilateral on the same side. ischaemia RELATED: hypoxia, anoxia 9830 Cessation of blood flow. This is a normal condition in some tissues, for example in many muscles during maximal voluntary contractions. If continued for too long, the products of metabolism build up, substrates become depleted, and temporary or irreversible loss of function (infarction) may result. iso - RELATED: hypo-, hyper - 9830 Having the same value, or property. Z. B. isotonic, isomer isolated RELATED: in vitro 9830 A tissue separated from its normal inputs. It might be kept in the body for study (in situ) or it might be studied in vitro. An isolated stimulator is an electrical stimulator in which neither of the output terminals is connected to earth this is useful for reducing the current during a stimulus that may flow through a recording device, causing a stimulus artefact. isotropic RELATED: homogeneous 9830 Having the same properties in all directions. Distinguish carefully from homogeneous. iteration A step that is repeated many times in trying to achieve a goal (e. g. to solve an equation, or straighten a picture on a wall). If the procedure is convergent, the steps eventually make almost no further difference, and you are close to a solution. If it is divergent, the steps get further from the goal, and the procedure may be useless. For example, you can find sqrt(2) by starting with any guess (except zero) and using the iteration formula (x21x) to alter the current estimate (x) again and again. (This is an example of the widely useful Newton-Rhapson formula for iterations to solve an equation of the form f(x)0: xx-f(x)(dfdx).) i-m Intramuscular (usually referring to an injection site). i-p Intraperitoneal. An injection given into the abdominal cavity (belly). iso - equal, same, uniform isotonic RELATED: isosmolar 9830 (1) Having the same tonicity. or the same osmotic effect on cells as the fluid in their normal environment. This is not necessarily the same as having the same osmolarity (see tonicity ) because some solutes contributing to the osmolarity of a solution may be permeant and equilibrate across the membrane, and so have no effect on cell volume, or only a transient effect. (2) In muscle physiology, an isotonic contraction is one during which the tension is constant (contrast isometric ). - itis SUF Inflammation of. its and its 9830 Get these straight. One of them means it is. One is like his or hers. Which is which Dont try to rote-learn it. Think about the relationship: the apostrophe represents the missing i in it is, while in his or hers you would probably never be tempted to put an apostrophe. i-v Intravenous (an injection or infusion into a vein). joule ABBREV: J RELATED: calorie 9830 The SI unit of energy. For mechanical energy it is equivalent to a 1 Newton force moving 1 meter distance. One watt (power) is 1Js. 1J10 7 ergs (cgs unit of energy). kal - Relating to potassium (Latin Kalium, hence symbol K). Z. B. hypokalaemia low blood potassium. Distinguish carefully from calci-. keyword RELATED: database 9830 A word used to gain access to information in a database an index entry. kilo - ABBREV: k RELATED: SI units 9830 One thousand. 10 3. E. g. 1kg 1000g labile CONVERSE: stable 9830 Transient, short-lived, or fragile. laminar flow RELATED: vector, turbulence 9830 A pattern of flow of a fluid (e. g. blood) in which the velocity and direction of movement vary smoothly as you go from one place to another. A graph of velocity against position would be a smooth curve, usually increasing monotonically from the walls to the middle of a vessel. You can describe the flow in terms of laminae (layers) of fluid flowing steadily past each other. The physical laws governing such flow are simple (e. g. Poiseuilles Law). language RELATED: program 9830 A computer language is a set of rules for expressing instructions to a computer. Examples are BASIC, FORTRAN, PASCAL, C, Machine Language or Assembler. A low level language (e. g. the machine language for a specific computer) is one in which each instruction carries out very simple operations, and many instructions are required. A high level language includes very powerful instructions that lead to complex sets of operations. High level languages must be translated into low level instructions before they are used: this is usually carried out automatically by programs called compilers or interpreters. latency A time delay between a stimulus and the beginning of a response. Dont use the term latency when you are talking about the time to the peak of a response. The word literally means hidden time: the time after the stimulus when there is still no sign that any response is going to occur. lateral On one or other side of the body. Far (or farther) from the midline. leak In membrane physiology, a leak is a passive flux of ions by a mechanism that is either artefactual and undesired (e. g. through damaged membrane around a site of electrode penetration) or relatively unselective between different species of ions. lesion RELATED: trauma 9830 A region of injury. The verb to lesion is sometimes used for the deliberate induction of tissue damage for experimental purposes. ligand A chemical or ion that binds to another chemical. ligate RELATED: ligature 9830 To tie closed, for example, a blood vessel or duct from a gland. limit A mathematical limit is a process in which some parameter gets closer and closer to a specified value, but doesnt actually reach it. Sometimes a function is not defined actually at the value that is approached. For example, if yxsin(x), the value of y is not straightforwardly defined at x0 since both the top and bottom of the expression for y are then zero. In the limit, as x approaches zero, y nevertheless gets closer and closer to the value 1. Integration limits are the values on the x axis between which the area under a graph is calculated. line RELATED: mains 9830 USA term for mains. linear RELATED: proportional 9830 A relation between two parameters, for which the graph is a straight line. The equation relating them is of the form yabtimesx. Note that linear is not the same as proportional. A proportional relationship is always linear, since its graph is a straight line through the origin. A linear relation is not necessarily a proportional one (i. e. the line doesnt necessarily go through the origin). logarithm ABBREV: log(x) RELATED: natural logarithm 9830 Logarithms strictly are to a certain base, which should be specified. If none is specified, the base is 10, while for natural logarithms it is e. Log(x) (to base 10) is the exponent (or power) to which 10 must be raised to give the number itself. Thus if ylog(x), then x10 y. For example, log(10)1, log(100)2, log(20)1.3010, etc. Logarithm tables used to be useful because they simplified complex multiplications and divisions. With calculators and computers, you wont need them. However, logarithms are enormously useful and important in the presentation of data (see logarithmic scales) and you should know by instinct that if log(X)-6.2, then X is between 10 -7 and 10 -6 . logarithmic scale Graphs are sometimes plotted with distance along one or both axes proportional to the logarithm of a variable, rather than to the variable itself. There are two reasons. One is to separate data points that would otherwise be crammed near one axis. The other is because some relationships give a straight line plotted in this way. For example, an exponential relationship can become linear if you use a vertical log scale, while a power law becomes linear if you use two log scales. You can buy log-linear and log-log graph paper to save you having to calculate the logs. You can identify a log scale by seeing that the values change by a constant factor (e. g.times10) when you move a constant distance. lyse To break, dissolve or destroy. Often refers to cells bursting, for example, due to a hypotonic extracellular solution. macro - CONVERSE: micro - 9830 Large. Z. B. macrophage a large cell that engulfs particles. In computer jargon, a macro is a single command that initiates a complex set of commands. macroscopic CONVERSE: microscopic 9830 Relating to large-scale features of something magnetic resonance ABBREV: MRS, MRI RELATED: NMR 9830 Magnetic resonance. A technique for studying the internal structure and chemistry of tissue by observing its properties in a high magnetic field. MR spectroscopy (MRS) gives information about the different chemicals present. Imaging techniques (MRI) give images of the structures that differ in their chemistry, which can reveal tumours, dead tissue, etc. mains RELATED: line 9830 The domestic electricity supply. Usually 220-240V, 50Hz in Europe and 110V, 60Hz in the USA. mains hum RELATED: noise, interference 9830 A type of interference that may be picked up during electrical recording, from mains operated circuits and cables nearby. It has the frequency of the mains, and may therefore be identified by seeing whether it has a period of 20ms (16.7ms in the USA). It is usually sinusoidal, but may include higher frequency components (harmonics) giving a jagged appearance to the waveform on an oscilloscope, especially if fluorescent lights are the source of the interference. If the signal is fed to a loudspeaker, it sounds like a deep hum. malignant RELATED: cancer CONVERSE: benign 9830 A condition that gets worse if not treated. Particularly refers to a tumour that invades and destroys other tissues. maximum CONVERSE: minimum 9830 The largest value that a parameter can have (e. g. the maximum age of a particular species), or a value on a graph that is larger than values on either side (E. g. levels of growth hormone often have several maxima during the day: i. e. the graph of concentration against time has several peaks). mean RELATED: average 9830 The sum of a set of quantities, divided by how many there are. It is nonsensical to take the mean of a set of quantities that are not in the same units. For a weighted mean, each quantity is multiplied by a coefficient, or weight before summing, and the result is divided by the sum of the weights. If the weights are all equal, then the weighted mean is the same as an ordinary mean. For example, a chemicals concentration in excreted urine will be the weighted mean of the concentrations produced by each kidney, weighted in proportion to the urine flow rates produced by each kidney. mechanism RELATED: why 9830 The sequence of events, steps and interactions involved in a process. When a physiologist asks why something happens, he usually wants to know the mechanism. median RELATED: quartile, percentile 9830 The value within a distribution that is exceeded by half of the data points. The 50 percentile. medium RELATED: culture 9830 Nutrient fluid suitable for growth or maintenance of cells or tissue in vitro . mega - ABBREV: M RELATED: SI units 9830 One million. 106 or 10 6 . megaly SUF Large. Z. B. megalomania delusion of grandeur. membrane potential ABBREV: V m Voltage difference between the inside and outside of a membrane. V m is normally taken as the inside voltage relative to the outside, taken as the reference: V0. So V m is normally negative at rest (the resting potential). Note that some cells (e. g. in endothelia involved in transport, V m may be different on different faces, and positive on some. messenger RELATED: second messenger 9830 A chemical released in one place, that has an influence on processes in another place, e. g. a hormone, transmitter, or intracellular messenger. Its role is essentially to act as a signal, conveying information. metabolism The chemical reactions that occur in the body. Chemicals ingested or manufactured in the body are either metabolised, excreted or accumulated. metabolite A product of metabolism of nutrients or of a particular specified substance. meter SUF Measure, or measuring instrument. E. g. manometer instrument for measuring vacuum or pressure. micro - ABBREV: u (Gr mu) RELATED: SI units 9830 One millionth: 10 -6. E. g. 1000 microvolts 1mV. micron ABBREV: um) 9830 An old-fashioned word for a micrometre (1um). It used to be abbreviated as 1u, but this is confusing and strongly discouraged within SI units. The unit mu (meaning milli-micron, or 1nm) was used by spectroscopists, and is also discouraged. milli - ABBREV: m RELATED: SI units 9830 One thousandth. 10 -3. For example, the commonest unit of voltage used in physiology is the millivolt (mV). Note that the abbreviation (m) is the same as that for a metre. This does not lead to confusion if you use units correctly. If milli - is used, it always precedes a symbol for an ordinary unit, and never stands on its own. Separate units that are multiplied together should always be separated by a dot (period). Thus 1ms 1 millisecond 1m. s 1 meter second. minimal RELATED: minimum, maximal 9830 Something that is almost small enough to have no effect. Distinguish from minimum, which means the smallest value under consideration or (in mathematics) one that is smaller than its neighbours. For example: Standing up leads to a transient fall in blood pressure, but this usually has minimal effects on brain function. At its minimum, the blood pressure may have dropped by 40mm Hg. minimum CONVERSE: maximum 9830 The lowest value a parameter can have (e. g. the minimum water temperature in which a person can survive), or a value on a graph that is lower than points on either side. mks RELATED: SI, cgs 9830 System of units based on metres, kilograms amp seconds mmHg The unit of pressure most commonly used for measuring blood pressure. 1mmHg is approximately 133 Pa (pascals). The unit is retained, despite not being an SI unit, because the commonest and most accurate instrument for measuring blood pressure is a mercury sphygmomanometer, which gives a direct reading in mmHg. mode RELATED: mean 9830 The most common, or most probable value in a distribution. Seldom a useful concept in physiology, though it is often about the same as the mean or median. modulator A chemical that influences (decreases or increases) the response to another stimulus. molality RELATED: molarity 9830 A way of expressing the ratios of the amounts of substances in solution. The molality of a solute is the number of mols of solute per kg of solvent. In physiology, dealing with aqueous solutions, this is for most practical purposes almost the same as the number of mols per litre of solution (i. e. the molar concentration of the solution). Molarity is the simpler and more commonly used concept, though there are some advantages in relation to thermodynamics in expressing concentrations as molalities. Also it is useful where a significant fraction of fluid volume is non-aqueous - e. g. lipid or protein. molarity ABBREV: moll, M RELATED: concentration 9830 A common way of expressing concentrations. The unit of molarity is the moll, often abbreviated as M, or molar. A solution having a concentration of 0.2M (200mM) contains 0.2mol of solute in each litre of volume. That is the same as 0.2mmol in each ml, etc. The molar concentration is the concentration in gl divided by the molecular weight of the solute. mol, mole RELATED: molarity 9830 A unit of quantity of a substance. If the molecular weight of a substance is X, then 1mol is X grams. For example, the MW of NaCl is 48.5 (2335.5), and therefore 1mol of NaCl is 48.8g. A 1M solution would therefore contain 48.8g of NaCl in 1litre. You can usually find the molecular weight of a compound (or formula weight, e. g. for a hydrated crystalline compound such as MgSO 4 ,7H 2 O) by looking on the label, to save you going to a set of chemical tables to work it out. monotonic A relation whose gradient has the same sign at all points, at least within a specified range. Linear, exponential and sigmoid relations are all monotonic. The relation between rate of sweating and body temperature is monotonic within the physiological range. That between mental performance and body temperature is not monotonic (performance declines at both high and low temperatures). morbid Diseased. Distinguish morbidity (the extent to which something, for example an infection, causes disease) from mortality (the extent to which it causes death). motility Movement, particularly of cells or parts of cells. motor Associated with movement, or production of force, e. g. motor nerves, vasomotor tone (action potentials producing a steady contraction of blood vessels). M-current Outward K current through channels that are opened by prolonged depolarisation and closed by acetylcholine acting at muscarinic receptors. Possibly important in control of adaptation and excitability of several types of nerve cell. nano - ABBREV: n RELATED: SI units 9830 One thousand millionth. 10 -9 . natri - Relating to sodium (Latin Natrium, symbol Na). Z. B. Natriuretic factor something leading to extra sodium in the urine. natural logarithm ABBREV: ln(x) RELATED: exponential function 9830 Logarithm to the base e (approx. 2.718). If yln(x), then xe y. A natural logarithm is 2.303 times the ordinary logarithm of the same number: ln(x)2.303log(x). It is natural because in certain respects it is mathematically simple. For example, ln(1948) where 948 is a small fraction (ltlt1) is approximately equal to 948 (whereas log 10 (1948) 0.43 948 ). The gradient or derivative of ln(x) is 1x. Hence the integral of 1x is ln(x). negligible RELATED: minimal 9830 Capable of being neglected, not worth considering. Less than minimal. Note that negligible may only be meaningful in a clearly defined context. What can be neglected from one point of view may be important in another context. Z. B. a negligible alcohol consumption in relation to its effect on behaviour may not be negligible if you are trying to study alcohol metabolism. nephro - RELATED: renal 9830 Relating to kidney. Z. B. nephritis inflammation of kidney. Nernst equation RELATED: equilibrium potential, Goldman equation 9830 This is the equation to calculate the equilibrium potential for a particular ion, i. e. the voltage difference across a membrane that would be just big enough to counter any net flux of that ion due to a concentration gradient. If ion X (e. g. Na ) has concentrations C i and C o on the inside and outside of the membrane, and a charge z (e. g. z 1 for Na , z -1 for Cl - ), then the equilibrium potential on the inside (relative to the outside) is: V eq(X) - RT(zF) log e (C i C o ) where R is the gas constant, T the absolute temperature and F Faradays constant. At 20 o C the value of RTF is 25mV. Converting the log e to log 10 (multiplying by 2.303), the expression becomes V eq(X) -58mV z log 10 (C i C o ). At 37 o C the constant is 61mV instead of 58mV. neural network A system of neurons that are coupled together in such a way as to process information. For example, a network might produce activity in one particular neuron only when a certain class of patterns is presented (classification or feature detection), or it might generate a pattern of outputs (perhaps leading to a coordinated movement) whenever a simple input is received. The study of the behaviour of neural networks (real nervous systems, simulated nervous systems and artificial systems resembling neurons in some respects) is a large area of information science that bridges neuroscience, computer science, physics and engineering. newton SI unit of force, that which would accelerate a 1kg mass by 1ms -2. The force that gravity exerts (at sea level) on a mass of about 102g. It is reputed to be a coincidence that this is close to the mass of a 17th century Lincolnshire apple, said to have triggered an understanding of such matters. NMR RELATED: Magnetic resonance 9830 Nuclear magnetic resonance. The same as magnetic resonance. The technique is based on the physics of the nuclei within certain atoms. The word nuclear has recently tended to be dropped from the terminology in hospitals, because it is reputed to scare patients The technique has nothing to do with radioactivity, however: which is presumably what patients might be scared of. nomogram A graphical device for solving equations. A chart is prepared specially for solving a particular problem. You draw on this a straight line between points corresponding to known values, and you find the unknown value by reading where your line crosses one of the prepared lines on the chart. For example, the pH of the blood is affected, according to quite complex formulae, both by the chronic condition of a patient (reflected by metabolic acidosis or alkalosis), and by the current rate of ventilation and CO 2 levels. If you know the pH and the PCO 2 . you can use a nomogram to find the degree of metabolic acidosis directly. non-invasive CONVERSE: invasive 9830 A technique that doesnt require entry into the tissue being studied, or damage to it. Many recent medical advances have arisen through the development of non-invasive techniques that assist diagnosis (e. g. Magnetic resonance). non-parametric test A statistical test that does not require assumptions about the probability distributions of the measured parameters. It may use, for example, just the rank order of a set of data. Such tests are much used in psychology. normal RELATED: physiological, pathological 9830 1. Not a sign of disease or trauma, or a risk factor for disease. Z. B. A normal range of blood pressure or body weights. Definitions of normal are often arbitrary or contentious: where is the borderline of unusual behaviour and mental illness 2. A chemical unit meaning containing 1M H or OH - ions. 3. Perpendicular. normalise To divide values for some measured variable by another parameter, in order to take account of some known relationship. For example, if you wanted to see if male and female muscle can produce the same force, you might measure the forces produced by muscles in men and women. Since you know, however, that a larger muscle can produce a larger force, you would have to normalise the data with measurements of the cross-sectional area of the muscles (and perhaps the lever ratios). Otherwise you might come to the wrong conclusion because of differences in the size and geometry of muscles in men and women. normo - RELATED: eu - 9830 Normal. Z. B. normocapnic having normal CO 2 levels. notch filter RELATED: band pass filter 9830 An electrical filter that cuts out a narrow range of frequencies. Most commonly used to cut out mains hum (at a well defined frequency), while passing other signals of interest. noxious A stimulus that is painful or unpleasant. null hypothesis RELATED: statistical test, significance limits 9830 A hypothesis that there is no real effect underlying a difference suggested by data, and that the apparent effect is due to random variations within the data. A null hypothesis must be clear, and in some circumstances may have to be quite precise and quantitative. For example, if you know from large surveys that the mean male-female height difference between adult siblings in England is 12cm and you make a small survey in France that gives a mean difference of 15cm, your null hypothesis might be that the difference in France is really 12cm. In this way you could test whether there is a significant difference between the two populations in this respect. numerator RELATED: denominator 9830 The top line of a quotient. A in the expression AB. Avoid the word unless you are quite sure not to confuse it. numerical aperture (N. A.) RELATED: resolving power, depth of focus 9830 A quantity that describes the light gathering power and the resolving power of a lens. The N. A. is greater with a larger diameter lens, and also if the medium between the object and the lens has a high refractive index (as with an oil immersion microscope objective). This increases the resolving power (i. e. means that smaller objects can be distinguished) but reduces the depth of focus of the lens (so that objects slightly out of the focal plane are blurred). In a camera, the f-stop number (e. g. f16) is 1N. A. a small f number (e. g. f1.8) gives you lots of light, but little depth of focus. numerical methods RELATED: analytical 9830 Methods for solving mathematical problems in specific cases (with known parameters), by using calculations and approximations. Usually this requires a computer. For example, you can integrate any function numerically there are some functions that you cannot integrate analytically (e. g. exp(-x 2 )). observation A measurement, or observation of a qualitative feature. Observations of the responses to skin trauma might include changes of skin colour, swelling, changes of heart rate, vocalisation, etc. occlusion A blockage in for example, a blood vessel. The response to one stimulus is sometimes said to occlude the response to another if the response to both stimuli presented together is less than the sum of the two separately. This occurs in the nervous system, for example, where each stimulus induces an all-or-none response in some of the same neurons. oedema RELATED: edema (US) 9830 Swelling offset RELATED: shift 9830 An offset control on a recording instrument allows you to add or subtract an adjustable steady signal at the input to the instrument. This has a similar effect to a shift control (operating at the output), in that it shifts the record up or down. The amount of the shift increases in proportion to the sensitivity of the instrument, however. An offset allows you to but it shifts the record by an amount that off-scale A measurement that is beyond the range that is satisfactorily registered by a measuring instrument. This may lead to disappearance of the record (as usually on an oscilloscope) or to saturation of the record so as to give a flat recording, as on a pen recorder. In these circumstances it may be possible to use a shift or offset control to bring the recording on-scale. Alternatively, it may be convenient and satisfactory to use AC-coupling of the signal. Ohms law RELATED: resistance, conductance, current, potential difference 9830 This states that current through a material is proportional to the potential difference (or voltage) across it: IVR where R is a constant called the electrical resistance. This relation can also be written as VIR or RVI. Ohms law holds closely for most ordinary materials, like metal wires and ionic solutions (electrolytes). It doesnt hold for many special electrical components like rectifiers, or for membrane channels, or even for ordinary wires if you pass so much current through them that they get hot (e. g. light bulbs): these things have a different resistance under different conditions. olfactory Relating to smell. operator A mathematical symbol indicating an operation. Some operators are unary, i. e. act only on one number. For example, - and. indicate respectively the negative and the factorial of a number. Some are binary, acting on two numbers, e. g.,times (or ),, indicating addition, multiplication, division and exponentiation. Conventional formulae often use the relative position of numbers to indicate operations (e. g. superscripts to indicate exponentiation). Formulae cannot easily be put into a computer in this form, so conventions are adopted that use symbols all on one line (e. g. , , and instead of times to avoid confusion). Use brackets whenever there might be ambiguity without brackets: e. g. 3(2x), not 32x. order of magnitude A useful but imprecise expression. Be careful with it. 1. Used to indicate that quantities are so different in size that the difference itself rules out some hypotheses. Z. B. The size of a large mammal is a quite different order of magnitude from the distances over which diffusion can take place. 2. Sometimes people use order of magnitude to mean roughly a factor of ten. Z. B. an elephant (2000kg) is about 5 orders of magnitude heavier than a shrew (ca. 15g). 3. Mathematicians use order in a more precise way, to indicate that a ratio tends asymptotically to zero or 1 under specific conditions. ordinate ABBREV: Y axis RELATED: abscissa 9830 The vertical, or Y axis, usually used for plotting a dependent variable in an experiment. ortho - Straight, normal. Z. B. orthodontics straightening of teeth. - osis SUF Diseased condition involving the preceding part of the word. Z. B. Psychosis, tuberculosis. osmolarity ABBREV: osmoll RELATED: tonicity 9830 This is the sum of the molar concentrations of all the ions or molecules in solution. 150mM NaCl, 100mM Na 2 SO 4 and 300mM sucrose each have the same osmolarity, 300mosmoll. The osmolarity is a measure of how many particles are in solution. If two solutions are separated by a membrane that is permeable to water, water will diffuse into the solution with greater osmolarity (i. e. more particles in solution), unless there is a pressure difference to oppose this movement. output RELATED: projection CONVERSE: input 9830 A structure leading from a system or something (a chemical, signal or a form of energy) produced by the system. overshoot RELATED: undershoot, transient 9830 Part of a response to a continuing stimulus, in which the response transiently exceeds the level at which it finally settles. Note that it is not really the converse of an undershoot. paired comparison RELATED: students t test 9830 A comparison in which measurements under one condition are paired in some way with measurements under another. This is to ensure that apart from the deliberate difference in conditions, each pair of measurements has as much as possible in common. For example, the paired measurements might be made on the same subject. It isnt always possible, however, to use the same subjects twice: for example, you may be comparing different treatments for a disease. In such cases you may be able to match subjects to some extent (e. g. for similar age, sex and symptomatology). Differences between the paired measurements are calculated, and statistical tests carried out on the mean difference. para - Alongside, resembling. Z. B. Z. B. parathyroid gland beside the thyroid, paraesthesia abnormal (but not absent) sensation, paramedical alongside medicine. Can also mean a defence against something (e. g. parasol), and in chemistry two positions opposite each other on a molecule. paradigm An idealised example. The logic that defines a difficult concept, for example how one defines anaemia, alertness or clinical depression. parameter RELATED: quantity, unit, dimension 9830 The value of a quantity, including its units. partial derivative RELATED: derivative 9830 The derivative with respect to one parameter (with the others fixed), of a function that depends on two or more parameters. For example, the concentration of a chemical in solution depends in general on position and time. It has partial derivatives with respect to time (i. e. the rate of change of concentration at each place) and with respect to the three directions in space (i. e. the concentration gradients in each direction at any one time). A partial differential equation (the diffusion equation) relates these derivatives. partial pressure in a gas mixture RELATED: vapour pressure 9830 The portion of the total pressure of a gas mixture that is due to a particular constituent. The total pressure is the sum of the partial pressures, and the proportions are the same as the proportions of the quantities of gas, either by numbers of molecules or moles, or by volume (measured at a fixed pressure). For example, normal expired air contains (after drying) about 5 CO 2 by volume (5 of the molecules are CO 2 ). The CO 2 partial pressure (P CO 2 ) is therefore about 0.05 of an atmosphere (38 mmHg or 5.0 kPa). Since part of the pressure in the alveoli (about 47 mmHg or 6.3 kPa) is water vapour pressure the CO 2 partial pressure in the alveoli would be less: 0.05 of (760-47) mmHg 36 mmHg, or 0.05 of (101-6.3) kPa 4.7 kPa partial pressure in a solution RELATED: partial pressure in a gas mixture 9830 The partial pressure of a gas (like O 2 or CO 2 ) in a solution is the partial pressure in a gas mixture in equilibrium with the solution. It is not directly related to how much of the gas is in the solution. Under normal conditions, arterial blood has P O 2 100 mmHg and P CO 2 40 mmHg, close to the values in the alveolar gas mixture with which it has equilibrated. At these normal partial pressures, the amount of O 2 and CO 2 in the blood may vary depending on how many red cells and much haemoglobin the blood contains. passive RELATED: electrochemical gradient CONVERSE: active 9830 A process or event that doesnt require energy, or that doesnt require the active participation of some system. It is often wise to clarify the senses in which active and passive are being used. For example, it is perfectly correct to say that an action potential (representing neural activity) is a purely passive event, in that it involves nothing but the passive movement of ions. In the context of membrane transport, passive movement is transport down an electrochemical gradient. Passive movement of a limb is movement induced elsewhere, not by contraction of the muscles that normally act on the limb. pathogen An organism or chemical that causes disease. pathological Diseased, disordered, or abnormal. pathophysiology Study of the function of tissue under pathological conditions. pCa RELATED: pH 9830 A way of expressing very low calcium concentrations, by analogy with pH. pCa-log 10 (molar Ca concentration). Z. B. pCa 5 means Ca 2 10 -5 M. peak CONVERSE: trough 9830 A point on a graph that is higher than those on either side (i. e. a maximum). percentage ABBREV: RELATED: proportional 9830 A quantity expressed relative to a reference as 100. It is most commonly used to describe changes. Note carefully that a 150 increase means a final value 2.5 times the original, while an increase to 150 means a final value 1.5 times the original. Unless otherwise stated, the initial value immediately before the change is always the reference. Thus if a parameter falls by 40 and then rises by 40, its final value is 84 of the initial value, not 100. There is obviously a risk of misunderstanding in this kind of expression, so it is usually best to make it exactly clear what you mean, e. g. The parameter fell to 60 and then rose to 84 of its initial value. percentile The X percentile within a distribution is the value below which X of the data points lie. perception Awareness of something, especially a sensation due to a sensory input. There are many sensory inputs that do not lead to conscious perceptions (e. g. afferents from arterial baroreceptors and chemoreceptors). Curiously, subjects can deny any perception, or any knowledge at all of a stimulus, yet be able to identify accurately some of its properties when forced to guess what they are (e. g. in the phenomenon of blindsight in patients who have total lesions of the primary visual cortex). perfuse RELATED: superfuse, infuse 9830 To pass fluid through. Z. B. an isolated salivary gland might be perfused with saline. peri - RELATED: epi - 9830 Surrounding, around. Z. B. perineurium sheath around nerve, perinatal around the time of birth. perinatal Around the time of birth. permeability RELATED: diffusion, transport 9830 Passage of a substance by diffusion across a membrane. A membrane is said to be permeable to a substance the substance is said to be permeant. The permeability of a membrane only allows a passive net flux to take place, i. e. in the direction down the electrochemical gradient of the permeant substance. If net movement occurs in the other direction, the substance must be subject to active transport. Quantitatively, the permeability coefficient for an uncharged substance, or for an ion under conditions when the membrane potential is zero, is the flux per unit area, divided by the concentration difference between the two sides of the membrane (dimensions: LT -1 ). personal computer ABBREV: PC) 9830 A computer used by just one person, as opposed to a computer that is connected to many terminals for separate users, or a set of computers that are all connected together in a network. An IBM-compatible PC is a computer on which you can use the same software as on a common type of PC made by IBM. pH RELATED: pCa 9830 A measure of acidity. pH - log 10 (molar H concentration). Note (a) that it is a logarithmic measure, so a change of 1 unit in pH corresponds to a 10-fold change in H concentration, and 0.3 units to a 2-fold change in concentration. (b) it is an inverse measure: low pH corresponds to high H concentration and high acidity. It is easy to remember that pH7 corresponds to 10 -7 M and pH8 to 10 -8 M. Normal plasma pH, ca. 7.4, is of course in between. phage SUF Eating, engulfing. Z. B. phagocyte. phase RELATED: time course, amplitude 9830 1. One of the parts of the time course of an event. For example, the rising or falling phase of an action potential the recovery phase after exercise. 2. For a sinusoidal function: a parameter that indicates where you are on the waveform, relative to when the waveform crosses the axis in a positive-going direction (phase0). This is measured as an angle: 2960acutetT radians or 360timestT degrees, where t is the time relative to the crossover and T is the period. A phase shift is the amount you have to shift one sinusoidal waveform relative to another (of the same frequency) to make them have the same crossovers. photomultiplier tube An extremely sensitive light sensing device that transduces a weak light signal into an electrical signal. physiological CONVERSE: unphysiological 9830 Characteristic of the normal workings of the tissue. If an experimental condition or a type of stimulation is said to be physiological, this means that it is within the range of conditions normally experienced by the tissue within the animal. Experiments under unphysiological conditions are often enormously helpful in understanding how the tissue works. For example, study of the force produced by muscle cells when stretched farther than the skeleton will normally permit them to be stretched (i. e. beyond their physiological range) were instrumental in establishing the sliding filament theory of muscle contraction. - physis SUF Growth. Z. B. hypophysis outgrowth under the brain, i. e. pituitary. pi 960 3.142 (approx.) For reference: Circumference of a circle 2960acuter. Area of circle 960acuter 2. Surface of sphere 4960acuter 2. Volume of sphere(43)timespacuter 3. Volume of cone (13)960acuter 2 timesh. pico - ABBREV: p RELATED: SI units 9830 One million millionth. 10 -12 . pixel The smallest unit capable of having a range of colours or shades, in a picture made up of dots. The picture on a computer screen usually consists of at least 640x400 pixels. placebo An inactive chemical given, as a control, to a subject in an experiment. New drugs cannot be claimed to be effective unless they are better than a placebo in a controlled, preferably blind, study. Many clinical conditions show a surprising improvement in many subjects following administration of a placebo (a placebo effect). It has been suggested that the size of a placebo effect is a measure of the social and psychological skills of a doctor, since undoubtedly these play a part in therapy, and with a placebo there is nothing else to help. plasma RELATED: serum 9830 The extracellular fluid of the blood, in which the cells are suspended. If blood is prevented from clotting, the cells will settle out leaving the relatively clear, yellowish plasma. plasticity The capacity to be modified after the changes associated with development have occurred. plateau A horizontal part of a graph, where the vertical parameter ceases to be influenced along with changes in the horizontal parameter. Many dose-response curves exhibit a plateau at high drug concentrations, because the concentration is more than enough to interact fully with all the receptors practically all of the time. pool Pooled data is data analysed together, ignoring some differences in conditions, or in how it was gathered. For example, you might look at the effects of a heavy meal on exercise performance, including both male and female subjects because you thought there might be an interesting difference. If you then found no significant difference between males and females, you might pool the data from all the subjects to get the best estimate of the effects of the meal itself. post - After, behind. Z. B. post-ischaemic hyperaemia increase of blood flow after a cessation of blood flow. posterior Near or nearer to the back end or tail. potential difference (p. d.) RELATED: voltage, electrochemical potential 9830 You can think of this as the driving force that is tending to push electric charge from one place to another through an electric conductor. It is like a more familiar temperature difference, which makes heat flow through a thermal conductor. Potential difference is measured in volts (V). Energy is dissipated (i. e. turned into heat or work) when a charge moves between places with a p. d. 1 Joule is dissipated if 1 Coulomb moves between places with a p. d. of 1 Volt. Conversely, it takes this much energy to move a unit of charge (1 C) in the opposite direction. Thus 1 V 1 JouleCoulomb. potentiation RELATED: facilitation CONVERSE: depression 9830 An increase in the power of something a persistent increase in the amplitude of a response. The increase may last for a few milliseconds after the cause of potentiation, or for many days (for example, the potentiation of muscle strength that results from training, or the long term potentiation of synaptic strength that may be involved in memory). Facilitation, on the other hand does not outlast whatever induces it. power In mathematics: exponent. In physics and physiology, it also means rate of doing work or rate of expending energy (measured in Joules. s -1. or Watts). power law RELATED: logarithm 9830 A relationship in which one parameter is proportional to the other raised to a fixed power: yatimesx p. If you study animals of different sizes, you will find that many of their parameters scale with size according to an approximate power law. For example if x is body mass, metabolic rate and heart rate follow approximate power law relationships with p0.72 and p-0.25 respectively. (Note that the relation for heart rate is an inverse relation: heart rate is faster in a mouse than an elephant.) You can verify whether something is a power law relationship by plotting log(y) against log(x): you get a straight line with a slope of (p) if you have a power law: log(y)log(a)ptimeslog(x). prandial Relating to a meal. preparation A part of an animal, tissue, or cell, made ready for experimentation. pressure RELATED: partial pressure 9830 The degree to which a fluid pushes on boundary surfaces. It is measured as force per area, in Pascals (Pa: 1Nm -2 ). Alternative units are millimetres of mercury (mmHg: 133 Pa), standard atmospheres (760 mmHg or 101 kPa) or bar (100 kPa). Often, (e. g. when talking about arterial presure) pressure really means relative pressure - the excess above the external atmospheric pressure. Pressure differences between parts of a fluid, unless caused and balanced by gravity, cause fluid flow. The total pressure of a gas mixture (e. g. air) is the sum of partial pressures of its constituents. principal RELATED: principle 9830 Distinguish these carefully. Principal means chief - either as an adjective ( principal features ) or as a noun ( school principal ). As an aid to memory, think of a pal who is a prince and principal of a principality principle RELATED: principal 9830 Distinguish these carefully. A principle is a basic idea or mechanism. New medical principles would mean advances in medicine. New medical principals would mean a clearout of senior staff process (1) An event or set of events. (2) A long thin branch of a cell (e. g. the dendrites and axon of a neuron). profile A graph plotted against position, showing the distribution of a parameter. For example, you might plot the profile of temperature along a diameter of the arm. prognosis The predicted course of a disease or disorder. program RELATED: language 9830 A set of instructions that can be obeyed by a computer. Programs must be written in a specific language. Computers are of no value without programs. Sophisticated programs like wordprocessors or spreadsheets can allow the user to perform complex tasks by giving commands in a form that is easier to understand than a programming language. The word program in relation to computers is usually spelt in this way even in England, where the ordinary word programme (as in a programme of work) is spelt differently. prophylactic A drug or a preventative measure taken to avoid disease or infection. proportional RELATED: linear, fractional change, percentage 9830 A relationship between two parameters in which they always change together by the same factor: if you double X, you double Y, etc. They change in proportion. The equation is of the form yatimesx, for which the graph is a straight line through the origin. An inverse proportional relationship is one in which doubling X halves Y, etc. i. e. yax. The graph for this is a hyperbola. A proportional change in a parameter is the same as a fractional change, i. e. (new value - old value)(old value). proteinuria Presence of protein in urine, sometimes indicative of kidney or heart disorders. protocol The plan for an experiment. pylorus The narrow end of the stomach (pylorus) leading to the duodenum. Q 10 The coefficient often used to express the temperature dependence of chemical, biological or physical processes. It is the factor by which the rate of the process increases when there is a 10oC rise in temperature. The Q 10 is often approximately constant over a restricted temperature range, and typically may have values typically around 1.02 for diffusion in gases, 1.3 for diffusion in liquids, 2-3 for biochemical reactions and up to 20 or more for some chemical reactions. quadratic RELATED: linear 9830 A relation of the form yax 2 bxc. The last two terms are a general linear function. The first makes it curvilinear, in fact in the shape of a parabola. This is one of the simplest non-linear functions that you may use to try to get a better fit to some data than by using a straight line. quadratic formula The formula for solving a quadratic equation. If ax 2 bxc0, then x(-bplusmnsqrt(b 2 -4ac))(2a) qualitative RELATED: quantitative 9830 Relating to the nature or qualities of something, not just to the values of parameters associated with it. For example: It is uncertain whether there are qualitative, not just quantitative, differences between the brains of monkeys and those of humans. quantitative RELATED: qualitative 9830 Relating to the value of a parameter. quantity RELATED: parameter 9830 Something you can, or in principle could, measure. quartile RELATED: median 9830 A quartile is the value within a distribution, beyond which only 25 of the data lies. A distribution has upper and lower quartiles, the 25 and 75 percentiles. quotient RELATED: denominator 9830 One parameter divided by another. If the parameters have dimensions (i. e. are not simple numbers), then the dimensions and units of the quotient are those of the top line (numerator) divided by those of the bottom (the denominator). Z. B. peripheral resistance is the quotient of arterio-venous pressure difference and blood flow: its units are those of pressure (Pascals) divided by those of flow (mlmin), i. e. Pa. ml -1.min. q. v. quod vide (LATIN) which see: Refers you to something else you could look up, usually a definition (q. v.) in a dictionary or glossary. radian A unit of angle. 1 radian 57.3 degrees (180 deg 960). The radian is a natural unit. The distance along the curve of a circle is simply radius times angle subtended (in radians). If x is in radians, sin(x)x for small angles (within 5 for angles less than 30 degrees, or 0.5 radians). If x is in radians, the gradient of the graph ysin(x) is cos(x). rate constant RELATED: time constant 9830 If the rate of change of a quantity is proportional to its present value, then the rate constant is the proportionality constant: rate of change rate constant times value. The resulting graph of the quantity against time is exponential, with a time constant equal to the reciprocal of the rate constant. The dimensions of a rate constant are time -1. In complex dynamic systems, in which several influences may tend to cause changes in a parameter (e. g. in complex chemical reactions), each influence may be separately characterised by a rate constant the graphs of the parameters (e. g. concentrations) in such situations are not generally exponential curves. rate of change Gradient. Most often but not always refers to the gradient of something plotted against time. You might talk of the rate of change of sweat production with temperature. ratio RELATED: quotient 9830 The numerical relationship between two things, regardless of units. It is nonsense to talk about the ratio of two quantities unless they have the same dimensions. Z. B. The ratio of males to females in the population is 48. 52, or 1. 1.08. People sometimes give just one number for a ratio. If you do, it must be the quotient of the first thing divided by the second. It would be very confusing to say the ratio of males to females was 1.08 in the above situation. In general, a ratio expressed with one number is likely to elicit the question: Which way round reactance (capacitative) The equivalent of resistance, but for a capacitor instead of a resistor. Its units are ohms. Current will only flow in and out of a capacitor if you apply an ALTERNATING voltage to it. Therefore, its reactance is infinite for a steady voltage (i. e. if the frequency f0). The higher the frequency, the lower the reactance: X 1(2960fC) where X is the reactance (in 937), C the capacitance (in Farads) and f the frequency (in Hz). Reactance is the ratio of the peak voltage to the peak current (XVI) just like Ohms Law, though the voltage and current are 90degrees out of phase. receptor (1) A binding site, usually on a cell membrane, for a particular chemical or class of chemicals (ligands). Some functional property of the cell is usually altered depending on whether the binding site is occupied or empty (e. g. an ion channel may be opened or shut). (2) A sense organ or sensory cell: a structure that is affected by changes in the external or internal environment of an organism and that produces signals (usually action potentials) that influence other parts of the organism. reciprocal ABBREV: x -1 RELATED: inverse 9830 The reciprocal of x is the quantity that when multiplied by x gives 1. This may be a simple number, or it may be a quantity with dimensions, or a unit. For example electrical conductance is the reciprocal of resistance and is measured in reciprocal ohms (also known as mhos, siemens). recording A continuous measurement, usually plotted as a graph against time. rectifier An electrical device that has a low resistance for current in one direction and a high resistance in the other direction. Often a semiconductor diode. recurrent In the nervous system, recurrent collaterals are branches of axons that come back into a structure from which they originated. Likewise, recurrent inhibition means inhibition of a set of cells that results from activity in the cells, amounting to a form of negative feedback. Recurrent also has the ordinary meaning of something that repeats again and again. reflex A response to a stimulus in which the signals are relayed by neurons, and are not normally subject to voluntary control. reflex arc The set of structures involved in a reflex: usually afferent and efferent nerves and one or more sets of synapses. refractive index A quantity (n) that describes the ability of a transparent material to refract (bend) light. refractory period A period in which a cell or tissue is unresponsive to stimuli (absolute refractory period) or has a raised threshold (relative refractory period) following a preceding period of activity. regression RELATED: correlation 9830 The line of closest fit to a graph exhibiting a correlation. This is usually a straight line (linear regression), though sometimes a quadratic, exponential, or other curve may be fitted if the data shows a clear relationship that departs from a straight line. The criterion for closest fit is usually that the sum of the squares of the deviations of all the points from the line (either horizontally or vertically) is a minimum. If a correlation is not statistically significant, then a regression line is not, in general, of any interest and it is a bit naughty to plot it since this may suggest there is a relationship evident in the data. regulate RELATED: control 9830 To control, in the sense of keeping something constant (e. g. body core temperature) or constantly adjusted to suit current requirements (e. g. fluid excretion in the kidney). relationship RELATED: correlation 9830 Two quantities are related if a graph shows that knowledge of one enables you to predict, to some extent, the value of the other. The line of the graph must, over the range considered, be neither horizontal nor vertical. The relationship may be strict (if the graph is a definite line through all the points) or statistical (if the points are scattered, and the prediction is simply a statement about the probability distribution of the second parameter). A statistical relationship is usually called a correlation. relative humidity Water vapour pressure as a percentage of saturated water vapour pressure. In comfortable conditions about 50-70. Relative humidity increases as air is cooled, until it reaches 100 (dewpoint), when condensation occurs. relative refractory period: see refractory period renal Relating to the kidney. resistance (electrical) RELATED: Ohms law 9830 A measure of how much something (e. g. a wire or a resistor) resists the passage of electric current. The bigger the resistance, the bigger the voltage (potential difference) needed to produce a given current: RVI. Units: ohms or 937 (for V in volts and I in amps). For many objects and circuits, R is nearly or exactly constant. In other words, the current is proportional to the potential difference. This is a statement of Ohms Law. But note that Ohms Law (q. v.) does not hold for everything. resistance vessels The arterioles and small arteries, which provide the greatest resistance to blood flow of all the vessels through which the blood flows in sequence through a tissue. Consequently, the biggest drop of pressure is along the resistance vessels. resistivity RELATED: conductivity 9830 An intrinsic property of an electrical conductor. It is the resistance of a section with unit cross-sectional area and unit length. Thus the resistance along the cytoplasm of a length L of an axon with cross-sectional area A and resistivity ampro would be amproLA. Units of resistivity are 937.m. The resistivity of tissue fluids is typically 0.5-2937.m, while for copper metal it is 0.02m937.m, i. e. 10 million times less. Conductivity is 1resistivity (units 937 -1 m -1 or Siemensm). resolution 1. The degree of detail contained in a visual image (e. g. expressed by the number of pixels). 2. The acuity or resolving power of a sensory system or an instrument. 3. The termination of an acute phase of a disease, especially a stage at which inflammation disappears. resolution of measurement RELATED: accuracy 9830 Ability of a measurement to distinguish slightly different conditions. Resolution may be limited by the size of incremental steps in the measurement (e. g. a digital pH meter may give readings to 2, 3, or 4 decimal places) or by inconsistencies in behaviour. It may be possible to identify the sources of some inconsistencies and reduce them (e. g. by placing the instrument in a standard state immediately prior to a measurement). Limitations due to fluctuations that are truly random can usually be improved by a factor SQRTn by averaging n independent measurements. Resolution is just one of the factors that limits the accuracy of a measurement. resolving power (resolution) of a microscope The minimum distance between two objects at which they appear as separate objects when viewed through a microscope. respiration (1) The act of breathing. (2) metabolic reactions involving oxygen as a reactant. response RELATED: stimulus 9830 A change caused by a stimulus. retrograde Moving backwards or in an abnormal direction or (as in retrograde axonal transport) in the opposite direction to something else (the action potentials). Reynolds number ABBREV: R RELATED: turbulence 9830 A dimensionless number that characterises the transition from laminar to turbulent fluid flow in a particular geometrical situation. For flow in a straight tube, R qtimesp(960acutertimesn) where q volume flow rate, r radius, p fluid density, n viscosity. If R is greater than a critical value (ca. 1000) then the flow becomes turbulent. Transition from laminar flow to turbulence might occur because of an increase of q (in a tube with constant r) or a decrease of r under conditions with constant q. Thus turbulence in the aorta (giving a heart murmur) may occur above a critical cardiac output, or when there is narrowing (stenosis) of the aorta. - rhea SUF Flowing, running. Z. B. diarrheaflowing through. Ringer solution RELATED: Krebs solution, 9830 A simple saline solution that is sufficiently similar to the normal environment of a tissue that the tissue continues to behave fairly normally when immersed in it. Named after Sidney Ringer, who discovered that calcium ions are an essential component of the physiological environment of cardiac cells. Appropriate Ringer solutions vary for different tissues and different species, and according to the needs of a particular experiment. Ringer solutions are usually not bubbled with a gas mixture containing CO 2 . and therefore normally have a lower than normal bicarbonate concentration to ensure a physiological pH. risk factor Something statistically associated with an undesired occurrence, such as a disease or accident. This may be a causal factor (e. g. cigarette smoking in relation to lung cancer) or something that suggests the possible existence of a causal factor (e. g. having a relative who suffers from a genetically related disease). root CONVERSE: power 9830 The nth root of x is the number that, multiplied by itself n times, gives x. This is x raised to the power 1n. root mean square ABBREV: rms) 9830 A measure of the typical size of a quantity, regardless of whether it is positive or negative. Take all the values. Square them. Take the mean of the squares. Then take the square root of the mean: this is the rms value. The rms value has the same dimensions as the original quantity, and may therefore be measured in the same units. Z. B. the rms value of the mains voltage in the UK is 220-240V. The mean voltage is zero (because it is negative for half the time) and the peak values are plusmn ca. 320V. saline RELATED: Ringer solution 9830 A solution of salts, usually one suitable for bathing or injecting into tissues. The simplest saline for clinical and mammalian use is 0.9 NaCl (approx. 150mM), which is roughly isosmotic with cells. More elaborate solutions for maintaining tissues in good physiological condition are often named after scientists who worked out their formulae, e. g. Ringer, Krebs. scalar RELATED: vector 9830 A quantity that simply has a magnitude, and no direction in space. For example: concentration is a scalar, flow or flux is a vector. science citation ind ABBREV: SCI RELATED: Index medicus 9830 A reference publication in the library. Useful if you want to find published literature about a specific topic. It lists all the papers referred to (citations) in everything that is published during the year. It is particularly useful if you want to find recent work following up something published earlier: you can expect the recent work to refer to the older work, and therefore to be traceable. Available on computer operated compact disc (CD ROM). - scope SUF Instrument that allows viewing of something. selectivity RELATED: specificity 9830 Membranes and ion channels exhibit selectivity, or selective permeability: they have a higher permeability for certain substances or ions. serum RELATED: plasma 9830 The fluid that separates from blood when it clots. Approximately equivalent to the plasma without much of its dissolved proteins. shift RELATED: balance, offset 9830 A shift or position control on an amplifier allows you to add or subtract an adjustable voltage at the output of the amplifier so as to bring the recording on-scale or to a convenient height. The size of the shift is usually independent of the sensitivity of the amplifier. SI units Standard International system of units. This is based mainly on metres, kg, seconds, amps, degrees Kelvin. Larger and smaller units are named in multiples of 1000. Units larger than the standard are named kilo-, Mega-, Giga-, Tera-. Units smaller than the standard are named milli-, micro-, nano-, pico-, femto-, atto-. The prefixes deci-, centi-, deca-, hecto - are separate from the 10 3 sequence, and are used rather seldom. You should certainly know the main sequence from Mega - down to pico-, and their abbreviations: M, k, m, micro, n, p. You dont often need the other prefixes in physiology. sigmoid A curved graph that always rises as you move to the right, but for which the gradient increases at first and then decreases. If you sketched a graph of the gradient, this would rise and then fall. This is a common shape of graph in biology, for example for dose-response curves, stimulus-response curves and for chemical reactions that involve cooperative phenomena, such as the oxygen dissociation curve for haemoglobin. The word means S-shaped, but its really more like the shape of an integral sign. sign RELATED: symptom 9830 Evidence that a physician can obtain, suggesting a disorder, that is not necessarily evident to the patient. Some symptoms and signs are not related in any obvious or well understood way to the nature of the disease. signal The waveform of a parameter that varies in time. In experiments, physiological signals are often converted into voltages (electric signals) that can be conveniently processed and recorded. significance level ABBREV: P RELATED: null hypothesis, statistical test 9830 The probability that, assuming a null hypothesis, you would get by chance an effect as large as was seen in a particular experiment. This is the end result of doing a statistical test. It is usually expressed, for example, as Plt0.01, along with details of the test. Usually if Pgt0.05 a result is described as not significant (n. s.). meaning that there isnt much certainty at all that the result was not a chance one. There is no universal answer to what is an acceptable significance level. If it would challenge firm ideas to reject the null hypothesis, then you must weigh the probability that these ideas are wrong against the probability P that your results might be due to chance. sine function ABBREV: sin(x) RELATED: cosine, tangent 9830 The sine of an angle is the opposite side to that angle in a right angled triangle, divided by the hypotenuse (longest side). This can easily be generalised to negative angles and angles greater than 90deg (9602 radians) by thinking about an arm that sweeps around from the origin of a graph, making a steadily increasing angle (A) with the horizontal axis: it always intersects a circle of unit radius around the origin at a height of sin(A) and at a horizontal displacement cos(A), generating two sinusoidal functions. sink CONVERSE: source 9830 See source. sinusoidal waveform RELATED: frequency components 9830 A repetitive waveform with the equation yatimessin(wtimestp). It is often but not necessarily a function of time (t), as is described here. a is the amplitude, w the angular frequency (in radianssec), and p the phase (in radians or degrees). The signal fluctuates between a and - a, with a repeat interval (or period) of 2960w sec. The frequency (i. e. how many times the waveform repeats itself per second) is w(2960) Hz. The phase p doesnt affect the shape of the waveform, but shifts it along the time axis. Note that a cosine function, e. g. cos(wt), is simply a sinusoidal function with a phase shift: cos(wt)sin(wt9602). sketch You understand what it is to sketch an object: to illustrate its main features without necessarily producing a perfectly neat drawing with exactly straight lines and precise quantitative relationships. If you are asked to sketch a graph, much the same thing is expected. It should be clear whether lines slope up or down, which way they are curved (if at all), and where lines intersect. If quantitative information is important (e. g. you might want to indicate maximum and minimum values or normal values), mark a number against the points: dont try to plot exact axes. Try sketching the heights of people as a function of age, marking puberty and any other ages important in the context. skewed A distribution or profile that is not symmetrical about its mean. smoothing RELATED: filter, frequency components 9830 A process for removing the high frequency components of a graph. This is often useful if the original data contains a lot of random fluctuation that obscures some consistent relationship. A histogram can be smoothed by using larger bin widths. Other graphs can be smoothed by averaging adjacent points, or by taking a weighted mean of several points around each value on the horizontal axis. Smoothing leads to distortion, since sharp peaks in the graph become smaller and broader. software RELATED: database, spreadsheet, wordprocessor 9830 Computer programs. These may be highly specific to a task (e. g. for running a particular piece of equipment), or they may be very general purpose aids to doing jobs (e. g. wordprocessors). Whether it is easy to use a computer depends on the software, not on the computer. solve RELATED: explicit, implicit 9830 To solve an equation means to find the value that a parameter must have for the equation to be correct. It is always possible to write an equation involving just a single variable x in the form f(x)0. A solution is then a value of x for which the graph of yf(x) meets or crosses the x-axis. In general there may be one, or many, or no solutions depending on the shape of the graph. If there are solutions, you can always find them by plotting a graph. Sometimes it is possible to find a formula for an explicit solution. If there are several (n) unknown variables to be found, then you need at least n equations to find all the unknowns and you cannot always solve the problem graphically. soma Body. Z. B. cell soma cell body somato-sensory sensation on the surface of the body (touch, etc.). source CONVERSE: sink 9830 In analysing changes that occur around electrically active cells, a current source is a region where current flows out across the membranes of active cells and a sink is where it flows in. It is sometimes possible to infer the current source density from measurements of voltage change at a number of sites within the tissue. space RELATED: compartment 9830 A fluid compartment (e. g. extracellular space), or the equivalent volume that a simple fluid compartment would have to have to account for the distribution of a chemical. For example, sucrose usually remains largely in extracellular space, so the sucrose space, i. e. the amount of sucrose in the tissue divided by the sucrose concentration with which it is equilibrated, may serve as an estimate of the extracellular space fraction. space constant ABBREV: 923 (Greek lambda) RELATED: time constant, cable theory 9830 Parameters may decline exponentially with distance, as well as with time. For example, if you give a weak stimulus to a long thin cell electrically at one place, then the resulting change of voltage across the membrane falls off exponentially as you go further away (in either direction). The space constant is the normal way to measure the degree of spread: the distance for the change to fall to 36.8, exactly equivalent in other respects to a time constant. specific (1) Relating to a particular one, or a small group of things. A specific drug, inhibitor, etc. is one that performs exclusively, or almost exclusively, the function described. Specific binding of a substance in a tissue is binding to a receptor that is selective, usually with high affinity, for that substance. Specific also may relate specifically to a biological species (e. g. a specific name). (2) A parameter that characterises a property of a substance or tissue, irrespective of how much is actually present. Specific membrane resistance is the resistance of unit area of membrane (in ohm. m 2 ), and specific conductance the resistance per unit area (in mho. m -2 ). spike RELATED: impulse 9830 A brief transient deflection on a record. An action potential is often referred to as a spike, especially when recorded on a slow trace, so that details of the timecourse of the individual action potentials are not apparent. spreadsheet RELATED: database, wordprocessor 9830 A general purpose computer program to help with calculations and (usually) drawing graphs. A quite revolutionary tool for scientists (and for business), which enables you to do elaborate calculations and to lay the results out clearly, without learning to write programs. standard 1. Something having a parameter with a known fixed value, used for calibration purposes, e. g. a standard battery (with a known voltage) or a standard solution with known concentration. 2. A way of assessing something according to an agreed rule, e. g. a standard deviation. standard deviation ABBREV: s. d. RELATED: variance, standard error 9830 This is the commonest measure of the variability of a quantity. It is the square root of the variance, and is usually more convenient than the variance because it has the same dimensions as the quantity itself (and therefore can be measured in the same units). For example, if you measured urine production in 20 of your colleagues, you might express the results in the form 230 plusmn 35 mlhr (mean plusmn s. d. n20). Generally about 70 of the values will fall within plusmn 1 s. d. of the mean (i. e. in this case, between 195 and 265 mlhr). standard error of mean ABBREV: s. e.m. RELATED: standard deviation, error bars 9830 An estimate of how much in error the mean of a set of measurements is likely to be, compared with the true mean you would get with very many measurements. It is the estimated standard deviation of the mean. With a small number (n) of measurements, the s. e.m. is larger. It is equal to the estimated standard deviation of the measurements (which tells how variable they themselves are) divided by sqrt(n). When you do an experiment, you may not be particularly interested in the variability of the original data (i. e. in the s. d.), but if you calculate a mean you should always be interested in how uncertain that is (i. e. in the s. e.m.). Calculators or spreadsheets do most of the work for you. stasis Constancy cessation of movement. Z. B. homeostasis, haemostasis. statistical test RELATED: null hypothesis, significance level 9830 A procedure to estimate the probability that an observed experimental result (or one even stronger) might have been obtained by chance, on the assumption of a null hypothesis. A test may in general be one-tailed or two-tailed. A one-tailed test gives the probability that the result would be as large or larger in the observed direction. A two-tailed test gives the probability (often just twice as great) that it be as large in either direction. If you predicted the effect in advance, and that is how the experiment turned out, then a 1-tailed test is appropriate. In other circumstances, a 2-tailed test should be used. std. dev. of functions If a quantity (y) is calculated from parameters x 1,x 2,etc. then it may be possible to calculate the standard deviation (sd) of y from the sds of the other parameters. With only one parameter (i. e. yf(x)), then sd(y)sd(x)timesdfdx, where dfdx is the absolute value of the gradient of y plotted against x. If yatimesx p (a power law), then the sd expressed as a percentage (sd) is simple: sd(y)ptimessd(x). For example, a 3 sd in the diameters of spheres corresponds to a 9 sd in their volumes. With 2 or more parameters, with statistically independent variations, the variance V(y)931 i (V(x i )(dfdx i ) 2 ). These formulae are not always exact, but are good approximations for small variations. std. dev. of sums amp products Two special cases of the calculation of the standard deviation (sd) of functions are common and important. If a quantity y is calculated from variable parameters x 1,x 2 . whose variations are statistically independent, then simple rules apply. If y is the sum or difference of x 1,x 2 . then the square of sd(y) is the sum of the squares of the sds for all the x i . If y is the product or quotient of x 1,x 2 . then a similar rule applies but in relation to the sds expressed as percentages (sd): the square of sd(y) is (approximately) the sum of the squares of sd for all the x i . regardless of whether they appear on the top or the bottom of the formula for y. steady state RELATED: equilibrium 9830 A state in which all parameters are constant (i. e. not changing with time). In biological experiments, this is really a matter of all important parameters being considered constant. For example, there may be continuing fluctuations of concentration or voltage within the tissue. Age is a relevant parameter in many experiments and is never strictly constant If you place a cell in a new solution, its resting membrane potential may rapidly (within seconds) reach a new steady state, but the concentrations of chemicals in its cytoplasm may change slowly and take hours to reach a new steady state. You need to use the concept with care. stimulus RELATED: response 9830 Strictly urging on, this means something that activates a tissue or process. Z. B. arterial CO 2 is a stimulus to respiration. Any external intervention applied to a tissue is described as a stimulus, however, even if the effect is inhibition or depression of function. This can be confusing: a stimulus can stimulate (i. e. activate) or inhibit some function. The usage is sensible in as much as interventions act by inducing some change in the tissue, which may itself either activate or inhibit particular processes. The effect of one tissue on another (e. g. nerve on muscle) is not stimulation unless it its effect is excitatory. The vagus certainly does not stimulate the heart. stomy SUF RELATED: - tomy 9830 Mouth. Z. B. tracheostomy making an artificial opening (mouth) in the trachea (windpipe). Distinguish from - tomy (e. g. tracheotomy). Students t test RELATED: Null hypothesis, significance level 9830 A very useful statistical test in which you compare the mean value of an observation with the value that you might expect according to a null hypothesis. t is the difference from the expected value, divided by the standard error. You need to know the number of degrees of freedom ( the number of observations, less 1) and you can then look up the minimum value of t for the required significance level in a set of tables. As a rule of thumb, the difference is never significant if tlt2, while tgt2.5 will always be significant (Plt0.05) unless you have very few observations (lt6). A more complex t test is required if you want to compare 2 means. sub - RELATED: hypo-, oligo - CONVERSE: super - 9830 Under, beneath. Z. B. subnormal, sub-lingual (under the tongue). subject Human experimental animal. A patient participating in an experiment or a clinical trial is a subject a normal subject participating in an experiment, even in a hospital, will not appreciate being called a patient summation ABBREV: 931 (Greek Sigma) 9830 1. Mathematically, this means to add a set of numbers: Sigma(x) means the sum of all the numbers like x. For example, in calculating a line of closest fit (a regression) you choose the parameters in a function f(x) so as to minimise Sigma((y-f(x)) 2 ). 2. Physiologically, summation means the addition of influences that arrive at a cell either at separate times (temporal summation) or at separate places (spatial summation). super - RELATED: supra-, hyper - CONVERSE: sub - 9830 Above. superfuse RELATED: perfuse, infuse 9830 To pass fluid over something. Z. B. the tongue might be superfused with solutions containing chemicals with different tastes. supra - RELATED: super-, hyper - CONVERSE: sub - 9830 Above. supramaximal RELATED: maximal, threshold 9830 Above maximal. A supramaximal stimulus is more than big enough to have the full effect: increasing it further will not increase the response. The stimulus is therefore on the plateau of a stimulus - response graph. This may be because the stimulus is above the threshold for all of the cells contributing to a response. suture A stitch made with needle and thread or a metal clamp, to hold tissue together. sweep The left to right movement of the spot on an oscilloscope. symptom RELATED: sign 9830 A change noticed by a patient, that indicates an underlying disorder. A presenting symptom is one that leads the patient to seek medical advice: it is not necessarily indicative of the most serious aspects of the disorder. syncytium A set of cells that are coupled in some way, so that they behave in certain respects as if their cytoplasm was continuous. For example, electric current can pass through the gap junctions between cells in the heart, allowing an action potential to propagate throughout the heart without synaptic transmission. syndrome A set of symptoms andor signs that are characteristic of a particular disorder. systole RELATED: diastole 9830 The time of contraction of the ventricles of the heart, when arterial blood is expelled into the aorta. Systolic pressure is the maximum arterial pressure reaches during the cycle, at the end of systole. tangent RELATED: gradient, slope 9830 A straight line that meets a curve and also has the same gradient at the point of contact. teleological Relating to the purpose of a tissue or organ. A teleological argument whereby, for example, you say I know what this hormone is for, so it must have this effect because that is how it would easily achieve its purpose is sometimes useful in helping to remember facts or guess at them. But it isnt very reliable, since biological evolution may not always have led to the same principles of successful design that you think would be sensible temporal 1. Relating to time. 2. Relating to the temple, or side of the head. tera - ABBREV: T RELATED: SI units 9830 One million million, 10 12 . tetanus RELATED: twitch 9830 In muscle physiology, a continuous contraction produced by stimuli or action potentials at a high frequency. A fused tetanus is one in which the frequency is high enough that responses to individual stimuli cannot be distinguished. Tetanus (or lockjaw) is also a disease in which sustained muscular contractions occur. The word is used in neurophysiology to denote high frequency stimulation, though this is often considered improper since the origin of the word has to do with the tautness of muscle, not with the frequency of stimulation. - thermic SUF Relating to temperature. threshold RELATED: excitability 9830 Minimum strength of stimulus that elicits a response. time constant ABBREV: 964 (Greek tau) RELATED: exponential constant, half life, rate constant 9830 The exponential constant for a parameter that varies exponentially as a function of time. The equation for the parameter is of the form ya. e t964 or ya. e - t964. depending on whether the exponential is rising or falling. In either case, a is the value at time t0. One time constant 1.443 half lives. The reciprocal of 964 is the rate constant. Z. B. the time constant for cooling of a cadaver is (according to Agatha Christie) 3.5 hrs. You should be able to sketch the cooling graph and mark the time constant on it by eye. time course RELATED: latency, rise time, overshoot, undershoot 9830 The temporal (i. e. time-related) characteristics of a response or event. In general, if you are asked to describe the time course of a response you should consider whether there is a latency, what the rise time or the time to peak is, whether the response is transient or maintained, whether there is an overshoot or undershoot, how long the recovery takes, and whether the effect of the stimulus is reversible. Not all these factors may be relevant, and there may be others (e. g. perhaps several peaks in a response). You dont need to make precise measurements, but you should make approximate quantitative statements. Try describing, from experience, the time course of effects of running a mile. timebase RELATED: trigger 9830 The part of an oscilloscope that moves the spot steadily from left to right. It always has a control for varying the speed of movement (the sweep speed) and various controls for determining when the sweep begins (trigger controls). The trigger options are usually FREE RUN, i. e. it starts to sweep as soon as the last sweep is complete, EXT TRIG, i. e. it starts when a pulse is fed through a cable into a socket on the front of the timebase, INT TRIG, i. e. it starts when the vertical deflection on one of the traces exceeds an adjustable level, LINE, i. e. it starts at a constant phase of the mains voltage supply - tomy RELATED: - ectomy 9830 Cutting. Z. B. lobotomy incising a lobe of an organ. tonic CONVERSE: phasic 9830 Continuous. A tonic response is one that is maintained during the period of a stimulus, i. e. that does not show complete adaptation. Muscle tone is a continuous level of contraction, arising usually from tonic activity in the innervating nerves (e. g. in skeletal muscles and vascular smooth muscles). tonicity RELATED: osmolarity 9830 In physical chemistry, this is the same as osmolarity. In physiology, it relates specifically to the behaviour of cells in a solution. It is a measure of the tendency of a solution to make cells swell or shrink. An isotonic solution leaves cells at normal volume. A hypotonic solution (e. g. a more dilute solution, with lower osmolarity) makes cells swell a hypertonic solution makes them shrink. Substances in solution that readily pass through membranes (e. g. urea) contribute to the osmolarity of a solution, but not to its tonicity. A 1M urea solution has a higher osmolarity than blood plasma, but is hypotonic. Water will enter the cells along with the urea, and make the cells burst. toxin A poisonous or harmful substance. Many useful drugs have toxic effects. transducer RELATED: transduction 9830 Something that converts a signal (in more rigorous terms: energy or information) into a different form. For example, the conversion of a light signal into an electrical signal by a photomultiplier tube. Sensory receptors are transducers, though the term is more usually applied to instruments. trace A record from a measuring instrument, in graphical form. transient RELATED: phasic CONVERSE: maintained 9830 Not maintained. Z. B. Cigarette smoking gives a transient feeling of well-being and contributes to a long term health risk. transmitter RELATED: modulators 9830 A chemical messenger released at a synapse by the pre-synaptic cell, and acting on receptors in the postsynaptic membrane. Transmitters have a rapid local action, most often acting by opening channels in the postsynaptic membrane. The same chemicals may also be released as hormones (e. g. noradrenaline) or as modulators. transport In the context of membrane physiology, (verb) to move across a membrane. trauma RELATED: lesion 9830 A painful, harmful, or destructive event, or the wound caused by such an event. The word is used in relation to both physical and psychological damage. trend RELATED: regression, correlation 9830 1. An approximate relation, or a generalisation that is true on average but not in every individual case (as in a correlation). Z. B. There is a trend for taller people to be heavier. There is a trend towards lower calorie food intake in the summer. 2. Some people use trend to mean a difference found in an experiment, that doesnt reach statistical significance. Usually it is a waste of time to talk about such differences. Certainly it is dangerous to suggest, by giving them a special name, that they are worth paying attention to. The whole idea of a statistical test is to show whether a difference is too small to be worth paying attention to. trigger RELATED: all-or-none 9830 Something that starts something else off. Z. B. An action potential may be said to be triggered by a stimulus that is above threshold a fit of coughing may be triggered by a deep breath the start of the sweep of an oscilloscope may be triggered by a brief pulse coming from a stimulator circuit. The essential thing here is that the triggering event doesnt merely affect what is triggered, but it causes the start of a stereotyped chain of events. The relation between the trigger and the triggered event is usually all-or-none. The analogy with the trigger of a gun is fairly obvious. trophic Relating to nutrition or growth. A trophic influence is one that influences growth or maintenance of a tissue. tropic SUF Related to direction. Turning. Z. B. trophotropic turning or moving towards food. trough CONVERSE: peak 9830 A point on a graph that is lower than those on either side (i. e. a minimum). turbid Muddy, milky (e. g. a suspension of cells). turbulence RELATED: laminar flow, Reynolds number 9830 A state in which fluid flow fluctuates markedly from one place to another and from one time to another. The pattern of flow is then governed by the physics of chaos (which is not yet well understood) rather than the physics of laminar flow. Transition from laminar flow to turbulence often occurs quite suddenly as the rate of flow is increased or as a constriction is narrowed (e. g. in a cardiac valve). The transition can sometimes be characterised by a Reynolds number. You can picture it as the transition from dark to white water in the flow of a river. Energy is dissipated in additional ways (e. g. by sound), and different stresses are placed on the walls of a vessel. turgid Swollen, rigid (e. g. a cell in a hypotonic solution). twitch RELATED: tetanus 9830 The response of a muscle cell to a single action potential. undershoot RELATED: overshoot 9830 A phase of the time course of a response in which the measured parameter may cross below the baseline level and be shifted in the opposite direction from the initial response, before final recovery. For example, if you hyperventilate deliberately, your respiration rate will normally show an undershoot subsequently. Terminology is rather ambiguous (and should be explained more clearly) if you are discussing a response in which the initial effect is a decrease. For example if you deliberately hypoventilate (or hold your breath), the subsequent hyperventilation is best not described as either an undershoot or an overshoot. uniform RELATED: homogeneous 9830 Having the same value, usually in different places or between different subjects (not necessarily at different times). Z. B. Oedema due to over-drinking is relatively uniform throughout all tissue compartments. If you do experiments on students, you usually have a population with very uniform ages. unilateral RELATED: ipsi-, contralateral CONVERSE: bilateral 9830 On one side only. unit RELATED: dimension 9830 The standard to which a quantity is compared, in assigning it a numerical value. It is useless to give numerical values to parameters without specifying the units, and dangerous to compare values without converting them to the same units (NB if you insist on doing this, you have to bear in mind the relation between the units as well as the relation between the two values - unnecessary mental gymnastics). Z. B. metre (m) or millimetre (mm) for length pascal (Pa Nm -2 ) or mm Hg (ca. 133 Pa) for pressure. upregulation Increase in something (usually the expression of a signal or a receptor), in response to a stimulus. - uresis Relating to, or appearing in, the urine. Z. B. diuresis extra urine, proteinuresis protein in the urine. valid Sound, logical. Note that an argument may be invalid, even if the conclusion is correct. (The patient may have cancer even though your reasons for thinking this were invalid.) vapour pressure RELATED: relative humidity 9830 The partial pressure of a vapour (evaporated liquid) within a gas mixture. When in equilibrium with a liquid at a particular temperature, the gas has a vapour pressure equal to the saturated vapour pressure. For water, this is 6.3kPa (47mmHg) at 37 o C and 2.3kPa (18mmHg) at 20 o C. variable RELATED: parameter, constant, dependent CONVERSE: constant 9830 A parameter that you can alter or expect to vary during an experiment. For example, during an experiment on a human subject, the inspired oxygen concentration and body core temperature may be variables, but body height is a constant parameter. In experiments on several subjects, height becomes a variable, that may or may not affect the results. Variables can be dependent or independent. If you look at how body temperature is affected by exercise, temperature is a dependent variable. If you vary body temperature directly (e. g. in a hot or cold bath) and look at its effect on mental capacity, temperature is the independent variable. variance RELATED: standard deviation 9830 A measure of how variable a set of numbers is. You first have to think about the individual differences of all the numbers from the mean value for all of them. These differences will be both ve and - ve, with a mean of zero. If you square them before taking the mean (making them all positive), then you get the variance. In other words, it is the mean square difference from the mean, or strictly the limit that this would approach if you take more and more samples. The standard deviation is the square root of the variance. vaso - Relating to a vessel (i. e. in anatomy, a tube). Usually relating to a blood vessel (e. g. vasoactive affecting blood vessels), but NB vasectomy removal of a part of the vas deferens. vector RELATED: scalar 9830 A quantity that has direction as well as magnitude. You can represent it visually as an arrow. For example, the velocity of blood flow is a vector, having magnitude and direction everywhere within a blood vessel. If the flow is laminar in a straight vessel, the direction is everywhere the same, but the magnitude falls off towards the vessel walls. At a branch point, the vectors in different places have different directions. If there is turbulent flow, the vectors fluctuate somewhat chaotically with both position and time. You can resolve a vector into components in 3 perpendicular directions. NB vectors with zero magnitude do not have a defined direction. vector differentiation ABBREV: grad, div, curl) 9830 3 types of vector differentiation are defined. The first is differentiation of something (such as concentration C) that isnt itself a vector. You can take the derivative of this with respect to position in each direction and form a vector from the 3 components: this is grad(C) (vC), proportional to the flux of substance that will diffuse in the concentration gradient. If a vector A is defined at every point (e. g. flux or velocity of movement) then the divergence div(A) (v. A) corresponds to the rate at which moving particles are being added locally to the system. (NB often v. A0.) Curl(A) (vxA) is a vector corresponding to the circulation (like a vortex) of particles locally. vector multiplication ABBREV: A. B, AxB) 9830 Two types of vector multiplication are defined. Both are generalisations of the ordinary multiplication of simple numbers. A scalar product A. B is the magnitude of vector A times the component of vector B in the direction of A. It arises, for example, if A is a force applied to a point and B is its displacement: A. B is then the work done during the movement (NB work is a scalar: it doesnt have direction). The vector product AxB is twice the area formed by the triangle defined by A and B. This has direction (perpendicular to the plane of the triangle) as well as magnitude, i. e. it is a vector. It arises, for example, in calculating the force due to a current (A) in a magnetic field (B). vectorcardiography A way of analyzing electrocardiogram signals in which the signals are displayed as a spot moving in two or three dimensions, corresponding to the changes of both amplitude and electrical axis of the electrocardiogram during the cycle. The spot traverses loops, which give a direct visual indication of the electrical axis. ventilate RELATED: breathe 9830 To cause air to flow through the airways. vivisection Literally, means to cut something living. Refers to experiments on living (including anaesthetised) animals. Anti-vivisectionists are those who oppose the use of animals for experiments. Opposition to animal experiments should be distinguished from opposition to cruelty to animals. Most people who perform animal experiments for biomedical and veterinary research are wholly opposed to cruelty and would argue strongly that their work causes little or no suffering to animals, and that where suffering is caused (as is inevitable, for example, in some research on pain) it is more than balanced by the alleviation of suffering due to the successes of such research in leading to clinical advances. voltage see potential difference waveform RELATED: time course, profile 9830 The shape of the graph of a signal plotted against time, showing its timecourse. wavelength The distance between two points of equal phase on a (sinusoidal) waveform, for example between wave crests. For a light wave, wavelength is inversely related to frequency. In the visible spectrum the shortest wavelengths (ca. 0.4nm) correspond to violet light and the longest (ca. 0.8nm) correspond to red light. white noise RELATED: hum 9830 A signal that fluctuates randomly in time, with a large range of different frequency components. If you played it through a loudspeaker it would sound like a hiss. All amplifiers generate a certain amount of such noise. The term white comes by analogy with white light, which usually contains all different frequencies (or wavelengths) of light. The energy in white noise is proportional to the bandwidth. You can learn to distinguish white noise on an oscilloscope from, for example, sinusoidal hum due to signals picked up from the mains (50Hz). why A why question in physiology may relate either to the mechanism by which something happens (As a result of what processes) or to the role that it plays in affecting other things, i. e. its consequences (For what benefit). A full answer (e. g. to the question Why does peripheral resistance rise when a person stands up) would include both aspects: in this case the reflex mechanisms, and also the consequences if these did not exist. Try to avoid the ambiguity if possible, and if in doubt (e. g. in an exam) say how you are interpreting the question. wordprocessor RELATED: spreadsheet, database 9830 A computer program used to help in the preparation and editing of text documents. 967 2 RELATED: students t test, significance 9830 Chi squared test. Often used for testing the significance of the differences of two proportions. For example, if 70100 patients given a new drug recover, while only 2050 given a placebo recover, is there significant evidence that the drug has an effect