, De manière générale (Chapitre 2, Section 2.1), plus le pas de temps est petit et plus l'approximation s'avère précise. En revanche, le choix d'un petit pas s'accompagne d'une augmentation du coût calculatoire

. Dans-notre-contexte-;-grün, des événements sont généralement dénis comme étant synchrones lorsqu'ils se produisent ensemble dans une fenêtre temporelle de 1 à 5 millisecondes, 1999.

, De plus, an d'observer les processus de sommation, ce pas doit être bien inférieur aux paramètres synaptiques? et? . Pour les simulations de modèles très détaillés, qui s'intéressent à des phénomènes aussi précis que la forme des potentiels d'actions, un pas de 0.01 milliseconde semble approprié, Börgers and Nectow, 2013.

. Ici-;-nordlie, Dans notre contexte, un pas de temps de 0.1 milliseconde semble approprié et en accord avec les simulations de modèles de type Integrate-and-Fire que l'on peut trouver dans la littérature, considère des spikes discrets et cette approximation montre bien qu'un pas de temps si petit ne nous est pas nécessaire, 2002.

, Il s'agit là d'un ordre de grandeur et la valeur exacte du pas de temps (que l'on note ?) peut naturellement être modiée au besoin : le processus de discrétisation reste alors le même. La discrétisation consiste nalement à exprimer tous les paramètres temporels du modèle en multiples de ?

, Discrétisation aux synapses

, Étant donnée une synapse s, cette fonction, lorsqu'elle est linéaire, est dénie par deux paramètres temporels et son poids : le temps durant lequel la valeur absolue de la fonction est croissante (? s ) jusqu'à atteindre sa valeur maximale |w s |

, il sut d'exprimer ces paramètres temporels,? s et? s , en multiples de ?. Lors de la réception d'un spike à la synapse s, la valeur de la charge locale évolue alors de manière discontinue par sauts de w? ? à chaque pas de temps ? jusqu'à atteindre la valeur w s

, Lorsque le neurone initial émet un spike, le neurone change au temps suivant et l'état reste le même (Figure 9.3). À partir de ce nouvel état initial, le neurone (modié) suit de nouveau sa dynamique habituelle. De manière plus détaillée : à tout temps t (non nul) tel qu'un spike est émis sur la sortie, le neurone reste le même qu'à ? plus tôt (où ? est inférieur à la période réfractaire, Le paramètre? s (aussi appelé time-to-peak) varie entre une et plusieurs dizaines de milneurone n'émet pas de spike

, Remarque: Lorsqu'un neurone émet un spike sur sa sortie, le poids des synapses de ce neurone peut changer. À cet instant même, l'état du neurone n'est potentiellement plus en continuité avec le signal d'entrée (Chapitre 4, Section 4.2, Dénition 13)

. ?-n-?-n-est-un-neurone,

N. ?-?-?-?-n-est-un-État-du-neurone, E. , I. Ir-+-?-e-et-o-e, and I. Ir-+-?-{0,

. ?-e-?-=,

?. Pour-tout-t-?-ir-+-tel-que-o-n-t, I t (t) = 1, en notant I t la fonction I t (h) = I(h+t)

, N t = N t?? avec 0 < ? < e ? (e ? est la période réfractaire absolue de N 0 , Dénitions 5 et 6 du Chapitre 4) et ? t = d N t ,I t (t) où t = max{, vol.0

*. , N t , ? t+? ) où ? t+? = d N t ,I t (?) avec ? t pour état initial

, CONCLUSION ET PERSPECTIVES ciences, à la fois à l'échelle d'un neurone unique et à l'échelle des réseaux

, Cette piste est motivée par les théorèmes de réduction et de normalisation que nous avons prouvés (Chapitre 5). Eectivement, ces théorèmes mettent en évidence des classes d'équivalence et nuancent le rôle de la structure précise des dendrites dans la fonction des neurones : l'arborisation dendritique ne contribuerait à la fonction d'entrée/sortie des neurones, que par l'apport de délais entre les synapses et le soma, dans un cadre de conduction passive. Notre point de vue est que l'atténuation est une conséquence de l'arborisation dendritique, la direction de recherche privilégiée concerne le rôle des dendrites dans la fonction neuronale

, La mise en évidence des classes d'équivalence mène à une question intéressante : si la morphologie des neurones n'est pas dictée de manière unique par la fonction d'entrée/sortie, comment expliquer les morphologies typiques des neurones biologiques (Figure 1.2, Chapitre 1) ? Pour investiguer cette problématique, nous pourrions, à partir des formes normalisées, reconstruire les arborescences dendritiques qui préservent la fonction d'entrée/sortie sous contraintes. Par exemple, nous pourrions contraindre la reconstruction par des critères tels que la limitation des redondances, l'économie de membrane, l'optimisation de la surface de contact, etc, 2016.

, L'idée serait alors d'identier des critères menant aux formes caractéristiques des neurones biologiques. Ceci permettrait potentiellement d'expliquer pourquoi une morphologie est privilégiée vis-à-vis d'autres morphologies permettant de remplir la même fonction d'entrée/sortie

, On peut alors se poser la question suivante : cette adaptation de la STDP bénécierait-elle à l'apprentissage automatique ? Comme on le voit, nos travaux ouvrent de nombreuses perspectives et la plupart d'entre elles n'étaient pas attendues à l'origine. Ces perspectives sont nombreuses et nous espérons que notre formalisme, à la croisée de la biologie théorique et de l'informatique fondamentale

, // creation du noeud Lustre correspondant -etat initial = 0. O public String toString () { String node = " node " + this . nodeName + " ( I_s : bool ) returns

. \-n,

, ArrayList < String > pastSpikes = new ArrayList < String >(

+. }-node,

, -1; i ++) { node = node + pastSpikes . get ( i ) +

, } node = node + pastSpikes . get ( pastSpikes . size () -1) + " : bool

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