Academic literature on the topic 'Kalikow decomposition'

Abstract In this paper we propose a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity in this paper is that we deal with an infinite number of components. We propose a graphical construction of the process and build, by means of a perfect simulation algorithm, a stationary version of the process. To implement this algorithm, we make use of a Kalikow-type decomposition technique. Two models are described in this paper. In the first model, we associate to each edge of the interaction graph a saturation threshold that controls the influence of a neuron on another. In the second model, we impose a structure on the interaction graph leading to a cascade of spike trains. Such structures, where neurons are divided into layers, can be found in the retina.

Aggregate alkaline corrosion of cement in concrete is going to respond in sodium and potassium hydroxide (lye) with active SiO2 found in some aggregates. During this reaction, the concrete has resulted in significant internal stresses which cause deformation of the concrete, cracking and disintegration. The reaction is slow and concrete signs of decomposition appear only after a few months or years. The study used two different aggregates quarries. Studies show that Lithuania gravel contaminated with reactive particles having amorphous silicon dioxide reacting with cement in sodium and potassium hydroxide and the resulting alkaline concrete corrosion. It was found that, according to AAR 2 large aggregates include Group II – potentially reactive because of their expansion after 14 days, higher than 0.1%. Užpildų šarminė korozija betone vyksta reaguojant cemente esantiems natrio ir kalio hidroksidams (šarmams) su aktyviu SiO2, esančiu kai kuriuose užpilduose. Vykstant šiai reakcijai betone susidaro didelių vidinių įtempių, kurie sukelia betono deformacijas, pleišėjimą ir suirimą. Reakcija vyksta lėtai, betono irimo požymių atsiranda tik po kelių mėnesių ar metų. Tyrimams buvo naudojami dviejų skirtingų karjerų užpildai. Atlikus tyrimus nustatyta, kad Lietuvos žvyro karjerai užteršti reaktyviomis dalelėmis, turinčiomis amorfinio silicio dioksido, reaguojančio su cemente esančiais natrio ir kalio šarmais, ir sukeliančiomis betono šarminę koroziją. Nustatyta, kad pagal AAR 2 stambieji užpildai priskiriami II grupei – galimai reaktyviems užpildams, nes jų plėtra po 14 parų viršija 0,1 %.

L'objectif de cette thèse est de construire des algorithmes capables de simuler l'activité d'un réseau de neurones. L'activité du réseau de neurones peut être modélisée par le train de spikes de chaque neurone, qui sont représentés par un processus ponctuel multivarié. La plupart des approches connues pour simuler des processus ponctuels rencontrent des difficultés lorsque le réseau sous-jacent est de grande taille.Dans cette thèse, nous proposons de nouveaux algorithmes utilisant un nouveau type de décomposition de Kalikow. En particulier, nous présentons un algorithme permettant de simuler le comportement d'un neurone intégré dans un réseau neuronal infini sans simuler l'ensemble du réseau. Nous nous concentrons sur la preuve mathématique que notre algorithme renvoie les bons processus ponctuels et sur l'étude de sa condition d'arrêt. Ensuite, une preuve constructive montre que cette nouvelle décomposition est valable pour divers processus ponctuels.Enfin, nous proposons des algorithmes, qui peuvent être parallélisés et qui permettent de simuler une centaine de milliers de neurones dans un graphe d'interaction complet, sur un ordinateur portable. Plus particulièrement, la complexité de cet algorithme semble linéaire par rapport au nombre de neurones à simuler
The goal of this thesis is to construct algorithms which are able to simulate the activity of a neural network. The activity of the neural network can be modeled by the spike train of each neuron, which are represented by a multivariate point processes. Most of the known approaches to simulate point processes encounter difficulties when the underlying network is large.In this thesis, we propose new algorithms using a new type of Kalikow decomposition. In particular, we present an algorithm to simulate the behavior of one neuron embedded in an infinite neural network without simulating the whole network. We focus on mathematically proving that our algorithm returns the right point processes and on studying its stopping condition. Then, a constructive proof shows that this new decomposition holds for on various point processes.Finally, we propose algorithms, that can be parallelized and that enables us to simulate a hundred of thousand neurons in a complete interaction graph, on a laptop computer. Most notably, the complexity of this algorithm seems linear with respect to the number of neurons on simulation