Publications (2)0 Total impact
Conference Proceeding: Synchrony and Asynchrony in Neural Networks.Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2010, Austin, Texas, USA, January 17-19, 2010; 01/2010
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ABSTRACT: The dynamics of large networks is an important and fasci-nating problem. Key examples are the Internet, social net-works, and the human brain. In this paper we consider a model introduced by DeVille and Peskin  for a stochastic pulse-coupled neural network. The key feature and novelty in their approach is that they describe the interactions of a neuronal system as a discrete-state stochastic dynamical network. This idealiza-tion has two benefits: it captures essential features of neu-ronal behavior, and it allows the study of spontaneous syn-chronization, an important phenomenon in neuronal net-works that is well-studied but unfortunately far from being well-understood. In synchronous behavior the firing of one neuron leads to the firing of other neurons, which in turn may set off a chain reaction that often involves a substantial proportion of the neurons. In this paper we rigorously analyze their model. In par-ticular, by applying methods and tools that are frequently used in theoretical computer science, we provide a very pre-cise picture of the dynamics and the evolution of the given system. In particular, we obtain insights into the coexis-tence of synchronous and asynchronous behavior and the conditions that trigger a "spontaneous" transition from one state to another.