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Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity…
Neuron is the most important building block in our brain, and information processing in individual neuron involves the transformation of input synaptic spike trains into an appropriate output spike train. Hardware implementation of neuron…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
The structure of the axon-dendrite connections of neurons of the brain creates a rich spatial structure in which provided various combinations of signals surrounding neurons. Structure of dendritic trees and shape of dendritic spines allow…
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural…
An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…
Understanding the basic operational logics of the nervous system is essential to advancing neuroscientific research. However, theoretical efforts to tackle this fundamental problem are lacking, despite the abundant empirical data about the…
This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
A hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks (ANN), is proposed to model time series generated by complex dynamic systems. We introduce well known features used in the study of dynamic…
Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input…
A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to…
The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…
We introduce probabilistic neural networks that describe unsupervised synchronous learning on an atomic Hardy space and space of bounded real analytic functions, respectively. For a stationary ergodic vector process, we prove that the…
The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions. Though a wide variety of nonlinear activation functions have been proposed for use in artificial neural networks, a…
Characterising the interactions between spiking neurons is central to our understanding of cognitive processes such as memory, perception and decision making. In this work, we consider the problem of inferring connectivity in the brain…
The relationship between brain structure and function has been probed using a variety of approaches, but how the underlying structural connectivity of the human brain drives behavior is far from understood. To investigate the effect of…