相关论文: Quadratic Sinusoidal Analysis of Neurons in Voltag…

The nonlinear properties of the dendrites in prepositus hypoglossi neurons are involved in maintenance of eye position. The biophysical properties of these neurons are essential for the operation of the vestibular neural integrator that…

This article develops a fundamental insight into the behavior of neuronal membranes, focusing on their responses to stimuli measured with power spectra in the frequency domain. It explores the use of linear and nonlinear (quadratic…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and 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…

Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…

In this paper, we present a novel method for analysis and segmentation of laminar structure of the cortex based on tissue characteristics whose change across the gray matter underlies distinctive between cortical layers. We develop and…

Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…

We extend the hyperplane arrangement framework for neural network expressivity from the braid to discriminantal arrangements. Compatible piecewise linear functions are characterized by circuit relations and admit a matroidal description via…

This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems.…

Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a…

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent…

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…

Splitting algorithms are well-established in convex optimization and are designed to solve large-scale problems. Using such algorithms to simulate the behavior of nonlinear circuit networks provides scalable methods for the simulation and…

Inspired by the diversity of biological neurons, quadratic artificial neurons can play an important role in deep learning models. The type of quadratic neurons of our interest replaces the inner-product operation in the conventional neuron…

The origin of nonlinear responses in cells has been suggested to be crucial for various cell functions including the propagation of the nervous impulse. In physics nonlinear behavior often originates from phase transitions. Evidence for…

Inspired by neuronal diversity in the biological neural system, a plethora of studies proposed to design novel types of artificial neurons and introduce neuronal diversity into artificial neural networks. Recently proposed quadratic neuron,…

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…

In recent years many methods have been developed to understand the internal workings of neural networks, often by describing the function of individual neurons in the model. However, these methods typically only focus on explaining the very…

Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…

In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…