Source author record

Wilten Nicola

Wilten Nicola appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record

Neurons and Cognition math.DS Biological Physics quant-ph

Catalog footprint

What is connected

6works

4topics

4close collaborators

Actions

Connect this record

Open graph Browse works

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

preprint2026arXiv

Approximate Macroscopic Dynamics of Spiking Neural Networks Based on Solutions to the Transport Equation

Firing rate fluctuations in neural populations are observed experimentally over multiple time scales, in single neurons, across trials when elicited by stimuli, and across populations. In this work, we examine how firing rate fluctuations emerge in networks of coupled integrate-and-fire neurons as a function of the initial distribution of voltages in networks with time-varying inputs. We analytically derive an approximation for the evolution of the instantaneous population rate or flux as a function of the initial voltage distribution through a Fokker-Planck system. Unlike earlier mean field approaches based on asynchronous or constant flux steady state solutions to the Fokker-Planck system, the approach considered here is based on the transport solution to the advection equation and assumes that the time-varying inputs are slow, and the neurons are in the excitation-driven regime. The transport mean field system predicts how firing rate fluctuations emerge from a dynamic interaction between time-varying inputs, initial densities, and coupling in populations of neurons.

preprint2022arXiv

Photons guided by axons may enable backpropagation-based learning in the brain

Despite great advances in explaining synaptic plasticity and neuron function, a complete understanding of the brain's learning algorithms is still missing. Artificial neural networks provide a powerful learning paradigm through the backpropagation algorithm which modifies synaptic weights by using feedback connections. Backpropagation requires extensive communication of information back through the layers of a network. This has been argued to be biologically implausible and it is not clear whether backpropagation can be realized in the brain. Here we suggest that biophotons guided by axons provide a potential channel for backward transmission of information in the brain. Biophotons have been experimentally shown to be produced in the brain, yet their purpose is not understood. We propose that biophotons can propagate from each post-synaptic neuron to its pre-synaptic one to carry the required information backward. To reflect the stochastic character of biophoton emissions, our model includes the stochastic backward transmission of teaching signals. We demonstrate that a three-layered network of neurons can learn the MNIST handwritten digit classification task using our proposed backpropagation-like algorithm with stochastic photonic feedback. We model realistic restrictions and show that our system still learns the task for low rates of biophoton emission, information-limited (one bit per photon) backward transmission, and in the presence of noise photons. Our results suggest a new functionality for biophotons and provide an alternate mechanism for backward transmission in the brain.

preprint2020arXiv

Normalized Connectomes Show Increased Synchronizability with Age Through Their Second Largest Eigenvalue

The synchronization of different brain regions is widely observed under both normal and pathological conditions such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity between them, and the ability to synchronize remains an open question. We investigated the problem of inter-region synchronization in networks of Wilson-Cowan/Neural field equations with homeostatic plasticity, each of which acts as a model for an isolated brain region. We considered arbitrary connection profiles with only one constraint: the rows of the connection matrices are all identically normalized. We found that these systems often synchronize to the solution obtained from a single, self-coupled neural region. We analyze the stability of this solution through a straightforward modification of the Master Stability Function (MSF) approach and found that synchronized solutions lose stability for connectivity matrices when the second largest positive eigenvalue is sufficiently large, for values of the global coupling parameter that are not too large. This result was numerically confirmed for ring systems and lattices and was also robust to small amounts of heterogeneity in the homeostatic set points in each node. Finally, we tested this result on connectomes obtained from 196 subjects over a broad age range (4-85 years) from the Human Connectome Project. We found that the second largest eigenvalue tended to decrease with age, indicating an increase in synchronizability that may be related to the increased prevalence of epilepsy with old age.

preprint2014arXiv

Non-smooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons

Mean-field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [14]. The mean-field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network. These differential equations are non-smooth, and in particular are piecewise smooth continuous (PWSC). Here, we analyze the smooth and non-smooth bifurcation structure of these equations and show that the system is organized around a pair of co-dimension two bifurcations that involve, respectively, the collision between a Hopf equilibrium point and a switching manifold, and a saddle-node equilibrium point and a switching manifold. These two co-dimension 2 bifurcations can coalesce into a co-dimension 3 non-smooth bifurcation. As the mean-field system we study is a non-generic piecewise smooth continuous system, we discuss possible regularizations of this system and how the bifurcations which occur are related to non-smooth bifurcations displayed by generic PWSC systems.

preprint2014arXiv

One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the mean-field systems have a degree of frequency error and the networks analyzed often do not include noise when there is adaptation. Here, we derive a one-dimensional partial differential equation (PDE) approximation for the marginal voltage density under a first order moment closure for coupled networks of integrate-and-fire neurons with white noise inputs. The PDE has substantially less frequency error than the mean-field system, and provides a great deal more information, at the cost of analytical tractability. The convergence properties of the mean-field system in the low noise limit are elucidated. A novel method for the analysis of the stability of the asynchronous tonic firing solution is also presented and implemented. Unlike previous attempts at stability analysis with these network types, information about the marginal densities of the adaptation variables is used. This method can in principle be applied to other systems with nonlinear partial differential equations.

preprint2013arXiv

Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Models

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons, and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons.