Publications by Tilo Schwalger

On a Finite-Size Neuronal Population Equation

Valentin Marc Schmutz, Tilo Schwalger, Eva Löcherbach

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

SIAM PUBLICATIONS2023

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Valentin Marc Schmutz, Tilo Schwalger

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal rep ...

PUBLIC LIBRARY SCIENCE2022

When shared concept cells support associations: Theory of overlapping memory engrams

Wulfram Gerstner, Tilo Schwalger, Chiara Gastaldi, Emanuela De Falco

Assemblies of neurons, called concepts cells, encode acquired concepts in human Medial Temporal Lobe. Those concept cells that are shared between two assemblies have been hypothesized to encode associations between concepts. Here we test this hypothesis in ...

2021

Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons

Tilo Schwalger

The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects and nonstationary responses of the populati ...

AMER PHYSICAL SOC2020

Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

Wulfram Gerstner, Valentin Marc Schmutz, Tilo Schwalger

Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static s ...

2020

How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

Wulfram Gerstner, Tilo Schwalger, Samuel Pavio Muscinelli

While most models of randomly connected neural networks assume single-neuron models with simple dynamics, neurons in the brain exhibit complex intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of single neurons and recurr ...

2019

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

Wulfram Gerstner, Moritz Deger, Tilo Schwalger

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacti ...

Public Library of Science2017

A Model of Synaptic Reconsolidation

Wulfram Gerstner, Lorric Ziegler, Tilo Schwalger, David Barak Kastner

Reconsolidation of memories has mostly been studied at the behavioral and molecular level. Here, we put forward a simple extension of existing computational models of synaptic consolidation to capture hippocampal slice experiments that have been interprete ...

Frontiers Research Foundation2016

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

Tilo Schwalger

Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in t ...

Springer2015

Interspike interval correlation in a stochastic exponential integrate-and-fire model with subthreshold and spike-triggered adaptation

Tilo Schwalger

We study the spike statistics of an adaptive exponential integrate-and-fire neuron stimulated by white Gaussian current noise. We derive analytical approximations for the coefficient of variation and the serial correlation coefficient of the interspike int ...

Springer2015

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Tilo Schwalger

The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability den ...

2015

Slow fluctuations in recurrent networks of spiking neurons

Tilo Schwalger

Networks of fast nonlinear elements may display slowfluctuations if interactions are strong. We find a transition in the long-term variability of a sparse recurrent network of perfect integrate-and-fire neurons at which the Fano factor switches from zero t ...

Amer Physical Soc2015

Fluctuations and information filtering in coupled populations of spiking neurons with adaptation

Wulfram Gerstner, Richard Naud, Moritz Deger, Tilo Schwalger

Finite-sized populations of spiking elements are fundamental to brain function but also are used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasirenewal description of neurons ...

2014

Relation between cooperative molecular motors and active Brownian particles

Tilo Schwalger

2011