40 research outputs found
AN ADAPTATIVE EVOLUTIONARY MODEL OF FINANCIAL INVESTORS
The main purpose of the paper is to determine a general behavior of a multi-agent model capable of describing the process of deliberation of an investors group witch may repeatedly decide whether to buy or sell an asset. Each adaptive agent was modeled asProgramming Models, Genetic algorithms, Information efficiency
Coarse-grained dynamics of an activity bump in a neural field model
We study a stochastic nonlocal PDE, arising in the context of modelling
spatially distributed neural activity, which is capable of sustaining
stationary and moving spatially-localized ``activity bumps''. This system is
known to undergo a pitchfork bifurcation in bump speed as a parameter (the
strength of adaptation) is changed; yet increasing the noise intensity
effectively slowed the motion of the bump. Here we revisit the system from the
point of view of describing the high-dimensional stochastic dynamics in terms
of the effective dynamics of a single scalar "coarse" variable. We show that
such a reduced description in the form of an effective Langevin equation
characterized by a double-well potential is quantitatively successful. The
effective potential can be extracted using short, appropriately-initialized
bursts of direct simulation. We demonstrate this approach in terms of (a) an
experience-based "intelligent" choice of the coarse observable and (b) an
observable obtained through data-mining direct simulation results, using a
diffusion map approach.Comment: Corrected aknowledgement
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
A biophysical observation model for field potentials of networks of leaky integrate-and-fire neurons
We present a biophysical approach for the coupling of neural network activity
as resulting from proper dipole currents of cortical pyramidal neurons to the
electric field in extracellular fluid. Starting from a reduced threecompartment
model of a single pyramidal neuron, we derive an observation model for
dendritic dipole currents in extracellular space and thereby for the dendritic
field potential that contributes to the local field potential of a neural
population. This work aligns and satisfies the widespread dipole assumption
that is motivated by the "open-field" configuration of the dendritic field
potential around cortical pyramidal cells. Our reduced three-compartment scheme
allows to derive networks of leaky integrate-and-fire models, which facilitates
comparison with existing neural network and observation models. In particular,
by means of numerical simulations we compare our approach with an ad hoc model
by Mazzoni et al. [Mazzoni, A., S. Panzeri, N. K. Logothetis, and N. Brunel
(2008). Encoding of naturalistic stimuli by local field potential spectra in
networks of excitatory and inhibitory neurons. PLoS Computational Biology 4
(12), e1000239], and conclude that our biophysically motivated approach yields
substantial improvement.Comment: 31 pages, 4 figure
Stochastic neural field theory and the system-size expansion
We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N â â) we recover standard activityâbased or voltageâbased rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N ) can be truncated to form a closed system of equations for the first and second order moments. Taking a continuum limit of the moment equations whilst keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the meanâfield dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately\ud
determine exponentially small transitions
Metastability in a stochastic neural network modeled as a velocity jump Markov process
One of the major challenges in neuroscience is to determine how noise that is
present at the molecular and cellular levels affects dynamics and information
processing at the macroscopic level of synaptically coupled neuronal
populations. Often noise is incorprated into deterministic network models using
extrinsic noise sources. An alternative approach is to assume that noise arises
intrinsically as a collective population effect, which has led to a master
equation formulation of stochastic neural networks. In this paper we extend the
master equation formulation by introducing a stochastic model of neural
population dynamics in the form of a velocity jump Markov process. The latter
has the advantage of keeping track of synaptic processing as well as spiking
activity, and reduces to the neural master equation in a particular limit. The
population synaptic variables evolve according to piecewise deterministic
dynamics, which depends on population spiking activity. The latter is
characterised by a set of discrete stochastic variables evolving according to a
jump Markov process, with transition rates that depend on the synaptic
variables. We consider the particular problem of rare transitions between
metastable states of a network operating in a bistable regime in the
deterministic limit. Assuming that the synaptic dynamics is much slower than
the transitions between discrete spiking states, we use a WKB approximation and
singular perturbation theory to determine the mean first passage time to cross
the separatrix between the two metastable states. Such an analysis can also be
applied to other velocity jump Markov processes, including stochastic
voltage-gated ion channels and stochastic gene networks