13 research outputs found
Event-driven simulation of spiking neurons with stochastic dynamics
We present a new technique, based on a proposed event-based strategy (Mattia & Del Giudice, 2000), for efficiently simulating large networks of simple model neurons. The strategy was based on the fact that interactions among neurons occur by means of events that are well localized in time (the action potentials) and relatively rare. In the interval between two of these events, the state variables associated with a model neuron or a synapse evolved deterministically and in a predictable way. Here, we extend the event-driven simulation strategy to the case in which the dynamics of the state variables in the inter-event intervals are stochastic. This extension captures both the situation in which the simulated neurons are inherently noisy and the case in which they are embedded in a very large network and receive a huge number of random synaptic inputs. We show how to effectively include the impact of large background populations into neuronal dynamics by means of the numerical evaluation of the statistical properties of single-model neurons under random current injection. The new simulation strategy allows the study of networks of interacting neurons with an arbitrary number of external afferents and inherent stochastic dynamics
DAMNED: A Distributed and Multithreaded Neural Event-Driven simulation framework
In a Spiking Neural Networks (SNN), spike emissions are sparsely and
irregularly distributed both in time and in the network architecture. Since a
current feature of SNNs is a low average activity, efficient implementations of
SNNs are usually based on an Event-Driven Simulation (EDS). On the other hand,
simulations of large scale neural networks can take advantage of distributing
the neurons on a set of processors (either workstation cluster or parallel
computer). This article presents DAMNED, a large scale SNN simulation framework
able to gather the benefits of EDS and parallel computing. Two levels of
parallelism are combined: Distributed mapping of the neural topology, at the
network level, and local multithreaded allocation of resources for simultaneous
processing of events, at the neuron level. Based on the causality of events, a
distributed solution is proposed for solving the complex problem of scheduling
without synchronization barrier.Comment: 6 page
A Markovian event-based framework for stochastic spiking neural networks
In spiking neural networks, the information is conveyed by the spike times,
that depend on the intrinsic dynamics of each neuron, the input they receive
and on the connections between neurons. In this article we study the Markovian
nature of the sequence of spike times in stochastic neural networks, and in
particular the ability to deduce from a spike train the next spike time, and
therefore produce a description of the network activity only based on the spike
times regardless of the membrane potential process.
To study this question in a rigorous manner, we introduce and study an
event-based description of networks of noisy integrate-and-fire neurons, i.e.
that is based on the computation of the spike times. We show that the firing
times of the neurons in the networks constitute a Markov chain, whose
transition probability is related to the probability distribution of the
interspike interval of the neurons in the network. In the cases where the
Markovian model can be developed, the transition probability is explicitly
derived in such classical cases of neural networks as the linear
integrate-and-fire neuron models with excitatory and inhibitory interactions,
for different types of synapses, possibly featuring noisy synaptic integration,
transmission delays and absolute and relative refractory period. This covers
most of the cases that have been investigated in the event-based description of
spiking deterministic neural networks
Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics
Nearly all neuronal information processing and interneuronal communication in the brain involves action potentials, or spikes, which drive the short-term synaptic dynamics of neurons, but also their long-term dynamics, via synaptic plasticity. In many brain structures, action potential activity is considered to be sparse. This sparseness of activity has been exploited to reduce the computational cost of large-scale network simulations, through the development of event-driven simulation schemes. However, existing event-driven simulations schemes use extremely simplified neuronal models. Here, we implement and evaluate critically an event-driven algorithm (ED-LUT) that uses precalculated look-up tables to characterize synaptic and neuronal dynamics. This approach enables the use of more complex (and realistic) neuronal models or data in representing the neurons, while retaining the advantage of high-speed simulation. We demonstrate the method's application for neurons containing exponential synaptic conductances, thereby implementing shunting inhibition, a phenomenon that is critical to cellular computation. We also introduce an improved two-stage event-queue algorithm, which allows the simulations to scale efficiently to highly connected networks with arbitrary propagation delays. Finally, the scheme readily accommodates implementation of synaptic plasticity mechanisms that depend on spike timing, enabling future simulations to explore issues of long-term learning and adaptation in large-scale networks.This work has been supported by the EU projects SpikeFORCE (IST-2001-35271), SENSOPAC (IST-028056) and the Spanish National Grant (DPI-2004-07032
Introducing numerical bounds to improve event-based neural network simulation
Although the spike-trains in neural networks are mainly constrained by the
neural dynamics itself, global temporal constraints (refractoriness, time
precision, propagation delays, ..) are also to be taken into account. These
constraints are revisited in this paper in order to use them in event-based
simulation paradigms.
We first review these constraints, and discuss their consequences at the
simulation level, showing how event-based simulation of time-constrained
networks can be simplified in this context: the underlying data-structures are
strongly simplified, while event-based and clock-based mechanisms can be easily
mixed. These ideas are applied to punctual conductance-based generalized
integrate-and-fire neural networks simulation, while spike-response model
simulations are also revisited within this framework.
As an outcome, a fast minimal complementary alternative with respect to
existing simulation event-based methods, with the possibility to simulate
interesting neuron models is implemented and experimented.Comment: submitte
Simulation of networks of spiking neurons: A review of tools and strategies
We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of
Computational Neuroscience, in press (2007
Applications of The Reflected Ornstein-Uhlenbeck Process
An Ornstein-Uhlenbeck process is the most basic mean-reversion model and has been used in various fields such as finance and biology. In some instances, reflecting boundary conditions are needed to restrict the state space of this process. We study an Ornstein-Uhlenbeck diffusion process with a reflecting boundary and its application to finance and neuroscience. In the financial application, the Vasicek model which is an Ornstein-Uhlenbeck process has been used to capture the stochastic movement of the short term interest rate in the market. The shortcoming of applying this model is that it allows a negative interest rate theoretically. Thus we use a reflected Ornstein-Uhlenbeck process as an interest rate model to get around this problem. Then we price zero-coupon bond and European options with respect to our model. In the application to neuroscience, we study integrate-and-fire (I-F) neuron models. We assume that the membrane voltage follows a reflected Ornstein-Uhlenbeck process and fires when it reaches a threshold. In this case, the interspike intervals (ISIs) are the same as the first hitting times of the process to a certain barrier. We find the first passage time density given ISIs using numerical inversion integration of the Laplace transform of the first passage time pdf. Then we estimate the unknown identifiable parameters in our model