3,962 research outputs found
An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model
Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings
subject to white noises, has been studied by using both direct simulations and
a semi-analytical augmented moment method (AMM) which has been proposed in a
recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For -unit FN neuron
ensembles, AMM transforms original -dimensional {\it stochastic} delay
differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs
for means and correlation functions of local and global variables.
Infinite-order recursive DEs are terminated at the finite level in the
level- AMM (AMM), yielding -dimensional deterministic DEs. When a
single spike is applied, the oscillation may be induced if parameters of
coupling strength, delay, noise intensity and/or ensemble size are appropriate.
Effects of these parameters on the emergence of the oscillation and on the
synchronization in FN neuron ensembles have been studied. The synchronization
shows the {\it fluctuation-induced} enhancement at the transition between
non-oscillating and oscillating states. Results calculated by AMM5 are in
fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos,
accepted in Phys. Rev. E with some change
Effective traffic management based on bounded rationality and indifference bands
Constrained cognitive abilities cause imperfections in drivers' choice behaviour and appear largely systematic and predictable. This study introduces the concept of 'effective control space' to build upon this knowledge as an opportunity to increase the effectiveness of Dynamic Traffic Management (DTM). Within the control space boundaries it is assumed that drivers do not act upon the effects of DTM measures, they behave as being indifferent to them. This study debates that: (i) drivers' ability to detect changes in attributes of their trip or the performance of a traffic system is limited, (ii) drivers make mistakes in estimating the value of such changes and (iii) drivers apply a great diversity of choice patterns but do not necessary adapt their choice. Hence, for some DTM measures to be effective effects should not exceed the control space boundaries, whereas other DTM measures need to give drivers an incentive that exceeds these boundaries. Knowledge on the effective control space may support road authorities to operationalise their measures most effectively. With the theories of indifference bands and decision-making as starting point a theoretical and conceptual framework are provided, supported by a numerical example to demonstrate how application can steer a system towards its optimal state
Adaptation Reduces Variability of the Neuronal Population Code
Sequences of events in noise-driven excitable systems with slow variables
often show serial correlations among their intervals of events. Here, we employ
a master equation for general non-renewal processes to calculate the interval
and count statistics of superimposed processes governed by a slow adaptation
variable. For an ensemble of spike-frequency adapting neurons this results in
the regularization of the population activity and an enhanced post-synaptic
signal decoding. We confirm our theoretical results in a population of cortical
neurons.Comment: 4 pages, 2 figure
Phase-locking in weakly heterogeneous neuronal networks
We examine analytically the existence and stability of phase-locked states in
a weakly heterogeneous neuronal network. We consider a model of N neurons with
all-to-all synaptic coupling where the heterogeneity is in the firing frequency
or intrinsic drive of the neurons. We consider both inhibitory and excitatory
coupling. We derive the conditions under which stable phase-locking is
possible. In homogeneous networks, many different periodic phase-locked states
are possible. Their stability depends on the dynamics of the neuron and the
coupling. For weak heterogeneity, the phase-locked states are perturbed from
the homogeneous states and can remain stable if their homogeneous conterparts
are stable. For enough heterogeneity, phase-locked solutions either lose
stability or are destroyed completely. We analyze the possible states the
network can take when phase-locking is broken.Comment: RevTex, 27 pages, 3 figure
Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles
We study the global dynamics of integrate and fire neural networks composed
of an arbitrary number of identical neurons interacting by inhibition and
excitation. We prove that if the interactions are strong enough, then the
support of the stable asymptotic dynamics consists of limit cycles. We also
find sufficient conditions for the synchronization of networks containing
excitatory neurons. The proofs are based on the analysis of the equivalent
dynamics of a piecewise continuous Poincar\'e map associated to the system. We
show that for strong interactions the Poincar\'e map is piecewise contractive.
Using this contraction property, we prove that there exist a countable number
of limit cycles attracting all the orbits dropping into the stable subset of
the phase space. This result applies not only to the Poincar\'e map under
study, but also to a wide class of general n-dimensional piecewise contractive
maps.Comment: 46 pages. In this version we added many comments suggested by the
referees all along the paper, we changed the introduction and the section
containing the conclusions. The final version will appear in Journal of
Mathematical Biology of SPRINGER and will be available at
http://www.springerlink.com/content/0303-681
VLT observations of GRB 990510 and its environment
We present BVRI photometry and spectrophotometry of GRB990510 obtained with
the ESO VLT/Antu telescope during the late decline phase. Between days 8 and 29
after the burst, the afterglow faded from R=24.2 to ~26.4. The spectral flux
distribution and the light curve support the interpretation of the afterglow as
synchrotron emission from a jet. The light curve is consistent with the optical
transient alone but an underlying SN with maximum brightness R>27.4 or a galaxy
with R>27.6 (3-sigma upper limits) cannot be ruled out. To a 5-sigma detection
threshold of R=26.1, no galaxy is found within 6'' of the transient. A very
blue V~24.5 extended object which may qualify as a starburst galaxy is located
12'' SE, but at unknown redshift.Comment: 5 pages A&A Latex, accepted for publication in A&A Letter
- …