125 research outputs found
System-Size Effects on the Collective Dynamics of Cell Populations with Global Coupling
Phase-transitionlike behavior is found to occur in globally coupled systems
of finite number of elements, and its theoretical explanation is provided. The
system studied is a population of globally pulse-coupled integrate-and-fire
cells subject to small additive noise. As the population size is changed, the
system shows a phase-transitionlike behavior. That is, there exits a
well-defined critical system size above which the system stays in a monostable
state with high-frequency activity while below which a new phase characterized
by alternation of high- and low frequency activities appears. The mean field
motion obeys a stochastic process with state-dependent noise, and the above
phenomenon can be interpreted as a noise-induced transition characteristic to
such processes. Coexistence of high- and low frequency activities observed in
finite size systems is reported by N. Cohen, Y. Soen and E. Braun[Physica A249,
600 (1998)] in the experiments of cultivated heart cells. The present report
gives the first qualitative interpretation of their experimental results
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
We study synchronization properties of general uncoupled limit-cycle
oscillators driven by common and independent Gaussian white noises. Using phase
reduction and averaging methods, we analytically derive the stationary
distribution of the phase difference between oscillators for weak noise
intensity. We demonstrate that in addition to synchronization, clustering, or
more generally coherence, always results from arbitrary initial conditions,
irrespective of the details of the oscillators.Comment: 6 pages, 2 figure
Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
An effective white-noise Langevin equation is derived that describes
long-time phase dynamics of a limit-cycle oscillator subjected to weak
stationary colored noise. Effective drift and diffusion coefficients are given
in terms of the phase sensitivity of the oscillator and the correlation
function of the noise, and are explicitly calculated for oscillators with
sinusoidal phase sensitivity functions driven by two typical colored Gaussian
processes. The results are verified by numerical simulations using several
types of stochastic or chaotic noise. The drift and diffusion coefficients of
oscillators driven by chaotic noise exhibit anomalous dependence on the
oscillator frequency, reflecting the peculiar power spectrum of the chaotic
noise.Comment: 16 pages, 6 figure
Effective phase description of noise-perturbed and noise-induced oscillations
An effective description of a general class of stochastic phase oscillators
is presented. For this, the effective phase velocity is defined either by
invariant probability density or via first passage times. While the first
approach exhibits correct frequency and distribution density, the second one
yields proper phase resetting curves. Their discrepancy is most pronounced for
noise-induced oscillations and is related to non-monotonicity of the phase
fluctuations
Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise
We discuss control techniques for noisy self-sustained oscillators with a
focus on reliability, stability of the response to noisy driving, and
oscillation coherence understood in the sense of constancy of oscillation
frequency. For any kind of linear feedback control--single and multiple delay
feedback, linear frequency filter, etc.--the phase diffusion constant,
quantifying coherence, and the Lyapunov exponent, quantifying reliability, can
be efficiently controlled but their ratio remains constant. Thus, an
"uncertainty principle" can be formulated: the loss of reliability occurs when
coherence is enhanced and, vice versa, coherence is weakened when reliability
is enhanced. Treatment of this principle for ensembles of oscillators
synchronized by common noise or global coupling reveals a substantial
difference between the cases of slightly non-identical oscillators and
identical ones with intrinsic noise.Comment: 10 pages, 5 figure
Finite-size and correlation-induced effects in Mean-field Dynamics
The brain's activity is characterized by the interaction of a very large
number of neurons that are strongly affected by noise. However, signals often
arise at macroscopic scales integrating the effect of many neurons into a
reliable pattern of activity. In order to study such large neuronal assemblies,
one is often led to derive mean-field limits summarizing the effect of the
interaction of a large number of neurons into an effective signal. Classical
mean-field approaches consider the evolution of a deterministic variable, the
mean activity, thus neglecting the stochastic nature of neural behavior. In
this article, we build upon two recent approaches that include correlations and
higher order moments in mean-field equations, and study how these stochastic
effects influence the solutions of the mean-field equations, both in the limit
of an infinite number of neurons and for large yet finite networks. We
introduce a new model, the infinite model, which arises from both equations by
a rescaling of the variables and, which is invertible for finite-size networks,
and hence, provides equivalent equations to those previously derived models.
The study of this model allows us to understand qualitative behavior of such
large-scale networks. We show that, though the solutions of the deterministic
mean-field equation constitute uncorrelated solutions of the new mean-field
equations, the stability properties of limit cycles are modified by the
presence of correlations, and additional non-trivial behaviors including
periodic orbits appear when there were none in the mean field. The origin of
all these behaviors is then explored in finite-size networks where interesting
mesoscopic scale effects appear. This study leads us to show that the
infinite-size system appears as a singular limit of the network equations, and
for any finite network, the system will differ from the infinite system
Ab initio many-body calculations on infinite carbon and boron-nitrogen chains
In this paper we report first-principles calculations on the ground-state
electronic structure of two infinite one-dimensional systems: (a) a chain of
carbon atoms and (b) a chain of alternating boron and nitrogen atoms. Meanfield
results were obtained using the restricted Hartree-Fock approach, while the
many-body effects were taken into account by second-order M{\o}ller-Plesset
perturbation theory and the coupled-cluster approach. The calculations were
performed using 6-31 basis sets, including the d-type polarization
functions. Both at the Hartree-Fock (HF) and the correlated levels we find that
the infinite carbon chain exhibits bond alternation with alternating single and
triple bonds, while the boron-nitrogen chain exhibits equidistant bonds. In
addition, we also performed density-functional-theory-based local density
approximation (LDA) calculations on the infinite carbon chain using the same
basis set. Our LDA results, in contradiction to our HF and correlated results,
predict a very small bond alternation. Based upon our LDA results for the
carbon chain, which are in agreement with an earlier LDA calculation
calculation [ E.J. Bylaska, J.H. Weare, and R. Kawai, Phys. Rev. B 58, R7488
(1998).], we conclude that the LDA significantly underestimates Peierls
distortion. This emphasizes that the inclusion of many-particle effects is very
important for the correct description of Peierls distortion in one-dimensional
systems.Comment: 3 figures (included). To appear in Phys. Rev.
A Measurement of the Cross Section in Two-Photon Processes
We have measured the inclusive production cross section in a
two-photon collision at the TRISTAN collider. The mean of
the collider was 57.16 GeV and the integrated luminosity was 150 . The
differential cross section () was obtained in the
range between 1.6 and 6.6 GeV and compared with theoretical predictions, such
as those involving direct and resolved photon processes.Comment: 8 pages, Latex format (article), figures corrected, published in
Phys. Rev. D 50 (1994) 187
Emergent complex neural dynamics
A large repertoire of spatiotemporal activity patterns in the brain is the
basis for adaptive behaviour. Understanding the mechanism by which the brain's
hundred billion neurons and hundred trillion synapses manage to produce such a
range of cortical configurations in a flexible manner remains a fundamental
problem in neuroscience. One plausible solution is the involvement of universal
mechanisms of emergent complex phenomena evident in dynamical systems poised
near a critical point of a second-order phase transition. We review recent
theoretical and empirical results supporting the notion that the brain is
naturally poised near criticality, as well as its implications for better
understanding of the brain
- …