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## Stable Stochastic Dynamics in Yeast Cell Cycle

Okabe, Yurie; Sasai, Masaki
Fonte: The Biophysical Society Publicador: The Biophysical Society
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
35.95%
Chemical reactions in cells are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of the cell is kept stable against those noisy perturbations. In this study, a stochastic model of the cell cycle of budding yeast was constructed to analyze the effects of noise on the cell-cycle oscillation. The model predicts intense noise in levels of mRNAs and proteins, and the simulated protein levels explain the observed statistical tendency of noise in populations of synchronous and asynchronous cells. Despite intense noise in levels of proteins and mRNAs, the cell cycle is stable enough to bring the largely perturbed cells back to the physiological cyclic oscillation. The model shows that consecutively appearing fixed points are the origin of this stability of the cell cycle.

## Stochastic steady state gain in a gene expression process with mRNA degradation control

Kuwahara, Hiroyuki; Schwartz, Russell
Fonte: The Royal Society Publicador: The Royal Society
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
26.2%
Recent analyses with high-resolution single-molecule experimental methods have shown highly irregular and variable bursting of mRNA in a wide range of organisms. Noise in gene expression is thought to be beneficial in cell fate specifications, as it can lay a foundation for phenotypic diversification of isogenetic cells in the homogeneous environment. However, because the stability of proteins is, in many cases, higher than that of mRNAs, noise from transcriptional bursting can be considerably buffered at the protein level, limiting the effect of noisy mRNAs at a more global regulation level. This raises a question as to what constructive role noisy mRNAs can play in the system-level dynamics. In this study, we have addressed this question using the computational models that extend the conventional transcriptional bursting model with a post-transcriptional regulation step. Surprisingly, by comparing this stochastic model with the corresponding deterministic model, we find that intrinsic fluctuations can substantially increase the expected mRNA level. Because effects of a higher mRNA level can be transmitted to the protein level even with slow protein degradation rates, this finding suggests that an increase in the protein level is another potential effect of transcriptional bursting. Here...

## Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation

Luo, Chao; Wang, Xingyuan
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.01%
A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.

## Stochastic environmental fluctuations drive epidemiology in experimental host–parasite metapopulations

Duncan, Alison B.; Gonzalez, Andrew; Kaltz, Oliver
Fonte: The Royal Society Publicador: The Royal Society
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.94%
Environmental fluctuations are important for parasite spread and persistence. However, the effects of the spatial and temporal structure of environmental fluctuations on host–parasite dynamics are not well understood. Temporal fluctuations can be random but positively autocorrelated, such that the environment is similar to the recent past (red noise), or random and uncorrelated with the past (white noise). We imposed red or white temporal temperature fluctuations on experimental metapopulations of Paramecium caudatum, experiencing an epidemic of the bacterial parasite Holospora undulata. Metapopulations (two subpopulations linked by migration) experienced fluctuations between stressful (5°C) and permissive (23°C) conditions following red or white temporal sequences. Spatial variation in temperature fluctuations was implemented by exposing subpopulations to the same (synchronous temperatures) or different (asynchronous temperatures) temporal sequences. Red noise, compared with white noise, enhanced parasite persistence. Despite this, red noise coupled with asynchronous temperatures allowed infected host populations to maintain sizes equivalent to uninfected populations. It is likely that this occurs because subpopulations in permissive conditions rescue declining subpopulations in stressful conditions. We show how patterns of temporal and spatial environmental fluctuations can impact parasite spread and host population abundance. We conclude that accurate prediction of parasite epidemics may require realistic models of environmental noise.

## GADIA: A Greedy Asynchronous Distributed Interference Avoidance Algorithm

Fonte: Institute of Electrical and Electronics Engineers Publicador: Institute of Electrical and Electronics Engineers
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
36.07%
In this paper, the problem of distributed dynamic frequency allocation is considered for a canonical communication network, which spans several networks such as cognitive radio networks and digital subscriber lines (DSLs). A greedy asynchronous distributed interference avoidance (GADIA) algorithm for horizontal spectrum sharing has been proposed that achieves performance close to that of a centralized optimal algorithm. The convergence of the GADIA algorithm to a near-optimal frequency allocation strategy is proved and several asymptotic performance bounds have been established for various spatial configurations of the network nodes. Furthermore, the near-equilibrium dynamics of the GADIA algorithm has been studied using the Glauber dynamics, by identifying the problem with the antiferromagnetic inhomogeneous long-range Potts model. Using the near-equilibrium dynamics and methods from stochastic analysis, the robustness of the algorithm with respect to time variations in the activity of network nodes is studied. These analytic results along with simulation studies reveal that the performance is close to that of an optimum centralized frequency allocation algorithm. Further simulation studies confirm that our proposed algorithm outperforms the iterative water-filling algorithm in the low signal-to-interference-plus-noise ratio (SINR) regime...

## Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update

Luo, Chao; Wang, Xingyuan; Liu, Hong
Fonte: Nature Publishing Group Publicador: Nature Publishing Group
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.08%
In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme.

## Asynchronous stochastic dynamics and the spatial prisioner's dilemma game

Grilo, Carlos Fernando Almeida; Correia, Luís
Tipo: Conferência ou Objeto de Conferência
Relevância na Pesquisa
96.27%
We argue that intermediate levels of asynchronism should be explored when one uses evolutionary games to model biological and sociological systems. Usually, only perfect synchronism and continuous asynchronism are used, assuming that it is enough to test the model under these two opposite update methods. We believe that biological and social systems lie somewhere between these two extremes and that we should inquire how the models used in these situations behave when the update method allows more than one element to be active at the same time but not necessarily all of them. Here, we use an update method called Asynchronous Stochastic Dynamics which allows us to explore intermediate levels of asynchronism and we apply it to the Spatial Prisoner’s Dilemma game. We report some results concerning the way the system changes its behaviour as the synchrony rate of the update method varies.

## The influence of asynchronous dynamics in the spatial prisioner's dilemma game

Grilo, Carlos Fernando Almeida; Correia, Luís
Tipo: Conferência ou Objeto de Conferência
Relevância na Pesquisa
25.94%
We examine the influence of asynchronism in the Spatial Prisoner’s Dilemma game. Previous studies reported that less cooperation is achieved with the asynchronous version of the game than with the synchronous one. Here, we show that, in general, the opposite is the most common outcome. This conclusion is only possible because a larger number of scenarios was tested, namely, different interaction topologies, a transition rule that can be tuned to emulate different levels of determinism in the choice of the next strategy to be adopted and different rates of asynchronism. The influence of stochastic and deterministic periodic updating in the outcome of the system is also compared. We found that these two update disciplines lead basically to the same result. This is an important issue in the simulation of social and biological behavior.

## Learning Stationary Correlated Equilibria in Constrained General-Sum Stochastic Games

Hakami, Vesal; Dehghan, Mehdi
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.12%
We study constrained general-sum stochastic games with unknown Markovian dynamics. A distributed constrained no-regret Q-learning scheme (CNRQ) is presented to guarantee convergence to the set of stationary correlated equilibria of the game. Prior art addresses the unconstrained case only, is structured with nested control loops, and has no convergence result. CNRQ is cast as a single-loop three-timescale asynchronous stochastic approximation algorithm with set-valued update increments. A rigorous convergence analysis with differential inclusion arguments is given which draws on recent extensions of the theory of stochastic approximation to the case of asynchronous recursive inclusions with set-valued mean fields. Numerical results are given for the exemplary application of CNRQ to decentralized resource control in heterogeneous wireless networks (HetNets).; Comment: 25 pages, 2 figures, 5 tables in IEEE Transactions on Cybernetics, Vol. XX, No. XX, 2015

## Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems

Huang, Zhi-Feng; Solomon, Sorin
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.9%
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents $\alpha$ of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Levy regime $\alpha < 2$, the power law decay with large exponent ($\alpha > 2$), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement.; Comment: 9 pages with 5 figures; Proceedings of EPS conference "Applications of Physics in Financial Analysis 2", 13 to 15 July 2000 Liege, Belgium (to appear in Eur. Phys. J. B)

## The dynamics of critical Kauffman networks under asynchronous stochastic update

Greil, Florian; Drossel, Barbara
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.04%
We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is in strong contrast to the synchronous case, where the number of attractors grows faster than any power law.; Comment: submitted to PRL

## Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice

Camia, Federico; Newman, Charles M.; Sidoravicius, Vladas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.01%
We investigate zero-temperature dynamics on the hexagonal lattice H for the homogeneous ferromagnetic Ising model with zero external magnetic field and a disordered ferromagnetic Ising model with a positive external magnetic field h. We consider both continuous time (asynchronous) processes and, in the homogeneous case, also discrete time synchronous dynamics (i.e., a deterministic cellular automaton), alternating between two sublattices of H. The state space consists of assignments of -1 or +1 to each site of H, and the processes are zero-temperature limits of stochastic Ising ferromagnets with Glauber dynamics and a random (i.i.d. Bernoulli) spin configuration at time 0. We study the speed of convergence of the configuration $\sigma^t$ at time t to its limit $\sigma^{\infty}$ and related issues.; Comment: 20 pages, to appear in "In and out of equilibrium: probability with a physics flavor", Progress in Probability, Birkhauser

## Transient Information Flow in a Network of Excitatory and Inhibitory Model Neurons: Role of Noise and Signal Autocorrelation

Mayor, Julien; Gerstner, Wulfram
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.9%
We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes. We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation on the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.; Comment: 27 pages, 7 figures, to appear in J. Physiology (Paris) Vol. 98

## Progresses in the Analysis of Stochastic 2D Cellular Automata: a Study of Asynchronous 2D Minority

Regnault, Damien; Schabanel, Nicolas; Thierry, Éric
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.09%
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under asynchronous updates. Still, the few mathematical analyses of asynchronism focus on one-dimensional probabilistic cellular automata, either on single examples or on specific classes. As for other classic dynamical systems in physics, extending known methods from one- to two-dimensional systems is a long lasting challenging problem. In this paper, we address the problem of analysing an apparently simple 2D asynchronous cellular automaton: 2D Minority where each cell, when fired, updates to the minority state of its neighborhood. Our experiments reveal that in spite of its simplicity, the minority rule exhibits a quite complex response to asynchronism. By focusing on the fully asynchronous regime, we are however able to describe completely the asymptotic behavior of this dynamics as long as the initial configuration satisfies some natural constraints. Besides these technical results, we have strong reasons to believe that our techniques relying on defining an energy function from the transition table of the automaton may be extended to the wider class of threshold automata.

## Does brain activity stem from high-dimensional chaotic dynamics? Evidence from the human electroencephalogram, cat cerebral cortex and artificial neuronal networks

Boustani, Sami El; Destexhe, Alain
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.09%
Nonlinear time series analyses have suggested that the human electroencephalogram (EEG) may share statistical and dynamical properties with chaotic systems. During slow-wave sleep or pathological states like epilepsy, correlation dimension measurements display low values, while in awake and attentive subjects, there is not such low dimensionality, and the EEG is more similar to a stochastic variable. We briefly review these results and contrast them with recordings in cat cerebral cortex, as well as with theoretical models. In awake or sleeping cats, recordings with microelectrodes inserted in cortex show that global variables such as local field potentials (local EEG) are similar to the human EEG. However, in both cases, neuronal discharges are highly irregular and exponentially distributed, similar to Poisson stochastic processes. To attempt reconcile these results, we investigate models of randomly-connected networks of integrate-and-fire neurons, and also contrast global (averaged) variables, with neuronal activity. The network displays different states, such as "synchronous regular" (SR) or "asynchronous irregular" (AI) states. In SR states, the global variables display coherent behavior with low dimensionality, while in AI states...

## Asynchronous Event-Driven Particle Algorithms

Donev, Aleksandar
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.08%
We present, in a unifying way, the main components of three asynchronous event-driven algorithms for simulating physical systems of interacting particles. The first example, hard-particle molecular dynamics, is well-known. We also present a recently-developed diffusion kinetic Monte Carlo algorithm, as well as a novel stochastic molecular-dynamics algorithm that builds on the Direct Simulation Monte Carlo. We explain how to effectively combine asynchronous event-driven with classical time-driven or with synchronous event-driven handling. Finally, we discuss some promises and challenges for event-driven simulation of realistic physical systems.; Comment: To appear in Simulation: Transactions of the Society for Modeling and Simulation International, 2008

## Stochastic Minority on Graphs

Rouquier, Jean-Baptiste; Regnault, Damien; Thierry1, Eric
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.93%
Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical Minority rule. Minority has been well-studied for synchronous updates and is thus a reasonable choice to begin with. Yet, beyond its apparent simplicity, this rule yields complex behaviors when asynchronism is introduced. We investigate the transitory part as well as the asymptotic behavior of the dynamics under full asynchronism (also called sequential: only one random vertex updates at each time step) for several types of graphs. Such a comparative study is a first step in understanding how the asynchronous dynamics is linked to the topology (the graph). Previous analyses on the grid [1,2] have observed that Minority seems to induce fast stabilization. We investigate here this property on arbitrary graphs using tools such as energy, particles and random walks. We show that the worst case convergence time is, in fact, strongly dependent on the topology. In particular, we observe that the case of trees is non trivial.

## Asynchronous Networks and Event Driven Dynamics

Bick, Christian; Field, Michael
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.33%
Real-world networks in physics, biology and technology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. We make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a theorem about the spatiotemporal factorization of the dynamics for a class of deadlock free functional asynchronous networks of feedforward type. We conclude with some examples and applications related to asynchronous networks with a stochastic connection structure.

## Activity-dependent stochastic resonance in recurrent neuronal networks

Tipo: Artigo de Revista Científica