Mass synchronization: occurrence and its control with possible applications to brain dynamics

Occurrence of strong or mass synchronization of a large number of neuronal populations in the brain characterizes its pathological states. In order to establish an understanding of the mechanism underlying such pathological synchronization, we present a model of coupled populations of phase oscillators representing the interacting neuronal populations. Through numerical analysis, we discuss the occurrence of mass synchronization in the model, where a source population which gets strongly synchronized drives the target populations onto mass synchronization. We hypothesize and identify a possible cause for the occurrence of such a synchronization, which is so far unknown: Pathological synchronization is caused not just because of the increase in the strength of coupling between the populations but also because of the strength of the strong synchronization of the drive population. We propose a demand controlled method to control this pathological synchronization by providing a delayed feedback where the strength and frequency of the synchronization determine the strength and the time delay of the feedback. We provide an analytical explanation for the occurrence of pathological synchronization and its control in the thermodynamic limit.     

与地理环境相关的中国铁路客运网拓扑结构

以中国铁路车站作为“节点”,每辆列车经过的相邻两个停靠车站之间连接一条“边”,构成有方向有权重的中国铁路客运网.首先研究了该网络的拓扑结构,包括连接度、聚集系数、最短路径和强度,结果表明中国铁路客运网的连接度分布,强度分布都是介于指数分布和幂率分布之间,是一个具有小世界性质的阶层网络.修建铁路需考虑人口分布,行政区域等因素.铁路固定设施成本高,修建完成后很难做变动,因此需考虑诸多空间地理环境对中国铁路客运网的影响,如站点的连接度和站点的相连站点之间的平均行驶距离之间的关系、车站的分布密度与人口密度的关系, 关键词： 铁路客运网 拓扑统计 小世界 地理环境     

The strength of the minority

In this paper, we focus on the problem of opinion formation by introducing a simple model with a certain community structure. To understand the strength of the community, we took a particular interest in a special problem of how the opinion of a small but cohesive community could persist or even be finally accepted by the majority of the society. Both simulation and analysis has been done in the absence and presence of noise. In the noiseless environment, assuming the population of the community is fixed, if the cohesion of the community reaches a certain level, then the phase transition will occur in the evolution process that the community will never be assimilated even if it can assimilate the other nodes in the network, which depends on the population of the community. On the other hand, in the presence of noise, the process of opinion formation seems more complex that two transition behaviors occur outside and inside the community as the noise level increases. And the outcomes of the evolution may be completely opposite under different noise conditions.     

Thermodynamic and magnetic properties of the hexagonal type Ising nanowire

wIn this paper, the role of multiplicative noise in synchronization of bidirectionally coupled chain is studied. For coupled chain with three nodes, we demonstrate that noise plays positive role in synchronization based on stability theory of stochastic differential equation, and numerical simulations show the theoretical results is correct. For coupled chain with more than three nodes, we discuss the noise’s effect on synchronization by numerical simulations. By the numerical results, one may conjecture that the noise also have positive effect on synchronization when node number is larger than three. However, the positive effect of noise on synchronization is weaken with node number increasing.     

多层单向耦合星形网络的特征值谱及同步能力分析

随着复杂网络同步的进一步发展,对复杂网络的研究重点由单层网络转向更加接近实际网络的多层有向网络.本文分别严格推导出三层、多层的单向耦合星形网络的特征值谱,并分析了耦合强度、节点数、层数对网络同步能力的影响,重点分析了层数和层间中心节点之间的耦合强度对多层单向耦合星形网络同步能力的影响,得出了层数对多层网络同步能力的影响至关重要.当同步域无界时,网络的同步能力与耦合强度、层数有关,同步能力随其增大而增强;当同步域有界时,对于叶子节点向中心节点耦合的多层星形网络,当层内耦合强度较弱时,层内耦合强度的增大会使同步能力增强,而层间叶子节点之间的耦合强度、层数的增大反而会使同步能力减弱;当层间中心节点之间的耦合强度较弱时,层间中心节点之间的耦合强度、层数的增大会使同步能力增强,层内耦合强度、层间叶子节点之间的耦合强度的增大反而会使同步能力减弱.对于中心节点向叶子节点耦合的多层星形网络,层间叶子节点之间的耦合强度、层数的增大会使同步能力增强,层内耦合强度、节点数、层间中心节点之间的耦合强度的增大反而会使同步能力减弱.     

Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise on the Gompertzian growth of tumours. Our results are obtained by solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study. We perform simulations to analyze various aspects, of the probability distribution, of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (τ) to the steady-state distribution as a function of (i) of the correlation strength (λ) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (α). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.     

基于复杂网络理论的北京公交网络拓扑性质分析

为分析公交复杂网络的拓扑性质, 本文以北京市为例, 选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据, 运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型. 该方法以公交站点作为节点, 相邻站点之间的公交线路作为边, 使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标. 对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示, 公交复杂网络的度和点强度分布极为不均, 网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%; 点强度与排列序数、累积强度分布都服从幂律分布, 具有无标度和小世界的网络特点, 少数关键节点在网络中发挥着重要的连接作用. 为分析复杂网络中的关键节点, 本文通过承载压力分析和基于"掠夺" 的区域中心节点提取两种方法, 得到了公交复杂网络中两类不同表现的关键节点. 这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.     

Modeling Dynamic Evolution of Online Friendship Network

In this paper,we study the dynamic evolution of friendship network in SNS (Social Networking Site).Our analysis suggests that an individual joining a community depends not only on the number of friends he or she has within the community,but also on the friendship network generated by those friends.In addition,we propose a model which is based on two processes:first,connecting nearest neighbors;second,strength driven attachment mechanism.The model reflects two facts:first,in the social network it is a universal phenomenon that two nodes are connected when they have at least one common neighbor;second,new nodes connect more likely to nodes which have larger weights and interactions,a phenomenon called strength driven attachment (also called weight driven attachment).From the simulation results,we find that degree distribution P(k),strength distribution P(s),and degree-strength correlation are all consistent with empirical data.     

Improvement of signal-to-noise ratio by stochastic resonance in sigmoid function threshold systems, demonstrated using a CMOS inverter

Stochastic resonance (SR) has become a well-known phenomenon that can enhance weak periodic signals with the help of noise. SR is an interesting phenomenon when applied to signal processing. Although it has been proven that SR does not always improve the signal-to-noise ratio (SNR), in a strongly nonlinear system such as simple threshold system, SR does in fact improve SNR for noisy pulsed signals at appropriate noise strength. However, even in such cases, when noise is weak, the SNR is degraded. Since the noise strength cannot be known in advance, it is difficult to apply SR to real signal processing. In this paper, we focused on the shape of the threshold at which SR did not degrade the SNR when noise was weak. To achieve output change when noise was weak, we numerically analyzed a sigmoid function threshold system. When the slope around the threshold was appropriate, SNR did not degrade when noise was weak and instead was improved at suitable noise strength. We also demonstrated SNR improvement for noisy pulsed voltages using a CMOS inverter, a very common threshold device. The input-output property of a CMOS inverter resembles the sigmoid function. By inputting the noisy signal voltage to a CMOS inverter, we measured the input and output voltages and analyzed the SNRs. The results showed that SNR was effectively improved over a wide range of noise strengths.     

Scaling Limits and Generic Bounds for Exploration Processes

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.     

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

Effects of spatial competition on the diversity of a quasispecies

The diversity harbored by populations of RNA viruses results from high mutation rates, as well as from the characteristics of the environment where they evolve. By means of a simple model for structured quasispecies, we quantify how competition for space among phenotypic types shapes their distribution at the mutation-selection equilibrium. We introduce a general framework to treat this problem and relate mutation rate and competition strength to the quasispecies composition. For diffusion limited competition, diversity typically increases and the asymptotic growth rate of the population diminishes as diffusion decreases. Limited mobility confers a relative advantage to worse competitors. The stationary state is characterized by an over-production of viral particles. Empirical data allow an estimation of mutation rates compatible with the diversity observed in viral populations infecting cellular monolayers.     

Boundary effects in a three-state modified voter model for languages

The standard three-state voter model is extended by including the outside pressure favouring one of the three language choices and by adding some biased internal noise. The Monte Carlo simulations are motivated by states with the population divided into three groups of various affinities to each other. We show the crucial influence of the boundaries for moderate lattice sizes like 500×500. By removing the fixed boundary at one side, we demonstrate that this can lead to the victory of one single choice. Noise in contrast stabilizes the choices of all three populations. In addition, we compute the persistence probability, i.e., the number of sites who have never changed their opinion during the simulation, and we consider the case of “rigid-minded” decision makers.     

电-声子耦合强度对量子点系统噪声的影响

利用Lang-Firsov正则变换和Keldysh非平衡格林函数方法研究了低温下具有电子-声子相互作用的量子点系统的噪声.我们特别注意了电-声子耦合强度的变化对量子点系统噪声的影响.数值结果表明:随着电-声子耦合强度的增大,系统的噪声增大,同时微分噪声谱中会出现一系列的声子伴带峰,峰的高度和数目对电-声子耦合强度的变化非常敏感.我们也研究了系统的Fano因子,它显示系统噪声对肖特基(Schottky)公式的偏离.在高偏压区,Fano因子随着电-声子耦合强度的增大而增大.     

电-声子耦合强度对量子点系统噪声的影响

利用Lang-Firsov正则变换和Keldysh非平衡格林函数方法研究了低温下具有电子-声子相互作用的量子点系统的噪声。我们特别注意了电-声子耦合强度的变化对量子点系统噪声的影响。数值结果表明：随着电-声子耦合强度的增大,系统的噪声增大,同时微分噪声谱中会出现一系列的声子伴带峰,峰的高度和数目对电-声子耦合强度的变化非常敏感。我们也研究了系统的Fano因子,它显示系统噪声对肖特基(Schottky)公式的偏离。在高偏压区,Fano因子随着电-声子耦合强度的增大而增大。     

Noise mitigation action plan of Pisa civil and military airport and its effects on people exposure

The “Galileo Galilei” airport is a civil and military airport quite close to central Pisa. Although the airport brings benefits in terms of tourism and different types of income, the air traffic growth exacerbates the exposition to aircraft noise. This could significantly affect public health. To this day, a small number of studies takes into account the standard indicators of Europe by considering noise emission data for military aircrafts. We estimated the noise impact produced by the airport and we evaluated the related exposed population by using the Integrated Noise Model (INM). The noise power levels of both commercial and military flights have been considered as an input to the model. Predicted levels were validated by means of a noise-monitoring network. A new tracking system (AirNav Radar) that captures Automatic Identification System (AIS) signals emitted by each aircraft has been used to emulate takeoff and landing procedures. This improves the accuracy of the input to the model. We simulated noise maps for present and future scenarios, including those following the application of noise reduction measures. For each situation, we also estimated the exposure of the population and the percentages of highly annoyed and highly sleep disturbed people. We show the utility of AIS data and their specific elaboration to draw up noise abatement measures in order to reduce the noise impact on population and allow the airport development.     

Evolution of donations on scale-free networks during a COVID-19 breakout

Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield for donors, and it has the characteristics of the prisoners' dilemma. This paper discusses why timely donations in the early stages of COVID-19 occurred. Based on the idea that donation is a strategy adopted by players during interconnection on account of their understanding of the environment, donation-related populations are placed on social networks and the inter-correlation structures in the population are described by scale-free networks. Players in donation-related populations are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi update rule, whereas the conversion between legal beneficiaries and the other three types is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters of the utility function, the noise intensity, the utility coefficient, the donation coefficient and the initial states of the population on the scale-free network change. For population sizes of 50, 100, 150, and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation and study the corresponding steady states and structural characteristics of the population. We identify the best ranges of the noise intensity K, the donation coefficient α and the utility coefficient β for promoting cooperation at different population sizes. Furthermore, with the increase of the population size, the donor traps are found. At the same time, it is discovered that the initial states of the population have a great impact on the steady states; thus the upper and lower triangle phenomena are proposed. We also find that the population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.     

The representation of periodic sounds in simulated sustained chopper units of the ventral cochlear nucleus

The nature of the neural processing underlying the extraction of pitch information from harmonic complex sounds is still unclear. Electrophysiological studies in the auditory nerve and many psychophysical and modeling studies suggest that pitch might be extracted successfully by applying a mechanism like autocorrelation to the temporal discharge patterns of auditory-nerve fibers. The current modeling study investigates the possible role of populations of sustained chopper (Chop-S) units located in the mammalian ventral cochlear nucleus (VCN) in this process. First, it is shown that computer simulations can predict responses to periodic and quasiperiodic sounds of individual Chop-S units recorded in the guinea-pig VCN. Second, it is shown that the fundamental period of a periodic or quasiperiodic sound is represented in the first-order, interspike interval statistics of a population of simulated Chop-S units. This is true across a wide range of characteristic frequencies when the chopping rate is equal to the f0 of the sound. The model was able to simulate the results of psychophysical studies involving the pitch height and pitch strength of iterated ripple noise, the dominance region of pitch, the effect of phase on pitch height and pitch strength, pitch of inharmonic stimuli, and of sinusoidally amplitude modulated noise. Simulation results indicate that changes in the interspike interval statistics of populations of Chop-S units compare well with changes in the pitch perceived by humans. It is proposed that Chop-S units in the ventral cochlear nucleus may play an important role in pitch extraction: They can convert a purely temporal pitch code as observed in the auditory nerve into a temporal place code of pitch in populations of cochlear-nucleus, Chop-S with different characteristic frequencies, and chopping rates. Thus, populations of cochlear-nucleus Chop-S units, together with their target units presumably located in the inferior colliculus, may serve to establish a stable rate-place code of pitch at the level of the auditory cortex.     

Some Analytical Properties of the Model for Stochastic Evolutionary Games in Finite Populations with Non-uniform Interaction Rate

Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, "The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations." In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to explain the emergence of cooperation in the Prisoner is Dilemma Games to some extent. Some specific examples are given to illustrate our results.     

The stabilizing effect of noise on the dynamics of a Boolean network

In this paper, we explore both numerically and analytically the robustness of a synchronous Boolean network governed by rule 126 of cellular automata. In particular, we explore whether or not the introduction of noise into the system has any discernable effect on the evolution of the system. This noise is introduced by changing the states of a given number of nodes in the system according to certain rules. New mathematical models are developed for this purpose. We use MATLAB to run the numerical simulations including iterations of the real system and the model, computation of Lyapunov exponents (LyE), and generation of bifurcation diagrams. We provide a more in-depth fixed-point analysis through analytic computations paired with a focus on bifurcations and delay plots to identify the possible attractors. We show that it is possible either to attenuate or to suppress entirely chaos through the introduction of noise and that the perturbed system may exhibit very different long-term behavior than that of the unperturbed system.