Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.     

Tsallis Mapping in Growing Complex Networks with Fitness

We introduce Tsallis mapping in Bianconi-Barab'asi (B-B) fitness model of growing networks.This mapping addresses the dynamical behavior of the fitness model within the framework of nonextensive statistics mechanics,which is characterized by a dimensionless nonextensivity parameter q.It is found that this new phenomenological parameter plays an important role in the evolution of networks:the underlying evolving networks may undergo a different phases depending on the q exponents,comparing to the original B-B fitness model,and the corresponding critical transition temperature T C is also identified.     

Dilute antiferromagnets: Imry-Ma argument,hierarchical model,and equivalence to random field Ising models

We discuss some aspects of the problem of the equivalence of dilute antiferromagnets and random field Ising models. We first investigate for dilute antiferromagnets the validity of the arguments of Imry and Ma. It turns out that they are applicable, but some care is required concerning the role played by the so-called internal Peierls contours. Next we consider a hierarchical version of a dilute antiferromagnetic Ising model in the presence of a uniform magnetic field and show that a renormalization group transformation maps it exactly into a hierarchical version of the random field Ising model, thus proving their equivalence as far as the critical behavior is concerned. In particular this implies that phase transition with spontaneous magnetization occurs only for dimensiond>2. Finally we show that in the absence of internal Peierls contours both models, in their hierarchical versions, exhibit phase transition already in dimensiond=2.     

Influence and dynamic behavior in random boolean networks

We present a rigorous mathematical framework for analyzing dynamics of a broad class of boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in boolean network analysis, and offer analogous characterizations for novel classes of random boolean networks. We show that some of the assumptions traditionally made in the more common mean-field analysis of boolean networks do not hold in general. For example, we offer evidence that imbalance (internal inhomogeneity) of transfer functions is a crucial feature that tends to drive quiescent behavior far more strongly than previously observed.     

三维钻石型等级晶格上量子Heisenberg系统的临界性质

利用重整化群方法,研究了三维钻石型等级晶格上的各向异性量子Heisenberg模型,获得了系统的相图和临界性质. 结果表明:对于铁磁系统,在各向同性Heisenberg极限下,系统存在有限温度的相变,并计算了系统的序参量和临界指数; 对于反铁磁系统,在各向同性Heisenberg极限下,临界温度不等于零,在临界线上不存在重入行为.     

First and second order transition in frustrated XY systems

The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte-Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte-Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as due to a fixed point in the complex plane. We review the experimental results in order to clarify the critical behavior observed. Received: 18 February 1998 / Revised: 24 April 1998 / Accepted: 30 April 1998     

Critical Behavior of the Kramers Escape Rate in Asymmetric Classical Field Theories

We introduce an asymmetric classical Ginzburg–Landau model in a bounded interval, and study its dynamical behavior when perturbed by weak spatiotemporal noise. The Kramers escape rate from a locally stable state is computed as a function of the interval length. An asymptotically sharp second-order phase transition in activation behavior, with corresponding critical behavior of the rate prefactor, occurs at a critical length ? _c , similar to what is observed in symmetric models. The weak-noise exit time asymptotics, to both leading and subdominant orders, are analyzed at all interval lengthscales. The divergence of the prefactor as the critical length is approached is discussed in terms of a crossover from non-Arrhenius to Arrhenius behavior as noise intensity decreases. More general models without symmetry are observed to display similar behavior, suggesting that the presence of a “phase transition” in escape behavior is a robust and widespread phenomenon.     

Epidemic spreading in scale-free networks

The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and persistence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.     

Self organization of social hierarchy and clusters in a challenging society with free random walks

Emergence of social hierarchy and clusters in a challenging equal-right society is studied on the basis of the agent-based model, where warlike individuals who have own power or wealth perform random walks in a random order on a lattice and when meeting others the individuals challenge the strongest among the neighbors. We assume that the winning probability depends on the difference in their wealth and after the fight the winner gets and the loser loses a unit of the wealth. We show that hierarchy is self organized when the population exceeds a critical value and the transition from egalitarian state to hierarchical state occurs in two steps. The first transition is continuous to the society with widespread winning-probability. At the second transition the variance of the winning fraction decrease discontinuously, which was not observed in previous studies. The second hierarchical society consists of a small number of extreme winners and many individuals in the middle class and losers. We also show that when the relaxation parameter for the wealth is large, the first transition disappears. In the second hierarchical society, a giant cluster of individuals is formed with a layered structure in the power order and some people stray around it. The structure of the cluster and the distribution of wealth are quite different from the results of the previous challenging model [M. Tsujiguchi and T. Odagaki, Physica A 375 (2007) 317] which adopts the preassigned order for random walk.     

Complex networks renormalization: flows and fixed points

Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.     

Localization length exponent,critical conductance distribution and multifractality in hierarchical network models for the quantum Hall effect

We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.     

Microtransitions in a 2 − d load bearing hierarchical network

We identify the existence of microtransitions in the process of avalanche transmission on $2?d$ load bearing hierarchical networks. It has been seen in earlier work that typical realizations of this network exhibit a second order transition, whereas the critical realization of the network, shows a first order transition. The microtransitions can be used to predict the transition point for both cases. Microtransitions are also seen in the correlation function and scale in a similar way for the critical realisation. We compare the ratios of the peaks of the Fourier spectrum of the correlation function with the structure factor of the network to infer information about the network structure.     

Noise induced transitions in fluid neural networks

We study the autosynchronization of temporal patterns of activity in Leptothorax ants, using to model this phenomenon the formalism of fluid neural networks. It is known that autosynchronization is involved in complex phenomena observed in ant colonies, such as task allocation and mutual exclusion. We have numerical evidence that this happens at the critical point of a noise induced transition.     

Nonuniversal routes to universality: critical phenomena in colloidal dispersions

We investigate critical phenomena in colloids by means of the renormalization-group based hierarchical reference theory of fluids. We focus on three experimentally relevant model systems: namely, the Asakura-Oosawa model of a colloidal dispersion under the influence of polymer-induced attractive depletion forces; fluids with competing short-range attractive and longer-range repulsive interactions; solutions of star polymers whose pair potential presents both an attractive well and an ultrasoft repulsion at shorter distance. Our results show that the ability to tune the effective interactions between colloidal particles allows one to generate a variety of crossovers to the asymptotic critical behavior, which are not observed in atomic fluids.     

Hierarchical cluster-tendency analysis of the group structure in the foreign exchange market

A hierarchical cluster-tendency (HCT) method in analyzing the group structure of networks of the global foreign exchange (FX) market is proposed by combining the advantages of both the minimal spanning tree (MST) and the hierarchical tree (HT). Fifty currencies of the top 50 World GDP in 2010 according to World Bank’s database are chosen as the underlying system. By using the HCT method, all nodes in the FX market network can be “colored” and distinguished. We reveal that the FX networks can be divided into two groups, i.e., the Asia-Pacific group and the Pan-European group. The results given by the hierarchical cluster-tendency method agree well with the formerly observed geographical aggregation behavior in the FX market. Moreover, an oil-resource aggregation phenomenon is discovered by using our method. We find that gold could be a better numeraire for the weekly-frequency FX data.     

Non-mean-field behavior of the contact process on scale-free networks

We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a nontrivial critical behavior that cannot be quantitatively accounted for by mean-field theory.     

The effect of TTL on the information traffic

In real communication protocols, the information packets have a finite Time-to-Live (TTL) to avoid the waste of network resources, such as infinite loop induced by routing error or too long transferring time. In this paper, we introduce TTL into the information traffic model on Barabási-Albert scale-free networks under local routing strategy and focus on its effect on the network capacity measured by the critical point (R_c) of phase transition from free flow to congestion. Simulations show that the network capacity and the communication velocity are improved. However, some packets are dropped before they arrived at destinations. It is found that the share of successfully arrived packets monotonously increases with the increment of TTL and it is considerably acceptable if TTL is not very small. We also examine the effect of TTL on the positive-feedback preference (PFP) internet model and the results are alike. Our work may be helpful in quantifying the effect of packet lifetime in real communication networks and in routing strategy designing.     

无序超导体磁通运动的两次退钉扎效应和重新进入超导相

考虑平面内和不同平面磁通之间的相互作用力，计算了无序各向异性超导体中磁通运动的平均速度、微分电阻随驱动力F_l的变化规律，用层间关联函数C_z的值来判断2D塑性流动和3D关联流动的运动图像.观察到随着外驱动力的增大微分电阻出现两个尖峰，它对应着磁通运动存在两次退钉扎现象.在一定层间耦合条件下，在微分电阻双峰之间，可观察到重新进入微分电阻为零的钉扎相.这与最近实验上新发现的无序弱钉扎超导体有重新进入超导相的巨大峰值效应相吻合.同时，也可发现随着驱动电流的增大，磁通运动出现由2D塑性流动到3D弹性流动的相变，这一维度的变化对应着微分电阻dV/dI曲线中的二次峰位置. 并证明当层间耦合(即代表磁场的大小)在一定范围时，3D-2D相变对应的临界电流随磁场的增大而增大, 反映了第二磁化峰附近的磁通格子软硬度改变的微观图像. 关键词： 第Ⅱ类超导体 磁通线格子 钉扎 峰值效应     

Oscillatory behavior of critical amplitudes of the Gaussian model on a hierarchical structure

We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display nonstandard critical behavior on the lattice under study. The leading singular behavior of the correlation length xi near the critical coupling K=K(c) is modulated by a function which is periodic in ln/ln(K(c)-K)/. We have also shown that the common finite-size scaling hypothesis, according to which for a finite system at criticality xi should be of the order of the size of the system, is not applicable in this case. As a consequence of this, the exact form of the leading singular behavior of xi differs from the one described earlier (which was based on the finite-size scaling assumption).     

Phase transition and critical behavior of spin–orbital coupled spinel ZnV_2O_4

We present the temperature-dependent susceptibility and specific heat measurement of spinel ZnV_2O_4.The structural transition with orbital ordering and the antiferromagnetic transition with spin ordering were observed at 50 K and 37 K,respectively.By analysis of the hysteresis behavior between the specific heat curves obtained in warming and cooling processes,the structural transition was confirmed to be the first-order transition,while the antiferromagnetic transition was found to be of the second-order type.At the structural transition,the latent heat and entropy change were calculated from the excess specific heat,and the derivative of pressure with respect to temperature was obtained using the Clausius-Clapayron equation.At the magnetic transition,the width of the critical fluctuation region was obtained to be about 0.5 K by comparing with Gaussian fluctuations.In the critical region,the critical behavior was analyzed by using renormalization-group theory.The critical amplitude ratio A~+/A~- = 1.46,which deviates from the 3D Heisenburg model;while the critical exponent α is-0.011,which is close to the 3D XY model.We proposed that these abnormal critical behaviors can be attributed to strong spin-orbital coupling accompanied with the antiferromagnetic transition.Moreover,in the low temperature range(2-5 K),the Fermi energy,the density of states near the Fermi surface,and the low limit of Debye temperature were estimated to be2.42 eV,2.48 eV~(-1),and 240 K,respectively.