arXiv subjects

Kevin E. Bassler

Publications and source records attributed to Kevin E. Bassler.

At least 55 records · Page 3Linked to original sources

arXiv2009

Attractor period distribution for critical Boolean networks

Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that control the dynamics of the entire network and thus determine the attractors. Assuming that the attractor period is equal to the least common multiple of the size of all relevant components, we show that the distribution in large networks is well approximated by a power-law with an exponent of -1. Numerical evidence based on sampling of attractors supports the conclusions of our analytic arguments.

cond-mat.dis-nn↗

arXiv2009

Depth-dependent critical behavior in V2H

Using X-ray diffuse scattering, we investigate the critical behavior of an order-disorder phase transition in a defective "skin-layer" of V2H. In the skin-layer, there exist walls of dislocation lines oriented normal to the surface. The density of dislocation lines within a wall decreases continuously with depth. We find that, because of this inhomogeneous distribution of defects, the transition effectively occurs at a depth-dependent local critical temperature. A depth-dependent scaling law is proposed to describe the corresponding critical ordering behavior.

cond-mat.mtrl-sci↗

arXiv2009

Improved community structure detection using a modified fine tuning strategy

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this unduely constrains their results, leading to a bias in the size of the communities they find and limiting their effectivness. To solve this problem, we propose adding a step to the existing algorithms that does not increase the order of their computational complexity. We show that, if this step is combined with a commonly used method, the identified constraint and resulting bias are removed, and its ability to find the optimal partitioning is improved. The effectiveness of this combined algorithm is also demonstrated by using it on real-world example networks. For a number of these examples, it achieves the best results of any known algorithm.

cs.CY↗

arXiv2008

Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.

math-ph↗

arXiv2008

Integration I(d) of Nonstationary Time Series: Stationary and nonstationary increments

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectations in standard economics. Detrended finance market returns are martingales, and martingales do not satisfy regression equations. We extend the standard discussion to discover the class of detrended processes beyond standard regression models that satisfy integration I(d). In the language of econometrics, the models of interest are unit root models, meaning martingales. Typical martingales do not have stationary increments, and those that do generally do not admit ergodicity. Our analysis leads us to comment on the lack of equilibrium observed earlier between FX rates and relative price levels.

physics.soc-ph↗

arXiv2007

Finite size effects and symmetry breaking in the evolution of networks of competing Boolean nodes

The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. It is found that finite size networks evolve in a fundamentally different way than infinitely large networks do. The symmetry of the evolutionary dynamics of infinitely large networks that selects for canalizing Boolean functions is broken in the evolutionary dynamics of finite size networks. In finite size networks there is an additional selection for input inverting Boolean functions that output a value opposite to the majority of input values. These results are revealed through an empirical study of the model that calculates the frequency of occurrence of the different possible Boolean functions. Classes of functions are found to occur with the same frequency. Those classes depend on the symmetry of the evolutionary dynamics and correspond to orbits of the relevant symmetry group. The empirical results match analytic results, determined by utilizing Polya's theorem, for the number of orbits expected in both finite size and infinitely large networks. The reason for the symmetry breaking in the evolutionary dynamics is found to be due to the need for nodes in finite size networks to behave differently in order to cooperate so that the system collectively performs as well as possible. The results suggest that both finite size effects and symmetry are important for understanding the evolution of real-world complex networks, including genetic regulatory networks.

cond-mat.stat-mech↗

arXiv2007

Martingales, the Efficient Market Hypothesis, and Spurious Stylized Facts

The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from systematic uneveness in noise traders' behavior. Spurious results arise mathematically from using a log increment with a 'sliding window'. We explain why a hard to beat market demands martingale dynamics , and martingales with nonlinear variance generate nonstationary increments. The nonstationarity is exhibited directly for Euro/Dollar FX data. We observe that the Hurst exponent H_s generated by the using the sliding window technique on a time series plays the same role as does Mandelbrot's Joseph exponent. Finally, Mandelbrot originally assumed that the 'badly behaved' second moment of cotton returns is due to fat tails, but that nonconvergent behavior is instead direct evidence for nonstationary increments. Summarizing, the evidence for scaling and fat tails as the basis for econophysics and financial economics is provided neither by FX markets nor by cotton price data.

q-fin.ST↗

arXiv2007

Martingales, Detrending Data, and the Efficient Market Hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic processes generate uncorrelated, generally nonstationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x- dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the efficient market hypothesis (EMH) to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the fair game condition in terms of serial correlations in Fama's paper on the EMH.

physics.soc-ph↗

arXiv2007

Optimal transport on wireless networks

We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on wireless networks. Our algorithm iteratively balances network traffic by minimizing the maximum node betweenness on the network. The variant we consider specifically accounts for the broadcast restrictions imposed by wireless communication by using a different betweenness measure. We compare the performance of our algorithm to two other known algorithms and find that our algorithm achieves the highest transport capacity both for minimum node degree geometric networks, which are directed geometric networks that model wireless communication networks, and for configuration model networks that are uncorrelated scale-free networks.

physics.soc-ph↗

arXiv2007

Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks

Canalization of genetic regulatory networks has been argued to be favored by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial canalization can arise in purely random networks in the absence of evolutionary pressures. We use a mapping of the Boolean functions in the Kauffman N-K model for genetic regulatory networks onto a k-dimensional Ising hypercube to show that the functions can be divided into different classes strictly due to geometrical constraints. The classes can be counted and their properties determined using results from group theory and isomer chemistry. We demonstrate that partially canalized functions completely dominate all possible Boolean functions, particularly for higher k. This indicates that partial canalization is extremely common, even in randomly chosen networks, and has implications for how much information can be obtained in experiments on native state genetic regulatory networks.

q-bio.QM↗

arXiv2007

Hurst Exponents, Markov Processes, and Fractional Brownian motion

There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H not equal to 1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case and nonstationary and uncorrelated in the other. The two- and one-point densities of fBm are constructed explicitly. The two-point density doesn't scale. The one-point density is identical with that for a Markov process with H not 1/2. We conclude that both Hurst exponents and histograms for one point densities are inadequate for deducing an underlying stochastic dynamical system from empirical data.

cond-mat.stat-mech↗

arXiv2007

Transport optimization on complex networks

We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the maximum node betweenness with as little path lengthening as possible. We show that by using this optimal routing, a network can sustain significantly higher traffic without jamming than in the case of shortest path routing. A formula is proved that allows quick computation of the average number of hops along the path and of the average travel times once the betweennesses of the nodes are computed. Using this formula, we show that routing optimization preserves the small-world character exhibited by networks under shortest path routing, and that it significantly reduces the average travel time on congested networks with only a negligible increase in the average travel time at low loads. Finally, we study the correlation between the weights of the links in the case of optimal routing and the betweennesses of the nodes connected by them.

cond-mat.dis-nn↗

arXiv2006

Nonlinear evolution of surface morphology in InAs/AlAs superlattices via surface diffusion

Continuum simulations of self-organized lateral compositional modulation growth in InAs/AlAs short-period superlattices on InP substrate are presented. Results of the simulations correspond quantitatively to the results of synchrotron x-ray diffraction experiments. The time evolution of the compositional modulation during epitaxial growth can be explained only including a nonlinear dependence of the elastic energy of the growing epitaxial layer on its thickness. From the fit of the experimental data to the growth simulations we have determined the parameters of this nonlinear dependence. It was found that the modulation amplitude don't depend on the values of the surface diffusion constants of particular elements.

cond-mat.mtrl-sci↗

arXiv2006

Emergent Criticality from Co-evolution in Random Boolean Networks

The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between topology and dynamics during the evolution. The final evolved state is shown to be independent of initial conditions. The network appears to be driven to a random Boolean network with uniform in-degree of two in the large network limit. However, for biologically realized network sizes, significant finite-size effects are observed including a broad in-degree distribution and an average in-degree connection between two and three. These results may be important for explaining properties of gene regulatory networks.

cond-mat.stat-mech↗

arXiv2006

Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets

Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade have reported that they arenon-Gaussian, scale in time, and have power-law(or fat) tails. However, because they use sliding interval methods of analysis, these studies implicitly assume that the underlying process has stationary increments. We explicitly show that this assumption is not valid for the Euro-Dollar exchange rate between 1999-2004. In addition, we find that fluctuations in returns of the exchange rate are uncorrelated and scale as power-laws for certain time intervals during each day. This behavior is consistent with a diffusive process with a diffusion coefficient that depends both on the time and the price change. Within scaling regions, we find that sliding interval methods can generate fat-tailed distributions as an artifact, and that the type of scaling reported in many previous studies does not exist.

physics.soc-ph↗

arXiv2006

Optimal routing on complex networks

We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing the maximum node betweenness with as little path lengthening as possible, thus being useful in cases when networks are jamming due to queuing overload. By using the resulting routing table, a network can sustain significantly higher traffic without jamming than in the case of traditional shortest path routing.

cond-mat.stat-mech↗

arXiv2006

Congestion-gradient driven transport on complex networks

We present a study of transport on complex networks with routing based on local information. Particles hop from one node of the network to another according to a set of routing rules with different degrees of congestion awareness, ranging from random diffusion to rigid congestion-gradient driven flow. Each node can be either source or destination for particles and all nodes have the same routing capacity, which are features of ad-hoc wireless networks. It is shown that the transport capacity increases when a small amount of congestion awareness is present in the routing rules, and that it then decreases as the routing rules become too rigid when the flow becomes strictly congestion-gradient driven. Therefore, an optimum value of the congestion awareness exists in the routing rules. It is also shown that, in the limit of a large number of nodes, networks using routing based on local information jam at any nonzero load. Finally, we study the correlation between congestion at node level and a betweenness centrality measure.

cond-mat.stat-mech↗

arXiv2006

Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance

We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motion. We construct a large set of scaling solutions of Fokker-Planck partial differential equations where H is not 1/2. Thus Markov processes, which by construction have no long time correlations, can have H not equal to 1/2. If a Markov process scales with Hurst exponent H then it simply means that the process has nonstationary increments. For the scaling solutions, we show how to reduce the calculation of the probability density to a single integration once the diffusion coefficient D(x,t) is specified. As an example, we generate a class of student-t-like densities from the class of quadratic diffusion coefficients. Notably, the Tsallis density is one member of that large class. The Tsallis density is usually thought to result from a nonlinear diffusion equation, but instead we explicitly show that it follows from a Markov process generated by a linear Fokker-Planck equation, and therefore from a corresponding Langevin equation. Having a Tsallis density with H not equal to 1/2 therefore does not imply dynamics with correlated signals, e.g., like those of fractional Brownian motion. A short review of the requirements for fractional Brownian motion is given for clarity, and we explain why the usual simple argument that H unequal to 1/2 implies correlations fails for Markov processes with scaling solutions. Finally, we discuss the question of scaling of the full Green function g(x,t;x',t') of the Fokker-Planck pde.

cond-mat.stat-mech↗