International Journal of Modern Physics C

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given “tuning” signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal’s fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach.

The paper modeled an evolution of cooperation in changing environment. A cooperation model of the evolving population was used. In this model, the individuals base the decisions to donate their resources solely on the similarity of evolved “tags” which are relative to evolved tag-difference tolerances. Two options of the cooperation model were analyzed with constant and random alterations of receiver’s and donor’s resources that change as a result of an interaction between the individuals. In both options of the cooperation model, the average of resources and the average cooperation rate follow the environmental changes, but in different ways. A comparison of the two models makes it evident that a common period of an adaptation for the changing environment is significantly greater for a cooperation model with constant alterations of the donor’s and the receiver’s resources than for a cooperation model with random alterations of them. Quantitative evaluation of the models to assess the influence of an environment on an evolution of cooperation is also provided.

We consider a dynamic group composed with a constant number of people and the people will change periodically. Every member in the community owns a value of confidence — a mechanism that measures the agent’s coherence to his or her own attitude. Based on Cellular Automata, the opinions of all agents are synchronously updated. As long as the updating frequency and updating proportion are appropriate, the open system can reach a democracy-like steady state. The majority of agents in the community will hold the same opinion.

As an important component in varieties of practical applications, understanding human urban mobility patterns draws intensive attention from researchers. In this paper, we investigate the urban mobility patterns and the impact of spatial distribution of places on the patterns using the data from a popular location-based social network Whrrl which are unrestricted to transportation modes. A movement region is demarcated for each city, which better depicts the concentrated active area of residents in the city than the administrative region. We show that the trip lengths in urban areas follow the exponential law unlike the power law in large scale of space. We find that the cities with larger sizes of place distribution area generally have smaller exponents of trip length distribution, larger means and deviations of trip lengths, while there are no apparent relationships between place densities and trip lengths. To examine the findings, we construct series of synthetic cities based on the power-law decay of place density and simulate urban human movement by the rank-based model. The simulations validate our findings and imply that the exponential distribution of urban trips is a combined result of power-law decay of place density and rank-based mobility preference.

Taking partial traces (PTrs) for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this paper, we present a thorough description of this function and analyze the number of elementary operations (ops) needed, under some possible alternative implementations, to compute it on a classical computer. As we note, it is worthwhile doing some analytical developments in order to avoid making null multiplications and sums, what can considerably reduce the ops. For instance, for a bipartite system ${{\mathscr{H}}}_a\otimes {{\mathscr{H}}}_b$ with dimensions $d_a=dim{{\mathscr{H}}}_a$ and $d_b=dim{{\mathscr{H}}}_b$ and for $d_a,d_b\gg 1$, while a direct use of PTr definition applied to ${{\mathscr{H}}}_b$ requires ${𝒪}(d_a^6{d}_b^6)$ ops, its optimized implementation entails ${𝒪}(d_a^2{d}_b)$ ops. In the sequence, we regard the computation of PTrs for general multipartite systems and describe Fortran code provided to implement it numerically. We also consider the calculation of reduced density matrices via Bloch’s parametrization with generalized Gell Mann’s matrices.

Community detection and analysis have attracted wide public concerns over the recent years. Meanwhile, many related algorithms in complex networks have been proposed. However, most of them concentrate on undirected and unweighted networks. Concerning the significant theoretical value and potential application foreground for directed-weighted networks, in this paper, a novel hierarchical communities detection algorithm (termed as DCBAI) has been proposed on the basis of asymmetric intimacy between nodes. Community structures are effectively detected by node clustering algorithm in directed-weighted network, and a set of optimal communities are generated. In addition, a new and asymmetric parameter is adopted to measure the intimate relationship between nodes. We make some simulation using the proposed algorithm in real-world networks and artificial networks, and the result obtained proves that the parameter can describe the direct and indirect relationships between two nodes. Eventually, comparison with similar algorithms shows that our proposed algorithm has better performance.

Gas–liquid two-phase flows are widely encountered in production processes of petroleum and chemical industry. Understanding the dynamic characteristics of multi-scale gas–liquid two-phase flow structures is of great significance for the optimization of production process and the measurement of flow parameters. In this paper, we propose a method of multi-scale symbolic time reverse (MSTR) analysis for gas–liquid two-phase flows. First, through extracting four time reverse asymmetry measures (TRAMs), i.e. Euclidean distance, difference entropy, percentage of constant words and percentage of reversible words, the time reverse asymmetry (TRA) behaviors of typical nonlinear systems are investigated from the perspective of multi-scale analysis, and the results show that the TRAMs are sensitive to the changing of dynamic characteristics underlying the complex nonlinear systems. Then, the MSTR analysis is used to study the conductance signals from gas–liquid two-phase flows. It is found that the multi-scale TRA analysis can effectively reveal the multi-scale structure characteristics and nonlinear evolution properties of the flow structures.

In this paper, we present a mechanism of generation of a class of switched dynamical system without equilibrium points that generates a chaotic attractor. The switched dynamical systems are based on piecewise linear (PWL) systems. The theoretical results are formally given through a theorem and corollary which give necessary and sufficient conditions to guarantee that a linear affine dynamical system has no equilibria. Numerical results are in accordance with the theory.

In the present work, it is shown that the Maxwell relations can effectively be used to partially verify the thermodynamic consistency of the entropic lattice kinetic models. As an example, we consider the Constant Speed Kinetic Model (CSKM) which has recently been introduced in [J. Comp. Phys. 274, 803 (2014); Phys Rev. E 91, 063311 (2015)] and show that, for the quasi-equilibrium flows and at low Mach numbers, the entropy variations are proportional to the pressure variations. The entropy variations of the CSKM are logarithmic (given by the Burg entropy) while the pressure variations obey a nonlogarithmic equation of state. The proportionality of these variations, which is in accordance with the Maxwell relations, can be used to partially verify the thermodynamic consistency of the model. A similar treatment of the previously introduced entropic lattice kinetic models (e.g. of the conventional ELBM of [I. V. Karlin, A. Ferrante and H. C. Öttinger, Europhys. Lett. 47, 182 (1999)]), can provide a new ground for comparing the thermodynamic consistency of the existing entropic lattice kinetic models with each other.

Building of hierarchy is inevitably associated with the constant competition for resources and attention. Here, we show how presence of two favored (leading) nodes affects properties of the network connecting individuals. In particular, we study how nodes characteristics depend on relative asymmetry between two leading nodes. It is shown that without strong and rigorous avoidance mechanism, individuals can support both dominating nodes. Slow redistribution of resources enhances this effect. Moreover, slow redistribution of resources results in development of social networks with a very limited number of layers.

In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known $L_2$, $L_{\infty }$ error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.

In this paper, a recently introduced accelerated sampling technique [D. Yevick, Int. J. Mod. Phys. C 27, 1650041 (2016)] for constructing transition matrices is further developed and applied to a two-dimensional $32\times 32$ Ising spin system. By permitting backward displacements up to a certain limit for each forward step while evolving the system to first higher and then lower energies within a restricted interval that is steadily displaced toward zero temperature as the computation proceeds, accuracy can be greatly enhanced. Simultaneously, the elements obtained from numerous independent calculations are collected in a single transition matrix. The relative accuracy of this novel method is established through a comparison to a transition matrix procedure based on the Metropolis algorithm in which the temperature is appropriately varied during the calculation and the results interpreted in terms of the distribution of realizations over both energy and magnetization.

In this paper, based on susceptible–infected–susceptible (SIS) scheme, we introduce a framework that allows us to describe the spreading dynamics of two interacting diseases with active nodes. Different from previous studies, the two different diseases, propagating concurrently on the same population, can interact with each other by modifying their transmission rates. Meanwhile, according to certain probabilities, each node on the complex networks rotates between active state and inactive state. Based on heterogeneous mean-field approach, we analyze the epidemic thresholds of the two diseases and compute the temporal evolution characterizing the spreading dynamics. In addition, we validate these theoretical predictions by numerical simulations with phase diagrams. Results show that the secondary thresholds for the two opposite scenarios (mutual enhancement scenario and mutual impairment scenario) are different. We also find that the value of critical threshold and the final size of spreading dynamics are reduced as the node activity rate decreases.

Identifying influential spreaders is crucial for developing strategies to control the spreading process on complex networks. Following the well-known K-Shell (KS) decomposition, several improved measures are proposed. However, these measures cannot identify the most influential spreaders accurately. In this paper, we define a Local K-Shell Sum (LKSS) by calculating the sum of the K-Shell indices of the neighbors within 2-hops of a given node. Based on the LKSS, we propose an Extended Local K-Shell Sum (ELKSS) centrality to rank spreaders. The ELKSS is defined as the sum of the LKSS of the nearest neighbors of a given node. By assuming that the spreading process on networks follows the Susceptible-Infectious-Recovered (SIR) model, we perform extensive simulations on a series of real networks to compare the performance between the ELKSS centrality and other six measures. The results show that the ELKSS centrality has a better performance than the six measures to distinguish the spreading ability of nodes and to identify the most influential spreaders accurately.