Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks

We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion a（t, L） = （∑i（mi - ρo ） ^2 / L ）1/2 is defined to describe the dynamical behaviour where Po is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ（t, L） follows a power-law scaling σ（ t, L） ~ t^δ1 and σ（ t, L） ~ t^δ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ（t, L） ~ t^δ2 when t 〈 T and 〈（t, L） ~ t^δ3 when t 〉 T. Moreover, it is found numerically that 62 is near to 61 for small rewiring probability q, and 63 hardly changes with varying q and it is almost the same as 64. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when t 〉 T for the small-world networks. We also show that the relaxation time r follows a power-law scaling τ ~ L^z and σ（t, L） in the stationary state follows a power-law Gs（L） - L^α for three different structures.     

A generalized thermodynamics for power-law statistics

We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that (i) the coupling between the systems is weak, (ii) the structure functions of the systems have a power-law dependence on the energy. It is found that the q values of two such systems at equilibrium must satisfy a relationship involving the respective numbers of degrees of freedom. The physical properties of a Tsallis distribution can be conveniently characterized by a new parameter η which can vary between 0 and +∞, these limits corresponding, respectively, to the two opposite situations of a microcanonical distribution and of a distribution with a predominant power-tail at high energies. We prove that the statistical expression of the thermodynamic functions is univocally determined by the requirements that (a) systems at thermal equilibrium have the same temperature, (b) the definitions of temperature and entropy are consistent with the second law of thermodynamics. We find that, for systems satisfying the hypotheses (i) and (ii) specified above, the thermodynamic entropy is given by Rényi entropy.     

Immunization of susceptible-infected model on scale-free networks

In this paper, we investigate two major immunization strategies, random immunization and targeted immunization, of the susceptible-infected (SI) model on the Barabási-Albert (BA) networks. For the heterogeneous structure, the random strategy is quite ineffective if the vaccinated proportion is small, while the targeted one which prefers to vaccinate the individuals with the largest degree can sharply depress the epidemic spreading even only a tiny fraction of population are vaccinated. The analytical solution is also obtained, which can capture the trend of velocity change vs. the amount of vaccinated population.     

From regular to growing small-world networks

We propose a growing model which interpolates between one-dimensional regular lattice and small-world networks. The model undergoes an interesting phase transition from large to small worlds. We investigate the structural properties by both theoretical predictions and numerical simulations. Our growing model is a complementarity for the important static Watts-Strogatz network model.     

Low-temperature thermodynamic properties of a one-dimensional disordered electron lattice system

A new method of low-temperature thermodynamic calculation of a one-dimensional generalized Wigner crystal on a disordered host-lattice is proposed. This method is based on the system statistical sum presentation in terms of modified transfer-matrixes. A gapless structure of the elementary excitations spectrum of the system under consideration is found.     

From unweighted to weighted networks with local information

In this paper, we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p. The model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned. With the increase in the local information, the degree correlation of the network transforms from assortative to disassortative. We also study the distribution of the degree, strength and edge weight, which all show crossover between exponential and scale-free. Finally, an application of the proposed model to the study of the synchronization is considered. It is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced.     

Robustness of Complex Networks under Attack and Repair

To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to the
understanding of robustness of complex networks with reparability.     

A Robustness Model of Complex Networks with Tunable Attack Information Parameter

We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.     

Limits on relief through constrained exchange on random graphs

Agents are represented by nodes on a random graph (e.g., “small world”). Each agent is endowed with a zero-mean random value that may be either positive or negative. All agents attempt to find relief, i.e., to reduce the magnitude of that initial value, to zero if possible, through exchanges. The exchange occurs only between the agents that are linked, a constraint that turns out to dominate the results. The exchange process continues until Pareto equilibrium is achieved. Only 40-90% of the agents achieved relief on small-world graphs with mean degree between 2 and 40. Even fewer agents achieved relief on scale-free-like graphs with a truncated power-law degree distribution. The rate at which relief grew with increasing degree was slow, only at most logarithmic for all of the graphs considered; viewed in reverse, the fraction of nodes that achieve relief is resilient to the removal of links.     

A dynamic model for city size distribution beyond Zipf 's law

We present a growth model for a system of cities. This model recovers not only Zipf's law but also other kinds of city size distributions (CSDs). A new positive exponent α, which yields Zipf's law only when equal to 1, was introduced. We define three classes of CSD depending on the value of α: larger than, smaller than, or equal to 1. The model is based on a random growth of the city population together with the variation of the number of cities in the system. The striking result is the peculiar behavior of the model: it is only statistical deterministic. Moreover, we found that the exponent α may be larger, smaller or equal to 1, just like in real systems of cities, depending on the rate of creation of new cities and the time elapsed during the growth. It is to our knowledge the first time that the influence of the time on the type of the distribution is investigated. The results of the model are in very good agreement with real CSD. The classification and model can be also applied to other entities like countries, incomes, firms, etc     

Effect of graded interlayer on the mode I edge delamination by residual stresses in multilayer coating-based systems

The mode I edge delamination could be initiated due to the presence of the interfacial peeling stresses near the edges of the multilayered systems due to the material mismatches between the adjacent layers. However, the exact peeling stress distributions could not be obtained by using the existing analytical and numerical models. It was proposed recently that the peeling moment resulting from the localized peeling stresses could be used to characterize mode I edge delamination. In this paper, the effect of the graded interlayer on the mode I edge delamination by thermal residual stresses in multilayer coating-based systems was investigated. Following the previous analysis approaches, the exact closed-form solutions for the peeling moments at individual interfaces and the curvatures for bilayer system, typical thermal barrier coating (TBC) system and TBC-based system with a graded interlayer inserted between the metallic layer and the ceramic layer were, respectively, derived. Case studies showed that the edge delamination by thermal stress could be impeded by properly selecting the coating materials and individual layer thicknesses. These studies may provide some important insights for developing fail-safe designing methodologies for multilayered systems.     

Uncertainty of cooperation in random scale-free networks

We study the spatial prisoner’s dilemma game where the players are located on the nodes of a random scale-free network. The prisoner’s dilemma game is a powerful tool and has been used for the study of mutual trust and cooperation among individuals in structured populations. We vary the structure of the network and the payoff values for the game, and show that the specific conditions can greatly influence the outcome of the game. A variety of behaviors are reproduced and the percentage of cooperating agents fluctuates significantly, even in the absence of irrational behavior. For example, the steady state of the game may be a configuration where either cooperators or defectors dominate, while in many cases the solution fluctuates between these two limiting behaviors.     

A new weighting method in network-based recommendation

In this paper, we propose a influence-based approach to investigate network-based recommendation systems. Different from the previous mass diffusion approach, we give a new expression of initial resource distribution and take into account the influence of resources associated with the receiver nodes. According to ranking score and two measures about the degree of personalization, we demonstrate that our method can outperform the previous methods greatly. It’s found that there exists an optimal initial resource distribution that leads to the best algorithmic accuracy and personalization strength. The optimal initial resource distribution indicates that we should increase the initial resource located on popular objects, rather than decrease them.     

Optimum designs for multi-layered film structures based on the knowledge on residual stresses

Residual stresses are inevitably generated within the multi-layered film structures due to the mismatches of material properties between the adjacent layers. Using the force and moment equilibrium conditions and beam bending theory, the residual stresses in each layer can be predicted and expressed as σ_i(z) = E_i[?′ + K(z + δ)], where E_i is the elastic modulus of the layer, ?′ the strain due to the in-plane force resulting from the misfit strain, K(z + δ) characterizes the bending contribution. For a bilayer system, the expression of the residual stress in the film is relatively simple. If the each layer thickness is much less than the substrate thickness, Stoney's equation will be derived. The assumption of a constant elastic modulus throughout the system is only applicable when the film and the substrate thickness ratio is less than 0.1. Specific analyses are performed for the thermal stresses in ZrO₂/NiCoCrAlY thermal barrier coatings (TBCs) to illustrate the implementation of the analytical model. Moreover, the effects of single interlayer and graded interlayer inserted between the metallic layer and the ceramic layer on the residual stress distributions in TBCs are investigated. Additionally, the zero-deflection design is also discussed for typically duplex-layer TBC system.     

Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node i is proportional to , where k_i is the degree of node i and ? is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter ? leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal ?.     

Negative specific heat, phase transition and particles spilling from a potential well

For a finite number of noninteracting particles in a box with a potential well in the center, the microcanonical kinetic energy in dependence on the total energy as it is negative can be classified into three categories. The first exhibits a monotonical rise and the specific heat is positive. The second shows a diminishing sawtooth wave with a global rise. The last corresponds to the extreme case and takes the regular sawtooth wave form. The sawtooth wave portion associates periodically a kinetic energy fall in spite of an increase of the total energy; and we attribute to such a fall the negative specific heat. The phase transition can be defined when the relatively dense particle state in the well and relatively dilute particle state in the rest volume of the box coexist, and the appearance of the negative specific heat is sufficient but not necessary for the onset of the phase transition.     

Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

Effects of high-order correlations on personalized recommendations for bipartite networks

In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user-user correlations are obtained by a diffusion process. Furthermore, by considering the second-order correlations, we design an effective algorithm that depresses the influence of mainstream preferences. Simulation results show that the algorithmic accuracy, measured by the average ranking score, is further improved by 20.45% and 33.25% in the optimal cases of MovieLens and Netflix data. More importantly, the optimal value depends approximately monotonously on the sparsity of the training set. Given a real system, we could estimate the optimal parameter according to the data sparsity, which makes this algorithm easy to be applied. In addition, two significant criteria of algorithmic performance, diversity and popularity, are also taken into account. Numerical results show that as the sparsity increases, the algorithm considering the second-order correlation can outperform the MCF simultaneously in all three criteria.     

Collaborative filtering based on multi-channel diffusion

In this paper, by applying a diffusion process, we propose a new index to quantify the similarity between two users in a user-object bipartite graph. To deal with the discrete ratings on objects, we use a multi-channel representation where each object is mapped to several channels with the number of channels being equal to the number of different ratings. Each channel represents a certain rating and a user having voted an object will be connected to the channel corresponding to the rating. Diffusion process taking place on such a user-channel bipartite graph gives a new similarity measure of user pairs, which is further demonstrated to be more accurate than the classical Pearson correlation coefficient under the standard collaborative filtering framework.