arXiv subjects

Xiaosong Chen

Publications and source records attributed to Xiaosong Chen.

51 records · Page 3Linked to original sources

arXiv2017

Abrupt transitions in collaborative social networks

Despite the wide use of networks as a versatile tool for exploring complex social systems, little is known about how to detect and forecast abrupt changes in social systems. In this report, we develop an early warning approach based on network properties to detect such changes. By analysing three collaborative social networks---one co-stardom, one patent and one scientific collaborative network, we discover that abrupt transitions inherent in these networks can serve as a good early warning signal, indicating, respectively, the dissolution of the Soviet Union, the emergence of the "soft matter" research field, and the merging of two scientific communities. We then develop a clique growth model that explains the universal properties of these real networks and find that they belong to a new universality class, described by the Gumbel distribution.

physics.soc-ph↗

arXiv2017

Finite size scaling theory for percolation phase transition

The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase transition, the finite-size scaling form for the reduced size of largest cluster has been extended to cluster ranked $R$. However, this is invalid for explosive percolation as our results show. Besides, the behaviors of largest increase of largest cluster induced by adding single link or node have also been used to investigate the critical properties of percolation and several new exponents $β_1$, $β_2$, $1/ν_1$ and $1/ν_2$ are defined while their relation with $β/ν$ and $1/ν$ is unknown. Through the analysis of asymptotic properties of size jump behaviors, we obtain correct critical exponents and develop a new approach to finite size scaling theory where sizes of ranked clusters are averaged at same distances from the sample-dependent pseudo-critical point in each realization rather than averaging at same value of control parameter.

cond-mat.stat-mech↗

arXiv2017

Revealing the phase transition behaviors of k-core percolation in random networks

The $k$-core percolation is a fundamental structural transition in complex networks. Through the analysis of the size jump behaviors of $k$-core in the evolution process of networks, we confirm that $k$-core percolation is continuous phase transition when $k=1,2$ while it is a hybrid first-order-second-order phase transition when $k\ge 3$. $2$-core percolation belongs to different universality class from that of $1$-core (giant component) percolation. The discontinuity of $k$-core percolation with $k\ge 3$ can be concluded from largest size jump of $k$-core which will not disappear in the thermodynamic limit while its continuous characteristic is reflected by second largest size jump which converges to zero in power law as $N\to \infty$. Furthermore, along with the previously known exponent $β=0.5$, we obtain a set of exponents which are independent of $k$ when $k\ge 3$ and also different from those critical exponents of $1$-core and $2$-core percolation.

cond-mat.stat-mech↗

arXiv2017

Finite size scaling theory for percolation with multiple giant clusters

A approach of finite size scaling theory for discontinous percolation with multiple giant clusters is developed in this paper. The percolation in generalized Bohman-Frieze-Wormald (BFW) model has already been proved to be discontinuous phase transition. In the evolution process, the size of largest cluster $s_1$ increases in a stairscase way and its fluctuation shows a series of peaks corresponding to the jumps of $s_1$ from one stair to another. Several largest jumps of the size of largest cluster from single edge are studied by extensive Monte Carlo simulation. $\overlineΔ_k(N)$ which is the mean of the $k$th largest jump of largest cluster, $\overline{r}_k(N)$ which is the corresponding averaged edge density, $σ_{Δ,k}(N)$ which is the standard deviation of $Δ_k$ and $σ_{r,k}(N)$ which is the standard deviation of $r_k$ are analyzed. Rich power law behaviours are found for $\overline{r}_k(N)$, $σ_{Δ,k}(N)$ and $σ_{r,k}(N)$ with critical exponents denoted as $1/ν_1$, $(β/ν)_2$ and $1/ν_2$. Unlike continuous percolation where the exact critical thresholds and critical exponent $1/ν_1$ are used for finite size scaling, the size-dependent pseudo critical thresholds $\overline{r}_k(N)$ and $1/ν_2$ works for the data collapse of the curves of largest cluster and its fluctuation in discontinuous percolation in BFW model. Further, data collapse can be obtained part by part. That is, $s_1(r,N)$ can be collapsed for each jump from one stair to another and its fluctuation can be collapsed around each peak with the corresponding $\overline{r}_k(N)$ and $1/ν_2$.

cond-mat.stat-mech↗

arXiv2017

Size Scaling of Velocity Field in Granular Flows through Apertures

For vertical velocity field $v_{\rm z} (r,z;R)$ of granular flow through an aperture of radius $R$, we propose a size scaling form $v_{\rm z}(r,z;R)=v_{\rm z} (0,0;R)f (r/R_{\rm r}, z/R_{\rm z})$ in the region above the aperture. The length scales $R_{\rm r}=R- 0.5 d$ and $R_{\rm z}=R+k_2 d$, where $k_2$ is a parameter to be determined and $d$ is the diameter of granule. The effective acceleration, which is derived from $v_{\rm z}$, follows also a size scaling form $a_{\rm eff} = v_{\rm z}^2(0,0;R)R_{\rm z}^{-1} θ(r/R_{\rm r}, z/R_{\rm z})$. For granular flow under gravity $g$, there is a boundary condition $a_{\rm eff} (0,0;R)=-g$ which gives rise to $v_{\rm z} (0,0;R)= \sqrt{ λg R_{\rm z}}$ with $λ=-1/θ(0,0)$. Using the size scaling form of vertical velocity field and its boundary condition, we can obtain the flow rate $W =C_2 ρ\sqrt{g } R_{\rm r}^{D-1} R_{\rm z}^{1/2} $, which agrees with the Beverloo law when $R \gg d$. The vertical velocity fields $v_z (r,z;R)$ in three-dimensional (3D) and two-dimensional (2D) hoppers have been simulated using the discrete element method (DEM) and GPU program. Simulation data confirm the size scaling form of $v_{\rm z} (r,z;R)$ and the $R$-dependence of $v_{\rm z} (0,0;R)$.

cond-mat.soft↗

arXiv2017

Universal scaling and critical exponents of the anisotropic quantum Rabi model

We investigate first- and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating- and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite? anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are relevant in a variety of systems able to realize strong coupling between light and matter, such as circuit QED setups where a finite anisotropy appears quite naturally.

quant-ph↗

arXiv2017

Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk

We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis-Hastings method. The gained efficiency increases with the spatial dimension (D), from approximately $10$ times in 2D to approximately $40$ times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a system with a linear size up to $L=128$, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents $ν^*=2/d$ and $γ/ν^*=d/2$. The critical point is determined, which is approximately $8$ times more precise than the best available estimate.

cond-mat.stat-mech↗

arXiv2016

Long-range Correlation and Market Segmentation in Bond Market

This paper looks into the analysis of the long-range auto-correlations and cross-correlations in bond market. Based on Detrended Moving Average (DMA) method, empirical results present a clear evidence of long-range persistence that exists in one year scale. The degree of long-range correlation related to maturities has an upward tendency with a peak in short term. These findings confirm the expectations of fractal market hypothesis (FMH). Furthermore, we have developed a method based on a complex network to study the long-range cross-correlation structure and apply it to our data, and found a clear pattern of market segmentation in the long run. We also detected the nature of long-range correlation in the sub-period 2007 to 2012 and 2011 to 2016. The result from our research shows that long-range auto-correlations are decreasing in the recent years while long-range cross-correlations are strengthening.

q-fin.ST↗

arXiv2016

Time and Frequency Structure of Causal Correlation Network in China Bond Market

There are more than eight hundred interest rates published in China bond market every day. Which are the benchmark interest rates that have broad influences on most interest rates is a major concern for economists. In this paper, multi-variable Granger causality test is developed and applied to construct a directed network of interest rates, whose important nodes, regarded as key interest rates, are evaluated with inverse Page Rank scores. The results indicate that some short-term interest rates have larger influences on the most key interest rates, while repo rates are the benchmark of short-term rates. It is also found that central bank bills'rates are in the core position of mid-term interest rates'network, and treasury bond rates are leading the long-term bonds rates. The evolution of benchmark interest rates is also studied from 2008 to 2014, and it's found that SHIBOR has generally become the benchmark interest rate in China. In the frequency domain we detect the properties of information flows between interest rates and the result confirms the existence of market segmentation in China bond market.

q-fin.ST↗

arXiv2015

Critical behaviors and universality classes of percolation phase transitions on two-dimensional square lattice

We have investigated both site and bond percolation on two dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked randomly, the site or bond with the smaller size product of two connected clusters is added when the product rule is taken. Not only the size of the largest cluster but also its size jump are studied to characterize the universality class of percolation. The finite-size scaling forms of giant cluster size and size jump are proposed and used to determine the critical exponents of percolation from Monte Carlo data. It is found that the critical exponents of both size and size jump in random site percolation are equal to that in random bond percolation. With the random rule, site and bond percolation belong to the same universality class. We obtain the critical exponents of the site percolation under the product rule, which are different from that of both random percolation and the bond percolation under the product rule. The universality class of site percolation differs different from that of bond percolation when the product rule is used.

cond-mat.stat-mech↗

arXiv2014

Hybrid evolving clique-networks and their communicability

Aiming to understand real-world hierarchical networks whose degree distributions are neither power law nor exponential, we construct a hybrid clique network that includes both homogeneous and inhomogeneous parts, and introduce an inhomogeneity parameter to tune the ratio between the homogeneous part and the inhomogeneous one. We perform Monte-Carlo simulations to study various properties of such a network, including the degree distribution, the average shortest-path-length, the clustering coefficient, the clustering spectrum, and the communicability.

cs.SI↗

arXiv2013

General Clique Percolation in Network Evolution

We introduce a general $(k,l)$ clique community, which consists of adjacent $k$-cliques sharing at least $l$ vertices with $k-1 \ge l \ge 1$. The emergence of a giant $(k,l)$ clique community indicates a $(k,l)$ clique percolation, which is studied by the largest size gap $Δ$ of the largest clique community during network evolution and the corresponding evolution step $T_c$. For a clique percolation, the averages of $Δ$ and $T_c$ and the root-mean-squares of their fluctuations have power law finite-size effects whose exponents are related to the critical exponents. The fluctuation distribution functions of $Δ$ and $T_c$ follow a finite-size scaling form. In the evolution of the Erdős-Rényi network, there are a series of $(k,l)$ clique percolation with $(k,l)=(2,1),(3,1),(3,2),(4,1),(4,2),(5,1),(4,3)$, and so on. The critical exponents of clique percolation depend on $l$, but are independent of $k$. The universality class of a $(k,l)$ clique percolation is characterized alone by $l$.

cond-mat.stat-mech↗

arXiv2012

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability $p$. At $p=0.5$, the GAP becomes the random growth model and leads to the minority product rule at $p=1$. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with $0.5 \le p \le 1$ are always continuous and their critical exponents depend on $p$. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter $p$ in addition.

cond-mat.stat-mech↗

arXiv2012

Continuous percolation phase transitions of random networks under a generalized Achlioptas process

Using the finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with minimum product of two connecting cluster sizes is taken with a probability $p$ from two randomly chosen edges. This model becomes the Erd\H os-Rényi network at $p=0.5$ and the random network under the Achlioptas process at $p=1$. Using both the fixed point of $s_2/s_1$ and the straight line of $\ln s_1$, where $s_1$ and $s_2$ are the reduced sizes of the largest and the second largest cluster, we demonstrate that the phase transitions of this model are continuous for $0.5 \le p \le 1$. From the slopes of $\ln s_1$ and $\ln (s_2/s_1)'$ at the critical point we get the critical exponents $β$ and $ν$, which depend on $p$. Therefore the universality class of this model should be characterized by $p$ also.

cond-mat.stat-mech↗

arXiv2010

Critical behavior of Binder ratios and ratios of higher order cumulants of conserved charges in QCD deconfinement phase transition

Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of high order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.

nucl-th↗