Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time

Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of particles of generation $n$ in a given region, we give the second and third orders asymptotic expansions of the central limit theorem under rather weak assumptions on the moments of the underlying branching and moving laws. The obtained results and the developed approaches shed light on higher order expansions. In the proofs, the Edgeworth expansion of central limit theorems for sums of independent random variables, truncating arguments and martingale approximation play key roles. In particular, we introduce a new martingale, show its rate of convergence, as well as the rates of convergence of some known martingales, which are of independent interest.Comment: Accepted by Bernoull

Statistical properties of online avatar numbers in a massive multiplayer online role-playing game

Massive multiplayer online role-playing games (MMORPGs) are very popular in past few years. The profit of an MMORPG company is proportional to how many users registered, and the instant number of online avatars is a key factor to assess how popular an MMORPG is. We use the on-off-line logs on an MMORPG server to reconstruct the instant number of online avatars per second and investigate its statistical properties. We find that the online avatar number exhibits one-day periodic behavior and clear intraday pattern, the fluctuation distribution of the online avatar numbers has a leptokurtic non-Gaussian shape with power-law tails, and the increments of online avatar numbers after removing the intraday pattern are uncorrelated and the associated absolute values have long-term correlation. In addition, both time series exhibit multifractal nature.Comment: 9 Elsart pages including 7 figure

Joint multifractal analysis based on the partition function approach: Analytical analysis, numerical simulation and empirical application

Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.Comment: 19 pages, 5 figure

Categorizing resonances X(1835), X(2120) and X(2370) in the pseudoscalar meson family

Inspired by the newly observed three resonances X(1835), X(2120) and X(2370), in this work we systematically study the two-body strong decays and double pion decays of $\eta(1295)/\eta(1475)$, $\eta(1760)/X(1835)$ and $X(2120)/X(2370)$ by categorizing $\eta(1295)/\eta(1475)$, $\eta(1760)/X(1835)$, X(2120) and X(2370) as the radial excitations of $\eta(548)/\eta^\prime(958)$. Our numerical results indicate the followings: (1) The obtained theoretical strong decay widths of three pseudoscalar states $\eta(1295)$, $\eta(1475)$ and $\eta(1760)$ are consistent with the experimental measurements; (2) X(1835) could be the second radial excitation of $\eta^\prime(958)$; (3) X(2120) and X(2370) can be explained as the third and fourth radial excitations of $\eta(548)/\eta^\prime(958)$, respectively.Comment: 16 pages, 15 figures, 3 tables. Accepted for publication in Phys. Rev.

Quantification of atherosclerotic plaque volume in coronary arteries by computed tomographic angiography in subjects with and without diabetes.

BackgroundDiabetes mellitus (DM) is considered a cardiovascular risk factor. The aim of this study was to analyze the prevalence and volume of coronary artery plaque in patients with diabetes mellitus (DM) vs. those without DM.MethodsThis study recruited consecutive patients who underwent coronary computed tomography (CT) angiography (CCTA) between October 2016 and November 2017. Personal information including conventional cardiovascular risk factors was collected. Plaque phenotypes were automatically calculated for volume of different component. The volume of different plaque was compared between DM patients and those without DM.ResultsAmong 6381 patients, 931 (14.59%) were diagnosed with DM. The prevalence of plaque in DM subjects was higher compared with nondiabetic group significantly (48.34% vs. 33.01%, χ = 81.84, P < 0.001). DM was a significant risk factor for the prevalence of plaque in a multivariate model (odds ratio [OR] = 1.465, 95% CI: 1.258-1.706, P < 0.001). The volume of total plaque and any plaque subtypes in the DM subjects was greater than those in nondiabetic patients significantly (P < 0.001).ConclusionThe coronary artery atherosclerotic plaques were significantly higher in diabetic patients than those in non-diabetic patients