Dynamical inference of hidden biological populations

Population fluctuations in a predator-prey system are analyzed for the case where the number of prey could be determined, subject to measurement noise, but the number of predators was unknown. The problem of how to infer the unmeasured predator dynamics, as well as the model parameters, is addressed. Two solutions are suggested. In the first of these, measurement noise and the dynamical noise in the equation for predator population are neglected; the problem is reduced to a one-dimensional case, and a Bayesian dynamical inference algorithm is employed to reconstruct the model parameters. In the second solution a full-scale Markov Chain Monte Carlo simulation is used to infer both the unknown predator trajectory, and also the model parameters, using the one-dimensional solution as an initial guess.     

Loop statistics in complex networks

We study a scaling property of the number M_h(N) of loops of size h in complex networks with respect to a network size N. For networks with a bounded second moment of degree, we find two distinct scaling behaviors: M_h(N) ~ (constant) and M_h(N) ~ lnN as N increases. Uncorrelated random networks specified only with a degree distribution and Markovian networks specified only with a nearest neighbor degree-degree correlation display the former scaling behavior, while growing network models display the latter. The difference is attributed to structural correlation that cannot be captured by a short-range degree-degree correlation.     

Modeling wealth distribution in growing markets

We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on how much they invest, and stochastically on how much they gain from the noisy market. The average wealth of the market could be fixed or growing. We show that in a market where investment capacity of agents differ, average wealth of agents generically follow the Pareto-law. In few cases, the individual distribution of wealth of every agentcould also be obtained exactly. We also show that the underlying dynamics of other well studied kinetic models of markets can be mapped to the dynamics of our auto-regressive model.     

不同腔结构下的声光调Q双包层光纤激光器特性研究

报道了半导体激光器端面抽运不同结构的声光调Q的双包层光纤激光器的脉冲输出特性. 对前向、后向不同抽运方式的掺镱调Q双包层光纤激光器在输出平均功率,调Q脉冲宽度及脉冲稳定性进行了对比及讨论;其中后向抽运的光纤激光器,在10kHz重复频率调制下,获得了斜效率为60％的平均功率输出,其脉冲宽度为52ns,单脉冲能量为03mJ. 最后利用不同抽运方式下的速率方程,理论分析调Q脉冲的特性,分析结果与实验相符. 关键词： 双包层光纤激光器 声光开关 前向抽运 后向抽运     

Pathway parameter and thermonuclear functions

In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell-Boltzmann distribution function were considered in a series of papers by Mathai and Haubold [A.M. Mathai, H.J. Haubold, Modern Problems in Nuclear and Neutrino Astrophysics, Akademie-Verlag, Berlin, 1988]. In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter α, so that when α→1 the thermonuclear functions in the Maxwell-Boltzmannian case are recovered. We will also give interpretations for the pathway parameter α in the case of cut-off and in terms of moments. Non-extensive statistical mechanics, as developed by Tsallis [C. Tsallis, What should a statistical mechanics satisfy to reflect nature? Physica D 193 (2004) 3-34], provides the physical basis for the generalized thermonuclear functions considered in this paper.     

轴向隐失波激励的回音壁模式光纤激光器

采用轴向隐失波激励增益的方式,使激光增益区域局限在光纤回音壁模式的模场区域内,显著地降低了回音壁模式光纤激光辐射的抽运阈值,由此形成一种低阈值的回音壁模式光纤激光器.在微焦耳量级的低抽运能量条件下,用回音壁模式光纤激光器研究了激光染料的浓度效应.实验结果表明,随着激光染料浓度的增加,回音壁模式激光辐射的波长向长波方向移动,激光波长范围变宽.用回音壁模式染料激光的四能级模型得到激光上能级和所有能级上的分子数比值γ(λ)曲线后,很好地解释了实验结果.低抽运阈值的回音壁模式光纤激光器,为研究液体激光现象提供了极为便利的手段.     

Implementation of upper limit calculation for a Poisson variable by Bayesian approach

The calculation of Bayesian confidence upper limit for a Poisson variable including both signal and background with and without systematic uncertainties has been formulated. A Fortran 77 routine, BPULE, has been developed to implement the calculation. The routine can account for systematic uncertainties in the background expectation and signal efficiency. The systematic uncertainties may be separately parameterized by a Gaussian, Log-Gaussian or flat probability density function (pdf). Some technical details of BPULE have been discussed.     

On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices

We prove the Law of Large Numbers and the Central Limit Theorem for analogs of U- and V- (von Mises) statistics of eigenvalues of random matrices as their size tends to infinity. We show first that for a certain class of test functions (kernels), determining the statistics, the validity of these limiting laws reduces to the validity of analogous facts for certain linear eigenvalue statistics. We then check the conditions of the reduction statements for several most known ensembles of random matrices. The reduction phenomenon is well known in statistics, dealing with i.i.d. random variables. It is of interest that an analogous phenomenon is also the case for random matrices, whose eigenvalues are strongly dependent even if the entries of matrices are independent.     

Energy Loss and Radial Force Variation Caused by Impeller Trimming in a Double-Suction Centrifugal Pump

Impeller trimming is an economical method for broadening the range of application of a given pump, but it can destroy operational stability and efficiency. In this study, entropy production theory was utilized to analyze the variation of energy loss caused by impeller trimming based on computational fluid dynamics. Experiments and numerical simulations were conducted to investigate the energy loss and fluid-induced radial forces. The pump’s performance seriously deteriorated after impeller trimming, especially under overload conditions. Energy loss in the volute decreased after trimming under part-load conditions but increased under overload conditions, and this phenomenon made the pump head unable to be accurately predicted by empirical equations. With the help of entropy production theory, high-energy dissipation regions were mainly located in the volute discharge diffuser under overload conditions because of the flow separation and the mixing of the main flow and the stalled fluid. The increased incidence angle at the volute’s tongue after impeller trimming resulted in more serious flow separation and higher energy loss. Furthermore, the radial forces and their fluctuation amplitudes decreased under all the investigated conditions. The horizontal components of the radial forces in all cases were much higher than the vertical components.     

Acceleration of heavy particles in isotropic turbulence

The paper concerns the effect of particle inertia on acceleration statistics. A simple analytical model for predicting the acceleration of heavy particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of describing the influence of both Stokes and Reynolds numbers on the particle acceleration variance. Comparisons of model predictions with numerical simulations are presented.