Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model.     

Local Energy Statistics in Spin Glasses

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies E _N < β _c N, where β _c is the critical temperature. We also explain the more complex behaviour that sets in at higher energies. Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from Physics and Biology” and by the European Science Foundation in the Programme RDSES.     

Probabilistic Analysis of Condition Numbers for Linear Programming

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C _R(A) introduced by Renegar (Ref. 2).     

Effect of long range interactions on the growth of compact clusters under deposition

In the paper the role of long range interactions on the growth of a volume conserving surface is studied using the Nonlocal Conserved Kardar-Parisi-Zhang (NCKPZ) equation. It is shown that previous theoretical predictions are inconsistent with an exact one-dimensional result. This serves as a motivation for construction of a Self-Consistent Expansion (SCE) that recovers the exact one-dimensional result, and gives the scaling exponents in higher dimensions as well. A possible application of this result to colloidal systems is discussed.     

焊接结构长寿命区疲劳累积损伤的概率模型

根据焊接结构在各种随机谱载荷下长寿命区疲劳试验的有关资料,对变幅载荷下焊接结构在长寿命区疲劳累积损伤的分布规律进行了统计分析,根据长寿命区疲劳高度离散性的特点,提出了一种变标准差的概率设计模型。     

通用模拟退火用于稳健多元分析校正

模拟退火是一种全局优化算法，具有跨越局部最优点的机制，最小一乘是一种较常用的最小二乘更为稳健的优化准则，更适用于可能偏离正态分布的实际数据集，本文探讨了用最小一乘为准则并利用模拟退火方法同时测定多组分体系的可能性。应用于2－3组分药物体系分析，获得了满意的结果，本文还探讨了改变步长提高模拟退火算法优化精度的方法。     

A probability distribution for precipitation data analysis

Hydrologic design is often based on assessments of large return interval measures; it is vital to be able to conclude them as precisely as possible. Henceforth, the selection of a probability distribution is very crucial for such cases. In view of this scenario, we propose and study a pliant probability distribution for precipitation data analysis. Some mathematical and statistical properties are analyzed. In order to make stronger predictions and judge the realistic return period, we have also characterized the model via Laplace transformation. We have estimated its parameters via the maximum likelihood estimation and constructed its information matrix for developing the confidence belt of population parameters. Moreover, a real-life setup is also considered by applying the model over precipitation data of diverse regions, including Jacksonville, Florida (USA), Barkhan (Pakistan), British Columbia (Canada), and Alexandria (Egypt). This investigated study is based on various statistical parametric and nonparametric tests, which indicates that the proposed model is one of the better strategies for precipitation data analysis when compared with the famous three-parameter Kappa model.     

Barriola-Vilenkin黑洞的统计熵

利用量子统计方法 ,直接计算Barriola_Vilenkin黑洞背景下玻色场和费米场的配分函数 ,然后利用砖墙膜模型计算和讨论黑洞背景下玻色场和费米场的熵     

An alternative approach to calculate the density of states in nonextensive statistical mechanics

A relation between the generalized partition function (Tsallis) and density of states is established by using the method of integral transform which enables reducing some integral equations into the algebraic equations. Inverse Mellin transformation of this equation gives the density of states. Similar relation is also hold the for standard partition function (Boltzmann-Gibbs) and the density of states. Using these relations, we recover the density of states for the classical ideal gas within both statistics.