Zero-range interaction in arbitrary dimensions and in the presence of external forces

We analyze zero-range interactions in arbitrary dimensions and in the presence of external forces in terms of non-local separable potentials. We show that in one-, two- and three-dimensional cases this approach is equivalent to the standard method with a renormalization operator. Our analysis indicates that the method of a projection operator is also useful for studying processes occurring under the influence of additional forces. As an example we present exact solutions for a particle interacting with a static electric field.     

线性比式和规划问题的输出空间分支定界算法

本文旨在针对线性比式和规划这一NP-Hard非线性规划问题提出新的全局优化算法.首先,通过引入p个辅助变量把原问题等价的转化为一个非线性规划问题,这个非线性规划问题的目标函数是乘积和的形式并给原问题增加了p个新的非线性约束,再通过构造凸凹包络的技巧对等价问题的目标函数和约束条件进行相应的线性放缩,构成等价问题的一个下界线性松弛规划问题,从而提出了一个求解原问题的分支定界算法,并证明了算法的收敛性.最后,通过数值结果比较表明所提出的算法是可行有效的.     

Identifying defective sets using queries of small size

We examine the following version of a classic combinatorial search problem introduced by Rényi: Given a finite set $X$ of $n$ elements we want to identify an unknown subset $Y$ of $X$, which is known to have exactly $d$ elements, by means of testing, for as few as possible subsets $A$ of $X$, whether $A$ intersects $Y$ or not. We are primarily concerned with the non-adaptive model, where the family of test sets is specified in advance, in the case where each test set is of size at most some given natural number $k$. Our main results are nearly tight bounds on the minimum number of tests necessary when $d$ and $k$ are fixed and $n$ is large enough.     

Performance appraisal based on distance function methods

Performance appraisal is a process used by some firms to evaluate their employees’ efficiency and productivity in order to plan their promotion policy, salary policy, layoffs policy, etc. Initially this process was just carried out by the executive staff, but recently it has evolved into an evaluation process based on the opinion of different reviewers, supervisors, collaborators, customers and the employees themselves (360-degree method). In such an evaluation process the reviewers evaluate some indicators related to employees performance appraisal. In this paper we propose an evaluation framework where there are different sets of reviewers taking part in the evaluation process. Since reviewers have a different knowledge about the evaluated employee, it seems suitable to offer a flexible framework in which different reviewers can express their assessments in different finite scales according to their knowledge. The final aim is to compute a global evaluation for each employee, that can be used by the management team to make their decisions regarding their human resources policy. In this way, to obtain a global evaluation for each employee, we propose a methodology able to aggregate individual valuation in a metric L_p framework. In this context, the associated optimization problems can be reduced to an Extended Goal Programming formulation that is very easy to compute.     

A flexible approach to ranking with an application to MBA Programs

We develop a model for flexibly ranking multi-dimensional alternatives/units into preference classes via Mixed Integer Programming. We consider a linear aggregation model, but allow the criterion weights to vary within pre-specified ranges. This allows the individual alternatives/units to play to their strengths. We illustrate the use of the model by considering the Financial Times Global MBA Program rankings and discuss the implications. We argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking, providing an argument for sorting or what we call flexible ranking.     

An Approximation Method for Improving Dynamic Network Model Fitting

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, that is, networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a nonnegligible computational burden, is much easier. This article examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail—networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.     

Languages for Statistics and Data Analysis

Abstract

Languages for data analysis and statistics must be able to cover the entire spectrum from improvisation and fast prototyping to the implementation of streamlined, specialized systems for routine analyses. Such languages must not only be interactive but also programmable, and the distinctions between language, operating system, and user interface get blurred. The issues are discussed in the context of natural and computer languages, and of the different types of user interfaces (menu, command language, batch). It is argued that while such languages must have a completely general computing language kernel, they will contain surprisingly few items specific to data analysis—the latter items more properly belong to the “literature” (i.e., the programs) written in the language.     

Wavelet-Based Estimation of Anisotropic Spatiotemporal Long-Range Dependence

In this article, the estimation of spatiotemporal long-range dependence is formulated in the spectral wavelet domain. Sample information is provided by functional spectral data. Their high local singularity at the origin is captured by the wavelet transform. Weak consistency of the spectral wavelet estimators proposed is derived. Two functional estimation algorithms are implemented. A simulation study is developed to illustrate the efficiency of the computational methods derived. An approximation to the empirical convergence rate of the spectral wavelet periodogram is computed in some simulated examples.     

Stochastic Dynamics for Passage Times and Diffusion Approximations for Finite Capacity Storage Models with Different Kinds of Barriers

In this article, we discuss a number of storage models of finite capacity with random inputs, random outputs, and linear release policy. They form a class of one-dimensional master equations with separable kernels. For this class of problems, the integral equations for first overflow or first emptiness can be transformed exactly into ordinary differential equations. Analysis is done with separable kernel. For all the stochastic models, two barriers are considered: one at X = 0 and the other at X = k, and the barriers are treated as absorbing or reflecting. The imbedding method is used to derive a third order differential equation. We consider first passage times for overflow without or with emptiness of the dam. We also study the passage times for first emptiness with and without overflows. The expected amount of overflows in a given time is also calculated. Finally, by suitable statistical features, all these models are converted into diffusion process with drift. Closed form solutions are obtained for all the problems in terms of Laplace transform functions. For the diffusion process with drift first passage time density is arrived at by treating X = 0 and X = k as absorbing barriers. One of the barriers as reflecting is also studied.     

On Lp -Theory of stochastic partialdifferential equations of divergence form with continuous coefficients

We develop an L_p -theory of stochastic PDEs of divergence form. Under natural assumptions on the coefficients and the data, we show that the solutions belong to some modified stochastic Sobolev spaces. As a consequence of this result and certain embedding theorem, we also show that the solutions are Holder continuous in space and time a.s. for sufficiently large p