A computational procedure for the asymptotic analysis of homogeneous semi-Markov processes

A new algorithm for classifying the states of a homogeneous Markov chain having finitely many states is presented, which enables the investigation of the asymptotic behavior of semi-Markov processes in which the Markov chain is embedded. An application of the algorithm to a social security problem is also presented.     

Some limit analysis of a three dimensional viscous compressible capillary model for plasma

In this study, we discuss some limit analysis of a viscous capillary model of plasma, which is expressed as a so‐called the compressible Navier‐Stokes‐Poisson‐Korteweg equation. First, the existence of global smooth solutions for the initial value problem to the compressible Navier‐Stokes‐Poisson‐Korteweg equation with a given Debye length λ and a given capillary coefficient κ is obtained. We also show the uniform estimates of global smooth solutions with respect to the Debye length λ and the capillary coefficient κ. Then, from Aubin lemma, we show that the unique smooth solution of the 3‐dimensional Navier‐Stokes‐Poisson‐Korteweg equations converges globally in time to the strong solution of the corresponding limit equations, as λ tends to zero, κ tends to zero, and λ and κ simultaneously tend to zero. Moreover, we also give the convergence rates of these limits for any given positive time one by one.     

The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results

Looking at the nonsymmetric case of a reaction-diffusion model known as the Keller-Segel model, we summarize known facts concerning (global in time) existence and prove new blowup results for solutions of this system of two strongly coupled parabolic partial differential equations. We show in Section 4, Theorem 4, that if the solution blows up under a condition on the initial data, blowup takes place at the boundary of a smooth domain . Using variational techniques we prove in Section 5 the existence of nontrivial stationary solutions in a special case of the system. Received April 2000     

A note on the central limit theorem for bipower variation of general functions

In this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006], where the central limit theorem was shown for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.     

Micro/macro viability analysis of individual‐based models: Investigation into the viability of a stylized agricultural cooperative

The mathematical viability theory proposes methods and tools to study at a global level how controlled dynamical systems can be confined in a desirable subset of the state space. Multilevel viability problems are rarely studied since they induce combinatorial explosion (the set of N agents each evolving in a p‐dimensional state space, can evolve in a Np dimensional state space). In this article, we propose an original approach which consists in solving first local viability problems and then studying the real viability of the combination of the local strategies, by simulation where necessary. In this article, we consider as multilevel viability problem a stylized agricultural cooperative which has to keep a minimum of members. Members have an economical constraint and some members have a simple model of the functioning of the cooperative and make assumptions on other members' behavior, especially proviable agents which are concerned about their own viability. In this framework, the model assumptions allow us to solve the local viability problem at the agent level. At the cooperative level, considering mixture of agents, simulation results indicate if and when including proviable agents increases the viability of the whole cooperative. © 2014 Wiley Periodicals, Inc. Complexity 21: 276–296, 2015     

On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals

We consider multiplexers in discrete time fed by the superposition of Ternary Markov Sources. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods.This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given.Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.     

The use of QP-free algorithm in the limit analysis of slope stability

In many mountainous areas, landslides and slope instabilities frequently occur after heavy rainfall and earthquake, and result in enormous casualties and huge economic losses. In order to mitigate the landslides hazard efficiently, a method is required for a better understanding of stability analysis. Fortunately, upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes. And in this approach, the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization. In general, the SQP-type algorithms are used to solve this optimization problem. However, it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the SQP-type algorithms. Fortunately, a QP-free algorithm based on penalty function and active-set strategy can be globally convergent toward the KKT points with arbitrary starting point, and the rate of convergence is local superlinear or even quadratic. Two classical problems of slope stability are solved by this QP-free algorithm. The results show that the QP-free algorithm would be the better choice than SQP-type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability.     

Long‐time stability and asymptotic analysis of the IFE method for the multilayer porous wall model

In this article, we study the long‐time stability and asymptotic behavior of the immersed finite element (IFE) method for the multilayer porous wall model for the drug‐eluting stents. First, with the IFE method for the spatial descretization, and the implicit Euler scheme for the temporal discretization, respectively, we deduce the global stability of fully discrete solution. Then, we investigate the asymptotic behavior of the discrete scheme which reveals that the multilayer porous wall model converges to the corresponding elliptic equation if approaches to a steady‐state in both and norms as . Finally, some numerical experiments are given to verify the theoretical predictions.     

Recent models in data envelopment analysis: Theory and applications

A critical review of the recent models of data envelopment analysis (DEA) is attempted here. Three new lines of approach involving dynamic changes in parameters, the error correction models and a stochastic sensitivity analysis are discussed in some detail. On the applications side, two new formulations are presented and discussed, e.g. a model of technical change and a cost frontier for testing economies of scale and adjustment due to risk factors. Thus the critical review of recent DEA models of productivity measurement provides new insight into the frontier of research in this field.     

Existence and zero‐electron‐mass limit of strong solutions to the stationary compressible Navier‐Stokes‐Poisson equation with large external force

In this study, we consider a viscous compressible model of plasma and semiconductors, which is expressed as a compressible Navier‐Stokes‐Poisson equation. We prove that there exists a strong solution to the boundary value problem of the steady compressible Navier‐Stokes‐Poisson equation with large external forces in bounded domain, provided that the ratio of the electron/ions mass is appropriately small. Moreover, the zero‐electron‐mass limit of the strong solutions is rigorously verified. The main idea in the proof is to split the original equation into 4 parts, a system of stationary incompressible Navier‐Stokes equations with large forces, a system of stationary compressible Navier‐Stokes equations with small forces, coupled with 2 Poisson equations. Based on the known results about linear incompressible Navier‐Stokes equation, linear compressible Navier‐Stokes, linear transport, and Poisson equations, we try to establish uniform in the ratio of the electron/ions mass a priori estimates. Further, using Schauder fixed point theorem, we can show the existence of a strong solution to the boundary value problem of the steady compressible Navier‐Stokes‐Poisson equation with large external forces. At the same time, from the uniform a priori estimates, we present the zero‐electron‐mass limit of the strong solutions, which converge to the solutions of the corresponding incompressible Navier‐Stokes‐Poisson equations.     

Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.     

An improved asymptotic analysis of the expected number of pivot steps required by the simplex algorithm

Leta ₁ ...,a _m be i.i.d. points uniformly on the unit sphere in ⁿ ,m n 3, and letX:= {x ⁿ |a _i ^T x1} be the random polyhedron generated bya ₁, ...,a _m . Furthermore, for linearly independent vectorsu, in ⁿ , letS _u , (X) be the number of shadow vertices ofX inspan(u,). The paper provides an asymptotic expansion of the expectation value¯S _n,m := _in4 ¹ E(S _u, ) for fixedn andm .¯S _n,m equals the expected number of pivot steps that the shadow vertex algorithm — a parametric variant of the simplex algorithm — requires in order to solve linear programming problems of type max u ^T ,xX, if the algorithm will be started with anX-vertex solving the problem max ^T ,x X. Our analysis is closely related to Borgwardt's probabilistic analysis of the simplex algorithm. We obtain a refined asymptotic analysis of the expected number of pivot steps required by the shadow vertex algorithm for uniformly on the sphere distributed data.     

Asymptotics for logical limit laws: When the growth of the components is in an RT class

Compton's method of proving monadic second-order limit laws is based on analyzing the generating function of a class of finite structures. For applications of his deeper results we previously relied on asymptotics obtained using Cauchy's integral formula. In this paper we develop elementary techniques, based on a Tauberian theorem of Schur, that significantly extend the classes of structures for which we know that Compton's theory can be applied.

     

On the asymptotic behavior of the parameter estimators for some diffusion processes: application to neuronal models

We consider a sample of i.i.d. times and we interpret each item as the first-passage time (FPT) of a diffusion process through a constant boundary. The problem is to estimate the parameters characterizing the underlying diffusion process through the experimentally observable FPT’s. Recently in Ditlevsen and Lánsky (Phys Rev E 71, 2005) and Ditlevsen and Lánsky (Phys Rev E 73, 2006) closed form estimators have been proposed for neurobiological applications. Here we study the asymptotic properties (consistency and asymptotic normality) of the class of moment type estimators for parameters of diffusion processes like those in Ditlevsen and Lánsky (Phys Rev E 71, 2005) and Ditlevsen and Lánsky (Phys Rev E 73, 2006). Furthermore, to make our results useful for application instances we establish upper bounds for the rate of convergence of the empirical distribution of each estimator to the normal density. Applications are also considered by means of simulated experiments in a neurobiological context.      

Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model

Although matrix model partition functions do not exhaust the entire set of -functions relevant for string theory, they are elementary blocks for constructing many other -functions and seem to capture the fundamental nature of quantum gravity an string theory properly. We propose taking matrix model partition functions as new special functions. This means that they should be investigated and represented in some standard form without reference to particular applications. At the same time, the tables and lists of properties should be sufficiently full to exclude unexpected peculiarities appearing in new applications. Accomplishing this task requires considerable effort, and this paper is only a first step in this direction. We restrict our consideration to the finite Hermitian one-matrix model an concentrate mostly on its phase and branch structure that arises when the partition function is considered as a D-module. We discuss the role of the CIV-DV prepotential (which generates a certain basis in the linear space of solutions of the Virasoro constraints, although an understanding of why and how this basis is distinguished is lacking) an evaluate several first multiloop correlators, which generalize the semicircular distribution to the case of multitrace and nonplanar correlators.Translated from Teoreticheskaya i Matematicheskaya Fizika,Vol. 142, No. 3, pp. 419–488, March, 2005.     

Modern analysis of customer satisfaction surveys: comparison of models and integrated analysis

Customer satisfaction is a key dimension driving business outcomes and performance of processes in service and product organizations. Measuring customer satisfaction is typically based on self‐declared or interview‐based questionnaires where users or consumers are asked to express opinions on statements, or satisfaction scales, mapping out various interactions with the service provider or product supplier. The topic has gained importance in recent years with researchers proposing new models and methods for designing, implementing, and analyzing customer satisfaction surveys. This paper builds on material presented in a recent edited book entitled Modern Analysis of Customer Satisfaction Surveys (Kenett and Salini, 2011). The book provides a comprehensive exposition of a variety of models that have all been applied to the same data set by leading experts. These models generate a variety of management insights. Combining models opens up opportunities for further research and applications. Specifically, we suggest that an integrated analysis, aggregating several approaches to survey data analysis, may prove effective in increasing the information quality derived from of a customer satisfaction survey. Copyright © 2011 John Wiley & Sons, Ltd.     

A class of mixture of experts models for general insurance: Theoretical developments

In the Property and Casualty (P&C) ratemaking process, it is critical to understand the effect of policyholders’ risk profile to the number and amount of claims, the dependence among various business lines and the claim distributions. To include all the above features, it is essential to develop a regression model which is flexible and theoretically justified. Motivated by the issues above, we propose a class of logit-weighted reduced mixture of experts (LRMoE) models for multivariate claim frequencies or severities distributions. LRMoE is interpretable, as it has two components: Gating functions, which classify policyholders into various latent sub-classes; and Expert functions, which govern the distributional properties of the claims. Also, upon the development of denseness theory in regression setting, we can heuristically interpret the LRMoE as a “fully flexible” model to capture any distributional, dependence and regression structures subject to a denseness condition. Further, the mathematical tractability of the LRMoE is guaranteed since it satisfies various marginalization and moment properties. Finally, we discuss some special choices of expert functions that make the corresponding LRMoE “fully flexible”. In the subsequent paper (Fung et al., 2019b), we will focus on the estimation and application aspects of the LRMoE.     

Dynamic style analysis of Spanish balanced pension plans: A Bayesian approach

This paper is focused on the dynamic allocations of Spanish balanced pension plans that invest predominantly in Euro‐zone equities. Applying a Bayesian method to a return‐based style analysis that includes the constraints of the strong version and time‐varying exposures, we provide evidence for no statistically significant changes over time in the main strategic asset allocations, namely, equity assets, long‐term debt and cash allocations. However, we find time‐varying selection abilities, indicating that the value added by managers is not the same over time. Although the investment style tends to be constant in each pension plan, these allocations are variable across plans which allow us to find different subsets of portfolios that present different mean returns and volatilities. Some pension plan features, such as size and type of financial institution that manages the portfolio, have been considered in trying to find concurrent characteristics in each subset. Copyright © 2010 John Wiley & Sons, Ltd.     

Forest management models and combinatorial algorithms: analysis of state of the art

Linear Programming and Mixed Integer Linear Programs have been used for forest planning since the 60's to support decision making on forest harvesting and management. In particular, during the last two decades of forest management there has been an increased interest in spatial issues. Further, new environmental concerns, such as resource sustainability and wildlife protection, impose that increased attention be paid to activities carried out on the ground. Road building needed for access also requires spatial definiton. As a result, more complex models must be used. We discuss the issues which have led to the combinatorial nature of some main forest management problems and the solution algorithms that have been proposed for these problems, including local search heuristics, random search approaches, strengthening of mixed integer model formulations and Lagrangian relaxation. In this survey, we discuss which of the proposed approaches have been used succesfully, the advantages and shortcomings of each and what are still open research problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference

From the results of convergence by sampling in linear principal component analysis (of a random function in a separable Hilbert space), the limiting distribution is given for the principal values and the principal factors. These results can be explicitly written in the normal case. Some applications to statistical inference are investigated.