Numerical Locking Problems for Parabolic Equations

We investigate the time evolution of a previous elliptic model. We study a parabolic model concerning the “numerical locking” phenomenon, namely a model for three-dimensional curved rods clamped at the endpoints. We show that the convergence of the numerical schemes is independent of the discretization parameters and the thickness of the rod. We present corresponding numerical experiments and we make a comparison with the results obtained for the hyperbolic model.     

Information storage and search complexity theory

We propose a new information-graph model for information storage and search. This model generalizes a number of known data-representation models. We study the main properties of the proposed model. We solve the problem of optimal informational graph synthesis for a wide class of search problems, including the most acute database search problems.     

Dimension Reduction and Optimality of the Uniform State in a Phase-Field-Crystal Model Involving a Higher-Order Functional

We study a phase-field-crystal model described by a free energy functional involving second-order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $$\Gamma $$-convergence result in an asymptotic thin-film regime leading to a reduced two-dimensional model. For the reduced model, we prove necessary and sufficient conditions for the global minimality of the uniform state. We also prove similar results for the Ohta–Kawasaki model.     

STOCHASTIC OPTIMIZATION FOR MULTISPECIES FISHERIES IN THE BARENTS SEA

We present a multispecies stochastic model that suggests optimal fishing policy for two species in a three‐species predator–prey ecosystem in the Barents Sea. We employ stochastic dynamic programming to solve a three‐dimensional model, in which the catch is optimized by using a multispecies feedback strategy. Applying the model to the cod, capelin, and herring ecosystem in the Barents Sea shows that the optimal catch for the stochastic interaction model is more conservative than that implied by the deterministic model. We also find that stochasticity has a stronger effect on the optimal exploitation policy for prey (capelin) than for predator (cod).     

A Lévy input fluid queue with input and workload regulation

We consider a controlled queuing model with Lévy input. The controls take place at random times. They involve the current workload and the input processes and may also depend on whether the workload process has reached certain critical values since the last control epoch. We propose a solution strategy for deriving the steady-state distribution of this model which is based on recent advances in the fluctuation theory of spectrally one-sided Lévy process. We provide illustrative examples involving a clearing model, an inventory model, and a model for the TCP protocol.     

Analysis of queueing policies in QoS switches

It is widely accepted that next-generation networks will provide guaranteed services, in contrast to the “best effort” approach today. We study and analyze queueing policies for network switches that support the QoS (Quality of Service) feature. One realization of the QoS feature is that packets are not necessarily all equal, with some having higher priorities than the others. We model this situation by assigning an intrinsic value to each packet. In this paper we are concerned with three different queueing policies: the nonpreemptive model, the FIFO preemptive model, and the bounded delay model. We concentrate on the situation where the incoming traffic overloads the queue, resulting in packet loss. The objective is to maximize the total value of packets transmitted by the queueing policy. The difficulty lies in the unpredictable nature of the future packet arrivals. We analyze the performance of the online queueing policies via competitive analysis, providing upper and lower bounds for the competitive ratios. We develop practical yet sophisticated online algorithms (queueing policies) for the three queueing models. The algorithms in many cases have provably optimal worst-case bounds. For the nonpreemptive model, we devise an optimal online algorithm for the common 2-value model. We provide a tight logarithmic bound for the general nonpreemptive model. For the FIFO preemptive model, we improve the general lower bound to 1.414, while showing a tight bound of 1.434 for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemptive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also show an improved lower bound of 1.618 for the 2-variable bounded delay model, matching the previously known upper bound.     

A Vasicek-Type Short Rate Model With Memory Effect

We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for the prices of bonds and bond options. Although the model is non-Markov, there exists an associated Markov process that allows one to apply usual numerical methods to the model. We derive analogs of an affine term structure and term structure equations for the model, and, using them, we present a numerical method to evaluate contingent claims.     

About the Power Law of the PageRank Vector Component Distribution. Part 2. The Buckley–Osthus Model,Verification of the Power Law for This Model,and Setup of Real Search Engines

This paper continues article [13]. Here we consider the Buckley–Osthus model for formation of an Internet network. We numerically calculate the PageRank vector for networks generated by this model.We show that the components of this vector are distributed according to a power law. We also discuss the computational aspects of this model with respect to the numerical methods for calculation of the PageRank vector, which were presented in the first part of the work. Finally, we describe a more general model for web-page ranking and some approaches to solve the optimization problem arising in this model learning.     

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.     

The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process,which is a stochastic fluid model itself

We introduce the Stochastic Fluid–Fluid Model, which offers powerful modeling ability for a wide range of real-life systems of significance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace–Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace–Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the first direct analysis of a stochastic fluid model that is Markovian on a continuous state space.     

CRM决策的序贯优化——以KDD98直邮决策为例

从多阶段、延迟回报的角度来看待CRM中的决策优化问题。以KDD98数据集为例,将邮寄序贯决策定义为一个部分可观察马尔可夫决策模型(POMDP)。提出了模型参数估计的EM算法并用MATLAB实现;用模型对数似然值、BIC统计量选择最佳模型;用向前一步预测对模型进行检验;用Incremental prune算法对模型求解。实证结果表明,POMDP模型可以很好的捕捉客户购买行为的动态变化,对客户的购买有很好的预测效果。在此基础上,说明了如何使用该模型以客户终生价值最大化为目标优化直邮策略。     

A new model for gas flow in pipe networks

We introduce a new model for gas dynamics in pipe networks by asymptotic analysis. The model is derived from the isothermal Euler equations. We present the derivation of the model as well as numerical results illustrating the validity and its properties. We compare the new model with existing models from the mathematical and engineering literature. We further give numerical results on a sample network. Copyright © 2009 John Wiley & Sons, Ltd.     

Forward–Backward Stochastic Differential Games and Stochastic Control under Model Uncertainty

We study optimal stochastic control problems with jumps under model uncertainty. We rewrite such problems as stochastic differential games of forward–backward stochastic differential equations. We prove general stochastic maximum principles for such games, both in the zero-sum case (finding conditions for saddle points) and for the nonzero sum games (finding conditions for Nash equilibria). We then apply these results to study robust optimal portfolio-consumption problems with penalty. We establish a connection between market viability under model uncertainty and equivalent martingale measures. In the case with entropic penalty, we prove a general reduction theorem, stating that a optimal portfolio-consumption problem under model uncertainty can be reduced to a classical portfolio-consumption problem under model certainty, with a change in the utility function, and we relate this to risk sensitive control. In particular, this result shows that model uncertainty increases the Arrow–Pratt risk aversion index.     

Two-component liquid model for the quark-gluon plasma

We discuss a two-component liquid model for the quark-gluon plasma. We show that the model explains the basic experimental observations of the plasma properties naturally on the qualitative level. From the standpoint of the dynamics, the model assumes the existence of an effective scalar field with a nonzero vacuum expectation value. The hypothesis that such a condensate exists is supported by lattice data. We formulate the kind of lattice data that would yield a possible verification of the model.     

Analysis of Multi-Unit Variance Components Models with State Space Profiles

We apply the Kalman Filter to the analysis of multi-unit variance components models where each unit's response profile follows a state space model. We use mixed model results to obtain estimates of unit-specific random effects, state disturbance terms and residual noise terms. We use the signal extraction approach to smooth individual profiles. We show how to utilize the Kalman Filter to efficiently compute the restricted loglikelihood of the model. For the important special case where each unit's response profile follows a continuous structural time series model with known transition matrix we derive an EM algorithm for the restricted maximum likelihood (REML) estimation of the variance components. We present details for the case where individual profiles are modeled as local polynomial trends or polynomial smoothing splines.     

On vector formulations of auction-type problems with applications

We propose an extension of the auction model with many divisible commodities for vector price (validity) functions. It can be viewed as a new general equilibrium model for complex systems with active elements. We give its sufficient vector variational inequality formulation and new general existence results for different ordering cones. We suggest vector extensions of network and spatial equilibrium problems with capacity bounds and show that they are particular cases of the general auction model. We also give new sufficient conditions for existence of solutions for these problems.     

Optimizing the simultaneous management of blood pressure and cholesterol for type 2 diabetes patients

We present a Markov decision process (MDP) model to determine the optimal timing of blood pressure and cholesterol medications. We study the use of our model for a high-risk population of patients with type 2 diabetes; however, the model and methods we present are applicable to the general population. We compare the optimal policies based on our MDP to published guidelines for initiation of blood pressure and cholesterol medications over the course of a patient’s lifetime. We also present a bicriteria analysis that illustrates the trade off between quality-adjusted life years and costs of treatment.     

A model of hysteresis with two inputs

We formulate and analyze a new model of vector hysteresis for the case of two-input signals. We prove the essential mathematical properties of this model and we present the solutions to two identification problems connected with our model.     

Global stability for a nonlocal reaction–diffusion population model

In this paper, we study a nonlocal reaction–diffusion population model. We establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution to the model. We then analyze the global stability for the model.