Optimality conditions for age-structured control systems

We consider a fairly general model (extension of the Gurtin-MacCamy model of population dynamics) of an age structured control system with nonlocal dynamics and nonlocal boundary conditions. A necessary optimality condition is obtained in the form of Pontryagin's maximum principle, which is applicable to a number of practically meaningful models where the previously known results fail. We discuss such models (an epidemic control, and a capital accumulation model) as illustrations.     

Linear regularity, equirregularity, and intersection mappings for convex semi-infinite inequality systems

We study the mixed-integer rounding (MIR) closures of polyhedral sets. The MIR closure of a polyhedral set is equal to its split closure and the associated separation problem is NP-hard. We describe a mixed-integer programming (MIP) model with linear constraints and a non-linear objective for separating an arbitrary point from the MIR closure of a given mixed-integer set. We linearize the objective using additional variables to produce a linear MIP model that solves the separation problem exactly. Using a subset of these additional variables yields an MIP model which solves the separation problem approximately, with an accuracy that depends on the number of additional variables used. Our analysis yields an alternative proof of the result of Cook et al. (1990) that the split closure of a polyhedral set is again a polyhedron. We also discuss a heuristic to obtain MIR cuts based on our approximate separation model, and present some computational results. Andrea Lodi was supported in part by the EU projects ADONET (contract n. MRTN-CT-2003-504438) and ARRIVAL (contract n. FP6-021235-2).     

A computational model for human eye-movements in military simulations

Models of eye movements of an observer searching for human targets are helpful in developing accurate models of target acquisition times and false positive detections. We develop a new model describing the distribution of gaze positions for an observer which includes both bottom-up (salience) and top-down (task dependent) factors. We validate the combined model against a bottom-up model from the literature and against the bottom up and top down parts alone using human performance data on stationary targets. The new model is shown to be significantly better. The new model requires a large amount of data about the terrain and the target that is obtained directly from the 3D simulation through an automated process.     

INARCH(1) processes: Higher-order moments and jumps

The INARCH(1) model is a simple but practically relevant, two-parameter model for processes of overdispersed counts with an autoregressive serial dependence structure. We derive closed-form expressions for the joint (central) moments and cumulants of the INARCH(1) model up to order 4. These expressions are applied to derive the moments of jumps in INARCH(1) processes. We illustrate this kind of application with a real-data example, and outline further potential applications.     

A Hessian Regularized Nonlinear Time Series Model

We introduce a nonparametric nonlinear time series model. The novel idea is to fit a model via penalization, where the penalty term is an unbiased estimator of the integrated Hessian of the underlying function. The underlying model assumption is very general: it has Hessian almost everywhere in its domain. Numerical experiments demonstrate that our model has better predictive power: if the underlying model complies with an existing parametric/semiparametric form (e.g., a threshold autoregressive model (TAR), an additive autoregressive model (AAR), or a functional coefficient autoregressive model (FAR)), our model performs comparably; if the underlying model does not comply with any preexisting form, our model outperforms in nearly all simulations. We name our model a Hessian regularized nonlinear model for time series (HRM). We conjecture on theoretical properties and use simulations to verify. Our method can be viewed as a way to generalize splines to high dimensions (when the number of variates is more than three), under which an analogous analytical derivation cannot work due to the curse of dimensionality. Supplemental materials are provided, and will help readers reproduce all results in the article.     

Inessential Combinations and Colorings of Models

We define the operations of an inessential combination and an almost inessential combination of models and theories. We establish basedness for an (almost) inessential combination of theories. We also establish that the properties of smallness and -stability are preserved upon passing to (almost) inessential combinations of theories. We define the notions of coloring of a model, colored model, and colored theory, and transfer the assertions about combinations to the case of colorings. We characterize the inessential colorings of a polygonometry.     

Robust investment–reinsurance optimization with multiscale stochastic volatility

This paper investigates the investment and reinsurance problem in the presence of stochastic volatility for an ambiguity-averse insurer (AAI) with a general concave utility function. The AAI concerns about model uncertainty and seeks for an optimal robust decision. We consider a Brownian motion with drift for the surplus of the AAI who invests in a risky asset following a multiscale stochastic volatility (SV) model. We formulate the robust optimal investment and reinsurance problem for a general class of utility functions under a general SV model. Applying perturbation techniques to the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation associated with our problem, we derive an investment–reinsurance strategy that well approximates the optimal strategy of the robust optimization problem under a multiscale SV model. We also provide a practical strategy that requires no tracking of volatility factors. Numerical study is conducted to demonstrate the practical use of theoretical results and to draw economic interpretations from the robust decision rules.     

An auxiliary server threshold queueing model and its application to the operational characteristics of web server system

This paper analyzes an auxiliary server queueing model in which secondary servers are added to the main server(s) when the queue length exceeds some predetermined threshold value at the main queue. We model this system by the level-dependent quasi-birth-death (QBD) process and develop computation algorithms. We apply this model to the web-server system to explore some specific operational characteristics and draw some useful conclusions.     

Who benefit from agency model: A strategic analysis of pricing models in distribution channels of physical books and e-books

We model a supply chain consisting of an author, a publisher, a physical bookstore (p-bookstore), and an electronic bookstore (e-bookstore). We employ game theory to examine and compare two types of pricing models of electronic books (e-books): wholesale model and agency model. Furthermore, we consider decentralized and horizontally centralized channels. The p-bookstore and e-bookstore are independent in the former but centralized in the latter. We adopt a simplified linear demand model to study when the publisher and the e-bookstore both benefit from the agency model. We find that a Pareto zone where both the publisher and e-bookstore benefit from the agency model always exists in the decentralized channels. In the agency model, the benefit from e-book sales may be more than the loss in physical book (p-book) sales. By contrast, a Pareto zone exists in the horizontally centralized channels if the wholesale price of p-books is not excessively low and the price elasticity is not extremely large. To check the robustness of our results, we relax model assumptions and conduct numerical studies in the Pareto zone to investigate how various parameters, such as authors royalty rate, affect profit improvement and readers welfare. We show that the publisher and bookstore have great potentials for profit improvement in the Pareto zone. Significant improvement is also observed in readers welfare.     

Effectiveness in RPL, with applications to continuous logic

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of ?ukasiewicz logic) and continuous logic, and prove effective versions of some related theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; we show that provability degree of a formula with respect to a linear theory is computable, and use this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory (such as that of a probability space or an L^p Banach lattice) is decidable.     

An input relaxation measure of efficiency in stochastic data envelopment analysis

We introduce stochastic version of an input relaxation model in data envelopment analysis (DEA). The input relaxation model, recently developed in DEA, is useful to resource management [e.g. G.R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion, Appl. Math. Comput. 151(1) (2004) 263–273]. This model allows more changes in the input combinations of decision making units than those in the observed inputs of evaluating decision making units. Using this extra flexibility in input combinations we can find better outputs. We obtain a non-linear deterministic equivalent to this stochastic model. It is shown that under fairly general conditions this non-linear model can be replaced by an ordinary deterministic DEA model. The model is illustrated using a real data set.     

Finite time ruin problems for the Erlang(2) risk model

We consider the Erlang(2) risk model and derive expressions for the density of the time to ruin and the joint density of the time to ruin and the deficit at ruin when the individual claim amount distribution is (i) an exponential distribution and (ii) an Erlang(2) distribution. We also consider the special case when the initial surplus is zero.     

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.     

Perfect information two-person zero-sum markov games with imprecise transition probabilities

Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an equilibrium value for the games formulated with the model in terms of a partial order and then establish the existence of an equilibrium policy pair that achieves the equilibrium value. We further analyze finite-approximation error bounds obtained from a value iteration-type algorithm and discuss some applications of the model.     

An operator splitting strategy for fluid–structure interaction problems with thin elastic structures in an incompressible Newtonian flow

We present a computational framework based on the use of the Newton and level set methods to model fluid–structure interaction problems involving elastic membranes freely suspended in an incompressible Newtonian flow. The Mooney–Rivlin constitutive model is used to model the structure. We consider an extension to a more general case of the method described in Laadhari (2017) to model the elasticity of the membrane. We develop a predictor–corrector finite element method where an operator splitting scheme separates different physical phenomena. The method features an affordable computational burden with respect to the fully implicit methods. An exact Newton method is described to solve the problem, and the quadratic convergence is numerically achieved. Sample numerical examples are reported and illustrate the accuracy and robustness of the method.     

A Combinatorial Approach to Piecewise Linear Time Series Analysis

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.     

On exact solutions to epidemic dynamic models

In this study, we address an SIR (susceptible-infected-recovered) model that is given as a system of first order differential equations and propose the SIR model on time scales which unifies and extends continuous and discrete models. More precisely, we derive the exact solution to the SIR model and discuss the asymptotic behavior of the number of susceptibles and infectives. Next, we introduce an SIS (susceptible-infected-susceptible) model on time scales and find the exact solution. We solve the models by using the Bernoulli equation on time scales which provides an alternative method to the existing methods. Having the models on time scales also leads to new discrete models. We illustrate our results with examples where the number of infectives in the population is obtained on different time scales.     

Random partition masking model for censored and masked competing risks data

We consider the parametric estimation with right-censored competing risks data and with masked failure cause. We propose a new model, called the random partition masking (RPM) model. The existing model based on the so called symmetry assumption, but the RPM model does not need the symmetry assumption. We propose a wide class of parametric distribution families of the failure time and cause, which does not need the assumption of independence between the components of the system. We also study the asymptotic properties of the maximum likelihood estimator under the new model, and apply our procedure to a medical and an industrial data sets.     

Weighted enumerations of boxed plane partitions and the inhomogeneous five-vertex model

We consider the five-vertex model on a square lattice with fixed boundary conditions which corresponds to weighted (with weight q per elementary cube) enumerations of boxed plane partitions. We calculate the one-point correlation function of the model which describes the probability of a given state on an edge (polarization). This generalizes an analogous result obtained previously by the authors for unweighted (weighted with weight q?=?1) enumerations of plane partitions. Bibliography: 14 titles.     

Spectral Gap of the Antiferromagnetic Lipkin–Meshkov–Glick Model

We study the spectral property of the supersymmetric (SUSY) antiferromagnetic Lipkin–Meshkov–Glick (LMG) model with an even number of spins and explicitly construct the supercharges of the model. Using the exact form of the SUSY ground state, we introduce simple trial variational states for the first excited states. We show numerically that they provide a relatively accurate upper bound for the spectral gap (the energy difference between the ground state and first excited states) in all parameter ranges, but because it is an upper bound, it does not allow rigorously determining whether the model is gapped or gapless. To answer this question, we obtain a nontrivial lower bound for the spectral gap and thus show that the antiferromagnetic SUSY LMG model is gapped for any even number of spins.