Low-order spectral models of the atmospheric circulation: A survey

A quasi-geostrophic potential vorticity equation is derived from the Navier-Stokes equations for atmospheric motions. It describes the evolution of a quasi-horizontally flow on time scales of a few days and more. The associated boundary-value problem is analyzed by projection of the equation onto orthonormal eigenfunctions (modes) of a Sturm-Liouville operator. The result is a spectral model, consisting of an infinite number of nonlinear ordinary differential equations for the evolution of the mode amplitudes. Low-order spectral models, in which only a few modes are resolved, appear to have properties which agree with observations of the atmospheric circulation. However, little justification is available for truncating the spectral expansion at low resolution numbers. It is argued that stochastic forcing terms should be added to the equations, but it is not a priori clear how they should be specified.A derivation is presented of a specific low-order spectral model of the quasi-geostrophic potential vorticity equation. Some of its subsystems are analyzed for their physical and mathematical properties. It appears that topography can act as a triggering mechanism to generate multiple equilibria. The corresponding flow patterns resemble preference states of the atmospheric circulation. The systems can vacillate between three characteristic regimes with transitions provided either by external or internal mechanisms. A discussion is presented on the validity of stochastically forced spectral models and deterministic chaotic models for the atmospheric circulation.Present affiliation: Institute of Meteorology and Oceanography, Princetonplein 5, 3584 CC, Utrecht, The Netherlands.     

A survey of game-theoretic models of cooperative advertising

The paper surveys the literature on cooperative advertising in marketing channels (supply chains) using game theoretic methods. During the last decade, in particular, this literature has expanded considerably and has studied static as well as dynamic settings. The survey is divided into two main parts. The first one deals with simple marketing channels having one supplier and one reseller only. The second one covers marketing channels of a more complex structure, having more than one supplier and/or reseller.     

Energy-economy simulation with the Argonne energy model for Portugal

This paper discusses energy-economy interactions in energy-poor newly industrializing countries (NICs), describes the structure and operation of the Argonne Energy Models (AEMs), and reports the results of an energy-economy simulation based upon the Argonne Energy Model for Portugal (AEM-P).The problem facing the energy-poor NICs is to achieve sufficient economic growth to pay for energy imports and energy sector development, with something left over. In addressing this issue, the energy-economy modeler finds that no existing analytic methodology is completely adequate. The AEMs contribute to the refinement of methodology by deriving least-cost energy-sector configurations in terms of energy flows and prices for specific energy transformation technologies.The energy-economy simulation for Portugal indicates that higher energy costs due to further industrialization could be offset substantially by application of energy conservation technologies, by adoption of fuel switching strategies, and by promotion of domestic energy production. Under varying economic scenarios, and with high world oil price assumptions, between 1977 and 1997 the energy sector would account for about 30 percent of GDP. As a proportion of total energy supply, imported oil would decrease from around 90 to 50 percent, imported coal would increase from under 1 to over 25 percent, and the contribution from domestic uranium and biomass would expand from about 9 to 14 percent.     

A survey on piecewise-linear models of regulatory dynamical systems

Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems. A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable of demonstrating the essential features of many non-linear dynamical systems is piecewise-linear systems. Implementation of piecewise-linear systems for modelling of regulatory dynamical systems requires different considerations depending on the status of the problem. In this work we considered three different cases. Firstly, we consider the inferential modelling problem based on the empirical observations and study the discrete piecewise-linear system, whose inverse problem is solvable under some assumptions. Secondly, we considered the problem of obtaining some complex regulatory systems by tractable piecewise-linear formulations and study the qualitative dynamic features of the systems and their piecewise-linear models. Finally, we considered Boolean delay equations for building abstract models of regulatory systems, which might be the simplest models demonstrating the essential qualitative features of our interest underlying adaption, learning and memorization.     

A survey of some mathematical programming models in transportation

Transportation problems constitute a fertile domain for the application of mathematical programming models and nonlinear optimization techniques, distribution problems, entropy models, traffic assigment problems and many others are good examples of this assertion. This paper provides a summary overview of the main modeling approaches in transportation and the related optimization models, symmetric and asymmetric, and an overview on the state-of-the-art of the origindestination adjustment problems and the related bilevel optimization methods.     

A survey of optimization models on cancer chemotherapy treatment planning

While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction of normal cells during the treatment. As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit. In this paper, we summarize the mathematical models applied to the optimal design of the cancer chemotherapy. We first elaborate on a typical optimization model and classify relevant literature with respect to modeling methods: Optimal control model (OCM) and others. We further classify the OCM models with respect to the solution method used. We discuss the limitations of the existing research and provide several directions for further research in optimizing chemotherapy treatment planning.     

Demographic change in models of endogenous economic growth. A survey

While in exogenous growth models demographic variables are linked to economic prosperity mainly via the population size, the structure of the workforce, and the capital intensity of workers, endogenous growth models and their successors also allow for interrelationships between demographic variables and technological change. However, most of the existing literature considers only the interrelationships based on population size and its growth rate and does not explicitly account for population aging. The aim of this paper is (a) to review the role of population size and population growth in the most commonly used endogenous economic growth models, (b) discuss models that also allow for population aging, and (c) sketch out the policy implications of the most commonly used endogenous growth models and compare them to each other.     

基于Logit离散选择模型的品类优化问题综述

品类优化问题(Assortment Optimization Problem)是收益管理的经典问题.它研究零售商在满足运营约束的前提下,应如何从给定产品集合中选择一个子集提供给消费者,以最大化预期收益.该问题的核心在于如何准确地刻画消费者在面对细分产品时的选择行为、建立相应的优化模型并设计高效率的求解算法.基于Logit离散选择模型的品类优化问题:首先,介绍了基于Multinomial Logit模型的品类优化问题.然后介绍了两个更复杂的变种:第一个是基于两层以及多层Nested Logit模型的品类优化问题,这类问题可合理刻画细分产品之间的"替代效应";第二个是基于Mixtures of Multinomial Logits模型的品类优化问题,这类问题可充分考虑消费者群体的异质性.随后,介绍了数据驱动的品类优化问题的相关进展.最后,指出该问题未来可能的若干研究方向.     

A survey of personalized treatment models for pricing strategies in insurance

We consider a model for price calculations based on three components: a fair premium; price loadings reflecting general expenses and solvency requirements; and profit. The first two components are typically evaluated on a yearly basis, while the third is viewed from a longer perspective. When considering the value of customers over a period of several years, and examining policy renewals and cross-selling in relation to price adjustments, many insurers may prefer to reduce their short-term benefits so as to focus on their most profitable customers and the long-term value. We show how models of personalized treatment learning can be used to select the policy holders that should be targeted in a company’s marketing strategies. An empirical application of the causal conditional inference tree method illustrates how best to implement a personalized cross-sell marketing campaign in this framework.     

A survey of lower bounding methodologies for production/inventory models

A review is undertaken of lower bounding methodologies for lot-sizing production/inventory models. This is done for both dynamic discrete time demand and continuous review, constant demand situations. The view is taken that lower bounds are an essential ingredient in the evaluation of heuristics when optima are unknown or too computationally complex to comfortably evaluate. Several directions of future research are suggested.     

A survey of Markov decision models for control of networks of queues

We review models for the optimal control of networks of queues. Our main emphasis is on models based on Markov decision theory and the characterization of the structure of optimal control policies.This research was partially supported by the National Science Foundation under Grant No. DDM-8719825. The Government has certain rights in this material. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The research was also partially supported by the C.I.E.S. (France), while the author was on leave at INRIA, Sophia-Antipolis, 1991–92.     

Stochastic models for risk estimation in volatile markets: a survey

Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and risk capital allocation with the average value-at-risk measure (AVaR). AVaR is the average loss provided that the loss is larger than a predefined value-at-risk level. We consider in some detail the AVaR calculation and estimation and investigate the stochastic stability.     

Counting dendrograms: A survey

A dendrogram is a tree representation of data, used in hierarchical cluster analysis. The enumeration of non-isomorphic dendrograms, with specified numbers of terminal or leaf nodes, is the problem addressed here. A number of sub-classes of this problem are distinguished, arising out of whether or not a dendrogram is considered to be binary, labelled and ranked, and results are reviewed for each.     

Wijsman convergence: A survey

A net A of nonempty closed sets in a metric space X, d is declaredWijsman convergent to a nonempty closed setA provided for eachx X, we haved(x, A)=lim d(x, A). Interest in this convergence notion originates from the seminal work of R. Wijsman, who showed in finite dimensions that the conjugate map for proper lower semicontinuous convex functions preserves convergence in this sense, where functions are identified with their epigraphs. In this paper, we review the attempts over the last 25 years to produce infinite-dimensional extensions of Wijsman's theorem, and we look closely at the topology of Wijsman convergence in an arbitrary metric space as well. Special emphasis is given to the developments of the past five years, and several new limiting counterexamples are presented.     

Bilevel programming: A survey

This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.Received: April 2005, Revised: May 2005, AMS classification: 90C05, 90C11, 90C20, 90C27, 90C3D, 65K05     

Supereulerian graphs: A survey

A graph is supereulerian if it has a spanning eulerian subgraph. There is a rduction method to determine whether a graph is supereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval number of a graph. We outline the research on supereulerian graphs, the reduction method, and its applications.     

A survey of deterministic models for the EOQ and EPQ with partial backordering

Models for the basic deterministic EOQ or EPQ problem with partial backordering or backlogging make all the assumptions of the classic EOQ or EPQ model with full backordering except that only a fraction of the demand during the stockout period is backordered. In this survey we review deterministic models that have been developed over the past 40 years that address the basic models and extensions that add other considerations, such as pricing, perishable or deteriorating inventory, time-varying or stock-dependent demand, quantity discounts, or multiple-warehouses.     

Conjugate-normal matrices: A survey

Conjugate-normal matrices play the same important role in the theory of unitary congruence as the conventional normal matrices do with respect to unitary similarities. However, unlike the latter, the properties of conjugate-normal matrices are not widely known. Motivated by this fact, we give a survey of the properties of these matrices. In particular, a list of more than forty conditions is given, each of which is equivalent to A being conjugate-normal.