凸函数的支撑凸集及其集映射

本文研究了线性空间中凸函数的支撑泛函存在性以及支撑泛函的数值域,利用子空间中支撑泛函延拓的方法,构造出在线性空间任意点的支撑泛函,确定在同一支撑点上支撑泛函的数值域,从而得到支撑泛函具有唯一性的充分必要条件,最后对支撑凸集到支撑泛函集的集映射进行讨论.     

Support vector machine classifiers with uncertain knowledge sets via robust optimization

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowledge is in the form of uncertain linear constraints, results in an uncertain convex optimization problem with a set containment constraint. Using a new extension of Farkas' lemma, we reformulate the robust counterpart of the uncertain convex optimization problem in the case of interval uncertainty as a convex quadratic optimization problem. We then reformulate the resulting convex optimization problems as a simple quadratic optimization problem with non-negativity constraints using the Lagrange duality. We obtain the solution of the converted problem by a fixed point iterative algorithm and establish the convergence of the algorithm. We finally present some preliminary results of our computational experiments of the method.     

Optimization of a highway project planning using a modified genetic algorithm

This paper proposes an optimization method for a national-level highway project planning based on a modified genetic algorithm. The proposed method adds to the existing methods by integrating various planning elements into a single system. A simulation model is used in order to determine the best investment strategy with regard to net present value, time deviation from the initial plan and discrepancy between available resources and investment costs by taking into account economical, social, traffic and political factors. The outcome is a project schedule with an optimized cash flow. The proposed method was tested using the example of the National Highway Programme in Slovenia.     

Relations between the convexity of a set and the differentiability of its support function

It is known that, in finite dimensions, the support function of a compact convex set with nonempty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper, we realize a thorough study of the relations between the differentiability of the support function on the interior of its domain and the convexity of the set, mainly for unbounded sets. Then, we revisit some results related to the differentiability of the cost function associated to a production function.     

Decision support system for mass dispensing of medications for infectious disease outbreaks and bioterrorist attacks

A simulation and decision support system, RealOpt^©, for planning large-scale emergency dispensing clinics to respond to biological threats and infectious disease outbreaks is described. The system allows public health administrators to investigate clinic design and staffing scenarios quickly. RealOpt^© incorporates efficient optimization technology seamlessly interfaced with a simulation module. The system's correctness and computational advantage are validated via comparisons against simulation runs of the same model developed on a commercial system. Simulation studies to explore facility layout and staffing scenarios for smallpox vaccination and for an actual anthrax-treatment dispensing exercise and post event analysis are presented. The system produces results consistent with the model built on the commercial system, but requires only a fraction of the computational time. Each smallpox scenario runs within 1 CPU minute on RealOpt^©, versus run times of over 5–10 h on the commercial system. The system's fast computational time enables its use in large-scale studies, in particular an anthrax response planning exercise involving a county with 864,000 households. The computational effort required for this exercise was roughly 30 min for all scenarios considered, demonstrating that RealOpt^© offers a very promising avenue for pursuing a comprehensive investigation involving a more diverse set of scenarios, and justifying work towards development of a robust system that can be widely deployed for use by state, local, and tribal health practitioners. Using our staff allocation and assignments for the Anthrax field exercise, DeKalb county achieved the highest throughput among all counties that simultaneously conducted the same scale of Anthrax exercise at various locations, with labor usage at or below the other counties. Indeed, DeKalb exceeded the targeted number of households, and it processed 50% more individuals compared to the second place county. None of the other counties achieved the targeted number of households. The external evaluators commented that DeKalb produced the most efficient floor plan (with no path crossing), the most cost-effective dispensing (lowest labor/throughput value), and the smoothest operations (shortest average wait time, average queue length, equalized utilization rate). The study proves that even without historical data, using our system one can plan ahead and be able to wisely estimate the required labor resources. The exercise also revealed many areas that need attention during the operations planning and design of dispensing centers. The type of disaster being confronted (e.g., biological attack, infectious disease outbreak, or a natural disaster) also dictates different design considerations with respect to the dispensing clinic, facility locations, dispensing and backup strategies, and level of security protection. Depending on the situation, backup plans will be different, and the level of security and military personnel, as well as the number of healthcare workers required, will vary. In summary, the study shows that a real-time decision support system is viable through careful design of a stand-alone simulator coupled with powerful tailor-designed optimization solvers. The flexibility of performing empirical tests quickly means the system is amenable for use in training and preparation, and for strategic planning before and during an emergency situation. The system facilitates analysis of “what-if'' scenarios, and serves as an invaluable tool for operational planning and dynamic on-the-fly reconfigurations of large-scale emergency dispensing clinics. It also allows for “virtual field exercises” to be performed on the decision support system, offering insight into operations flow and bottlenecks when mass dispensing is required for a region with a large population. The system, designed in modular form with a flexible implementation, enables future expansion and modification regarding emergency center design with respect to treatment for different biological threats or disease outbreaks. Working with emergency response departments, further fine-tuning and development of the system will be made to address different biological attacks and infectious disease outbreaks, and to ensure its practicality and usability.     

Feature Selection using Fuzzy Support Vector Machines

The feature selection consists of obtaining a subset of these features to optimally realize the task without the irrelevant ones. Since it can provide faster and cost-effective learning machines and also improve the prediction performance of the predictors, it is a crucial step in machine learning. The feature selection methods using support machines have obtained satisfactory results, but the noises and outliers often reduce the performance. In this paper, we propose a feature selection approach using fuzzy support vector machines and compare it with the previous work, the results of experiments on the UCI data sets show that feature selection using fuzzy SVM obtains better results than using SVM.     

On the role of heterogeneous and imperfect information in a laboratory financial market

In this paper, we analyze the behavior of a group of heterogeneously informed investors in an laboratory asset market. Our experimental setting is inspired by Huber et al. (On the benefit of information in markets with heterogeneously informed traders: an experimental study, 2004). However, instead of their system of cumulative and exogenously given information structure, we introduce an information market where the traders can buy an imperfect prediction of the future value of the dividend with a maximum anticipation of four periods. The accuracy of the prediction decreases with the chosen time horizon, whereas its price remains constant. Our results confirm a non-strictly monotonic increasing value of the information.     

Joint value-distribution theorems on Lerch zeta-functions. II

We give corrected statements of some theorems from [5] and [6] on joint value-distribution of Lerch zeta-functions (limit theorems, universality, functional independence). We also present a new direct proof of a joint limit theorem in the space of analytic functions and an extension of a joint universality theorem. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 332–350, July–September, 2006.     

Naive audience and communication bias

We introduce the possibility that the receiver naively believes the sender’s message in a game of information transmission with partially aligned objectives. We characterize an equilibrium in which the communication language is inflated, the action taken is biased, and the information transmitted is more precise than in the benchmark fully-strategic model. We provide comparative statics results with respect to the amount of asymmetric information, the proportion of naive receivers, and the size of the sender’s bias. As the state space grows unbounded, the equilibrium converges to the fully-revealing equilibrium that results in the limit case with unbounded state space.      

Construction of an atomic decomposition for functions with compact support

Chang, Krantz and Stein [D.-C. Chang, S.G. Krantz, E.M. Stein, Hp theory on a smooth domain in Rn and elliptic boundary value problems, J. Funct. Anal. 114 (1993) 286-347] proved that if f∈Hp(Rn) and f vanishes outside , then f has an atomic decomposition whose atoms are contained in Ω. The purpose of this paper is to give another proof for the case n/(n+1)<p?1 and Ω a cube. Our argument provides a simple, direct construction of the desired atomic decomposition, and it works in a class of function spaces more general than the usual Hardy spaces.