A Two-Step Smoothing Method for Varying-Coefficient Models with Repeated Measurements

Datasets involving repeated measurements over time are common in medical trials and epidemiological cohort studies. The outcomes and covariates are usually observed from randomly selected subjects, each at a set of possibly unequally spaced time design points. One useful approach for evaluating the effects of covariates is to consider linear models at a specific time, but the coefficients are smooth curves over time. We show that kernel estimators of the coefficients that are based on ordinary local least squares may be subject to large biases when the covariates are time-dependent. As a modification, we propose a two-step kernel method that first centers the covariates and then estimates the curves based on some local least squares criteria and the centered covariates. The practical superiority of the two-step kernel method over the ordinary least squares kernel method is shown through a fetal growth study and simulations. Theoretical properties of both the two-step and ordinary least squares kernel estimators are developed through their large sample mean squared risks.     

On a generalization of the Gallai-Roy-Vitaver theorem to the bandwidth coloring problem

We generalize to the bandwidth coloring problem a classical theorem, discovered independently by Gallai, Roy and Vitaver, in the context of the graph coloring problem. Two proofs are given, a simple one and a more complex one that is based on a series of equivalent mathematical programming models.     

Affirmative action algorithms

Affirmative action is a new variety of selection rule which employs historical information to favor the choice of elements that have not been selected in the past. We categorize three implementations of this principle and discuss their application to the simplex method, to Bard-type schemes for the linear complementarity problem, and to augmenting path methods for network flow problems. We present analytical and computational results, and some open questions.Research supported by the Georgia Institute of Technology.Research supported by the New Faculty Research Development Program of the Georgia Institute of Technology. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

On the combinatorial structure of chromatic scheduling polytopes

Chromatic scheduling polytopes arise as solution sets of the bandwidth allocation problem in certain radio access networks, supplying wireless access to voice/data communication networks for customers with individual communication demands. To maintain the links, only frequencies from a certain spectrum can be used, which typically causes capacity problems. Hence it is necessary to reuse frequencies but no interference must be caused by this reuse. This leads to the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-hard, and there do not even exist polynomial time algorithms with a fixed quality guarantee.As algorithms based on cutting planes have shown to be successful for many other combinatorial optimization problems, the goal is to apply such methods to the bandwidth allocation problem. For that, knowledge on the associated polytopes is required. The present paper contributes to this issue, exploring the combinatorial structure of chromatic scheduling polytopes for increasing frequency spans. We observe that the polytopes pass through various stages—emptyness, non-emptyness but low-dimensionality, full-dimensionality but combinatorial instability, and combinatorial stability—as the frequency span increases. We discuss the thresholds for this increasing “quantity” giving rise to a new combinatorial “quality” of the polytopes, and we prove bounds on these thresholds. In particular, we prove combinatorial equivalence of chromatic scheduling polytopes for large frequency spans and we establish relations to the linear ordering polytope.     

Generalized Fibonacci broadcasting: An efficient VOD scheme with user bandwidth limit

Broadcasting is attractive in delivering popular videos in video-on-demand service, because the server broadcast bandwidth is independent of the number of users. However, the required server bandwidth does depend on how much bandwidth each user can use, as well as on the user's initial waiting time. This paper addresses the issue of limiting the user bandwidth, and proposes a new broadcasting scheme, named Generalized Fibonacci Broadcasting (GFB). In terms of many performance graphs, we show that, for any given combination of the server bandwidth and user bandwidth, GFB can achieve the least waiting time among all the currently known fixed-delay broadcasting schemes. Furthermore, it is very easy to implement GFB. We also demonstrate that there is a trade-off between the user waiting time and the buffer requirement at the user.     

Continuous benchmark selections

The existence of benchmark selections that are continuous both in production factors and technology is examined. If the class of technologies display non-convexities, continuous selections do not exist in general. For probabilistic benchmarks, i.e., lotteries over efficient productions, existence of continuous selections holds only under additional conditions of well-behavedness.     

Bandwidth choice for local polynomial estimation of smooth boundaries

Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.     

螺旋波导TEm1-TE11模式转换器的设计

 基于耦合波理论，对螺旋波导(蛇形线微扰)94 GHz、6周期TE₀₁-TE₁₁模式转换器和10.24 GHz、4周期TE­31-TE11模式转换器进行了设计和数值分析。通过解耦合波方程得出模式转换器中各模式成分的比例关系，并对转换器的参数做进一步修正，然后利用电磁仿真软件进行模拟。两种转换器在中心频率处的模拟转换效率均达到98%以上，95%以上带宽超过2 GHz，仿真结果与理论分析吻合得较好。     

Parametric multiple regression risk models: Theory and statistical analysis

Parametric multiple regression models for the claim number and the claim amount of an individual risk are introduced allowing explanatory variables to influence the mean claim number (amount). A model for an entire portfolio of risks is established on this basis. Then an extensive and in many cases efficient statistical analysis of this model is presented.