Uniform-in-Bandwidth Functional Limit Laws

We provide uniform-in-bandwidth functional limit laws for the increments of the empirical and quantile processes. Our theorems, established in the framework of convergence in probability, imply new sharp uniform-in-bandwidth limit laws for functional estimators. In particular, they yield the explicit value of the asymptotic limiting constant for the uniform-in-bandwidth sup-norm of the random error of kernel density estimators. We allow the bandwidth to vary within the complete range for which the estimators are consistent.     

Products of mixed covering arrays of strength two

A covering array CA(N;t,k, v is an N × k array such that every N × t subarray contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple “cut‐and‐paste” construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t = 2 is derived. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 124–138, 2006     

Bihermitian Structures On Complex Surfaces

We correct the statements of Theorem 1 and Corollary 2 of theabove-mentioned paper and provide a new argument for Corollary2. We also update some parts of the paper in the light of recentmajor developments in the theory of bihermitian structures,due to M. Gualtieri and N. Hitchin. 2000 Mathematics SubjectClassification 53C26 (primary), 32J15, 53C56 (secondary).     

Weakly dependent chains with infinite memory

We prove the existence of a weakly dependent strictly stationary solution of the equation _Xt=F(_Xt−1,_Xt−2,_Xt−3,…;_ξt)$X_t=F(X_{t-1},X_{t-2},X_{t-3},\dots ;{\xi }_t)$ called a chain with infinite memory. Here the innovations  _ξt${\xi }_t$ constitute an independent and identically distributed sequence of random variables. The function F$F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F$F$ and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.     

X‐ray excited optical luminescence from crystalline silicon

Synchrotron based X‐ray excited optical luminescence (XEOL) has been measured with many direct bandgap semiconductors. We present XEOL measurements on crystalline silicon (Si), obtained despite of its indirect bandgap and the consequently low luminescence efficiency. Spectra of monocrystalline and multicrystalline (mc) Si at room temperature are compared to theoretical spectra. A possible application in the synchrotron‐based research on mc‐Si is exemplified by combining XEOL, X‐ray fluorescence (XRF) spectroscopy, photoluminescence (PL) spectroscopy, and microscope images of grain boundaries. This approach can be utilized to investigate the recombination activity of metal precipitates, to analyze areas of different lifetimes on mc‐Si samples and to correlate additional material parameters to XRF measurements. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An effective and simple heuristic for the set covering problem

This paper investigates the development of an effective heuristic to solve the set covering problem (SCP) by applying the meta-heuristic Meta-RaPS (Meta-heuristic for Randomized Priority Search). In Meta-RaPS, a feasible solution is generated by introducing random factors into a construction method. Then the feasible solutions can be improved by an improvement heuristic. In addition to applying the basic Meta-RaPS, the heuristic developed herein integrates the elements of randomizing the selection of priority rules, penalizing the worst columns when the searching space is highly condensed, and defining the core problem to speedup the algorithm. This heuristic has been tested on 80 SCP instances from the OR-Library. The sizes of the problems are up to 1000 rows × 10,000 columns for non-unicost SCP, and 28,160 rows × 11,264 columns for the unicost SCP. This heuristic is only one of two known SCP heuristics to find all optimal/best known solutions for those non-unicost instances. In addition, this heuristic is the best for unicost problems among the heuristics in terms of solution quality. Furthermore, evolving from a simple greedy heuristic, it is simple and easy to code. This heuristic enriches the options of practitioners in the optimization area.     

Cycles in dense digraphs

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?

We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:

• when V(G) is the union of two cliques
• when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.

     

Lytic cycle: A defining process in oncolytic virotherapy

The viral lytic cycle is an important process in oncolytic virotherapy. Most mathematical models for oncolytic virotherapy do not incorporate this process. In this article, we propose a mathematical model with the viral lytic cycle based on the basic mathematical model for oncolytic virotherapy. The viral lytic cycle is characterized by two parameters, the time period of the viral lytic cycle and the viral burst size. The time period of the viral lytic cycle is modeled as a delay parameter. The model is a nonlinear system of delay differential equations. The model reveals a striking feature that the critical value of the period of the viral lytic cycle is determined by the viral burst size. There are two threshold values for the burst size. Below the first threshold, the system has an unstable trivial equilibrium and a globally stable virus free equilibrium for any nonnegative delay, while the system has a third positive equilibrium when the burst size is greater than the first threshold. When the burst size is above the second threshold, there is a functional relation between the bifurcation value of the delay parameter for the period of the viral lytic cycle and the burst size. If the burst size is greater than the second threshold, the positive equilibrium is stable when the period of the viral lytic cycle is smaller than the bifurcation value, while the system has orbitally stable periodic solutions when the period of the lytic cycle is longer than the bifurcation value. However, this bifurcation value becomes smaller when the burst size becomes bigger. The viral lytic cycle may explain the oscillation phenomena observed in many studies. An important clinic implication is that the burst size should be carefully modified according to its effect on the lytic cycle when a type of a virus is modified for virotherapy, so that the period of the viral lytic cycle is in a suitable range which can break away the stability of the positive equilibria or periodic solutions.