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We provide a new upper bound for sampling numbers [Formula omitted] associated with the compact embedding of a separable reproducing kernel Hilbert space into the space of square integrable functions. There are universal constants [Formula omitted] (which are specified in the paper) such that gn2[less than or equal to]Clog(n)n[summation]k[greater than or equal to]âcn[right floor][sigma]k2,n[greater than or equal to]2,where [Formula omitted] is the sequence of singular numbers (approximation numbers) of the Hilbert-Schmidt embedding [Formula omitted]. The algorithm which realizes the bound is a least squares algorithm based on a specific set of sampling nodes. These are constructed out of a random draw in combination with a down-sampling procedure coming from the celebrated proof of Weaver's conjecture, which was shown to be equivalent to the Kadison-Singer problem. Our result is non-constructive since we only show the existence of a linear sampling operator realizing the above bound. The general result can for instance be applied to the well-known situation of [Formula omitted] in [Formula omitted] with [Formula omitted]. We obtain the asymptotic bound gn[less than or equal to]Cs,dn-slog(n)(d-1)s+1/2,which improves on very recent results by shortening the gap between upper and lower bound to [Formula omitted]. The result implies that for dimensions [Formula omitted] any sparse grid sampling recovery method does not perform asymptotically optimal., Author(s): Nicolas Nagel [sup.1], Martin Schäfer [sup.1], Tino Ullrich [sup.1] Author Affiliations: (1) grid.6810.f, 0000 0001 2294 5505, Faculty of Mathematics, TU Chemnitz, , 09107, Chemnitz, Germany Introduction > In [...]

The karyon-module (KM-) algorithm for expanding an algebraic number [alpha] = ([[alpha].sub.1], ..., [[alpha].sub.d]) from [R.sup.d] in a multidimensional continued fraction, i.e., in a sequence of rational numbers [P.sub.a]/[Q.sub.a] = ([P.sub.a.sub.1]/[Q.sup.a], ..., [P.sub.a.sub.d]/[Q.sup.a]) a = 1,2,3 ..., from [Q.sup.d] with numerators [P.sub.a.sub.1], ..., [P.sub.a.sub.d] [member of] Z and a common denominator [Q.sup.a] = 1, 2, 3, ... is proposed. The KM-algorithm belongs to the class of tuned algorithms and is based on constructing localized Pisot units [zeta] > 1, for which the moduli of all the conjugates [[zeta].sup.(i)] [not equal to] [zeta] are contained in the [theta]-neighborhood of the number [[zeta].sup.-1/d], where the parameter [theta] may take an arbitrary fixed value. It is proved that given a real algebraic point a of degree deg([alpha]) = d + 1, the KM-algorithm provides its approximation such that [absolute value of ([alpha] - [P.sub.a]/[Q.sub.a])] [less than or equal to] c/[Q.sup.1+1/d-[theta].sub.a] for all a [greater than or equal to] [a.sub.[alpha],[theta]], where the constants [a.sub.[alpha],[theta]] > 0 and c = [c.sub.[alpha],[theta]] > 0 are independent of a = 1, 2, 3, ..., and the convergents [P.sub.a]/[Q.sub.a] are computed from a certain recurrence relation with constant coefficients, determined by the choice of the localized unit [zeta]. Bibliography: 19 titles., UDC 511.3 INTRODUCTION 0.1. The karyon-module algorithm. The paper suggests the karyon-module (KM-) algorithm KM : [P.sub.a]/[Q.sub.a] [right arrow] [alpha] as a [right arrow] +[infinity] (0.1) for expanding an algebraic [...]

The karyon-module (KM-) algorithm for expanding an algebraic number [alpha] = ([[alpha].sub.1], ..., [[alpha].sub.d]) from [R.sup.d] in a multidimensional continued fraction, i.e., in a sequence of rational numbers [mathematical expression not reproducible] from [Q.sup.d] with numerators [P.sup.a.sub.1], ..., [P.sup.a.sub.d] [member of] Z and a common denominator [Q.sup.a] = 1, 2, 3, ... is proposed. The KM-algorithm belongs to the class of tuned algorithms and is based on constructing localized Pisot units [zeta] > 1, for which the moduli of all the conjugates [[zeta].sup.(i) [not equal to] [zeta] are contained in the [theta]-neighborhood of the number [[zeta].sup.-1/d], where the parameter [theta] may take an arbitrary fixed value. It is proved that given a real algebraic point [alpha] of degree deg([alpha]) = d + 1, the KM-algorithm provides its approximation such that [mathematical expression not reproducible] for all a [greater than or equal to] [a.sub.[alpha],[theta]], where the constants [a.sub.[alpha],[theta]] > 0 and c = [c.sub.[alpha],[theta]] > 0 are independent of a = 1, 2, 3, ..., and the convergents [[P.sub.a]/[Q.sub.a]] are computed from a certain recurrence relation with constant coefficients, determined by the choice of the localized unit [zeta]. Bibliography: 19 titles., UDC 511.3 INTRODUCTION 0.1. The karyon-module algorithm. The paper suggests the karyon-module (KM-) algorithm KM : [[P.sub.a]/[Q.sub.a] [right arrow] [alpha] as a [right arrow] + [infinity] (0.1) for expanding an [...]

A development of the simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions is proposed. To this end, localized Pisot matrices are constructed, whose eigenvalues with moduli less than one are contained in an interval of small length. Such Pisot matrices generate continued fractions whose convergents are arbitrarily close to the best approximations. Bibliography: 16 titles., UDC 511 INTRODUCTION 0.1. The simplex-module algorithm. The simplex-module (SM-) algorithm for expansion of algebraic numbers [[alpha].sub.1], ..., [[alpha].sub.d] in multidimensional continued fractions SM: [P.sub.a]/[Q.sub.a] = ([P.sub.a,1]/[Q.sub.a], ..., [P.sub.a,d]/[Q.sub.a]) [right [...]

The paper establishes the invariance of the simplex-module algorithm for expanding real numbers [alpha] = ([[alpha].sub.1], ..., [[alpha].sub.d]) in multidimensional continued fractions under linear-fractional Transformations [alpha] = ([[alpha]'.sub.1], ..., [[alpha]'.sub.d]) = U with matrices U from the unimodular group [GL.sub.d+1] (Z). It is shown that the convergents of the transformed collections of numbers [alpha]' satisfy the same recurrence relation and have the same approximation order. Bibliography: 20 titles., UDC 511 INTRODUCTION 0.1. The simplex-module algorithm. The simplex-module algorithm (SM-algorithm) for expansion of algebraic numbers [[alpha].sub.1], ..., [[alpha].sub.d]] in multidimensional continued fractions, SM : t [P.sub.a]/[Q.sub.a] = ([P.sub.a,1]/[Q.sub.a], ..., [...]

The simplex-module algorithm for expansion of algebraic numbers a = ([[alpha].sub.1], ..., [[alpha].sub.d]) in multidimensional continued fractions is suggested. The method is based on minimal rational simplices s, where [alpha] [member of] s, and Pisot matrices [P.sub.[alpha]], for which [??] = ([[alpha].sub.1], ..., [[alpha].sub.d], 1) is an eigenvector. A multidimensional generalization of the Lagrange theorem is proved. Bibliography: 19 titles., UDC 511 Introduction 0.1. Complete points. A point [alpha] = ([[alpha].sub.1], ..., [[alpha].sub.d]) and the corresponding set {[[alpha].sub.1], ..., [[alpha].sub.d]} of real algebraic numbers are said to be complete if [...]

Frequent distributions of the databases of the numerical values obtained by resolving algorithms, which describe physical and other processes, give a possibility for bonding the probability of that results the algorithms get. In the frequent distribution of the fractions of integers (rational numbers), local maxima which meet the ratios of masses of the elementary particles have been found., Consider a general case of an arbitrary function F(x, y, z,...). Take under consideration a region of the values of this function, split into numerous intervals. Filling up the intervals [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2008.02.032 Byline: A. Sedeno-Noda (a), E. Gonzalez-Davila (a), C. Gonzalez-Martin (a), A. Gonzalez-Yanes (b) Keywords: Small area estimation; Benchmarking property; Networks flows; Goal programming Abstract: National Statistical Agencies and Autonomous Institutions are extremely interested in using information from those areas that are actually smaller than the actual areas for which a survey is initially designed. As such, small area estimation and its application are valuable when conducting research on Official Statistics. A wide range of different methods are available which provide estimations to small area levels, being reasonable to guarantee that they add up to the published design-based estimations in a large area that includes these small areas. This requirement is known as benchmarking. Different algorithms, all based on distances between original data and modified data, are introduced in this paper, with the intention of satisfying the benchmarking property. We provide rules to apply these proposed calibrated methods according to user criteria. Goal programming with priorities methodology is used to represent user preferences. The result is a collection of different interdependent network flow problems. Some of these problems require the development of ad hoc methods. The introduced methods are assessed by a Monte Carlo simulation study using the Spanish Labour Force Survey in the Canary Islands. The results also show that the consistency of the estimator is independent of the used calibrated methods, but it does depend on the benchmarking weights. Author Affiliation: (a) Departamento de Estadistica, Investigacion Operativa y Computacion (DEIOC), Universidad de La Laguna, 38205- La Laguna, Tenerife, Spain (b) Instituto Canario de Estadistica (ISTAC), Gobierno de Canarias, 38003 S/C de Tenerife, Tenerife, Spain Article History: Received 7 May 2007; Accepted 29 February 2008

To purchase or authenticate to the full-text of this article, please visit this link: http://dx.doi.org/10.1111/j.1365-2745.2008.01421.x Byline: Olivier J. Hardy (*) Keywords: community ecology; neutral model; null model; phylogenetic structure; randomization test; simulation; Type I error rate Abstract: Summary Analyzing the phylogenetic structure of natural communities may illuminate the processes governing the assembly and coexistence of species. For instance, an association between species co-occurrence in local communities and their phylogenetic proximity may reveal the action of habitat filtering, niche conservatism and/or competitive exclusion. Different methods were recently proposed to test such community-wide phylogenetic patterns, based on the phylogenetic clustering or overdispersion of the species in a local community. This provides a much needed framework for addressing long standing questions in community ecology as well as the recent debate on community neutrality. The testing procedures are based on (i) a metric measuring the association between phylogenetic distance and species co-occurrence, and (ii) a data set randomization algorithm providing the distribution of the metric under a given 'null model'. However, the statistical properties of these approaches are not well-established and their reliability must be tested against simulated data sets. This paper reviews metrics and null models used in previous studies. A 'locally neutral' subdivided community model is simulated to produce data sets devoid of phylogenetic structure in the spatial distribution of species. Using these data sets, the consistency of Type I error rates of tests based on 10 metrics combined with nine null models is examined. This study shows that most tests can become liberal (i.e. tests rejecting too often the null hypothesis that only neutral processes structured spatially the local community) when the randomization algorithm breaks down a structure in the original data set unrelated to the null hypothesis to test. Hence, when overall species abundances are distributed non-randomly across the phylogeny or when local abundances are spatially autocorrelated, better statistical performances were achieved by randomization algorithms preserving these structural features. The most reliable randomization algorithm consists of permuting species with similar abundances among the tips of the phylogenetic tree. One metric, R.sub.PD-DO, also proved to be robust under most simulated conditions using a variety of null models. Synthesis. Given the suboptimal performances of several tests, attention must be paid to the testing procedures used in future studies. Guidelines are provided to help choosing an adequate test. Article History: Received 3 October 2007; accepted 18 June 2008Handling Editor: Christopher Lortie Article note: (*) Correspondence author. E-mail: ohardy@ulb.ac.be

The adequacy of hourly rainfall sampling was examined in terms of the detection of diurnal variations using 8 yr (1998-2005) of data observed by the precipitation radar on the Tropical Rainfall Measuring Mission (TRMM) satellite. It was found that the monthly and hourly rain samples for each 0.2[degrees] grid point over the 8-yr period are composed of multiple precipitation systems. In this study, a ''3-h-significant diurnal peak' was defined as the time of maximum rainfall with consecutive positive anomalies for more than 3 h. The fraction of the analyzed area with a 3-h-significant diurnal peak increased annually and accounted for 43% of the total global tropics at 0.2[degrees] resolution over the 8-yr period. The diurnal signature over Tibet and the Amazon showed a high degree of spatial uniformity (at >10[degrees] scale). The degree of similarity and locations of the regional diurnal characteristics are described in terms of seasonal variations and at multiple resolutions based on spatial uniformity. For example, uniform early-afternoon peaks generally appear over the coastal land and areas of high relief, whereas a seasonally invariant early-afternoon peak over the low-lying Amazon basin is recognized as a regional characteristic. In areas of coastal ocean, early-morning peaks appear in certain regions such as the area surrounding the so-called Maritime Continent and the area off the west coast of Mexico. These peaks are distinct from the global characteristics of late-morning rainfall maxima recorded over most coastal oceans and early-morning peaks recorded over open ocean. The results are also compared with those derived from TRMM Microwave Imager (TMI) data. In addition to obtaining a coherent signal, regional differences in the timing of maximum rainfall over the Tibetan Plateau were addressed; this discrepancy is attributed to limitations of the scattering algorithm used for TMI data in terms of detecting shallow convection and screening cold surfaces.

Oxford Industries, Inc., a leading US apparel manufacturer, implemented a scheduling algorithm that significantly reduced equipment changeovers in its in-house embroidery facility. The company was experiencing difficulties meeting due dates [...]

Early in 2003, with continually increasing product variety and production volumes, Dell, Inc. had reached the designed capacity limits of one of its main production facilities, the Morton L. Topfer [...]

Chair: Joseph Kolibal, University of Southern Mississippi Vice-chair: Andrew Harrell, CEWES-GM THURSDAY MORNING Hunter Henry Executive Room 12 9:30 COMPILED ENGLISH A. Louise Perkins (1*), Tom Rishel (2), Farnaz Zand [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.comnet.2005.09.022 Byline: J.J. Garcia-Luna-Aceves (b), Marc Mosko (b), Charles E. Perkins (a) Keywords: Routing protocol; Loop-free; Algorithm analysis; Ad hoc network Abstract: A new protocol is presented for on-demand, loop-free routing in ad hoc networks. The new protocol, called the labeled distance routing (LDR) protocol, uses a distance invariant to establish an ordering criterion and per-destination sequence numbers to reset the invariant resulting in loop-freedom at every instant. The distance invariant allows nodes to change their next hops or distances to destinations without creating routing-table loops. The destination sequence number, which only the destination may increment, permits nodes to reset the values of their distance invariants. The performance of LDR is compared against the performance of three other protocols that are representative of the state-of-the-art, namely AODV, DSR and OLSR; LDR's performance is shown to be far better than the other three protocols. Author Affiliation: (a) Communication Systems Laboratory, Nokia Research Center, 313 Fairchild Drive, Mountain View, CA 94043, United States (b) U.C. Santa Cruz, Jack Baskin School of Engineering, Santa Cruz, CA 95062, United States Article Note: (footnote) [star] This work was supported in part by the US Air Force/OSR under Grant No. F49620-00-1-0330, and by the Baskin Chair in Computer Engineering.