Algorithms for non-uniform size data placement on parallel disks

We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data items) that need to be assigned to a storage system consisting of N disks d₁,d₂,…,d_N. We are also given sets U₁,U₂,…,U_M such that U_i is the set of clients seeking the ith data item. Data item i has size s_i. Each disk d_j is characterized by two parameters, namely, its storage capacity C_j which indicates the maximum total size of data items that may be assigned to it, and a load capacity L_j which indicates the maximum number of clients that it can serve. The goal is to find a placement of data items to disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system.We study this data placement problem for homogeneous storage systems where all the disks are identical. We assume that all disks have a storage capacity of k and a load capacity of L. Previous work on this problem has assumed that all data items have unit size, in other words s_i=1 for all i. Even for this case, the problem is NP-hard. For the case where s_i{1,…,Δ} for some constant Δ, we develop a polynomial time approximation scheme (PTAS). This result is obtained by developing two algorithms, one that works for constant k and one that works for arbitrary k. The algorithm for arbitrary k guarantees that a solution where at least -fraction of all clients are assigned to a disk (under certain assumptions). In addition we develop an algorithm for which we can prove tight bounds when s_i{1,2}. In fact, we can show that a -fraction of all clients can be assigned (under certain natural assumptions), regardless of the input distribution.     

First high-resolution analysis of the 4ν1+ν3 band of nitrogen dioxide near 1.5 μm

The high-resolution absorption spectrum of the 4ν₁+ν₃ band of the ¹⁴N¹⁶O₂ molecule was recorded by CW-Cavity Ring Down Spectroscopy between 6575 and 6700 cm⁻¹. The assignments involve energy levels of the (4,0,1) vibrational state with rotational quantum numbers up to K_a=8 and N=48. A large majority of the spin-rotation energy levels were reproduced within their experimental uncertainty using a theoretical model which takes explicitly into account the Coriolis interactions between the spin-rotational levels of the (4,0,1) vibrational state and those of the (4,2,0) and of (0,9,0) dark states, the anharmonic interactions between the (4,2,0) and (0,9,0) states together with the electron spin-rotation resonances within the (4,0,1), (4,2,0) and (0,9,0) states. Precise vibrational energies, rotational, spin-rotational, and coupling constants were determined for the {(4,2,0), (0,9,0), (4,0,1)} triad of interacting states. Using these parameters and the value of the transition dipole-moment operator determined from a fit of a selection of experimental line intensities, the synthetic spectrum of the 4ν₁+ν₃ band was generated and is provided as Supplementary Material.     

Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators

We give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on Hilbert spaces, which is subject to a Lipschitz continuous perturbation depending on the state. These sets are not necessarily weakly closed as in [3], [4], while the invariance criteria are still written by using only the data of the system. So, no need to the explicit knowledge of neither the solution of this differential inclusion, nor the semi-group generated by the maximal monotone operator. These invariant/viability results are next applied to derive explicit criteria for a-Lyapunov pairs of lower semi-continuous (not necessarily weakly-lsc) functions associated to these differential inclusions. The lack of differentiability of the candidate Lyapunov functions and the consideration of general invariant sets (possibly not convex or smooth) are carried out by using techniques from nonsmooth analysis.     

New necessary and sufficient optimality conditions for strong bilevel programming problems

In this paper we are interested in a strong bilevel programming problem (S). For such a problem, we establish necessary and sufficient global optimality conditions. Our investigation is based on the use of a regularization of problem (S) and some well-known global optimization tools. These optimality conditions are new in the literature and are expressed in terms of \(\max \)–\(\min \) conditions with linked constraints.     

Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns

In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance‐gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off‐line Markov Chain Monte Carlo in synthetic and real data applications.     

Hinge peptide combinatorial libraries for inhilbitors of botulinum neurotoxins and saxitoxin: Deconvolution strategy

Combinatorial library screening offers a rapid process for identifying potential therapies to toxins. Hinge peptide libraries, which rely on conformational diversity rather than traditional molecular diversity, reduce the need for huge numbers of syntheses and screening steps and greatly expedite the discovery process of active molecules. Hinge peptide libraries having the structures: Acetyl-X₁–X₂–hinge–X₃–X₄–NH₂ (capped) and X₁–hinge–X₂–X₃ (uncapped), where X₁ through X₄ are near-equimolar mixtures of twelve L-amino acids and hinge = 4-aminobutyric acid, were screened for inhibitory activity in bioassays for botulinum neurotoxins A and B (BoNT/A, BoNT/B) and saxitoxin. The zinc protease activity of the reduced light chains of BoNT/A and /B was assayed by measuring the cleavage of synthetic substrates. Saxitoxin activity was measured by the restoration of the viability of neuroblastoma cells treated with ouabain and veratridine. Deconvolution of libraries was accomplished by fixing one position at a time beginning with the C-terminus. Primary library subsets in which position 4 was fixed showed moderate levels of inhibition for BoNT/A. Secondary library subsets showed stronger inhibition in the bioassays. In each of the bioassays, inhibitory potency was stronger when the second position to be fixed was on the opposite side of the hinge, rather than on the same side with respect to the C-terminus, suggesting that the hinge facilitates the interaction of side chains. Inhibitors for all three of the toxins studied were discovered within library subsets, although not necessarily in primary subsets. These studies demonstrate that (1) the best strategy for deconvoluting hinge peptide libraries is by fixing residues alternately on each side of the hinge moiety, and (2) it is essential to investigate secondary subsets even when primary subsets are inactive. The present findings support the concept that the increased flexibility imposed by the inclusion of a central hinge residue in small peptides increases the opportunity for side chain interactions, providing a distinct advantage for hinge peptide libraries over conventional peptide libraries. Hinge peptide libraries are a rich source of novel ligands for modulation of biomechanisms. The library subsets uncovered in this study may possess peptides that will lead to effective therapies to neurotoxin poisoning.     

C n -almost automorphic solutions for partial neutral functional differential equations

In this work, we study the existence of C ⁿ -almost periodic solutions and C ⁿ -almost automorphic solutions (n?≥?1), for partial neutral functional differential equations. We prove that the existence of a bounded integral solution on ?⁺ implies the existence of C ⁿ -almost periodic and C ⁿ -almost automorphic strict solutions. When the exponential dichotomy holds for the homogeneous linear equation, we show the uniqueness of C ⁿ -almost periodic and C ⁿ -almost automorphic strict solutions.     

AF-Domains and Their Generalizations

In this article, we are concerned with the study of the dimension theory of tensor products of algebras over a field k. We introduce and investigate the notion of generalized AF-domain (GAF-domain for short) and prove that any k-algebra A such that the polynomial ring in one variable A[X] is an AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain. Moreover, we compute the Krull dimension of A? _k B for any k-algebra A such that A[X] is an AF-domain and any k-algebra B generalizing the main theorem of Wadsworth in [16 Wadsworth , A. R. ( 1979 ). The Krull dimension of tensor products of commutative algebras over a field . J. London Math. Soc. 19 : 391 – 401 .[Crossref], [Web of Science ®] , [Google Scholar]].     

A new method for solving Pareto eigenvalue complementarity problems

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNM_min and SNM_FB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201–213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125–137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method.