Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.     

A simple and inexpensive "solvent in silicone tube extraction" approach and its evaluation in the gas chromatographic analysis of pesticides in fruits and vegetables

A novel, simple, and inexpensive approach to sorptive extraction, which we call solvent in silicone tube extraction (SiSTEx), was applied to pesticide residue analysis and its effectiveness and efficiency were evaluated. In SiSTEx, which is a form of open tubular sorptive extraction, a piece of silicone tubing (4 cm long, 1.47 mm ID, 1.96 mm OD in this study) is attached to the cap of a 20 mL glass vial that contains the aqueous sample. The tubing is plugged at the end dangling in the sample solution, and MeCN (e.g., 40 microL) added by syringe to the inner tube volume through a septum in the cap. A stir-bar is used to mix the sample for a certain time (e.g., 60 min), which allows chemicals to partition into the tubing where they diffuse across the silicone and partition into the MeCN. The final MeCN extract is then analyzed for the concentrated analytes. In this study, the SiSTEx approach was evaluated for the analysis of organophosphorus (OP) and organochlorine (OC) pesticides in fruits and vegetables using GC/pulsed flame photometric (PFPD) and halogen specific (XSD) detectors for analysis. The produced samples were initially extracted by a rapid MeCN procedure, and 5 mL of the initial extract was diluted four-fold with water to undergo sorptive extraction for 60 min. The final extract was analyzed by GC/PFPD + XSD for 14 OP and 22 OC pesticides. This simple approach was able to detect 26 of the 36 pesticides at 10 ng/g or less original equivalent sample concentration with average reproducibility of 11% RSD. For those 26 pesticides, a 44-fold lower detection limit on average was achieved in matrix extracts using SiSTEx despite the four-fold dilution with water.     

Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at sqrt[S(NN)] =2.76 TeV with the ATLAS detector at the LHC

By using the ATLAS detector, observations have been made of a centrality-dependent dijet asymmetry in the collisions of lead ions at the Large Hadron Collider. In a sample of lead-lead events with a per-nucleon center of mass energy of 2.76 TeV, selected with a minimum bias trigger, jets are reconstructed in fine-grained, longitudinally segmented electromagnetic and hadronic calorimeters. The transverse energies of dijets in opposite hemispheres are observed to become systematically more unbalanced with increasing event centrality leading to a large number of events which contain highly asymmetric dijets. This is the first observation of an enhancement of events with such large dijet asymmetries, not observed in proton-proton collisions, which may point to an interpretation in terms of strong jet energy loss in a hot, dense medium.     

A note on regular Ramsey graphs

We prove that there is an absolute constant C>0 so that for every natural n there exists a triangle‐free regular graph with no independent set of size at least \({{C}}\sqrt{{{n}}\log{{n}}}\). © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 244–249, 2010     

Semicharacters of Groups

We define the notion of a semicharacter of a group G: A function from the group to ?*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is divisible by the order of the group. We prove that the conjecture holds for some important families of groups, including the Symmetric groups and the groups GL(2, q).     

Fragmented metastable states exist in an attractive bose-einstein condensate for atom numbers well above the critical number of the Gross-Pitaevskii theory

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number N(cr)(GP) of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above N(cr)(GP). The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.     

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Approximating the independence number via theϑ-function

We describe an approximation algorithm for the independence number of a graph. If a graph onn vertices has an independence numbern/k + m for some fixed integerk 3 and somem > 0, the algorithm finds, in random polynomial time, an independent set of size , improving the best known previous algorithm of Boppana and Halldorsson that finds an independent set of size (m ^1/(k–1)) in such a graph. The algorithm is based on semi-definite programming, some properties of the Lovász-function of a graph and the recent algorithm of Karger, Motwani and Sudan for approximating the chromatic number of a graph. If the-function of ann vertex graph is at leastMn ^1–2/k for some absolute constantM, we describe another, related, efficient algorithm that finds an independent set of sizek. Several examples show the limitations of the approach and the analysis together with some related arguments supply new results on the problem of estimating the largest possible ratio between the-function and the independence number of a graph onn vertices. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Research supported in part by a USA—Israel BSF grant and by the Fund for Basic Research administered by the Israel Academy of Sciences and by the Minkowski Minerva Center for Geometry at Tel Aviv University.This work was partly done while the author was at XEROX PARC and partly at DIMACS.     

Synthesis of Nitrogen‐Containing Rubicene and Tetrabenzopentacene Derivatives

Carbon‐based materials, such as acenes, fullerenes, and graphene nanoribbons, are viewed as the potential successors to silicon in the next generation of electronics. Although a number of methodologies provide access to these materials’ all‐carbon variants, relatively fewer strategies readily furnish their nitrogen‐doped analogues. Herein, we report the rational design, preparation, and characterization of nitrogen‐containing rubicenes and tetrabenzopentacenes, which can be viewed either as acene derivatives or as molecular fragments of fullerenes and graphene nanoribbons. The reported findings may prove valuable for the development of electron transporting organic semiconductors and for the eventual construction of larger carbonaceous systems.