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Characterization of maximally random jammed sphere packings: Voronoi correlation functions

Physical Review E 2014年第5期90卷 052120-052120页

作者： Michael A. Klatt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in th

关键词： RANDOM variables VORONOI polygons MINKOWSKI space POISSON processes FUNCTIONS (mathematics)

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An integrative approach to investigate the respective roles of single-nucleotide variants and copy-number variants in Attention-Deficit/Hyperactivity Disorder (vol 6, 22851, 2016)

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SCIENTIFIC REPORTS 2016年第1期6卷 22851-22851页

作者： Lima, Leandro de Araujo Feio-dos-Santos, Ana Cecilia Belangero, Sintia Iole Gadelha, Ary Bressan, Rodrigo Affonseca Salum, Giovanni Abrahao Pan, Pedro Mario Moriyama, Tais Silveira Graeff-Martins, Ana Soledade Tamanaha, Ana Carina Alvarenga, Pedro Krieger, Fernanda Valle Fleitlich-Bilyk, Bacy Jackowski, Andrea Parolin Brietzke, Elisa Sato, Joao Ricardo Polanczyk, Guilherme Vanoni Mari, Jair de Jesus Manfro, Gisele Gus do Rosario, Maria Conceiao Miguel, Euripedes Constantino Puga, Renato David Tahira, Ana Carolina Souza, Viviane Neri Chile, Thais Gouveia, Gisele Rodrigues Simoes, Sergio Nery Chang, Xiao Pellegrino, Renata Tian, Lifeng Glessner, Joseph T. Hashimoto, Ronaldo Fumio Rohde, Luis Augusto Sleiman, Patrick M. A. Hakonarson, Hakon Brentani, Helena Inter-institutional Grad Program on Bioinformatics University of São Paulo São Paulo SP Brazil Center for Applied Genomics The Children’s Hospital of Philadelphia Philadelphia PA USA Department & Institute of Psychiatry University of São Paulo Medical School São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Federal University of São Paulo São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Federal University of São Paulo São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Federal University of São Paulo São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Hospital de Clínicas de Porto Alegre Federal University of Rio Grande do Sul Porto Alegre RS Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Federal University of São Paulo São Paulo SP Brazil Department & Institute of Psychiatry University of São Paulo Medical School São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Federal University of São Paulo São Paulo SP Brazil Department & Institute of Psychiatry University of São Paulo Medical School São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil National Institute of Developmental Psychiatry for Children and Adolescents (INCT-CNPq) São Paulo SP Brazil Department of Psychiatry Federal University of São Paulo São Paulo SP Brazil Department & Institute of Psychiatry University of S

Many studies have attempted to investigate the genetic susceptibility of Attention-Deficit/Hyperactivity Disorder (ADHD), but without much success. The present study aimed to analyze both single-nucleotide and copy-number variants contributing to the genetic architecture of ADHD. We generated exome data from 30 Brazilian trios with sporadic ADHD. We also analyzed a Brazilian sample of 503 children/adolescent controls from a High Risk Cohort Study for the Development of Childhood Psychiatric Disorders, and also previously published results of five CNV studies and one GWAS meta-analysis of ADHD involving children/adolescents. The results from the Brazilian trios showed that cases with de novo SNVs tend not to have de novo CNVs and vice-versa. Although the sample size is small, we could also see that various comorbidities are more frequent in cases with only inherited variants. Moreover, using only genes expressed in brain, we constructed two “in silico” protein-protein interaction networks, one with genes from any analysis, and other with genes with hits in two analyses. Topological and functional analyses of genes in this network uncovered genes related to synapse, cell adhesion, glutamatergic and serotoninergic pathways, both confirming findings of previous studies and capturing new genes and genetic variants in these pathways.

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Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 465-476页

作者： Weinan E Jian-feng LU Xu YANG Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University School of Mathematical Sciences Peking University

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

关键词： semiclassical limit Bloch-Wigner transform Bloch dynamics Berry phase asymptotic analysis

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Downlink analysis for a heterogeneous cellular network

Downlink analysis for a heterogeneous cellular network

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2014 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2014

作者： Madhusudhanan, Prasanna Restrepo, Juan G. Liu, Youjian Eugene Brown, Timothy X. Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309-0425 United States Department of Applied Mathematics University of Colorado Boulder CO 80309-0425 United States Interdisciplinary Telecommunications Program University of Colorado Boulder CO 80309-0425 United States

ISBN: (纸本)9783901882630

In this paper, a comprehensive study of the downlink performance in a heterogeneous cellular network (or hetnet) is conducted. A general hetnet model is considered consisting of an arbitrary number of open-access and closed-access tier of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs of each tier have a constant transmission power, random fading coefficient with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability and average rate at an arbitrary mobile-station (MS), and average per-tier load are derived for the max-SINR connectivity model. Using stochastic ordering, interesting properties and simplifications for the hetnet downlink performance are derived by relating this connectivity model to the maximum instantaneous received power (MIRP) connectivity model, providing good insights about the hetnets and the downlink performance in these complex networks. Furthermore, the results also demonstrate the effectiveness and analytical tractability of the stochastic geometric approach to study the hetnet performance. © 2014 IFIP.

关键词： Fading channels

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Hydrodynamic interaction between overlapping domains during recurrence of registration within planar lipid bilayer membranes

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Physical Review E 2014年第3期89卷 032717-032717页

作者： Tao Han Trevor P. Bailey Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Due to a thermodynamic coupling between the two leaflets comprising a lipid bilayer, compositional lipid domains residing within opposing leaflets are often found in registry. If the system is perturbed by displacing one domain relative to the other, diffusive and advective lipid fluxes are established to restore equilibrium and reestablish domain overlap. In this work, we focus on the advective part of the process, and first derive an analytical expression for the hydrodynamic drag coefficient associated with the advective flow for the special case of perfect domain overlap. The resulting expression identifies parameter regions where sliding friction between the leaflets dominates over viscous dissipation within the leaflets or vice versa. It is shown that in all practically relevant cases, sliding friction between the leaflets is the dominant factor. Finally, we investigate the domain separation dependence of the hydrodynamic drag coefficient via direct simulations of a continuum diffuse interface model, and provide useful empirical expressions for its behavior.

关键词： HYDRODYNAMICS BILAYER lipid membranes DRAG coefficient ENERGY dissipation SLIDING friction FLUX (Energy)

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Erratum to: Some Joys and Trials of Mathematical Neuroscience

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Journal of Nonlinear Science 2014年第2期24卷 243-244页

作者： Holmes, Philip Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton USA Princeton Neuroscience Institute Princeton University Princeton USA

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Hybrid LS-SA-PS methods for solving fuzzy non-linear programming problems

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MATHEMATICAL AND COMPUTER MODELLING 2013年第1-2期57卷 180-188页

作者： Vasant, Pandian Engineering Mathematics Program Fundamental & Applied Sciences Department University Technology Petronas Malaysia

The fuzzy optimization problem is one of the prominent topics in the broad area of artificial intelligence. It is applicable in the field of non-linear fuzzy programming. Its application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem was solved by hybrid optimization techniques like Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). An industrial production planning problem with a cubic objective function, eight decision variables and 29 constraints was solved successfully using the LS-SA-PS hybrid optimization techniques. The computational results for the objective function with respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Nonlinear fuzzy programming Simulated annealing Pattern search Line search Vagueness factor Level of satisfaction

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Angular momentum dependent orbital-free density functional theory: Formulation and implementation

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Physical Review B 2014年第15期89卷 155112-155112页

作者： Youqi Ke Florian Libisch Junchao Xia Emily A. Carter []Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

Orbital-free density functional theory (OFDFT) directly solves for the ground-state electron density. It scales linearly with respect to system size, providing a promising tool for large-scale material simulations. Removal of the orbitals requires use of approximate noninteracting kinetic energy density functionals. If replacing ionic cores with pseudopotentials, removal of the orbitals also requires these pseudopotentials to be local. These are two severe challenges to the capabilities of conventional OFDFT. While main group elements are often well described within conventional OFDFT, transition metals remain intractable due to their localized d electrons. To advance the accuracy and general applicability of OFDFT, we have recently reported a general angular momentum dependent formulation as a next-generation OFDFT. In this formalism, we incorporate the angular momenta of electrons by devising a hybrid scheme based on a muffin tin geometry: inside spheres centered at the ionic cores, the electron density is expanded in a set of atom-centered basis functions combined with an onsite density matrix. The explicit treatment of the angular momenta of electrons provides an important basis for accurately describing the important ionic core region, which is not possible in conventional OFDFT. In addition to the conventional OFDFT total energy functional, we introduce a nonlocal energy term containing a set of angular momentum dependent energies to correct the errors due to the approximate kinetic energy density functional and local pseudopotentials. Our approach greatly increases the accuracy of OFDFT while largely preserving its numerical simplicity. Here, we provide details of the theoretical formulation and practical implementation, including the hybrid scheme, the derivation of the nonlocal energy term, the choice of basis functions, the direct minimization of the total energy, the procedure to determine the angular momentum dependent energies, the force formula with Pu

关键词： ANGULAR momentum (Nuclear physics) DENSITY functional theory GROUND state (Quantum mechanics) ELECTRON density SIMULATION methods & models DENSITY functionals

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Local paths to global coherence: Cutting networks down to size

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Physical Review E 2014年第3期89卷 032802-032802页

作者： Yu Hu James Trousdale Krešimir Josić Eric Shea-Brown Department of Applied Mathematics University of Washington Seattle Washington 98195 USA Department of Mathematics University of Houston Houston Texas 77204-5001 USA Department of Biology and Biochemistry University of Houston Houston Texas 77204-5001 USA Program in Neurobiology and Behavior University of Washington Seattle Washington 98195 USA Department of Physiology and Biophysics University of Washington Seattle Washington 98195 USA

How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale, we consider the coherence of overall network dynamics. We show that such global coherence in activity can often be predicted from the local structure of the network. To characterize local network structure, we use “motif cumulants,” a measure of the deviation of pathway counts from those expected in a minimal probabilistic network model. We extend previous results in three ways. First, we give acombinatorial formulation of motif cumulants that relates to the allied concept in probability theory. Second, we show that the link between global network dynamics and local network architecture is strongly affected by heterogeneity in network connectivity. However, we introduce a network-partitioning method that recovers a tight relationship between architecture and dynamics. Third, for a particular set of models, we generalize the underlying theory to treat dynamical coherence at arbitrary orders (i.e., triplet correlations and beyond). We show that at any order, only a highly restricted set of motifs impacts dynamical correlations.

关键词： PROBABILISTIC generative models PROBABILITY theory COHERENT states NETWORK computers COMPUTER architecture DYNAMICS COMPUTER network resources

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A connectionist model of context-based memory reconsolidation in the hippocampus: the role of sleep

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BMC Neuroscience 2014年第1期15卷 1-2页

作者： Justin Lines Jean-Marc Fellous Kelsey Nation Department of Psychology University of Arizona Tucson Arizona 85721 USA Neuroscience Graduate Interdisciplinary Program University of Arizona Tucson Arizona 85719 USA Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA

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