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Optimization-Based String Method for Finding Minimum Energy Path

Communications in Computational Physics 2013年第7期14卷 265-275页

作者： Amit Samanta Weinan E Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA Beijing International Center for Mathematical Research Peking UniversityBeijingChina

We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understanding of transition pathways between metastable *** method relies on the original formulation of the string method[***.B,66,052301(2002)],*** evolve a smooth curve along a direction normal to the *** algorithm works by performing minimization steps on hyperplanes normal to the *** the problem of finding MEP on the PES is remodeled as a set of constrained minimization *** provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method[***.,126(16),164103(2007)].At the same time,it provides a more direct analog of the finite temperature string *** applicability of the algorithm is demonstrated using various examples.

关键词： Rare events string method minimum energy path dislocation nucleation

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Density-based and transport-based core-periphery structures in networks

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Physical Review E 2014年第3期89卷 032810-032810页

作者： Sang Hoon Lee Mihai Cucuringu Mason A. Porter Oxford Centre for Industrial and Applied Mathematics Mathematical Institute University of Oxford Oxford OX2 6GG United Kingdom Program in Applied and Computational Mathematics (PACM) Princeton University Fine Hall Washington Road Princeton New Jersey 08544-1000 USA Department of Mathematics University of California Los Angeles Los Angeles California 90095 USA CABDyN Complexity Centre University of Oxford Oxford OX1 1HP United Kingdom

Networks often possess mesoscale structures, and studying them can yield insights into both structure and function. It is most common to study community structure, but numerous other types of mesoscale structures also exist. In this paper, we examine core-periphery structures based on both density and transport. In such structures, core network components are well-connected both among themselves and to peripheral components, which are not well-connected to anything. We examine core-periphery structures in a wide range of examples of transportation, social, and financial networks—including road networks in large urban areas, a rabbit warren, a dolphin social network, a European interbank network, and a migration network between counties in the United States. We illustrate that a recently developed transport-based notion of node coreness is very useful for characterizing transportation networks. We also generalize this notion to examine core versus peripheral edges, and we show that the resulting diagnostic is also useful for transportation networks. To examine the properties of transportation networks further, we develop a family of generative models of roadlike networks. We illustrate the effect of the dimensionality of the embedding space on transportation networks, and we demonstrate that the correlations between different measures of coreness can be very different for different types of networks.

关键词： MESOSCALE convective complexes -- Computer simulation COMMUNITY organization TRANSPORTATION SOCIAL networks DENSITY MARKOV processes DEPENDENCY (Imperialism)

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Evolutionary Features and Parameter Optimization of Spiking Neural Networks for Unsupervised Learning

Evolutionary Features and Parameter Optimization of Spiking ...

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International Joint Conference on Neural Networks

作者： Marco Silva Adriano Koshiyama Marley Vellasco Edson Cataldo Department of Electrical Engineering Pontifical Catholic University of Rio de Janeiro (PUC-Rio) Applied Mathematics Department Graduate Program in Telecommunications Engineering Federal Fluminense University (UFF)

ISBN: (纸本)9781479914821

This paper introduces two new hybrid models for clustering problems in which the input features and parameters of a spiking neural network (SNN) are optimized using evolutionary algorithms. We used two novel evolutionary approaches, the quantum-inspired evolutionary algorithm (QIEA) and the optimization by genetic programming (OGP) methods, to develop the quantum binary-real evolving SNN (QbrSNN) and the SNN optimized by genetic programming (SNN-OGP) neuro-evolutionary models, respectively. The proposed models are applied to 8 benchmark datasets, and a significantly higher clustering accuracy compared to a standard SNN without feature and parameter optimization is achieved with fewer iterations. When comparing QbrSNN and SNN-OGP, the former performed slightly better but at the expense of increased computational effort.

关键词： Neurons Sociology Statistics Neural networks Evolutionary computation Optimization Biological cells

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A lower bound on the Rényi entropy of convolutions in the integers

A lower bound on the Rényi entropy of convolutions in the i...

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IEEE International Symposium on Information Theory

作者： Liyao Wang Jae Oh Woo Mokshay Madiman Department of Physics Yale University New Haven CT USA Applied Mathematics Program Yale University New Haven CT USA Department of Mathematical Sciences University of Delaware Newark DE USA

A simple new lower bound is provided for the Rényi entropy of the convolution of probability distributions on the integers in terms of certain (discrete) rearrangements of these distributions. This inequality may... 详细信息

关键词： Entropy Random variables Information theory Educational institutions Additives Convex functions

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Mean field limit of a dynamical model of polymer systems

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Science China mathematics 2013年第12期56卷 2591-2598页

作者： E Weinan SHEN Hao School of Mathematical Sciences and BICMR Peking University Department of Mathematics and PACM Princeton UniversityPrinceton NJ 08544 USA Program in Applied and Computational Mathematics Princeton UniversityPrinceton NJ 08544 USA

This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.

关键词： polymers mean field limit stochastic PDEs McKean-Vlasov equation

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Marginal stability in jammed packings: Quasicontacts and weak contacts

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Physical Review E 2014年第2期90卷 022114-022114页

作者： Yoav Kallus Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Maximally random jammed (MRJ) sphere packing is a prototypical example of a system naturally poised at the margin between underconstraint and overconstraint. This marginal stability has traditionally been understood in terms of isostaticity, the equality of the number of mechanical contacts and the number of degrees of freedom. Quasicontacts, pairs of spheres on the verge of coming in contact, are irrelevant for static stability, but they come into play when considering dynamic stability, as does the distribution of contact forces. We show that the effects of marginal dynamic stability, as manifested in the distributions of quasicontacts and weak contacts, are consequential and nontrivial. We study these ideas first in the context of MRJ packing of d-dimensional spheres, where we show that the abundance of quasicontacts grows at a faster rate than that of contacts. We reexamine a calculation of Jin et al. [Phys. Rev. E 82, 051126 (2010)], where quasicontacts were originally neglected, and we explore the effect of their inclusion in the calculation. This analysis yields an estimate of the asymptotic behavior of the packing density in high dimensions. We argue that this estimate should be reinterpreted as a lower bound. The latter part of the paper is devoted to Bravais lattice packings that possess the minimum number of contacts to maintain mechanical stability. We show that quasicontacts play an even more important role in these packings. We also show that jammed lattices are a useful setting for studying the Edwards ensemble, which weights each mechanically stable configuration equally and does not account for dynamics. This ansatz fails to predict the power-law distribution of near-zero contact forces, P(f)∼fθ.

关键词： SPHERE packings POWER law (mathematics) COMPUTATIONAL complexity NP-hard problems BRAVAIS lattice

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Relationship between pore size and velocity probability distributions in stochastically generated porous media

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Physical Review E 2014年第1期89卷 013018-013018页

作者： M. Siena M. Riva J. D. Hyman C. L. Winter A. Guadagnini Dipartimento di Ingegneria Civile e Ambientale Politecnico di Milano Piazza L. Da Vinci 32 20133 Milano Italy Department of Hydrology and Water Resources University of Arizona Tucson Arizona 85721 USA Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA

We perform a set of detailed numerical simulations of single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (ϕ) and degrees of connectivity, and analyze the probability density functions (PDFs) of the pore sizes, S, and vertical velocity components, w, which are aligned with the mean flow direction. Both of the PDFs are markedly skewed with pronounced positive tails. This feature of the velocity PDF is dictated by the pore structure and determines the shortest travel times, one of the key transport attributes that underpins the success or the failure of environmental remediation techniques. Using a maximum likelihood approach, we determine that the PDFs of S and w decay according to an exponential and a stretched exponential model, respectively. A strong correlation between the key parameters governing the decay of the upper tails of the two PDFs is found, which provides a quantitative result for this analogy that so far has been stated only qualitatively. The parameter governing the concavity of the tail of the velocity PDF varies linearly with porosity over the entire range of tested values (0.2≤ϕ≤0.6). The parameters controlling the spread of the upper tails of the PDFs of S and w appear to be linked by a power-law relationship.

关键词： PORE size distribution DISTRIBUTION (Probability theory) STOCHASTIC analysis POROUS materials CONCAVE functions

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Near optimal feedback guidance design and the planar restricted three-body problem 24

Near optimal feedback guidance design and the planar restric...

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24th AAS/AIAA Space Flight Mechanics Meeting, 2014

作者： Dinius, Joseph Furfaro, Roberto Topputo, Francesco Selnick, Scott Program in Applied Mathematics University of Arizona 617 N Santa Rita Ave TucsonAZ85721 United States Department of Systems and Industrial Engineering University of Arizona 1127 E James E. Rogers Way TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona 1130 N Mountain Ave TucsonAZ85721 United States Department of Aerospace Science and Technology Politecnico di Milano Via La Masa 34 Milan20156 Italy

ISBN: (纸本)9780877036111

In this paper, we present the application of the ZEM/ZEV guidance algorithm to the planar restricted three-body problem (PR3BP). The ZEM/ZEV guidance law as a feedback guidance strategy is presented and applied to the PR3BP. The fuel optimal solution to the PR3BP for a transfer from GTO to L1 in the Earth-Moon system is presented as a point for comparison, showing the near optimality of the closed-loop guidance approach. Challenges of the approach and strategies for implementation in spacecraft mission design are discussed.

关键词： Feedback

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Noise- and stimulus-dependence of the optimal encoding nonlinearities in a simple ON/OFF retinal circuit model

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BMC Neurosci 2014年第SUPPL 1期15卷 P47-P47页

作者： Braden A W Brinkman Alison Weber Fred Rieke Eric Shea-Brown Department of Applied Mathematics University of Washington Seattle WA 98195 USA Department of Physiology and Biophysics University of Washington Seattle WA 98195 USA Program in Neurobiology and Behavior University of Washington Seattle WA 98195 USA Howard Hughes Medical Institute University of Washington Seattle WA 98195 USA

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An Empirical Analysis of Meta-learning for the Automatic Choice of Architecture and Components in Ensemble Systems

An Empirical Analysis of Meta-learning for the Automatic Cho...

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Brazilian Conference on Intelligent Systems (BRACIS)

作者： Diego S.C. Nascimento Anne M.P. Canuto André L.V. Coelho Information System Group. Federal Institute of Rio Grande do Norte (IFRN) Ipanguaçu RN Brazil Informatics and Applied Mathematics Department Federal University of Rio Grande do Norte (UFRN) Natal RN Brazil University of Fortaleza (UNIFOR) Graduate Program in Applied Informatics Fortaleza CE Brazil

Studies with ensemble systems have gained attention recently and, most of them, propose new methods for the design (generation) of different components in these systems. In parallel, new contributions of meta-learning have been presented as an efficient alternative to automatic recommendation of algorithms. In this paper, we apply meta-learning in the process of recommendation of important parameters of ensemble systems, which are: architecture and individual classifiers. The main goal is to provide an efficient way to design ensemble systems. In order to validate the proposed approach, an empirical investigation is conducted, recommending three possible types of ensemble architectures (Bagging, Boosting and Multi-Boosting) and five possible types of learning algorithms to compose the ensemble systems (individual classifiers or components). An initial analysis of the results confirms that meta-learning can be a promising tool to be used in the automatic choice of important parameters in ensemble systems.

关键词： Barium Boosting Bagging Support vector machines Error analysis Algorithm design and analysis Niobium

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