Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While CS literature has mostly focused on problems involving 1-D and 2-D signal...
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ISBN:
(纸本)9781424442959
Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While CS literature has mostly focused on problems involving 1-D and 2-D signals, many important applications involve signals that are multidimensional. We propose the use of Kronecker product matrices in CS for two purposes. First, we can use such matrices as sparsifying bases that jointly model the different types of structure present in the signal. Second, the measurement matrices used in distributed measurement settings can be easily expressed as Kronecker products. This new formulation enables the derivation of analytical bounds for sparse approximation and CS recovery of multidimensional signals.
Two significant indices that measure a country's development are related to science and education. To address the people’s peculiar needs as developing nations, which include the aspiration to develop and the des...
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Two significant indices that measure a country's development are related to science and education. To address the people’s peculiar needs as developing nations, which include the aspiration to develop and the desire to compete in a competitive global village, a scientific education that addresses the specific needs of the people has to be in place. Every nation must create and maintain a scientifically educated culture to become developed or sustain its development. In the light of developing economies, they need to establish a program that addresses literacy efficiency in the technical labor force and world aware citizenry. This paper examines how the scientific but people-oriented education, EarthSpace educational system, and EarthSpace, climate change and the renewable energy education initiative may impact sustainable development in the states of its deployment.
Premelting describes the confluence of phenomena that are responsible for the stable existence of the liquid phase of matter in the solid region of its bulk phase diagram. Here we develop a theoretical description of ...
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Premelting describes the confluence of phenomena that are responsible for the stable existence of the liquid phase of matter in the solid region of its bulk phase diagram. Here we develop a theoretical description of the premelting of water ice contained in a porous matrix, made of a material with a melting temperature substantially larger than ice itself, to predict the amount of liquid water in the matrix at temperatures below its bulk freezing point. Our theory combines the interfacial premelting of ice in contact with the matrix, grain-boundary melting in the ice, and impurity and curvature induced premelting, with the latter occurring in regions which force the ice-liquid interface into a high curvature configuration. These regions are typically found at points where the matrix surface is concave, along contact lines of a grain boundary with the matrix, and in liquid veins. Both interfacial premelting and curvature induced premelting depend on the concentration of impurities in the liquid, which, due to the small segregation coefficient of impurities in ice are treated as homogeneously distributed in the premelted liquid. Our principal result is an equation for the fraction of liquid in the porous medium as a function of the undercooling, which embodies the combined effects of interfacial premelting, curvature induced premelting, and impurities. The result is analyzed in detail and applied to a range of experimentally relevant settings.
The problem of fault tolerant state estimation is considered. We propose a unified, general formulation of the problem in which two different types of faults affect the system's output simultaneously. This problem...
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The problem of fault tolerant state estimation is considered. We propose a unified, general formulation of the problem in which two different types of faults affect the system's output simultaneously. This problem statement generalizes previously reported formulations that may be obtained as special cases. Three families of state estimation methods for fault-prone systems are presented, generalizing several classical estimation algorithms. These families include: one-step near-optimal filters, which are closely related to the GPB filter family, IMM-based filters, and linear optimal estimators.
We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem ca...
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We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d-dimensional Euclidean space Rd, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in Rd for d=2, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408…], where π/18=0.7408… corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d=2, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust an
Most common complex traits such as obesity, hypertension, diabetes, and cancers are known to be associated with multiple genes, environmental factors, and epistasis. Recently, the development of advanced genotyping te...
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Most common complex traits such as obesity, hypertension, diabetes, and cancers are known to be associated with multiple genes, environmental factors, and epistasis. Recently, the development of advanced genotyping technologies allows us to perform the genome-wide association studies (GWAS). For detecting the effects of multiple genes on complex traits, many approaches have been proposed for GWAS. Multifactor dimensionality reduction (MDR) proposed by Ritchie et al. (2001) is one of the powerful methods for detecting epistasis, which detects high order interactions among genes. However, MDR is computationally intensive due to its requirement of testing all possible n-way combinations. Thus, it is not practically feasible to apply MDR directly to analyzing large-scale GWAS data. We propose an efficient strategy to perform MDR analysis for GWAS data. First, select a subset of genetic factors such as SNPs with some marginal significance. Second, perform MDR analysis only for the selected genetic factors. Third, provide MDR summary results through network graph. Even for the MDR analysis for the selected SNPs, a fast computing system is required. We developed our own GPU based system for the large-scale GWAS data. We applied our strategy to Korean Association REsource (KARE) (8,838 individuals with 101,837 SNPs) for detecting two-way interactions of genetic factors associated with body mass index (BMI). We identified several genes and pathways which have been known to be associated with obesity.
作者:
S. TorquatoF. H. Stillinger[]Department of Chemistry
Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute of Advanced Study Princeton New Jersey 08540 USA
Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and into selected aspects of biological systems. Th...
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Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and into selected aspects of biological systems. This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide and (in the large system limit) continuous range of intensive properties, including packing fraction ϕ, mean contact number Z, and several scalar order metrics. Application of these analytical tools to spheres in three dimensions (an analog to the venerable Ising model) covers a myriad of jammed states, including maximally dense packings (as Kepler conjectured), low-density strictly jammed tunneled crystals, and a substantial family of amorphous packings. With respect to the last of these, the current approach displaces the historically prominent but ambiguous idea of “random close packing” with the precise concept of “maximally random jamming.” Both laboratory procedures and numerical simulation protocols can and, frequently, have been used for creation of ensembles of jammed states. But while the resulting distributions of intensive properties may individually approach narrow distributions in the large system limit, the distinguishing varieties of possible operational details in these procedures and protocols lead to substantial variability among the resulting distributions, some examples of which are presented here. This review also covers recent advances in understanding jammed packings of polydisperse sphere mixtures, as well as convex nonspherical particles, e.g., ellipsoids, “
作者:
Adam B. HopkinsFrank H. StillingerSalvatore TorquatoDepartment of Chemistry
Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA
The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a sto...
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The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of configuration space. The knowledge of Rmin(N) in d-dimensional Euclidean space Rd allows for the construction both of a realizability condition for pair-correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings in Rd. In this paper, we focus on the two-dimensional circular disk problem. We find and present the putative densest packings and corresponding Rmin(N) for selected values of N up to N=348 and use this knowledge to construct such a realizability condition and an upper bound. We additionally analyze the properties and characteristics of the maximally dense packings, finding significant variability in their symmetries and contact networks, and that the vast majority differ substantially from the triangular lattice even for large N. Our work has implications for packaging problems, nucleation theory, and surface physics.
The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introd...
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The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.
The aim of this work is the development of a numerical technique for the reduction of reaction mechanisms of common hydrocarbon and oxygenated fuels, such as methane, ethylene, propane, methanol and ethanol, using ste...
The aim of this work is the development of a numerical technique for the reduction of reaction mechanisms of common hydrocarbon and oxygenated fuels, such as methane, ethylene, propane, methanol and ethanol, using steady‐state and partial equilibrium assumptions. Numerical tests are carried to establish the basic chain for each fuel as well as to determine the amount of small products of combustion, whose concentration depends on the turbulent mixing and needs to be controlled due to environmental restrictions. The results are in agreement with data in the literature.
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