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Unexpected Density Fluctuations in Jammed Disordered Sphere Packings

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Physical Review Letters 2005年第9期95卷 090604-090604页

作者： Aleksandar Donev Frank H. Stillinger Salvatore Torquato Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k)∼|k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r)∼−r−4, and a long-ranged direct correlation function c(r).

关键词： .saturated power-law structure factor hard-sphere damped sphere packings jammed hyperuniform local density fluctuations nonanalytic direct correlation function

A field equation for induction-transduction of activation-deactivation probability on measurable space

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arXiv 2022年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Chemistry Princeton University Princeton NJ08544 United States

Induction-transduction of activating-deactivating points are fundamental mechanisms of action that underlie innumerable systems and phenomena, mathematical, natural, and anthropogenic, and can exhibit complex behaviors such as self-excitation, phase transitions, hysteresis, polarization, periodicity, chaos, wave behavior, geometry, and energy transfer. We describe a class of primitives for induction-transduction based on dynamics on images of marked random counting measures under graphical random transformations. We derive a field equation for the law of the activation-deactivation (Bernoulli) process on an arbitrary measurable space and describe some mechanisms of action on the unit *** Codes 37A50, 60G57, 60G60, 60G55 © 2022, CC BY-NC-SA.

关键词： Energy transfer

Use of the Boltzmann Equation to Simulate Lattice-Gas Automata

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Physical Review Letters 1988年第20期61卷 2332-2332页

作者： Guy R. McNamara Gianluigi Zanetti Research Institutes University of Chicago Chicago IL 60637 5640 South Ellis Avenue United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

We discuss an alternative technique to the lattice-gas automata for the study of hydrodynamic properties, namely, we propose to model the lattice gas with a Boltzmann equation. This approach completely eliminates the statistical noise that plagues the usual lattice-gas simulations and therefore permits simulations that demand much less computer time. It is estimated to be more efficient than the lattice-gas automata for intermediate to low Reynolds number R≲100.

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Benchmark Tests of Principal Fissile Nuclide Data in JENDL-3 with Simple Fast Critical Assemblies

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Journal of Nuclear Science and Technology 1993年第11期30卷 1087页

作者： TIAN, Dongfeng HASEGAWA, Akira NAKAGAWA, Tsuneo KIKUCHI, Yasuyuki Nuclear Data Center Department of PhysicsTokai Research EstablishmentJapan Atomic Energy Research Institute A visiting scientist through STA Scientist Exchange Program from Institute of Applied Physics and Computational Mathematics

A series of benchmark tests was made to check the neutron nuclear data of main fissile nuclides (239Pu, 236U and 233U) of JENDL-3 for fast reactors. A total of nine critical assemblies were analyzed. They are assemblies of single material, high enrichment and simple geometry with small volume and therefore suitable for nuclear data testing. Criticality calculation was made by ANISN with S16P5 using the VITAMIN-J 175-energy-group. Discussions are made on ken, spectral indices at core center and leakage spectra. From the study, a problem was pointed out relating to the interpolation of secondary-neutron energy distributions for threshold reactions near the threshold energy point adopted in the original JENDL-3 and its remedy was proposed. By the benchmark tests of thus revised JENDL-3 (JENDL-3.1), it was shown that integral experiments for 239Pu and 235U cores were reproduced quite satisfactorily. On the contrary, it was revealed that large deviations for 233U cores from the experiment were due to uncertainties of the fission spectrum and the inelastic scattering cross sections, In the present work, sensitivity of "a" parameter (level density parameter) of Madland-Nix's fission spectrum formula to the integral data was extensively studied. Some recommendations are made to improve JENDL-3.1.

关键词： JENDL-3 fast reactors benchmarks neutrons nuclear data cross section plutonium-239 uranium-235 uranium-233 Madland-Nix's fission spectra k eff spectral index leakage spectra accuracy

Locality and low-dimensions in the prediction of natural experience from fMRI 07

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Locality and low-dimensions in the prediction of natural exp...

Proceedings of the 21st International Conference on Neural Information Processing Systems

作者： François G. Meyer Greg J. Stephens Center for the Study of Brain Mind and Behavior Program in Applied and Computational Mathematics Princeton University Center for the Study of Brain Mind and Behavior Department of Physics Princeton University

ISBN: (纸本)9781605603520

Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding; how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-defined Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke's area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ~ 0.8) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience.

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On the cross-validation bias due to unsupervised preprocessing

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arXiv 2019年

作者： Moscovich, Amit Rosset, Saharon Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics and Operations Research Tel-Aviv University Tel-Aviv Israel

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection;(ii) grouping of rare categorical features;and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional *** Codes 62-07 Copyright © 2019, The Authors. All rights reserved.

关键词： Regression analysis

Structural characterization of many-particle systems on approach to hyperuniform states

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arXiv 2021年

作者： Torquato, Salvatore Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The study of hyperuniform states of matter is an emerging multidisciplinary field, impinging on topics in the physical sciences, mathematics and biology. The focus of this work is the exploration of quantitative descriptors that herald when a many-particle system in d-dimensional Euclidean space Rd approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes as well as the crossover point between them in terms of the "volume" coefficient A and "surface-area" coefficient B associated with the local number variance σ2(R) for a spherical window of radius R. The larger the ratio B/A, the larger the hyperuniform scaling regime, which becomes of infinite extent in the limit B/A → ∞. To complement the known direct-space representation of the coefficient B in terms of the total correlation function h(r), we derive its corresponding Fourier representation in terms of the structure factor S(k), which is especially useful when scattering information is available experimentally or theoretically. We also demonstrate that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio B/A, as well as other diagnostic measures of hyperuniformity, including the hyperuniformity index H and the direct-correlation function length scale ξc, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. Specifically, we analyze equilibrium systems of hard rods and "sticky" hard-sphere systems in arbitrary space dimension d as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "steal

关键词： Temperature

Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman–Bucy Filters

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arXiv 2022年

作者： Álvarez Ballesteros, Miguel Ángel Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the development of an unbiased estimator for the ensemble Kalman–Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit N → ∞, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein–Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods. © 2022, CC BY-NC-SA.

关键词： Continuous time systems

Uncertainity quantification for atomistic reaction models: An equation-free stochastic simulation algorithm example

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Multiscale Modeling and Simulation 2007年第4期6卷 1217-1233页

作者： Zou, Yu Keverekidis, Ioannis G. Citigroup 388 Greenwhich Street New York NY 10013 United States Department of Chemical Engineering and Program in Applied and COmputational Mathematics Princeton University Princeton NJ 08544 United States

We describe a computational framework linking uncertainty quantification (UQ) methods for continuum problems depending on random parameters with equation-free (EF) methods for performing continuum deterministic numerics by acting directly on atomistic/stochastic simulators. Our illustrative example is a heterogeneous catalytic reaction mechanism with an uncertain atomistic kineticparameter;the "inner" dynamic simulator of choice is a Gillespie stochastic simulation algorithm(SSA). We demonstrate UQ computations at the coarse-grained level, in a nonintrusive way, throughthe design of brief, appropriately initialized computational experiments with the SSA code. The system is thus observed at three levels: (a) a fine scale for each stochastic simulation at each value of the uncertain parameter;(b) an intermediate coarse-grained state for the expected behavior of the SSA at each value of the uncertain parameter;and (c) the desired fully coarse-grained level: distributions of the coarse-grained behavior over the range of uncertain parameter values The latter are computed in the form of generalized polynomial chaos (gPC) coefficients in terms of the random parameter. Coarse projective integration and coarse fixed point computation are employed to accelerate the computational evolution of these desired observables, to converge on random stable/ unstable steady states, and to perform parametric studies with respect to other (nonrandom) system parameters. © 2008 Society for Industrial and applied mathematics.

关键词： Stochastic systems