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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

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

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

NERNST-PLANCK-NAVIER-STOKES SYSTEMS NEAR EQUILIBRIUM

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arXiv 2020年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States DEPARTMENT OF MATHEMATICS TEMPLE UNIVERSITY PHILADELPHIAPA19122 United States PROGRAM IN APPLIED AND COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States

The Nernst-Planck-Navier-Stokes system models electrodiffusion of ions in a fluid. We prove global existence of solutions in bounded domains in three dimensions with either blocking (no-flux) or uniform selective (special Dirichlet) boundary conditions for ion concentrations. The global existence of strong solutions is established for initial conditions that are sufficiently small perturbations of steady state solutions. The solutions remain close to equilbrium in strong norms. The main two steps of the proof are (1) the decay of the sum of relative entropies (Kullback-Leibler divergences) and (2) the control of L2 norms of deviations by the sum of relative *** Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Navier Stokes equations

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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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

random graphs by product random measures

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arXiv 2022年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted random graphs, directed or undirected, labeled or unlabeled, where (i) the composition of the test function and transformation is a non-negative edge weight function, (ii) the mean measures encode edge density/weight and vertex degree density/weight, and (iii) the mean edge weight, when square-integrable, encodes generalized spectral and Sobol representations. We develop a number of properties of these random graphs, and we give simple examples of some of their possible *** Codes 60G57, 60G55 © 2022, CC BY-NC-SA.

关键词： Encoding (symbols)

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

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arXiv 2024年

作者： Xie, Pinchen Chen, Yixiao Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Materials Institute Princeton University PrincetonNJ08544 United States

We report an extensive molecular dynamics study of ab-initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium upon crossing the transition temperature. We find that the macroscopic polarization appears/disappears due to dipolar switching at the nanometer scale. We also compute the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. For a long time, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation due to the thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases. © 2024, CC BY.

关键词： Ferroelectricity

Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach

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arXiv 2017年

作者： Aminzare, Zahra Dey, Biswadip Davison, Elizabeth N. Leonard, Naomi Ehrich Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Mechanical and Aerospace Engineering Princeton University NJ08540 United States

Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with neuronal spiking dynamics, we show that our new sufficient condition is tighter than those found in previous analyses which used nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex oscillatory systems. Copyright © 2017, The Authors. All rights reserved.

关键词： Synchronization