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Method for measuring promptγ-rays generated by D-T neutrons bombarding a depleted uranium spherical shell

Chinese Physics C 2016年第1期40卷 37-46页

作者：秦建国赖财锋蒋励刘荣张信威叶邦角朱通华 Department of Modern Physics University of Science and Technology of ChinaHefei 230026China Institute of Nuclear Physics and Chemistry CAEPP.O.Box 213Mianyang 621900China Graduate School China Academy of Engineering PhysicsMianyang 621900China Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088China

The prompt T-ray spectrum from depleted uranium （DU） spherical shells induced by 14 MeV D-T neutrons is measured. Monte Carlo （MC） simulation gives the largest prompt 2/ flux with the optimal thickness of the DU spherical shells 3-5 cm and the optimal frequency of neutron pulse 1 MHz. The method of time of flight and pulse shape coincidence with energy （DC-TOF） is proposed, and the subtraction of the background y-rays discussed in detail. The electron recoil spectrum and time spectrum of the prompt γ-rays are obtained based on a 2＇＇ × 2＇＇ BC501A liquid scintillator detector. The energy spectrum and time spectrum of prompt γ-rays are obtained based on an iterative unfolding method that can remove the influence of γ-rays response matrix and pulsed neutron shape. The measured time spectrum and the calculated results are roughly consistent with each other. Experimental prompt γ-ray spectrum in the 0.4-3 MeV energy region agrees well with MC simulation based on the ENDF/BVI.5 library, and the discrepancies for the integral quantities ofγ-rays of energy 0.4-1 MeV and 1 3 MeV are 9.2% and 1.1%, respectively.

关键词： D-T neutron depleted uranium prompt γ-ray delayed γ-ray time of flight

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Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

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Physical Review Research 2024年第3期6卷 033260页

作者： Peter K. Morse Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute of Materials Princeton Center for Theoretical Science Program in Applied and Computational Mathematics

In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions d=1–4, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d=2–8, which have only recently been made possible due to a highly parallelized algorithm.

关键词： Classical statistical mechanics Disordered systems

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WONDER: weighted one-shot distributed ridgeregression in high dimensions

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 2483-2534页

作者： Edgar Dobriban Yue Sheng Wharton Statistics Department University of Pennsylvania Philadelphia PA Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA

In many areas, practitioners need to analyze large data sets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high-dimensional random-effects model where each predictor has a small effect, we discover several new ***-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call "infinite-worker limit".Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are *** also propose a new Weighted ONe-shot DistributEd Ridge regression algorithm (WONDER). We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy.

关键词： distributed learning ridge regression high-dimensional statistics random matrix theory

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

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33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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NOMAD: nonlinear manifold decoders for operator learning 22

NOMAD: nonlinear manifold decoders for operator learning

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Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Jacob H. Seidman Georgios Kissas Paris Perdikaris George J. Pappas Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Department of Electrical and Systems Engineering University of Pennsylvania

ISBN: (纸本)9781713871088

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost.

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An information theoretic framework for eukaryotic gradient sensing 19

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20th Annual Conference on Neural Information Processing Systems, NIPS 2006

作者： Kimmel, Joseph M. Salter, Richard M. Thomas, Peter J. Computer Science Program Oberlin College Oberlin OH 44074 United States Department of Mathematics Biology and Cognitive Science Case Western Reserve University Cleveland OH 44106 United States Computational Neuroscience Graduate Program University of Chicago United States Center for Computation and Modeling United States

ISBN: (纸本)9780262195683

Chemical reaction networks by which individual cells gather and process information about their chemical environments have been dubbed "signal transduction" networks. Despite this suggestive terminology, there have been few attempts to analyze chemical signaling systems with the quantitative tools of information theory. Gradient sensing in the social amoeba Dictyostelium discoideum is a well characterized signal transduction system in which a cell estimates the direction of a source of diffusing chemoattractant molecules based on the spatiotemporal sequence of ligand-receptor binding events at the cell membrane. Using Monte Carlo techniques (MCell) we construct a simulation in which a collection of individual ligand particles undergoing Brownian diffusion in a three-dimensional volume interact with receptors on the surface of a static amoeboid cell. Adapting a method for estimation of spike train entropies described by Victor (originally due to Kozachenko and Leonenko), we estimate lower bounds on the mutual information between the transmitted signal (direction of ligand source) and the received signal (spatiotemporal pattern of receptor binding/unbinding events). Hence we provide a quantitative framework for addressing the question: how much could the cell know, and when could it know it? We show that the time course of the mutual information between the cell's surface receptors and the (unknown) gradient direction is consistent with experimentally measured cellular response times. We find that the acquisition of directional information depends strongly on the time constant at which the intracellular response is filtered.

关键词： Ligands

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Convolutional neural networks with low-rank regularization 4

Convolutional neural networks with low-rank regularization

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4th International Conference on Learning Representations, ICLR 2016

作者： Tai, Cheng Xiao, Tong Zhang, Yi Wang, Xiaogang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Electronic Engineering Chinese University of Hong Kong Hong Kong Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor United States

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves 91.31% accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. © ICLR 2016: San Juan, Puerto Rico. All Rights Reserved.

关键词： Iterative methods

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Ecumenical Modal Logic 1

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3rd International Workshop on Dynamic Logic, DaLí 2020

作者： Marin, Sonia Pereira, Luiz Carlos Pimentel, Elaine Sales, Emerson Department of Computer Science University College London London United Kingdom Philosophy Department PUC-Rio Rio de Janeiro Brazil Department of Mathematics UFRN Natal Brazil Graduate Program in Applied Mathematics and Statistics UFRN Natal Brazil

ISBN: (数字)9783030658403

ISBN: (纸本)9783030658397

The discussion about how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz’ system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In this work we extend Prawitz’ ecumenical idea to alethic K -modalities. © 2020, Springer Nature Switzerland AG.

关键词： Computer circuits

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LATTICE-VALUED BOTTLENECK DUALITY

arXiv

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arXiv 2024年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Department of Mathematics Department of Electrical & Systems Engineering and Program in Applied Mathematics & Computational Science University of Pennsylvania United States

This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth’s theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and *** Codes 06D05, 90C35, 06A07 © 2024, CC BY.

关键词： Combinatorial optimization

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Hyperuniformity order metric of Barlow packings

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Physical Review E 2019年第2期99卷 022111-022111页

作者： T. M. Middlemas F. H. Stillinger S. 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 New Jersey 08544 USA

The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ¯. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The “stealthy stacking” theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ¯ for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ¯ of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.

关键词： Classical statistical mechanics

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