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arXiv 2019年

作者： Lan, Ti-Yen Bendory, Tamir Boumal, Nicolas Singer, Amit Program in Applied and Computational Mathematics Mathematics Department Princeton University PrincetonNJ08544 United States

Motivated by the structure reconstruction problem in cryo-electron microscopy, we consider the multi-target detection model, where multiple copies of a target signal occur at unknown locations in a long measurement, further corrupted by additive Gaussian noise. At low noise levels, one can easily detect the signal occurrences and estimate the signal by averaging. However, in the presence of high noise, which is the focus of this paper, detection is impossible. Here, we propose two approaches—autocorrelation analysis and an approximate expectation maximization algorithm—to reconstruct the signal without the need to detect signal occurrences in the measurement. In particular, our methods apply to an arbitrary spacing distribution of signal occurrences. We demonstrate reconstructions with synthetic data and empirically show that the sample complexity of both methods scales as SNR−3 in the low SNR regime. Copyright © 2019, The Authors. All rights reserved.

关键词： Convolution

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Factor analysis for spectral estimation

arXiv

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arXiv 2017年

作者： Andén, Joakim Singer, Amit Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy. Copyright © 2017, The Authors. All rights reserved.

关键词： Power spectrum

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Probabilistic Theory of Mean Field Games with Applications I 1

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丛书名： Probability Theory and Stochastic Modelling

2018年

作者： René Carmona François Delarue

ISBN: (数字)9783319589206

ISBN: (纸本)9783319564371;9783030132606

Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems.

关键词： Probability Theory Calculus of Variations and Optimization Differential Equations Quantitative Economics

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Ab initio multi-scale modeling of ferroelectrics: The case of PbTiO3

arXiv

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arXiv 2022年

作者： Xie, Pinchen Chen, Yixiao Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We report an ab initio multi-scale study of lead titanate using the Deep Potential (DP) models, a family of machine learning-based atomistic models, trained on first-principles density functional theory data, to represent potential and polarization surfaces. Our approach includes anharmonic effects beyond the limitations of reduced models and of the linear approximation for the polarization. The calculated enthalpy, spontaneous polarization, specific heat and dielectric susceptibility agree well with experiments on single crystals. In addition, we study how the free energy depends on the polarization with enhanced sampling methods, further supporting the first-order and order-disorder character of the transition. The latter is evidenced by persistence of local dipoles above the transition temperature. The simulated free energy surface as a function of the global polarization leads to a Landau-Devonshire theory of the single domain crystal. © 2022, CC BY.

关键词： Free energy

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MULTI-TARGET DETECTION WITH ROTATIONS

arXiv

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arXiv 2021年

作者： Bendory, Tamir Lan, Ti-Yen Marshall, Nicholas F. Rukshin, Iris Singer, Amit School of Electrical Engineering Tel Aviv University Tel Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics Oregon State University Corvallis OR USA Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Program in Applied and Computational Mathematics and the Department of Mathematics Princeton University Princeton NJ USA

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

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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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Viscosity in water from first-principles and deep-neural-network simulations

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npj computational Materials 2022年第1期8卷 1318-1327页

作者： Cesare Malosso Linfeng Zhang Roberto Car Stefano Baroni Davide Tisi SISSA—Scuola Internazionale Superiore di Studi Avanzati 34136TriesteItaly Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ08544USA DP Technology Beijing100080PR China Department of Chemistry Department of Physicsand Princeton Institute for the Science and Technology of MaterialsPrinceton UniversityPrincetonNJUSA CNR Istituto Officina dei Materiali SISSA Unit34136TriesteItaly

We report on an extensive study of the viscosity of liquid water at near-ambient conditions,performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics(AIMD),based on density-functional theory(DFT).In order to cope with the long simulation times necessary to achieve an acceptable statistical accuracy,our ab initio approach is enhanced with deep-neural-network potentials(NNP).This approach is first validated against AIMD results,obtained by using the Perdew–Burke–Ernzerhof(PBE)exchange-correlation functional and paying careful attention to crucial,yet often overlooked,aspects of the statistical data ***,we train a second NNP to a dataset generated from the Strongly Constrained and Appropriately Normed(SCAN)*** the error resulting from the imperfect prediction of the melting line is offset by referring the simulated temperature to the theoretical melting one,our SCAN predictions of the shear viscosity of water are in very good agreement with experiments.

关键词： viscosity Strongly ambient

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Using a level set to model multiple myeloma induced bone loss

Using a level set to model multiple myeloma induced bone los...

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6th European Congress on computational Methods in applied Sciences and Engineering, ECCOMAS 2012

作者： Ayati, Bruce P. Graham, Jason M. Holstein, Sarah A. Department of Mathematics and Program in Applied Mathematical and Computational Sciences University of Iowa Iowa City IA 52242-1419 United States Department of Internal Medicine University of Iowa Iowa City IA 52242-1081 United States

ISBN: (纸本)9783950353709

Multiple myeloma is a hematological malignancy characterized by proliferation of malignant plasma cells and derangement of bone homeostasis. Myeloma bone disease results in significant morbidity as a result of bone pain, hypercalcemia, diffuse osteopenia, and pathologic fractures. We present a spatially explicit mathematical model of multiple myeloma and bone remodeling, synthesizing the existing model of local "microenvironment" interactions in Ayati et al. 2010 [1] with a level set approach for representing the sharp interface been bone and marrow introduced in [6]. computational results show the feasibility of using a level set to capture the spatial structure in the context of a geometrically straightforward interface, but one that nonetheless captures the essence of the rich geometries seen in bone marrow biopsy slides. In particular, we are able to model the formation of an osteolytic lesion in the case of multiple myeloma dysregulated bone remodeling, but not, using the same remodeling parameter set, in the case of normal bone remodeling.

关键词： Bone

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CHAOTIC TRANSPORT IN 2-DIMENSIONAL AND 3-DIMENSIONAL FLOW PAST A CYLINDER

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PHYSICS OF FLUIDS A-FLUID DYNAMICS 1991年第5期3卷 1051-1062页

作者： BATCHO, P KARNIADAKIS, GE Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

The response of transport measures (Nusselt number, drag and lift force) for two- and three-dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discretization at a Reynolds number Re = 500. The undisturbed two-dimensional flow remains periodic at this Reynolds number, unless a suitable forcing is applied on the naturally produced system. Three-dimensional simulations establish that three-dimensionality sets in at Re almost-equal-to 200. Successive supercritical states are established through a series of period-doublings, before a chaotic state is reached at a Re almost-equal-to 500. For the two-dimensional forced flow, all transport measures oscillate aperiodically in time and undergo a "crisis," i.e., a sudden and dramatic increase in their amplitude. The corresponding three-dimensional, naturally produced chaotic state corresponds to a less drastic change of the transport quantities with both rms and mean values lower than their two-dimensional counterparts.

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Inertial Hegselmann-Krause systems

Inertial Hegselmann-Krause systems

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American Control Conference (ACC)

作者： Bernard Chazelle Chu Wang Department of Computer Science Princeton University Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781467386838

We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of HK systems with closed-minded agents, which settles a conjecture of long standing. This paper also introduces anchored HK systems and show their equivalence to the symmetric heterogeneous model.

关键词： Convergence Communication networks Kinetic theory Protocols Nickel Mobile communication Turning

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