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arXiv 2025年

作者： Newby, Eli Shi, Wenlong Jiao, Yang Torquato, Salvatore Albert, Réka Department of Physics Pennsylvania State University University ParkPA16802 United States Department of Cardiovascular and Metabolic Sciences Lerner Research Institute Cleveland Clinic ClevelandOH44195 United States Arizona State University TempeAZ85287 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Biology Pennsylvania State University University ParkPA16802 United States

To be used as an analysis tool, it is important that a spatial network’s construction algorithm reproduces the structural properties of the original physical embedding. One method for converting a two-dimensional (2D) point pattern into a spatial network is the Delaunay triangulation. Here, we apply the Delaunay triangulation to seven different types of 2D point patterns, including hyperuniform systems. The latter are characterized by completely suppressed normalized infinite-wavelength density fluctuations. We demonstrate that the quartile coefficients of dispersion of multiple centrality measures are capable of rank-ordering hyperuniform and nonhyperuniform systems independently, but they cannot distinguish a system that is nearly hyperuniform from hyperuniform systems. Thus, in each system, we investigate the local densities of the point pattern ρP (ri;) and of the network ρG(ni;). We reveal that there is a strong correlation between ρP (ri;) and ρG(ni;) in nonhyperuniform systems, but there is no such correlation in hyperuniform systems. When calculating the pair-correlation function and local density covariance function on the point pattern and network, the point pattern and network functions are similar only in nonhyperuniform systems. In hyperuniform systems, the triangulation has a positive covariance of local network densities in pairs of nodes that are close together;such covariance is not present in the point patterns. Thus, we demonstrate that the Delaunay triangulation accurately captures the density fluctuations of the underlying point pattern only when the point pattern possesses a positive correlation between ρP (ri;) for points that are close together. Such positive correlation is seen in most real-world systems, so the Delaunay triangulation is generally an effective tool for building a spatial network from a 2D point pattern, but there are situations (i.e., disordered hyperuniform systems) where we caution that the Delaunay triangulation would not

关键词： Triangulation

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Comment on “Jamming at zero temperature and zero applied stress: The epitome of disorder”

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Physical Review E 2004年第4期70卷 043301-043301页

作者： Aleksandar Donev Salvatore Torquato Frank H. Stillinger Robert Connelly Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Materials Institute Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Mathematics Cornell University Ithaca New York 14853 USA

O’Hern, Silbert, Liu, and Nagel [Phys. Rev. E. 68, 011306 (2003)] claim that a special point J of a “jamming phase diagram” (in density, temperature, stress space) is related to random close packing of hard spheres and that it represents, for their suggested definitions of jammed and random, the recently introduced maximally random jammed state. We point out several difficulties with their definitions and question some of their claims. Furthermore, we discuss the connections between their algorithm and other hard-sphere packing algorithms in the literature.

关键词： .RCp Phys Rev Hard Spheres hard-sphere well-de jamming point out maximally claim special point nitions jammed MRJ OSLN

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

arXiv

引用

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

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Hyperuniform states of matter

arXiv

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arXiv 2018年

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties. Copyright © 2018, The Authors. All rights reserved.

关键词： Ground state

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Estimation in the group action channel

arXiv

引用

arXiv 2018年

作者： Abbe, Emmanuel Pereira, João M. Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

MSC Codes 94A15, 62B10We analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryoelectron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when N=σ2dis bounded from above, where N is the number of observations, σ is the noise standard deviation, and d is the so-called moment order cutoff. In contrast, the maximum likelihood estimator is shown to be consistent if N=σ2ddiverges. Copyright © 2018, The Authors. All rights reserved.

关键词： Mean square error

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Multireference alignment is easier with an aperiodic translation distribution

arXiv

引用

arXiv 2017年

作者： Abbe, Emmanuel Bendory, Tamir Leeb, William Pereira, João M. Sharon, Nir Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (the signal energy divided by the noise variance) in order to drive the mean-square error (MSE) to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as ω(1/SNR3). In this work, using a generalization of the Chapman-Robbins bound for orbits and expansions of the X2divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as ω(1/SNR2). This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation-maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model. Copyright © 2017, The Authors. All rights reserved.

关键词： Maximum principle

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COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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Computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

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Raman spectrum and polarizability of liquid water from deep neural networks

arXiv

引用

arXiv 2020年

作者： Sommers, Grace M. Calegari Andrade, Marcos F. Zhang, Linfeng Wang, Han Car, Roberto Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface, the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for H2O and D2O. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes. Copyright © 2020, The Authors. All rights reserved.

关键词： Liquids

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Beta expansions: a new approach to digitally corrected A/D conversion

Beta expansions: a new approach to digitally corrected A/D c...

引用

IEEE International Symposium on Circuits and Systems (ISCAS)

作者： I. Daubechies R. DeVore C.S. Gunturk V.A. Vaishampayan Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics University of South Carolina Columbia SC USA Department of Mathematics Courant Institute of Mathematical Sciences New York NY USA Information Sciences Research AT and T Research Laboratories Florham Park NJ USA

We introduce a new architecture for pipelined (and also algorithmic) A/D converters that give exponentially accurate conversion using inaccurate comparators. An error analysis of a sigma-delta converter with an imperfect comparator and a constant input reveals a self-correction property that is not inherited by the successive refinement quantization algorithm that underlies both pipelined multistage A/D converters and algorithmic A/D converters. Motivated by this example, we introduce a new A/D converter, the beta converter, which has the same self-correction property as a sigma-delta converter but which exhibits higher order (exponential) accuracy with respect to the bit rate as compared to a sigma-delta converter, which exhibits only polynomial accuracy.

关键词： mathematics Delta-sigma modulation Error analysis Quantization Redundancy Error correction Voltage Sampling methods Fourier transforms Computer architecture

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Hyperbolic procrustes analysis using riemannian geometry 21

Hyperbolic procrustes analysis using riemannian geometry

引用

Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Ya-Wei Eileen Lin Yuval Kluger Ronen Talmon Viterbi Faculty of Electrical and Computer Engineering Technion Program in Applied Mathematics Yale University and Interdepartmental Program in Computational Biology and Bioinformatics Yale University and Department of Pathology Yale University

ISBN: (纸本)9781713845393

Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.

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