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arXiv 2020年

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

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems like liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such systems involving spin chains are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform extensive analysis of these systems using density matrix renormalization group (DMRG) to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the "τ order metric" of the ground state, the measure of hyperuniformity and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of transverse magnetic field may remarkably lead to increase in the order of the ground state as measured by the "τ order metric," even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping on to a system of spinless ferm

关键词： Phase transitions

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Nonlocal effective electromagnetic wave characteristics of composite media: Beyond the quasistatic regime

arXiv

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arXiv 2020年

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

We derive exact nonlocal homogenized constitutive relations for the effective electromagnetic wave properties of disordered two-phase composites and metamaterials from first principles. This exact formalism enables us to extend the long-wavelength limitations of conventional homogenization estimates of the effective dynamic dielectric constant tensor Εe(kI, ω) for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where ω and kI are the frequency and wave vector of the incident radiation). We accomplish this task by deriving nonlocal strong-contrast expansions that exactly account for complete microstructural information (infinite set of n-point correlation functions) and hence multiple scattering to all orders for the range of wave numbers for which our extended homogenization theory applies, i.e., 0 ≤ |kI|. 1 (where is a characteristic heterogeneity length scale). Because of the fast-convergence properties of such expansions, their lower-order truncations yield accurate closed-form approximate formulas for Εe(kI, ω) that apply for a wide class of microstructures. These nonlocal formulas are resummed representations of the strong-contrast expansions that still accurately capture multiple scattering to all orders via the microstructural information embodied in the spectral density, which is easy to compute for any composite. The accuracy of these microstructure-dependent approximations is validated by comparison to full-waveform simulation computations for both 2D and 3D ordered and disordered models of composite media. Thus, our closed-form formulas enable one to predict accurately and efficiently the effective wave characteristics well beyond the quasistatic regime for a wide class of composite microstructures without having to perform full-blown simulations. We find that disordered hyperuniform media are generally less lossy than their nonhyperuniform counterparts. We also show that certain disordered hyperunif

关键词： Microstructure

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Characterizing the hyperuniformity of ordered and disordered two-phase media

arXiv

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arXiv 2020年

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

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σV2 (R) and the associated hyperuniformity order metrics BV . This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered/irregular packings, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have the minimal value of the hyperuniformity order metrics BV across all volume fractions. On the other hand, among all packings considered, the triangular-lattice packings have the smallest values of BV for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing has the minimal order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems by inverse design procedures. Copyright © 2020, The Authors. All rights reserved.

关键词： Wireless networks

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Nearest-neighbor functions for disordered stealthy hyperuniform many-particle systems

arXiv

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arXiv 2020年

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

Disordered stealthy many-particle systems in d-dimensional Euclidean space Rd are exotic amorphous states of matter that suppress any single scattering events for a finite range of wavenumbers around the origin in reciprocal space. They are currently the subject of intense fundamental and practical interest. We derive analytical formulas for the nearest-neighbor functions of disordered stealthy many-particle systems. First, we analyze asymptotic small-r approximations and expansions of the nearest-neighbor functions based on the pseudo-hard-sphere ansatz. We then consider the problem of determining how many of the standard n-point correlation functions are needed to determine the nearest neighbor functions, and find that a finite number suffice. Via theoretical and computational methods, we are able to compare the large-r behavior of these functions for disordered stealthy systems to those belonging to crystalline lattices. Such ordered and disordered stealthy systems have bounded hole sizes, and thus compact support for their nearest-neighbor functions. However, we find that the approach to the critical-hole size can be quantitatively different, emphasizing the importance of hole statistics in distinguishing ordered and disordered stealthy configurations. We argue that the probability of finding a hole close to the critical-hole size should decrease as a power law with an exponent only dependent on the space dimension d for ordered systems, but that this probability decays asymptotically faster for disordered systems, with either an increase in the exponent of the power law or a crossover into a decay faster than any power law. This implies that holes close to the critical-hole size are rarer in disordered systems. The rarity of observing large holes in disordered systems creates substantial numerical difficulties in sampling the nearest neighbor distributions near the critical-hole size. This motivates both the need for new computational methods for efficient samp

关键词： computational methods

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Recursive projection-aggregation decoding of Reed-Muller codes

arXiv

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arXiv 2019年

作者： Ye, Min Abbe, Emmanuel Mathematics Institute School of Computer and Communication Sciences EPFL Switzerland Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University Department of Electrical Engineering Princeton University United States

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding and code concatenation techniques. We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations. Copyright © 2019, The Authors. All rights reserved.

关键词： Decoding

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Optimized large hyperuniform binary colloidal suspensions in two dimensions

arXiv

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arXiv 2020年

作者： Ma, Zheng Lomba, Enrique Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Instituto de Química Física Rocasolano CSIC Calle Serrano 119 MadridE-28006 Spain 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 creation of disordered hyperuniform materials with potentially extraordinary optical properties requires a capacity to synthesize large samples that are effectively hyperuniform down to the nanoscale. Motivated by this challenge, we propose a fabrication protocol using binary paramagnetic colloidal particles confined in a 2D plane. The strong and long-ranged dipolar interaction induced by a tunable magnetic field is free from screening effects that attenuates long-ranged electrostatic interactions in charged colloidal systems. Specifically, we find a family of optimal size ratios that makes the two-phase system effectively hyperuniform. We show that hyperuniformity is a general consequence of low isothermal compressibilities, which makes our protocol suitable to systems with other long-ranged soft interactions, dimensionalities and/or polydispersity. Our methodology paves the way to synthesize large photonic hyperuniform materials that function in the visible to infrared range and hence may accelerate the discovery of novel photonic materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Suspensions (fluids)

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From point patterns to networks: to what extent does the Delaunay triangulation reproduce key spatial and density information?

arXiv

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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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Classification of datasets with imputed missing values: does imputation quality matter?

arXiv

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arXiv 2022年

作者： Shadbahr, Tolou Roberts, Michael Stanczuk, Jan Gilbey, Julian Teare, Philip Dittmer, Sören Thorpe, Matthew Torné, Ramon Viñas Sala, Evis Lió, Pietro Patel, Mishal Rudd, James H.F. Mirtti, Tuomas Rannikko, Antti Sakari Aston, John A.D. Tang, Jing Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Preller, Jacobus Stanczuk, Jan Babar, Judith Sánchez, Lorena Escudero Wassin, Marcel Holzer, Markus Walton, Nicholas Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Department of Mathematics University of Manchester Manchester United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom Department of Radiology University of Cambridge Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pathology University of Helsinki Helsinki University Hospital Finland iCAN-Digital Precision Cancer Medicine Flagship Helsinki Finland Department of Urology University of Helsinki Helsinki University Hospital Helsinki Finland Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Faculty of Mathematics University of Vienna Austria Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data. All code and data used in this paper are also released publicly at [inserted upon publication]. © 2022, CC BY.

关键词： Classification (of information)

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Parameter inference with non-linear galaxy clustering: accounting for theoretical uncertainties

arXiv

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arXiv 2021年

作者： Knabenhans, Mischa Brinckmann, Thejs Stadel, Joachim Schneider, Aurel Teyssier, Romain Institute for Computational Science University of Zurich Winterthurerstrasse 190 Zurich8057 Switzerland Dipartimento di Fisica Scienze della Terra Universitá degli Studi di Ferrara via Giuseppe Saragat 1 Ferrara44122 Italy Sezione di Ferrara Via Giuseppe Saragat 1 Ferrara44122 Italy C.N. Yang Institute for Theoretical Physics Department of Physics & Astronomy Stony Brook University Stony BrookNY11794 United States Department of Astrophysical Sciences Princeton University 4 Ivy Lane PrincetonNJ08544 United States The Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

We implement EuclidEmulator (version 1), an emulator for the non-linear correction of the matter power spectrum, into the Markov chain Monte Carlo (MCMC) forecasting code MontePython. We compare the performance of HALOFIT, HMCode, and EuclidEmulator1, both at the level of power spectrum prediction and at the level of posterior probability distributions of the cosmological parameters, for different cosmological models and different galaxy power spectrum wave number cutoffs. We confirm that the choice of the power spectrum predictor has a non-negligible effect on the computed sensitivities when doing cosmological parameter forecasting, even for a conservative wave number cut-off of 0.2 ℎMpc−1. We find that EuclidEmulator1 is on average up to 17% more sensitive to the cosmological parameters than the other two codes, with the most significant improvements being for the Hubble parameter of up to 42% and the equation of state of dark energy of up to 26%, depending on the case. In addition, we point out that the choice of the power spectrum predictor contributes to the risk of computing a significantly biased mean cosmology when doing parameter estimations. For the four tested scenarios we find biases, averaged over the cosmological parameters, of between 0.5 and 2σ (from below 1σ up to 6σ for individual parameters). This paper provides a proof of concept that this risk can be mitigated by taking a well-tailored theoretical uncertainty into account as this allows to reduce the bias by a factor of 2 to 5, depending on the case under consideration, while keeping posterior credibility contours small: the standard deviations are amplified by a factor of ≤ 1.4 in all cases. © 2021, CC BY-NC-SA.

关键词： Power spectrum

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Visualizing structure and transitions in high-dimensional biological data (vol 54, pg 781, 2019)

引用

NATURE BIOTECHNOLOGY 2020年第1期38卷 108-108页

作者： Moon, Kevin R. van Dijk, David Wang, Zheng Gigante, Scott Burkhardt, Daniel B. Chen, William S. Yim, Kristina van den Elzen, Antonia Hirn, Matthew J. Coifman, Ronald R. Ivanova, Natalia B. Wolf, Guy Krishnaswamy, Smita Department of Mathematics and Statistics Utah State University Logan USA Cardiovascular Research Center section Cardiology Department of Internal Medicine Yale University New Haven USA Department of Computer Science Yale University New Haven USA School of Basic Medicine Qingdao University Qingdao China Yale Stem Cell Center Department of Genetics Yale University New Haven USA Computational Biology and Bioinformatics Program Yale University New Haven USA Department of Genetics Yale University New Haven USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing USA Department of Mathematics Michigan State University East Lansing USA Applied Mathematics Program Yale University New Haven USA Department of Genetics Center for Molecular Medicine University of Georgia Athens USA Department of Mathematics and Statistics Université de Montréal Montréal Canada Mila—Quebec Artificial Intelligence Institute Montréal Canada

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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