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Characterizing the hyperuniformity of ordered and disordered two-phase media

Physical Review E 2021年第1期103卷 012123-012123页

作者： Jaeuk Kim Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

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 two-phase heterogeneous 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 B¯V. 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 or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics B¯V across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of B¯V for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the 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 with desirable bulk physical properties by inverse d

关键词： Patterns in complex systems

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Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

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Physical Review B 2021年第1期103卷 014118-014118页

作者： Amartya Bose Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

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 such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems 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 an extensive analysis of these systems using density matrix renormalization group simulations 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 a transverse magnetic field may lead remarkably to an 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 onto a system of spinless

关键词： Long-range interactions Quantum phase transitions Spin chains

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Principal Curvatures Estimation with Applications to Single Cell Data

arXiv

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arXiv 2025年

作者： Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian Université de Montréal Dept. of Math. & Stat. QC Montréal Canada Mila – Quebec AI Institute MontréalQC Canada Yale University Dept. of Comp. Sci. New HavenCT United States Dept. of Genetics New HavenCT United States Applied Mathematics Program New HavenCT United States Université de Fribourg Department of Informatics Fribourg Switzerland Helmholtz Zentrum München Institute of AI for Health Munich Germany

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation. © 2025, CC BY.

关键词： Spatio-temporal data

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Geomagnetic field influences probabilistic abstract decision-making in humans

arXiv

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arXiv 2023年

作者： Chae, Kwon-Seok Oh, In-Taek Jeong, Soo Hyun Kim, Yong-Hwan Kim, Soo-Chan Kim, Yongkuk Department of Biology Education Kyungpook National University Daegu41566 Korea Republic of Brain Science and Engineering Institute Kyungpook National University Daegu41566 Korea Republic of Department of Baduk Studies Myongji University Yongin17058 Korea Republic of Department of Biological Sciences Neuroscience program Delaware State University DoverDE19901-2277 United States Department of Electrical and Electronic Engineering Research Center for Applied Human Sciences Hankyong National University Anseong17579 Korea Republic of Department of Mathematics Kyungpook National University Daegu41566 Korea Republic of

To resolve disputes or determine the order of things, people commonly use binary choices such as tossing a coin, even though it is obscure whether the empirical probability equals to the theoretical probability. The geomagnetic field (GMF) is broadly applied as a sensory cue for various movements in many organisms including humans, although our understanding is limited. Here we reveal a GMF-modulated probabilistic abstract decision-making in humans and the underlying mechanism, exploiting the zero-sum binary stone choice of Go game as a proof-of-principle. The large-scale data analyses of professional Go matches and in situ stone choice games showed that the empirical probabilities of the stone selections were remarkably different from the theoretical probability. In laboratory experiments, experimental probability in the decision-making was significantly influenced by GMF conditions and specific magnetic resonance frequency. Time series and stepwise systematic analyses pinpointed the intentionally uncontrollable decision-making as a primary modulating target. Notably, the continuum of GMF lines and anisotropic magnetic interplay between players were crucial to influence the magnetic field resonance-mediated abstract decision-making. Our findings provide unique insights into the impact of sensing GMF in decision-makings at tipping points and the quantum mechanical mechanism for manifesting the gap between theoretical and empirical probability in 3-dimensional living space. © 2023, CC BY-NC-ND.

关键词： Decision making

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Exploiting self-organized criticality in strongly stratified turbulence

arXiv

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arXiv 2021年

作者： Chini, Gregory P. Michel, Guillaume Julien, Keith Rocha, Cesar B. Caulfield, Colm-Cille P. Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Institut Jean Le Rond d’Alembert Sorbonne Université CNRS UMR 7190 ParisF-75005 France Department of Applied Mathematics University of Colorado BoulderCO80309 United States Department of Marine Sciences University of Connecticut StorrsCT06269 United States BP Institute Department of Applied Mathematics & Theoretical Physics Cambridge University CambridgeCB3 0WA United Kingdom

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly-varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow-fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly-evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parameterizations. Copyright © 2021, The Authors. All rights reserved.

关键词： Asymptotic analysis

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RANDOMLY AGGREGATED LEAST SQUARES FOR SUPPORT RECOVERY

arXiv

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arXiv 2020年

作者： Steinerberger, Stefan Lindenbaum, Ofir Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States

We study the problem of exact support recovery: given an (unknown) vector θ ∈ {−1, 0, 1}D, we are given access to the noisy measurement y = Xθ + ω, where X ∈ RN×D is a (known) Gaussian matrix and the noise ω ∈ RN is an (unknown) Gaussian vector. How small we can choose N and still reliably recover the support of θ? We present RAWLS (Randomly Aggregated Unweighted Least Squares Support Recovery): the main idea is to take random subsets of the N equations, perform a least squares recovery over this reduced bit of information and then average over many random subsets. We show that the proposed procedure can provably recover an approximation of θ and demonstrate its use in support recovery through numerical examples. Copyright © 2020, The Authors. All rights reserved.

关键词： Recovery

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Ecumenical modal logic

arXiv

引用

arXiv 2020年

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

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 a recent work, Ecumenical sequent calculi and a nested system were presented, and some very interesting proof theoretical properties of the systems were established. In this work we extend Prawitz' Ecumenical idea to alethic *** Codes 03B45, 03F03 Copyright © 2020, The Authors. All rights reserved.

关键词： Computer circuits

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A SEMICIRCLE LAW FOR DERIVATIVES OF RANDOM POLYNOMIALS

arXiv

引用

arXiv 2020年

作者： Hoskins, Jeremy G. Steinerberger, Stefan Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States

Let x1, . . ., xn be n independent and identically distributed random variables with mean zero, unit variance, and finite moments of all remaining orders. We study the random polynomial pn having roots at x1, . . ., xn. We prove that for ` ∈ N fixed as n → ∞, the (n − `)−th derivative of pn behaves like a Hermite polynomial: for x in a compact interval, n`/2n`!! · p(nn−`) ( √xn ) → He`(x + γn), where He` is the `−th probabilists’ Hermite polynomial and γn is a random variable converging to the standard N(0, 1) Gaussian as n → ∞. Thus, there is a universality phenomenon when differentiating a random polynomial many times: the remaining roots follow a Wigner semicircle distribution. Copyright © 2020, The Authors. All rights reserved.

关键词： Polynomials

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Interior electroneutrality in nernst-planck-navier-stokes systems

arXiv

引用

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

We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions for the ionic concentrations, we prove that the ionic charge density ρ converges in time to zero in the interior of the domain, in the limit of vanishing Debye length (ǫ → 0). For the unstable regime of Dirichlet boundary conditions for the ionic concentrations, we prove bounds that are uniform in time and ǫ. We also consider electroneutral boundary conditions, for which we prove that electroneutrality ρ → 0 is achieved at any fixed ǫ > 0, exponentially fast in time in Lp, for all 1 ≤ p MSC Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Boundary conditions

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The ternary Goldbach problem with a prime with a missing digit and primes of special types

arXiv

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arXiv 2021年

作者： Maier, Helmut Rassias, Michael Th. Department of Mathematics University of Ulm Helmholtzstrasse 18 Ulm89081 Germany Department of Mathematics and Engineering Sciences Hellenic Military Academy Vari Attikis16673 Greece Moscow Institute of Physics and Technology Institutskiy per d. 9 Dolgoprudny141700 Russia Institute for Advanced Study Program in Interdisciplinary Studies 1 Einstein Dr PrincetonNJ08540 United States

Let 'Equation Presented' Let γ∗0= 1/γ0 be fixed. Let also a0∈ {0,1, ⋯, 9}. In [23] we proved on assumption of the Generalized Riemann Hypothesis (GRH), that each sufficiently large odd integer N0can be represented in the form N0= p1+ p2+ p3, where for i = 2,3 the primes piare Piatetski-Shapiro primes - primes of the form pi= [nic0], ni∈ - whereas the decimal expansion of p1does not contain the digit a0. In this paper we replace one of the Piatetski-Shapiro primes p2and p3by primes of the type p = x2+ y2+ 1. Copyright © 2021, The Authors. All rights reserved.

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