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arXiv 2024年

作者： Wang, Haina Huse, David A. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute of Materials and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The probability of finding a spherical "hole" of a given radius r contains crucial structural information about many-body systems. Such hole statistics, including the void conditional nearest-neighbor probability functions GV (r), have been well studied for hard-sphere fluids in d-dimensional Euclidean space Rd. However, little is known about these functions for hard-sphere crystals for values of r beyond the hard-sphere diameter, as large holes are extremely rare in crystal phases. To overcome these computational challenges, we introduce a biased-sampling scheme that accurately determines hole statistics for equilibrium hard spheres on ranges of r that far extend those that could be previously explored. We discover that GV (r) in crystal and hexatic states exhibits oscillations whose amplitudes increase rapidly with the packing fraction, which stands in contrast to GV (r) for fluid states that is monotonic in r. The oscillations in GV (r) for 2D crystals are strongly correlated with the local orientational order metric in the vicinity of the holes, and variations in GV (r) for 3D states indicate a transition between tetrahedral and octahedral holes, demonstrating the power of GV (r) as a probe of local coordination geometry. To further study the statistics of interparticle spacing in hard-sphere systems, we compute the local packing fraction distribution f(l) of Delaunay cells, and find that for d ≤ 3, the excess kurtosis of f(l) switches sign at a certain transitional global packing fraction. Our investigation facilitates the study of structural and bulk properties of materials that involve the creation of rare large holes, such as the solubility of alloys. © 2024, CC BY.

关键词： Spheres

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Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions

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Physical Review E 2025年第2期111卷 025105-025105页

作者： Alessia Ferraro Gregory P. Chini T. M. Schneider Emergent Complexity in Physical Systems Laboratory (ECPS) École Polytechnique Fédérale de Lausanne CH-1015 Lausanne Switzerland Nordita Royal Institute of Technology and Stockholm University Stockholm 106 91 Sweden Department of Mechanical Engineering and Program in Integrated Applied Mathematics University of New Hampshire Durham New Hampshire 03824 USA

We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this scale separation, an efficient hybrid fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability—and temporal scale separation—is maintained. For 2D systems, the fluctuation eigenfunctions are labeled by their Fourier wave numbers characterizing spatial variability in that extended spatial direction, and the marginal mode(s) must coincide with the fastest-growing mode(s) over all admissible Fourier wave numbers. Here we derive an ordinary differential equation governing the slow evolution of the wave number of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows and other strongly constrained forms of geophysical turbulence in extreme parameter regimes. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasicoherent structures in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows in which scale separation justifies a QL approximation of the dynamics.

关键词： Shear flow

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arXiv

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arXiv 2023年

作者： Stickler, Megan Ott, William Kilpatrick, Zachary P. Josic, Krešimir Karamched, Bhargav R. Department of Mathematics University of Houston HoustonTX United States Department of Applied Mathematics University of Colorado-Boulder BoulderCO United States Department of Biology and Biochemistry University of Houston HoustonTX United States Department of Mathematics Florida State University TallahasseeFL United States Institute of Molecular Biophysics Florida State University TallahasseeFL United States Program in Neuroscience Florida State University TallahasseeFL United States

Normative models are often used to describe how humans and animals make decisions. These models treat deliberation as the accumulation of uncertain evidence that terminates with a commitment to a choice. When extended to social groups, such models often assume that individuals make independent observations. However, individuals typically gather evidence from common sources, and their observations are rarely independent. Here we ask: For a group of ideal observers who do not exchange information, what is the impact of correlated evidence on decision accuracy? We show that even when agents are identical, correlated evidence causes decision accuracy to depend on temporal decision order. Surprisingly, the first decider is less accurate than a lone observer. Early deciders are less accurate than late deciders. These phenomena occur despite the fact that the rational observers use the same decision criterion, so they are equally confident in their decisions. We analyze discrete and continuum evidence-gathering models to explain why the first decider is less accurate than a lone observer when evidence is correlated. Pooling the decisions of early deciders using a majority rule does not rescue accuracy in the sense that such pooling results in only modest accuracy gain. Although we analyze an idealized model, we believe that our analysis offers insights that do not depend on exactly how groups integrate evidence and form *** Codes 92F05 © 2023, CC BY.

关键词： Decision making

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Exploring Multiscale Quantum Media: High-Precision Efficient Numerical Solution of the Fractional Schrödinger equation, Eigenfunctions with Physical Potentials, and Fractionally-Enhanced Quantum Tunneling

arXiv

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arXiv 2024年

作者： Lewis, Joshua M. Carr, Lincoln D. Quantum Engineering Program Colorado School of Mines GoldenCO80401 United States Department of Physics Colorado School of Mines GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States

Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and technology is the fractional Schrödinger equation, which describes sub-and super-dispersive behavior of quantum wavefunctions induced by multiscale media. We derive a computationally efficient sixth-order split-step numerical method to converge the eigenfunctions of the FSE to arbitrary numerical precision for arbitrary fractional order derivative. We demonstrate applications of this code to machine precision for classic quantum problems such as the finite well and harmonic oscillator, which take surprising twists due to the non-local nature of the fractional derivative. For example, the evanescent wave tails in the finite well take a Mittag-Leffer-like form which decay much slower than the well-known exponential from integer-order derivative wave theories, enhancing penetration into the barrier and therefore quantum tunneling rates. We call this effect fractionally enhanced quantum tunneling. This work includes an open source code for communities from quantum experimentalists to applied mathematicians to easily and efficiently explore the solutions of the fractional Schrödinger equation in a wide variety of practical potentials for potential realization in quantum tunneling enhancement and other quantum applications. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

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Wire Before You Walk

Wire Before You Walk

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Asilomar Conference on Signals, Systems & Computers

作者： Tesfa Asmara Dhananjay Bhaskar Ian Adelstein Smita Krishnaswamy Michael Perlmutter Department of Computer Science Pomona College Claremont CA USA Mathematics and Statistics Pomona College Claremont CA USA Department of Genetics Yale School of Medicine New Haven CT USA Department of Mathematics Yale University New Haven CT USA Department of Computer Science Yale University New Haven CT USA Program for Applied Mathematics Yale University New Haven CT USA Computational Biology and Bioinformatics Program Yale University New Haven CT USA Wu Tsai Institute Yale University New Haven CT USA Department of Mathematics Boise State University Boise ID USA

Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.

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DATA-DRIVEN MORI-ZWANZIG: REDUCED ORDER MODELING OF SPARSE SENSORS MEASUREMENTS FOR BOUNDARY LAYER TRANSITION

arXiv

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Michael Livescu, Daniel Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can be collected at fixed locations. Thus, in developing reduced models for predicting and controlling the flow at the sensor locations, the main challenge is in accounting for how the surrounding field of unobserved (or unresolved) variables interacts with the observed (or resolved) variables at the fixed sensor locations. This makes the Mori-Zwanzig (MZ) formalism a natural choice, as it results in the Generalized Langevin Equations which provides a mathematically sound framework for constructing non-Markovian reduced-order models that include the effects the unresolved variables have on the resolved variables. These effects are captured in the so called memory kernel and orthogonal dynamics, which, when using Mori's linear projection, provides a higher order approximation to the traditional approximate Koopman learning methods. In this work, we explore recently developed data-driven methods for extracting the MZ operators to two boundary-layer flows obtained from high resolution data;a low speed incompressible flow over a flat plate exhibiting bypass transition;and a high speed compressible flow over a flared cone at Mach 6 and zero angle of attack where transition was initiated using a broadband forcing approach ("natural" transition). In each case, an array of "sensors" are placed near the surface of the solid boundary, and the MZ operators are learned and the predictions are compared to the Extended Dynamic Mode Decomposition (EDMD), both using delay embedded coordinates. Further comparisons are made with Long Short-Term Memory (LSTM) and a regression based projection framework using neural networks for the MZ operators. First, we compare the effects of including delay embedded coordinates with EDMD and Mori based MZ and provide

关键词： Dynamic mode decomposition

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On Complex Analytic tools, and the Holomorphic Rotation methods

arXiv

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arXiv 2022年

作者： Coifman, Ronald R. Peyrière, Jacques Weiss, Guido Department of Mathematics Program in Applied Mathematics Yale University New HavenCT06510 United States Institut de Mathématiques d'Orsay CNRS Université Paris-Saclay Orsay91405 France

We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It is known [6] that all harmonic functions in higher dimensions are combinations of holomorphic functions on 2 dimensional planes, extended as, constant in normal directions. We derive representation theorems, with corresponding isometries, opening the door for applications in higher dimensions, to the processing of highly oscillatory multidimensional signals. © 2022, CC BY.

关键词： Harmonic functions

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Global-Local Active Contour for Segmenting Images with Simultaneous Inhomogeneity and Texture

SSRN

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SSRN 2024年

作者： Shao, Pei-Chiang Department of Applied Mathematics Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan Undergraduate Program in College of Electrical Engineering and Computer Science Chung Yuan Christian University Zhongli District Taoyuan City320314 Taiwan

Severe intensity inhomogeneity (InH) and complex real-world textures cause great difficulties and become two important issues in image segmentation and object extraction applications. Plenty of methods are proposed to tackle these issues, however, they usually perform poorly on images possess both InH and texture. In this paper, we propose a region-based active contour model for segmenting images with simultaneous inhomogeneity and texture. A new bias field possesses both global and local smoothness properties is proposed to handle the InH issue, and a pixel inhomogeneity factor (PIF) is employed to jointly deal with InH and textured images. We also employ the total variation (TV) regularization to further smooth and denoise the transformed PIF image, making the segmentation process to have the nice properties of global convergence and independence of contour initialization. A large number of numerical experiments and comparisons are conducted to demonstrate the effective performance of the newly proposed method. © 2024, The Authors. All rights reserved.

关键词： Textures

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Algebraic Constraints and Algorithms for Common Lines in Cryo-EM

arXiv

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arXiv 2024年

作者： Muller, Tommi Duncan, Adriana L. Verbeke, Eric J. Kileel, Joe Mathematical Institute University of Oxford OxfordOX2 6GG United Kingdom Department of Mathematics University of Texas at Austin AustinTX78712 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Oden Institute University of Texas at Austin AustinTX78712 United States

We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2n × n matrix storing properly-scaled basis vectors for the common lines between n projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated to the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental *** Codes 90C26, 14Q30 © 2024, CC BY.

关键词： Clustering algorithms

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The total phenolic and flavonoid contents of Aloe vera and Morinda citrifolia extracts as antibacterial material against Pseudomonas aeruginosa

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Materials Today: Proceedings 2023年 72卷 2796-2802页

作者： Royani, Ahmad Hanafi, Muhammad Julistiono, Heddy Manaf, Azwar Postgraduate Program of Materials Science Study Department of Physics Faculty of Mathematics and Natural Sciences Universitas Indonesia Depok 16424 Indonesia Research Center for Metallurgy National Research and Innovation Agency Puspiptek Area Tangerang Selatan 15314 Indonesia Research Center for Raw Material of Medicine and Traditional Medicine National Research and Innovation Agency Puspiptek Area Tangerang Selatan 15314 Indonesia Research Center for Applied Microbiology National Research and Innovation Agency Jl. Raya Bogor Km. 46 Cibinong Science Center Cibinong 16911 Indonesia

Pseudomonas aeruginosa is a pioneer bacterium initiating the biofilm formation process so that it is corrosive to some metals in the marine environment. One of the efforts to prevent and control corrosion due to environmentally friendly biofilms is using green biocides. The extraction of Aloe vera and Morinda citrifolia with methanol were carried out to obtain antibacterial material. The extract of those plants with multilevel maceration method. The study aimed to identify the total phenolic and flavonoid contents in A. vera and M. citrifolia crude extracts and compare the two antibacterial extract activities. The total phenolic and flavonoid contents were analyzed using the Folin-Ciocalteu and the aluminum chloride colorimetric methods. The antibacterial activity against P. aeruginosa was conducted using the microdilution method to determine the minimum inhibitory concentration (MIC). The structure of the bioactive components of both A. vera and M. citrifolia extracts were identified using a liquid chromatography-mass spectrometer (LC/MS-MS). The MIC of A. vera and M. citrifolia for P. aeruginosa bacteria is about 6144 µg/mL, while the MIC of antibiotic Enrofloxacin is 16 µg/mL. The mean of total phenolic and flavonoid contents for the methanolic extracts of A. vera and M. citrifolia were 1.39% and 4.03% (phenolic), and 0.26% and 0.28% (flavonoids), respectively. The chemical structure of A. vera consists of 2″-O-Feruloylaloesin, Kaempferol-3-O-rutinoside, and Natsudaidain. At the same time, the chemical structure of M. citrifolia consists of 7-Hydroxy-Methoxycoumarin and Cirsiumaldehyde. A. vera and M. citrifolia crude extracts had lower inhibition than antibacterial control (Enrofloxacin) for P. aeruginosa. The lower bacteria inhibition was due to the low active materials (phenolic and flavonoid contents). So, the purification methods of crude extracts to obtain active materials with high antibacterial activity were needed. © 2022

关键词： Bacteria

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