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Correlations in interacting electron liquids: Many-body statistics and hyperuniformity

Physical Review B 2024年第10期110卷 104201页

作者： Haina Wang Rhine Samajdar Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Materials Institute Program in Applied and Computational Mathematics

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple

关键词： Electronic structure Quantum many-body systems Two-dimensional electron gas

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Developing a mathematics Curriculum for the Biosciences

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PRIMUS 2022年第2期32卷 218-245页

作者： Gordon, Sheldon P. Gross, Sarah Bahamonde, Matthew Winn, Jack Seifert, Jessica Martin, Carla A. Yang, Yajun Farmingdale State College United States American Jewish University United States Applied Mathematics Program United States

This article describes the authors’ experiences developing and implementing an innovative curriculum connecting mathematics and the biological sciences. It describes the original plan, the modifications that were necessary, and some advice to readers who might want to develop comparable programs. © 2021 Taylor & Francis Group, LLC.

关键词： mathematics and biology education

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Essentially Commuting with a Unitary

arXiv

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arXiv 2025年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with R and obey a non-triviality condition, and prove it is bijective with Z. Copyright © 2025, The Authors. All rights reserved.

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Image-processing methods for electron microscopy of biological specimens

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Acta Crystallographica Section D: Structural Biology 2025年第Pt 6期81卷 276-277页

作者： Sorzano, Carlos Oscar S. Bartesaghi, Alberto Singer, Amit Centro Nacional de Biotecnología-CSIC C/Darwin 3 Cantoblanco Madrid 28049 Spain Department of Biochemistry Duke University School of Medicine Durham 27708 NC United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton 08540 NJ United States

The focused issue on Image-processing methods for electron microscopy of biological specimens is introduced. The virtual issue is available at https://***/special_issues/2025/imageprocessing .

关键词： electron microscopy image processing

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Novel Scheme for Robust Confusion Component Selection Based on Pythagorean Fuzzy Set

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Computers, Materials & Continua 2023年第3期74卷 6523-6534页

作者： Nabilah Abughazalah Mohsin Iqbal Majid Khan Iqtadar Hussain Department of Mathematical Sciences College of SciencePrincess Nourah bint Abdulrahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia Department of Mathematics&Statistics Riphah International UniversityIslamabadPakistan Department of Applied Mathematics&Statistics Institute of Space TechnologyIslamabadPakistan Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar Statistical Consulting Unit College of Arts and ScienceQatar UniversityDohaQatar

The substitution box,often known as an S-box,is a nonlinear component that is a part of several block *** purpose is to protect cryptographic algorithms from a variety of cryptanalytic assaults.A Multi-Criteria Decision Making(MCDM)problem has a complex selection procedure because of having many options and criteria to choose *** of this,statistical methods are necessary to assess the performance score of each S-box and decide which option is the best one available based on this *** the Pythagorean Fuzzy-based Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS)method,the major objective of this investigation is to select the optimal S-box to be implemented from a pool of twelve key *** the help of the Pythagorean fuzzy set(PFS),the purpose of this article is to evaluate whether this nonlinear component is suitable for use in a variety of encryption *** this article,we have considered various characteristics of S-boxes,including nonlinearity,algebraic degree,strict avalanche criterion(SAC),absolute indicator,bit independent criterion(BIC),sum of square indicator,algebraic immunity,transparency order,robustness to differential cryptanalysis,composite algebraic immunity,signal to noise ratio-differential power attack(SNR-DPA),and confusion coefficient variance on some standard S-boxes that are Advanced Encryption Following this,the findings of the investigation are changed into Pythagorean fuzzy numbers in the shape of a *** matrix is then subjected to an analysis using the TOPSIS method,which is dependent on the Pythagorean fuzzy set,to rank the most suitable S-box for use in encryption applications.

关键词： Decision making substitution box TOPSIS multi-criterion decision making fuzzy set Pythagorean fuzzy set

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A Flow Artist for High-Dimensional Cellular Data 33

A Flow Artist for High-Dimensional Cellular Data

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33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023

作者： MacDonald, Kincaid Bhaskar, Dhananjay Thampakkul, Guy Nguyen, Nhi Zhang, Joia Perlmutter, Michael Adelstein, Ian Krishnaswamy, Smita Yale University Department of Mathematics United States Pomona College Department of Mathematics United States University of Washington Department of Statistics United States Boise State University Department of Mathematics United States Yale University Department of Computer Science United States Yale University Applied Mathematics Program United States Yale University Computational Biology and Bioinformatics Program United States

ISBN: (纸本)9798350324112

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data. © 2023 IEEE.

关键词： RNA

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Local order metrics for many-particle systems across length scales

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Physical Review Research 2024年第3期6卷 033262页

作者： Charles Emmett Maher Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

关键词： Classical statistical mechanics

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Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality

arXiv

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arXiv 2024年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this abstract characterization, we define generalizations of this locality, which we term quasi-2D. We go on to calculate the path-connected components of spaces of unitaries or orthogonal projections which are quasi-2D-local and find a starkly different behavior compared with the actual 2D column of the Kitaev table, exhibiting e.g., in the unitary chiral case, infinitely many Z-valued indices. Copyright © 2024, The Authors. All rights reserved.

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An Ant Colony Algorithm Approach to the Vehicle Routing Problem and Variants

An Ant Colony Algorithm Approach to the Vehicle Routing Prob...

引用

IEEE Symposium on Systems and Information Engineering Design, SIEDS

作者： Tulio Tablada Cleon Davis Neil Palumbo Applied and Computational Mathematics Program Johns Hopkins University Electrical and Computer Engineering Program Johns Hopkins University

ISBN: (数字)9798350385144

ISBN: (纸本)9798350385151

In the basic vehicle routing problem (VRP), a vehicle must deliver goods from one centralized warehouse to multiple customers efficiently. Several VRP variants and constraints exist, including different product types, specific delivery times, multiple warehouses, vehicle fuel constraints, and pick-up from one location and delivery to another. This work proposes and demonstrates a flexible algorithm for solving the VRP via ant colony optimization (ACO) that can address many of the variants discussed above. ACO algorithms mimic the behavior of ants, learning optimal paths to a food source and back to the nest based on stigmergic behavior. This work compares a proposed, more flexible ACO algorithm to a traditional optimization algorithm that is implemented in the Google VRP solver. Readily available data were used to test and demonstrate results. Several VRP variants were implemented in both the (proposed) flexible ACO algorithm and the Google VRP solver. The flexible ACO algorithm performed better in terms of distance traveled versus the Google VRP solver for two variants and worse for three other cases. However, the Google VRP solver was not able to solve some of the VRP variant combinations considered here and failed when solving some backhaul datasets. Because the flexible ACO algorithm was able to better handle many case variations, it may be an attractive alternative optimization tool.

关键词： Ant colony optimization Vehicle routing Symbols Internet Fuels Optimization Backhaul networks

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Semi-analytical finite element method applied for characterizing micropolar fibrous composites

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applied mathematics and Mechanics(English Edition) 2024年第12期45卷 2147-2164页

作者： J.A.OTERO Y.ESPINOSA-ALMEYDA R.RODRIGUEZ-RAMOS J.MERODIO School of Engineering and Sciences Monterrey Institute of TechnologyEstado de Mexico 52926Mexico Institute of Engineering and Technology Autonomous University of Ciudad JuarezCiudad JuarezChihuahua 32310Mexico Postgraduate Program in Computational Modeling in Science and Technology Federal Fluminense UniversityRıo de Janeiro 27255-125Brazil Faculty of Mathematics and Computer Science University of HavanaLa Habana 10400Cuba Department of Mathematics Applied to ICT School of Informatics Systems EngineeringTechnical University of MadridMadrid 28031Spain

A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.

关键词： semi-analytical approach fiber-reinforced composite(FRC) effective property finite element method(FEM) asymptotic homogenization method(AHM) micropolar elasticity

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