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arXiv 2021年

作者： Sahneh, Faryad Darabi Fries, William Watkins, Joseph C. Lega, Joceline Department of Mathematics University of Arizona United States Interdisciplinary Program in Applied Mathematics University of Arizona United States Department of Epidemiology and Biostatistics University of Arizona United States BIO5 Institute University of Arizona TucsonAZ85721 United States

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic SIR (Susceptible, Infected, Recovered) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona. Copyright © 2021, The Authors. All rights reserved.

关键词： COVID-19

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From Dyson models to many-body quantum chaos

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Physical Review B 2025年第3期111卷 035147-035147页

作者： Alexei Andreanov Matteo Carrega Jeff Murugan Jan Olle Dario Rosa Ruth Shir Center for Theoretical Physics of Complex Systems Institute for Basic Science (IBS) Daejeon 34126 Korea Basic Science Program Korea University of Science and Technology (UST) Daejeon 34113 Korea CNR-SPIN Via Dodecaneso 33 16146 Genova Italy The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town 7701 South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland 7602 South Africa Max Planck Institute for the Science of Light 91058 Erlangen Germany ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP—University of Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Department of Physics and Materials Science University of Luxembourg L-1511 Luxembourg Luxembourg

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

关键词： Quantum chaos

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Cross-system biological image quality enhancement based on the generative adversarial network as a foundation for establishing a multi-institute microscopy cooperative network

arXiv

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arXiv 2024年

作者： Panek, Dominik Rząca, Carina Szczypior, Maksymilian Sorysz, Joanna Misztal, Krzysztof Baster, Zbigniew Rajfur, Zenon Doctoral School of Exact and Natural Sciences Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland Department of Molecular and Interfacial Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate Program in Biophysics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30‑348 Poland Undergraduate program in Biomedical Engineering Faculty of Electrical Engineering Automatics Computer Science and Biomedical Engineering AGH University of Science and Technology Al. A. Mickiewicza 30 Building B-1 Kraków30-059 Poland Division of Computational Mathematics Faculty of Mathematics and Computer Science Jagiellonian University 6 Lojasiewicza St. Kraków Poland

High-quality fluorescence imaging of biological systems is limited by processes like photobleaching and phototoxicity, and also in many cases, by limited access to the latest generations of microscopes. Moreover, low temporal resolution can lead to a motion blur effect in living systems. Our work presents a deep learning (DL) generative-adversarial approach to the problem of obtaining high-quality (HQ) images based on their low-quality (LQ) equivalents. We propose a generative-adversarial network (GAN) for contrast transfer between two different separate microscopy systems: a confocal microscope (producing HQ images) and a wide-field fluorescence microscope (producing LQ images). Our model proves that such transfer is possible, allowing us to receive HQ-generated images characterized by low mean squared error (MSE) values, high structural similarity index (SSIM), and high peak signal-to-noise ratio (PSNR) values. For our best model in the case of comparing HQ-generated images and HQ-ground truth images, the median values of the metrics are 6·10-4, 0.9413, and 31.87, for MSE, SSIM, and PSNR, respectively. In contrast, in the case of comparison between LQ and HQ ground truth median values of the metrics are equal to 0.0071, 0.8304, and 21.48 for MSE, SSIM, and PSNR respectively. Therefore, we observe a significant increase ranging from 14% to 49% for SSIM and PSNR respectively. These results, together with other single-system cross-modality studies, provide proof of concept for further implementation of a cross-system biological image quality enhancement. © 2024, CC BY-SA.

关键词： Fluorescence imaging

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Unbiased Estimation Using a Class of Diffusion Processes

SSRN

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SSRN 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

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DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

arXiv

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arXiv 2022年

作者： Bhaskar, Dhananjay MacDonald, Kincaid Fasina, Oluwadamilola Thomas, Dawson Rieck, Bastian Adelstein, Ian Krishnaswamy, Smita Department of Genetics Yale School of Medicine New HavenCT United States Department of Mathematics Yale University New HavenCT United States Program for Applied Mathematics Yale University New HavenCT United States Department of Physics Yale University New HavenCT United States Institute of AI for Health Helmholtz Pioneer Campus Munich Germany Department of Computer Science Yale University New HavenCT United States Program for Computational Biology and Bioinformatics Yale University New HavenCT United States

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes. © 2022, CC BY.

关键词： Geometry

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The quenching-activation behavior of the gradient descent dynamics for two-layer neural network models

arXiv

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arXiv 2020年

作者： Ma, Chao Wu, Lei Weinan, E. Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Institute of Big Data Research

A numerical and phenomenological study of the gradient descent (GD) algorithm for training two-layer neural network models is carried out for different parameter regimes when the target function can be accurately approximated by a relatively small number of neurons. It is found that for Xavier-like initialization, there are two distinctive phases in the dynamic behavior of GD in the under-parametrized regime: An early phase in which the GD dynamics follows closely that of the corresponding random feature model and the neurons are effectively quenched, followed by a late phase in which the neurons are divided into two groups: a group of a few "activated" neurons that dominate the dynamics and a group of background (or "quenched") neurons that support the continued activation and deactivation process. This neural network-like behavior is continued into the mildly over-parametrized regime, where it undergoes a transition to a random feature-like behavior. The quenching-activation process seems to provide a clear mechanism for "implicit regularization". This is qualitatively different from the dynamics associated with the "mean-field" scaling where all neurons participate equally and there does not appear to be qualitative changes when the network parameters are changed. Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

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Machine learning of microstructure–property relationships in materials leveraging microstructure representation from foundational vision transformers

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Acta Materialia 2025年

作者： Sheila E. Whitman Marat I. Latypov Graduate Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ 85721 USA Department of Materials Science and Engineering University of Arizona Tucson AZ 85721 USA

Machine learning of microstructure–property relationships from data is an emerging approach in computational materials science. Most existing machine learning efforts focus on the development of task-specific models for each microstructure–property relationship. We propose utilizing pre-trained foundational vision transformers for the extraction of task-agnostic microstructure features and subsequent light-weight machine learning of a microstructure-dependent property. We demonstrate our approach with pre-trained state-of-the-art vision transformers (CLIP, DINOv2, SAM) in two case studies on machine-learning: (i) elastic modulus of two-phase microstructures based on simulations data; and (ii) Vicker’s hardness of Ni-base and Co-base superalloys based on experimental data published in literature. Our results show the potential of foundational vision transformers for robust microstructure representation and efficient machine learning of microstructure–property relationships without the need for expensive task-specific training or fine-tuning of bespoke deep learning models.

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Uniqueness of weak solutions to the primitive equations in some anisotropic spaces

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Journal of Differential Equations 2025年 444卷

作者： Tim Binz Yoshiki Iida Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road Princeton 08544 NJ the United States of America Department of Pure and Applied Mathematics Graduate School of Fundamental Science and Engineering Waseda University Okubo 3-4-1 Shinjuku-ku Tokyo 169-8555 Japan

We consider the both 3D and 2D viscous primitive equations for ocean in the isothermal setting. While strong global well-posedness of the viscous primitive equations for large data in H 1 has already proved, the uniqueness of the weak solutions of Leray–Hope type for given initial data in L 2 remains an outstanding open problem. In this paper, we establish a new conditional uniqueness result for weak solutions to the primitive equations, that is, if a weak solution belongs some scaling invariant function spaces, and satisfies some additional assumptions, then the weak solution is unique. In particular, our result can be obtained as different one from z -weak solutions framework by adopting some anisotropic approaches with the homogeneous toroidal Besov spaces. As an application of the proof, we establish the energy equality for weak solutions in the uniqueness class given in the main theorem.

关键词： 35Q86 35K59 86A05 86A10 35Q35 Primitive equations Conditional uniqueness Anisotropic spaces Besov spaces Scaling invariance

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Identification of fishing ground hotspot of traditional purse seine fisher at northern waters of Aceh - A community-based data collection approach 1

Identification of fishing ground hotspot of traditional purs...

引用

1st International and National Symposium on Aquatic Environment and Fisheries, INSAEF 2020

作者： Haridhi, H.A. Rizal, S. Nanda, M. Muhammad Wilson, C.R. Department of Marine Sciences Faculty of Marine and Fisheries Syiah Kuala University Banda Aceh Indonesia Marine and Fisheries Research Center Syiah Kuala University Banda Aceh Indonesia Doctoral Program of Mathematics and Applied Science Graduate School Syiah Kuala University Banda Aceh Indonesia Asian Development Bank Mandaluyong Philippines

Fishing grounds are among the most important key of information kept by the fishermen. Understanding the fishing ground locations are considered important as an evaluation of the fishing effort being reached by the fishermen as well as understanding the pressure being received to the fish stock at the surrounding water. The recent study has shown that a community-based data collection approach was found successful in recording and analyzing the fishing ground locations and its properties. One of the few projects implementing this concept is the Community-Based Bathymetric Survey (CBBS), which was realized by the Body of Rehabilitation and Reconstruction (BRR) Nanggroe Aceh Darussalam (NAD) - Nias with funding from the Asian Development Bank (ADB). As many as 151 GPS-transducer recording devices were installed to the fishermen boats along the coast of Aceh, with 45 devices were installed to the traditional purse seine fisher at the northern water of Aceh. These devices were configured to automatically record locations each time the boat moved 30 m. Other important information, such as water depth, time, speed, and sea surface temperature (SST) were recorded as well. This study aims to examine the fishing ground and its fishing hotspot of the traditional purse seine fisher in the northern waters of Aceh. The data collection was performed between June 2007 and May 2009 and gathered as many as 922 data sets consist of 6,170,648 data points, from the 45 purse seine boats. Trough the data, we are able to identify the typical fishing activities of purse seiner and as many as 1,619 data points were being detected. The results indicate that there are five main regions of the fishing ground hotspot in the northern waters of Aceh, i.e. 1. Western offshore of Lhok Nga, 2. Northern offshore of Ulee Lheue, 3. Western offshore of Aceh Islands, 4. Eastern offshore of Aceh Island, and 5. Northern offshore of Krueng Raya. Among the fishing ground hotspot analyzed, the Western offshor

关键词： Location

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Fast principal component analysis for cryo-electron microscopy images

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Biological imaging 2023年 3卷 e2-e2页

作者： Nicholas F Marshall Oscar Mickelin Yunpeng Shi Amit Singer Department of Mathematics Oregon State University Corvallis Oregon 97331 USA. Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA. Department of Mathematics Princeton University Princeton New Jersey 08544 USA.

Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For images of size × , our method has time complexity ( + ) and space complexity ( + ). In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

关键词： Covariance estimation Fourier–Bessel cryo-EM denoising principal component analysis single particle reconstruction

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