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Efficient Power Transfer via Induced Virtual Critical Coupling in an Overcoupled Silicon Nitride Microresonator

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Efficient Power Transfer via Induced Virtual Critical Coupli...

2023 Conference on Lasers and Electro-Optics, CLEO 2023

作者： Hinney, Jakob Kim, Seunghwi Flatt, Graydon J.K. Datta, Ipshita Alii, Andrea Lipson, Michal Department of Electrical Engineering Columbia University New YorkNY10027 United States Photonics Advanced Science Research Catm City University of New Yor New YorkNY10031 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Physics Program Graduate Center City University of New York New YorkNY10016 United States

We induce virtual critical coupling in an overcoupled photonic microresonator using complex-frequency pulses. We observe efficient cavity storage as an incident pulse of time constant 138 ps suppresses the resonant tr... 详细信息

ISBN: (纸本)9781957171258

关键词： Microresonators

Dermatological Diagnostics: A Unified Deep Learning Framework for Skin Lesion and Cancer Classification 1

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Dermatological Diagnostics: A Unified Deep Learning Framewor...

1st IEEE International Conference on Advances in Computing, Communication and Networking, ICAC2N 2024

作者： Kumar, Vinod Jain, Isha Dongla, Durga Sritha Rai, Shivangi Rastogi, Vani Kaushik, Eva Kaushik, Rohit George Washington University School of Engineering and Applied Science WashingtonDC United States Dr. Akhilesh Das Gupta Institute of Technology and Management Computer Science and Engineering Department New Delhi India Gandhi Institute of Technology and Management Computer Science and Engineering Department Andhra Pradesh Visakhapatnam India Data Scientist DXC Technology Noida India Data Analytics Program University of Illinois CS and Mathematics Department Springfield United States

ISBN: (纸本)9798350356816

Skin pathologies encompass a spectrum of conditions, with malignancies such as melanoma representing a critical diagnostic urgency. This investigation delineates the deployment of Convolutional Neural Networks (CNNs) for the classification of dermatological anomalies, benchmarking CNN diagnostic fidelity against dermatological expert evaluations. The study underscores the efficacy of CNN classifiers in expediting the diagnostic workflow for various cutaneous disorders. Advocating for an automated diagnostic framework, the research introduces a CNN-based system aimed at reducing human diagnostic load, accelerating diagnostic timelines, and enhancing survival outcomes. Utilizing advanced image processing algorithms and deep learning architectures, the research presents an automated classification system for skin pathologies, addressing both benign and malignant presentations. The classification matrix includes nine dermatological conditions: actinic keratosis, basal cell carcinoma, benign keratosis, dermatofibroma, melanoma, nevus, seborrheic keratosis, squamous cell carcinoma, and vascular lesions. The objective is to engineer a CNN model with robust diagnostic performance across a diverse lesion dataset, ensuring accurate identification and categorization of dermatological conditions. © 2024 IEEE.

关键词： Convolutional neural networks

Evaluating COVID-19 Surveillance Testing Strategies at Colorado School of Mines: A Stochastic Modeling Approach

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arXiv 2024年

作者： Albrecht, Laura Leiderman, Karin Sindi, Suzanne S. Nychka, Douglas Applied Mathematics and Statistics Department Colorado School of Mines GoldenCO United States Mathematics Department University of North Carolina Chapel Hill Chapel HillNC United States UNC Blood Research Center University of North Carolina Chapel Hill Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel Hill Chapel HillNC United States Department of Applied Mathematics University of California Merced MercedCA United States

This study introduces a stochastic model of COVID-19 transmission tailored to the Colorado School of Mines campus and evaluates surveillance testing strategies within a university context. Enhancing the conventional SEIR framework with stochastic transitions, our model accounts for the unique characteristics of disease spread in a residential college, including specific states for testing, quarantine, and isolation. Employing an approximate Bayesian computation (ABC) method for parameter estimation, we navigate the complexities inherent in stochastic models, enabling an accurate fit of the model with the campus case data. We then studied our model under the estimated parameters to evaluate the efficacy of different testing policies that could be implemented on a university campus. This framework not only advances understanding of COVID-19 dynamics on the Mines campus but serves as a blueprint for comparable settings, providing insights for informed strategies against infectious diseases. © 2024, CC BY.

关键词： COVID-19

Machine learning from a continuous viewpoint,I

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Science China mathematics 2020年第11期63卷 2233-2266页

作者： Weinan E Chao Ma Lei Wu Department of Mathematics Princeton UniversityPrincetonNJ 08544USA The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Beijing Institute of Big Data Research Beijing 100871China

We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous *** also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous *** discuss how the issues of generalization error and implicit regularization can be studied under this framework.

关键词： machine learning continuous formulation flow-based model gradient flow particle approximation

STEFAN PROBLEM WITH SURFACE TENSION: GLOBAL EXISTENCE OF PHYSICAL SOLUTIONS UNDER RADIAL SYMMETRY

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arXiv 2022年

作者： Nadtochiy, Sergey Shkolnikov, Mykhaylo Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States ORFE Department Bendheim Center for Finance Program in Applied & Computational Mathematics Princeton University Princeton NJ08544 United States

We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the initial data we introduce a novel "probabilistic" notion of solution, which can accommodate the discontinuities in time (of the radius) of the evolving aggregate. Our main result establishes the global existence of a probabilistic solution satisfying the natural upper bound on the sizes of the discontinuities. Moreover, we prove that the upper bound is sharp in dimensions d ⩾ 3, in the sense that none of the discontinuities in the solution can be decreased in magnitude. The detailed analysis of the discontinuities, via appropriate stochastic representations, differentiates this work from the previous literature on weak solutions to the Stefan problem with surface *** Codes 80A22, 60H30, 35B44 Copyright © 2022, The Authors. All rights reserved.

关键词： Surface tension

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Physical Review Research 2023年第3期5卷 033020-033020页

作者： Megan Stickler William Ott Zachary P. Kilpatrick Krešimir Josić Bhargav R. Karamched Department of Mathematics University of Houston Houston Texas 77004 USA Department of Applied Mathematics University of Colorado Boulder Boulder Colorado 80309 USA Department of Biology and Biochemistry University of Houston Houston Texas 77004 USA Department of Mathematics Florida State University Tallahassee Florida 32306 USA Institute of Molecular Biophysics Florida State University Tallahassee Florida 32306 USA Program in Neuroscience Florida State University Tallahassee Florida 32306 USA

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. The first decider is less accurate than a lone observer, and 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 macroscopic 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 results in only a 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 decisions.

关键词： Social systems Decision making models Diffusion & random walks Markovian processes Stochastic analysis Stochastic differential equations

On the Ψ−Second Level Fractional Derivative

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SSRN

SSRN 2024年

作者： Bany-Ahmad, Rami Mohammad Ibrahim, Alawiah Noorani, Mohd Salmi Md. Abdeljawad, Thabet Department of Mathematical Sciences Faculty of Science and Technology University Kebangsaan Malaysia Selangor Bangi43600 Malaysia University Preparatory Program Dar Al Uloom University Riyadh Saudi Arabia Department of Mathematics and Sciences Prince Sultan University Riyadh Saudi Arabia Department of Medical Research China Medical University Taichung40402 Taiwan Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Medusa Garankuwa0204 South Africa Department of Mathematics Kyung Hee University 26 Kyungheedae-ro Dongdaemun-gu Seoul02447 Korea Republic of

In this article, we create another novel parametrization for the ψ−Hilfer fractional derivative, which can be easier to apply in some cases and cover the gaps between these concepts. Additionally, we unveil the most comprehensive variant of the second-level fractional derivative with respect to another function, so-called ψ−second level fractional derivative. Furthermore, we establish a comprehensive generalization termed as ψ−mth level FDs for the mth compositions of the nth−order derivative. Moreover, we obtain the remarkable derivatives that are widely studied, like ψ−Riemann Liouville, ψ−Caputo, and ψ−Hilfer fractional derivatives, which emerge as special cases of the transformative ψ−second level fractional derivative. Finally, the intricate interconnections between these derivatives across various parameter values and spaces are thoroughly explored, shedding light on some of their fundamental properties. © 2024, The Authors. All rights reserved.

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Unbiased Parameter Estimation for Bayesian Inverse Problems

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China 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

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

Existence and Stability of Nonequilibrium Steady States of Nernst-Planck-Navier-Stokes Systems

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arXiv 2022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

MSC Codes 35Q30, 35Q35, 35Q92We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of Rd, d = 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state solutions and present a sufficient condition in terms of only the boundary data that guarantees that these solutions have nonzero fluid velocity. We show that time evolving solutions are ultimately bounded uniformly, independently of their initial size. In addition, we consider one dimensional steady states with steady nonzero currents and show that they are globally nonlinearly stable as solutions in a three dimensional periodic strip, if the currents are sufficiently weak. © 2022, CC BY.

关键词： Navier Stokes equations