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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

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arXiv 2023年

作者： Beckers, Thomas Seidman, Jacob Perdikaris, Paris Pappas, George J. Department of Electrical and Systems Engineering University of Pennsylvania PhiladelphiaPA19104 United States graduate program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems. © 2023, CC BY-NC-ND.

关键词： Hamiltonians

The existence of the maximum likelihood estimate in multinomial logistic regression for mixed-membership models

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Communications in Statistics - Theory and Methods 2025年

作者： Nwaigwe, Dwight Rychlik, Marek Program in Applied Mathematics The University of Arizona TucsonAZ United States Department of Mathematics The University of Arizona TucsonAZ United States

It is known that the maximum likelihood estimate of a logistic regression model may not exist. Specifically, the maximum likelihood estimate only exists if the dataset is non separable. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset, a type of regularization. This is equivalent to treating logistic regression as a mixed-membership (grade-of-membership) model. © 2025 Taylor & Francis Group, LLC.

关键词： Maximum likelihood estimation

Reconsider photoplethysmogram signal quality assessment in the free living environment

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Physiological Measurement 2024年第6期45卷 06NT01-06NT01页

作者： Su, Yan-Wei Hao, Chia-Cheng Liu, Gi-Ren Sheu, Yuan-Chung Wu, Hau-Tieng Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu Taiwan Data Science Degree Program National Taiwan University Academia Sinica Taipei Taiwan Department of Mathematics National Cheng-Kung University Tainan Taiwan National Center for Theoretical Sciences National Taiwan University Taipei Taiwan Courant Institute of Mathematical Sciences New York University New YorkNY10012 United States

Objective. Assessing signal quality is crucial for biomedical signal processing, yet a precise mathematical model for defining signal quality is often lacking, posing challenges for experts in labeling signal qualities. The situation is even worse in the free living environment. Approach. We propose to model a PPG signal by the adaptive non-harmonic model (ANHM) and apply a decomposition algorithm to explore its structure, based on which we advocate a reconsideration of the concept of signal quality. Main results. We demonstrate the necessity of this reconsideration and highlight the relationship between signal quality and signal decomposition with examples recorded from the free living environment. We also demonstrate that relying on mean and instantaneous heart rates derived from PPG signals labeled as high quality by experts without proper reconsideration might be problematic. Significance. A new method, distinct from visually inspecting the raw PPG signal to assess its quality, is needed. Our proposed ANHM model, combined with advanced signal processing tools, shows potential for establishing a systematic signal decomposition based signal quality assessment model. © 2024 Institute of Physics and Engineering in Medicine.

关键词： free-living environment photoplethysmogram signal quality index synchrosqueezing transform

The Small-World Effect for Interferometer Networks

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arXiv 2023年

作者： Krawciw, Benjamin Carr, Lincoln D. Behn, Cecilia Diniz Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO United States Department of Physics Colorado School of Mines GoldenCO United States Quantum Engineering Program Colorado School of Mines GoldenCO United States

Complex network theory has focused on properties of networks with real-valued edge weights. However, in signal transfer networks, such as those representing the transfer of light across an interferometer, complex-valued edge weights are needed to represent the manipulation of the signal in both magnitude and phase. These complex-valued edge weights introduce interference into the signal transfer, but it is unknown how such interference affects network properties such as small-worldness. To address this gap, we have introduced a small-world interferometer network model with complex-valued edge weights and generalized existing network measures to define the interferometric clustering coefficient, the apparent path length, and the interferometric small-world coefficient. Using high-performance computing resources, we generated a large set of small-world interferometers over a wide range of parameters in system size, nearest-neighbor count, and edge-weight phase and computed their interferometric network measures. We found that the interferometric small-world coefficient depends significantly on the amount of phase on complex-valued edge weights: for small edge-weight phases, constructive interference led to a higher interferometric small-world coefficient;while larger edge-weight phases induced destructive interference which led to a lower interferometric small-world coefficient. Thus, for the small-world interferometer model, interferometric measures are necessary to capture the effect of interference on signal transfer. This model is an example of the type of problem that necessitates interferometric measures, and applies to any wave-based network including quantum networks. Copyright © 2023, The Authors. All rights reserved.

关键词： Interferometers

"Halfway to Rayleigh" and other Insights to the Rossby Wave Instability

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arXiv 2024年

作者： Chang, Eonho Youdin, Andrew N. Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Astronomy Steward Observatory University of Arizona TucsonAZ85721 United States Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States

The Rossby wave instability (RWI) is the fundamental non-axisymmetric radial shear instability in disks. The RWI can facilitate disk accretion, set the shape of planetary gaps and produce large vortices. It arises from density and/or temperature features, such as radial gaps, bumps or steps. A general, sufficient condition to trigger the RWI is lacking, which we address by studying the linear RWI in a suite of simplified models, including incompressible and compressible shearing sheets and global, cylindrical disks. We focus on enthalpy amplitude and width as the fundamental properties of disk features with various shapes. We find analytic results for the RWI boundary and growth rates across a wide parameter space, in some cases with exact derivations and in others as a description of numerical results. Features wider than a scale-height generally become unstable about halfway to Rayleigh instability, i.e. when the squared epicyclic frequency is about half the Keplerian value, reinforcing our previous finding. RWI growth rates approximately scale as enthalpy amplitude to the 1/3 power, with a weak dependence on width, across much of parameter space. Global disk curvature affects wide planetary gaps, making the outer gap edge more susceptible to the RWI. Our simplified models are barotropic and height-integrated, but the main results should carry over to more complex and realistic scenarios. © 2024, CC BY.

关键词： Shear flow

The Smart Analysis of Performing Scalable Inference for Big Data Analytics

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The Smart Analysis of Performing Scalable Inference for Big ...

2023 International Conference on Power Energy, Environment and Intelligent Control, PEEIC 2023

作者： Bhandarkar, Vishakha D. Rongali, Aruna Sri Shamout, Mohamed Dawood Pund, Sachin Nama, Gigih Forda Patil, Shrishailappa Yeshwantrao Chavan College of Engineering Applied Mathematics and Humanities India University of the Cumberlands Graduate Doctoral Information Technology Information Technology Emphasis/Information Technology United States College of Business Administration University of Sharjah Department of Management Sharjah United Arab Emirates Shri Ramdeobaba College of Engineering and Management Department of Industrial Engineering Maharashtra Nagpur India Doctoral Program of Environtmental Science University of Lampung Department of Informatics Bandar Lampung Indonesia Vishwakarma Institute of Technology Computer Engineering Pune India

ISBN: (纸本)9798350357769

This paper examines the reproducibility of massive information analytics under particular factors. The paper proposes the 'performing Scalable Inference' technique to cope with scalability troubles and to exploit current big statistics platforms for efficient computing and statistics garage of the statistics. In particular, the paper describes how to perform leak-free, parallelizable visible analytics over massive datasets using present extensive records analytics frameworks such as Apache Flink. This method presents an automated manner to execute analytics that preserves reproducibility and the ability to make adjustments without re-running the entire technique. The paper also demonstrates how these analytics may help several real-world use instances, explore affected person cohorts for studies, and develop stratified patient cohorts for hospital therapy. In the end, the paper observes how the proposed method may be exercised within the real world. Actively scalable inference for massive information analytics is pivotal in optimizing decision-making and allocation of assets. Typically, such inferences are made based on information accumulated from numerous sources, databases, unstructured data, and different digital sources. So one can ensure scalability, a complete cloud-primarily based platform has to be hired. This solution will permit the ***, deploying the essential records series and evaluation algorithms are prime here. It could permit the platform to recognize the styles inside the statistics and discover any ability correlations or traits. Additionally, predictive analytics and system mastering strategies may be incorporated to provide insights into the results of the information. In the long run, by leveraging those techniques, the platform can draw efficient inferences and appropriately compare situations in an agile and green way.. © 2023 IEEE.

关键词： adjustments an a lytics automated preserves statistics

random graphs by product random measures

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arXiv 2022年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted random graphs, directed or undirected, labeled or unlabeled, where (i) the composition of the test function and transformation is a non-negative edge weight function, (ii) the mean measures encode edge density/weight and vertex degree density/weight, and (iii) the mean edge weight, when square-integrable, encodes generalized spectral and Sobol representations. We develop a number of properties of these random graphs, and we give simple examples of some of their possible *** Codes 60G57, 60G55 © 2022, CC BY-NC-SA.

关键词： Encoding (symbols)

Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold

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arXiv 2025年

作者： Torquato, Salvatore Kim, Jaeuk Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Stealthy interactions are an emerging class of nontrivial, bounded long-ranged oscillatory pair potentials with classical ground states that can be disordered, hyperuniform, and infinitely degenerate. Their hybrid crystal-liquid nature endows them with novel physical properties with advantages over their crystalline counterparts. Here, we show the existence of nonequilibrium hard-sphere glasses within this unusual ground-state manifold as the stealthiness parameter χ tends to zero that are remarkably configurationally extremely close to hyperuniform 3D maximally random jammed (MRJ) sphere packings. The latter are prototypical glasses since they are maximally disordered, perfectly rigid, and perfectly nonergodic. Our optimization procedure, which leverages the maximum cardinality of the infinite ground-state set, not only guarantees that our packings are hyperuniform with the same structure-factor scaling exponent as the MRJ state, but they share other salient structural attributes, including a packing fraction of 0.638, a mean contact number per particle of 6, gap exponent of 0.44(1), and pair correlation functions g2(r) and structures factors S(k) that are virtually identical to one another for all r and k, respectively. Moreover, we demonstrate that stealthy hyperuniform packings can be created within the disordered regime (0 © 2025, CC0.

关键词： Liquid crystals

A field equation for induction-transduction of activation-deactivation probability on measurable space

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arXiv 2022年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Chemistry Princeton University Princeton NJ08544 United States

Induction-transduction of activating-deactivating points are fundamental mechanisms of action that underlie innumerable systems and phenomena, mathematical, natural, and anthropogenic, and can exhibit complex behaviors such as self-excitation, phase transitions, hysteresis, polarization, periodicity, chaos, wave behavior, geometry, and energy transfer. We describe a class of primitives for induction-transduction based on dynamics on images of marked random counting measures under graphical random transformations. We derive a field equation for the law of the activation-deactivation (Bernoulli) process on an arbitrary measurable space and describe some mechanisms of action on the unit *** Codes 37A50, 60G57, 60G60, 60G55 © 2022, CC BY-NC-SA.

关键词： Energy transfer