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arXiv 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 KSA 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 (d, B(d)) 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}tϵ[0,1]on d, d ϵ 0. 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, 16] 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 (which is random) 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 *** Codes 60J60, 62D05, 65C40 © 2022, CC BY.

关键词： Diffusion

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PHYSICS INFORMED MACHINE LEARNING WITH SMOOTHED PARTICLE HYDRODYNAMICS: HIERARCHY OF REDUCED LAGRANGIAN MODELS OF TURBULENCE

arXiv

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arXiv 2021年

作者： Woodward, Michael Tian, Yifeng Hyett, Criston Fryer, Chris Stepanov, Mikhail Livescu, Daniel Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics UArizona TucsonAZ85721 United States Department of Mathematics UArizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division LANL Los AlamosNM87544 United States

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH;and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Parameterization

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On the existence of the maximum likelihood estimate and convergence rate under gradient descent for multi-class logistic regression

arXiv

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arXiv 2020年

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

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The notion of data separability is not needed, which is in contrast to the classical set up of multi-class logistic regression in which each data sample belongs to one class. We also provide a general and constructive estimate of the convergence rate to the maximum likelihood estimate when gradient descent is used as the optimizer. Our estimate involves bounding the condition number of the Hessian of the maximum likelihood function. The approaches used in this article rely on a simple operator-theoretic *** Codes 62J12, 65K10, 47N10 Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

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Optimization production and characterization of fish protein hydrolysate (FPH) from Sardinella Lemuru head with papain protease

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AIP Conference Proceedings 2025年第1期3186卷

作者： Jannatul Firdaus Evi Susanti Suharti Suharti Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Negeri Malang Jl. Semarang 5 Malang 65145 Indonesia Biotechnology Program Department of Applied Science Faculty of Mathematics and Natural Sciences Universitas Negeri Malang Jl. Semarang 5 Malang 65145 Indonesia

Sardinella lemuru head has potential as Fish Protein Hydrolysate (FPH). This study aims to determine the optimum conditions and characterization of FPH from lemuru fish heads produced enzymatically with papain. This study was conducted through the following stages with (1) isolation of crude extract of papain, (2) optimization of papain enzymatic FPH production methods, (3) characterization of FPH including determined of proximate value, FTIR analysis, molecular weight, the antibacterial and antioxidant activity FPH produced from lemuru fish head powder was a short peptide measuring about 25 kDa and less. FPH has water, protein, and fat value of 24.54; 28.76; and 0.224 % (w/w). The resulting yield was at an optimum condition of 18.87% under the following conditions: 1 g of fish head powder was hydrolyzed with 0.705 U papain in 8 mL of phosphate buffer pH 7 0.1 M, incubated for 3 hours at room temperature, continued for 90 minutes at 75°C and at 90°C for 5 minutes. At a concentration of 10,000 ppm, the FPH can inhibit the growth of Escherichia coli bacteria by producing an inhibition zone diameter of 4.537±0.265 and Staphylococcus aureus bacteria by 5.5±0.212 and has an IC50 value to inhibit DPPH free radical oxidation of 70.175 ppm.

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Liquid-Liquid Transition in Water from First Principles

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Physical Review Letters 2022年第25期129卷 255702-255702页

作者： Thomas E. Gartner, III Pablo M. Piaggi Roberto Car Athanassios Z. Panagiotopoulos Pablo G. Debenedetti Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

关键词： Classical statistical mechanics First order phase transitions First-principles calculations Liquid-liquid phase transition Phase transitions Thermodynamics Deep learning Density functional theory Molecular dynamics

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Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order-disorder transitions in LixCoO2

arXiv

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arXiv 2023年

作者： Teichert, G.H. Das, S. Shojaei, M. Faghih Holber, J. Mueller, T. Hung, L. Gavini, V. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Toyota Research Institute Los AltosCA United States Department of Materials Science & Engineering University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States Applied Physics Program University of Michigan United States Materials Science & Engineering Johns Hopkins University United States

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes’ phase evolution in terms of temperature, morphology, charge cycling and particle size. © 2023, CC BY-NC-SA.

关键词： Cathodes

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Convergence of Mass Transfer Particle Tracking Schemes for the Simulation of Advection-Diffusion-Reaction Equations

SSRN

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SSRN 2024年

作者： Pankavich, Stephen D. Schauer, Lucas Schmidt, Michael J. Engdahl, Nicholas B. Bolster, Diogo Benson, David A. Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM87185 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States

Since their introduction, multi-species mass-transfer particle tracking (or MTPT) algorithms have been used to accurately simulate advective and dispersive transport of solutes, even within systems that feature nonlinear chemical reactions. The MTPT methods were originally derived from a probabilistic or first-principles perspective and have previously lacked a more rigorous derivation arising directly from the underlying advection-diffusion-reaction equation (ADRE). Herein, we provide a fully rigorous derivation of the MTPT method as a Lagrangian approximation of solutions to the ADRE, complete with a description of the error and order of accuracy generated by this approximation. Numerical simulations further detail the fidelity of MTPT methods and display parameter regimes wherein the numerical error is independent of the chosen time step, and thereby dependent only upon the numerical discretization of the spatial domain via the number of particles within a simulation. Finally, different normalizations of the local Green's function are shown to generate similar approximations of the underlying solution for stationary particles. © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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Grapenet_Lv1 for the Prediction of Optimum Hand-Picking Time of Nagano Purple Grapes

SSRN

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SSRN 2025年

作者： Islam, Md. Parvez Shinagawa, K. Hatou, K. Abdurrakhman, Arief Dian, K. Department of Biomechanical Systems Faculty of Agriculture Ehime University 3-5-7 Tarumi Matsuyama790-8566 Japan United Graduate School of Agriculture Ehime University 3-5-7 Tarumi Matsuyama790-8566 Japan Department of Instrumentation Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Business Mathematics Program Study School of Applied STEM Universitas Prasetiya Mulya BSD Campus BSD City Kav. Edutown I.1 Tangerang15339 Indonesia Indonesia

We investigated the optimum hand-picking time of Nagano Purple, a rare Japanese table grape variety. The color sensitivity between pure red–purple–black and pure purple–black makes it difficult for farmers to harvest these fruits at the right time while maintaining high sweetness level. We manually extracted 13 color parameters, namely, X, Y, Z, x, y, L*, a*, b*, L, a, b, C*, and h, from 355 grape skin samples using a colorimeter, which is a time-consuming and expensive process. In addition, we developed a 15-layer shallow long short-term memory (LSTM) and bidirectional long short-term memory (BLSTM) neural network, namely, GrapeNet_Lv1, with a learnable parameter of 1.39E+06. This network is compact and requires low computational cost for training. Furthermore, it has the ability to prevent the problems of vanishing gradient and overfitting. The combination of all the 13 aforementioned parameters yielded promising results in predicting color and sweetness levels, with test accuracies of 0.83 and 0.76, respectively. In the prediction of color level, our proposed network GrapeNet_Lv1 achieves a high validation accuracy of 0.92, F1 score of 0.88, recall of 0.87, low validation loss of 0.39, and RMSE of 0.31. However, in the prediction of sweetness level, GrapeNet_Lv1 achieves a relatively low validation accuracy of 0.79, F1 score of 0.70, recall of 0.69, high validation loss of 0.72, and RMSE of 0.33. Further research can help improve the accuracy. GrapeNet_Lv1 can be applied to other crops, where, predicting the whose optimal hand-picking time is difficult to predict based on color recognition. Keywords: Neural network;LSTM-BLSTM;Nagano Purple, color, sweetness © 2025, The Authors. All rights reserved.

关键词： Long short-term memory

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Periodicity Scoring of Time Series Encodes Dynamical Behavior of the Tumor Suppressor p53 ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 488-495页

作者： Caroline Moosmüller Christopher J. Tralie Mahdi Kooshkbaghi Zehor Belkhatir Maryam Pouryahya José Reyes Joseph O. Deasy Allen R. Tannenbaum Ioannis G. Kevrekidis C. Moosmüller and C. Tralie contributed equally to this work Department of Mathematics University of California San Diego La Jolla CA 92093 USA Department of Medical Physics Memorial Sloan-Kettering Cancer Center NY USA Department of Chemical and Biomolecular Engineering Johns Hopkins University Baltimore MD 21218 USA Department of Mathematics and Computer Science Ursinus College Collegeville PA USA Program in Applied and Computational Mathematics Princeton University NJ USA School of Engineering and Sustainable Development De Montfort University Leicester UK Cancer Biology and Genetics Program and Computational and Systems Biology Program Memorial Sloan-Kettering Cancer Center New York NY 10065 USA and Department of Systems Biology Harvard Medical School Boston MA 02115 USA Departments of Computer Science and Applied Mathematics & Statistics Stony Brook University NY USA

In this paper we analyze the dynamical behavior of the tumor suppressor protein p53, an essential player in the cellular stress response, which prevents a cell from dividing if severe DNA damage is present. When this response system is malfunctioning, e.g. due to mutations in p53, uncontrolled cell proliferation may lead to the development of cancer. Understanding the behavior of p53 is thus crucial to prevent its failing. It has been shown in various experiments that periodicity of the p53 signal is one of the main descriptors of its dynamics, and that its pulsing behavior (regular vs. spontaneous) indicates the level and type of cellular stress. In the present work, we introduce an algorithm to score the local periodicity of a given time series (such as the p53 signal), which we call Detrended Autocorrelation Periodicity Scoring (DAPS). It applies pitch detection (via autocorrelation) on sliding windows of the entire time series to describe the overall periodicity by a distribution of localized pitch scores. We apply DAPS to the p53 time series obtained from single cell experiments and establish a correlation between the periodicity scoring of a cell’s p53 signal and the number of cell division events. In particular, we show that high periodicity scoring of p53 is correlated to a low number of cell divisions and vice versa. We show similar results with a more computationally intensive state-of-the-art periodicity scoring algorithm based on topology known as Sw1PerS. This correlation has two major implications: It demonstrates that periodicity scoring of the p53 signal is a good descriptor for cellular stress, and it connects the high variability of p53 periodicity observed in cell populations to the variability in the number of cell division events.

关键词： Systems biology cellular systems time series modeling bioinformatics computational biology

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The concept of a ramjet electric propulsion for a low-orbit spacecraft 2nd

The concept of a ramjet electric propulsion for a low-orbit ...

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2nd IAA/AAS Conference on Space Flight Mechanics and Space Structures and Materials, SciTech Forum 2019

作者： Filatyev, Aleksander S. Gordeev, Sviatoslav V. Khartov, Sergey A. Popov, Garri A. Suvorov, Maksim O. Aerospace Research Program of TsAGI 1 Zhukovsky Str. Moscow Region Zhukovsky140180 Russia Department 13 of RIAME MAI 5 Leningradskoe Shosse Moscow125080 Russia RIAME MAI 5 Leningradskoe Shosse Moscow125080 Russia Keldysh Institute of Applied Mathematics 4 Miusskaya sq. Moscow125047 Russia

ISBN: (纸本)9780877036746

The key problems of developing a ramjet air-breathing electric propulsion operating with overboard atmosphere gases as propellant for a low-orbit spacecraft are considered. The schematic diagram is proposed and the intake device parameters are estimated. The laboratory model of the thrust unit based on the radio-frequency ion thruster is developed and tested. The model showed a steady operation in wide range of values of consumed radio-frequency power and atmosphere gases mass flow. The experimental results were analyzed and the ability of operation of a ramjet air-breathing electric propulsion in conditions corresponding to the spacecraft flight in orbits with altitude of 190-220 km confirmed. © 2021, Univelt Inc. All rights reserved.

关键词： Orbits

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