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ON THE STABILITY OF POSITIVE SEMIGROUPS

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arXiv 2021年

作者： Del Moral, Pierre Horton, Emma Jasra, Ajay Centre de Recherche Inria Bordeaux Sud-Ouest Talence 33405 France Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science & Technology Building 1 Thuwal23955-6900 Saudi Arabia

The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V -norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to a class of time-varying positive semigroups. In the context of time-homogeneous models, the regularity conditions discussed in the present article appear to be necessary and sufficient condition for the existence of leading eigenvalues. We review and illustrate the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and signal processing. Copyright © 2021, The Authors. All rights reserved.

关键词： Banach spaces

Fault Diagnosis of Wind Energy Conversion Systems Using Gaussian Process Regression-based Multi-Class Random Forest

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IFAC-PapersOnLine 2022年第6期55卷 127-132页

作者： Majdi Mansouri Radhia Fezai Mohamed Trabelsi Hajji Mansour Hazem Nounou Mohamed Nounou Electrical and Computer Engineering Program Texas A&M University at Qatar Doha Qatar Department of Mathematics and Sciences Prince Sultan University Riyadh 11586 Saudi Arabia Research Laboratory of Automation Signal Processing and Image National Engineering School of Monastir 5019 Tunisia Electronic and Communications Engineering Department Kuwait College of Science and Technology P. O. Box 27235 Kuwait Higher Institute of Applied Science and Technology of Kasserine University of Kairouan PO Box 471 1200 Kasserine Tunisia Chemical Engineering Program Texas A&M University at Qatar Doha Qatar

This work proposes a new fault diagnosis approach for a wind energy conversion (WEC) system. The proposed technique merges the benefits of feature extraction based on Gaussian Process Regression (GPR) and Multi-Class Random Forest (MCRF)-based fault classification where instances are classified into one or more classes. In the developed GPR-MCRF approach, the nonlinear statistical features including the mean vector M GPR and the variance matrix C GPR are computed using the GPR model with aim of extracting the most relevant features from the WEC system. Then, these features are introduced to the RF classifier for classification and diagnosis purposes. Therefore, the application of the GPR-MCRF technique for WEC systems aims to enhance the use of the classical raw data-based MCRF and diagnosis accuracy. Three kinds of faults (wear-out, open-circuit, and short-circuit faults) are considered in this work. Different case studies are investigated in order to illustrate the effectiveness and robustness of the developed technique compared to the state-of-the-art methods. The obtained results show that the the developed GPR-MCRF technique is an effective feature extraction and fault diagnosis technique for WEC systems.

关键词： Random Forest (RF) Multi-Class Gaussian Process Regression (GPR) Fault Diagnosis Wind Energy Conversion Systems

ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

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

Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning

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arXiv 2020年

作者： Weinan, E. Han, Jiequn Jentzen, Arnulf Department of Mathematics Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Faculty of Mathematics and Computer Science University of Münster Germany

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are potentially free of the curse of dimensionality for many different applications and have been proven to be so in the case of some nonlinear Monte Carlo methods for nonlinear parabolic PDEs. In this paper, we review these numerical and theoretical advances. In addition to algorithms based on stochastic reformulations of the original problem, such as the multilevel Picard iteration and the Deep BSDE method, we also discuss algorithms based on the more traditional Ritz, Galerkin, and least square formulations. We hope to demonstrate to the reader that studying PDEs as well as control and variational problems in very high dimensions might very well be among the most promising new directions in mathematics and scientific computing in the near *** Codes 65C05, 65K10, 65M75, 90C06 Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods

DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

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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

Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit

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Open Journal of Modelling and Simulation 2021年第2期9卷 159-171页

作者： Camila de Andrade Kalil Maria Clícia Stelling de Castro Dilson Silva Célia Martins Cortez Postgraduate Program in Computational Sciences Rio de Janeiro State University Rio de Janeiro Brazil Department of Informatics and Computer Science Rio de Janeiro State University Rio de Janeiro Brazil Department of Applied Mathematics Rio de Janeiro State University Rio de Janeiro Brazil

The aim of the present study is to contribute to the knowledge about the functioning of the neuronal circuits. We built a mathematical-computational model using graph theory for a complex neurophysiological circuit consisting of a reverberating neuronal circuit and a parallel neuronal circuit, which could be coupled. Implementing our model in C++ and applying neurophysiological values found in the literature, we studied the discharge pattern of the reverberant circuit and the parallel circuit separately for the same input signal pattern, examining the influence of the refractory period and the synaptic delay on the respective output signal patterns. Then, the same study was performed for the complete circuit, in which the two circuits were coupled, and the parallel circuit could then influence the functioning of the reverberant. The results showed that the refractory period played an important role in forming the pattern of the output spectrum of a reverberating circuit. The inhibitory action of the parallel circuit was able to regulate the reverberation frequency, suggesting that parallel circuits may be involved in the control of reverberation circuits related to motive activities underlying precision tasks and perhaps underlying neural work processes and immediate memories.

关键词： Mathematical-Computational Modelling Neurophysiological Circuit Reverberating Circuit Parallel Circuit

The Smart Analysis of Performing Scalable Inference for Big Data Analytics

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

International Conference on Power Energy, Environment and Intelligent Control (PEEIC)

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

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..

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Prediction and Prevention of Pandemics via Graphical Model Inference and Convex programming

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arXiv 2021年

作者： Krechetov, Mikhail Sikaroudi, Amir Mohammad Esmaieeli Efrat, Alon Polishchuk, Valentin Chertkov, Michael Skolkovo Institute of Science and Technology Moscow121205 Russia University of Arizona Department of Computer Science TucsonAZ85721 United States University of Arizona Program in Applied Mathematics TucsonAZ85721 United States Linköping Univeristy Communications and Transport Systems Norrkoping60174 Sweden University of Arizona Department of Mathematics TucsonAZ85721 United States

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge: assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g. any N of possible single node infections, any N(N-1)=2 of possible two node infections, etc, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census tract and each edge factor represents the strength of the pairwise interaction between a pair of nodes, e.g. representing the inter-node travel, road closure and related, and each local bias/field represents the community level of immunization, acceptance of the social distance and mask wearing practice, etc. Resolving the Inference Challenge requires finding the Maximum-A-Posteriory (MAP), i.e. most probable, state of the Ising Model constrained to the set of initially infected nodes. (An infected node is in the +1 state and a node which remained safe is in the-1 state.) We show that almost all attractive Ising Models on dense graphs result in either of the two possibilities (modes) for the MAP state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected (susceptible). This bi-modal solution of the Inference Challenge allows us to re-sta

关键词： Ising model