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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

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

Second-order nonlinear Hall effect in Weyl semimetals

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Physical Review B 2020年第24期102卷 245116-245116页

作者： Yang Gao Furu Zhang Wei Zhang Institute of Applied Physics and Computational Mathematics Beijing 100088 China College of Computer Science and Engineering Anhui University of Science and Technology Huainan 232001 China

We investigate the second-order nonlinear Hall effect of Weyl semimetals using a quantum theory, paying attention to the interband process and quantum interference effect. The Drude-type nonlinear Hall conductivity due to the intraband process is found for each Weyl node in the low-frequency regime (the photon energy of the incident field is much smaller than the chemical potential). While in the high-frequency regime with the interband process dominated, the nonlinear photoconductivity shows a two-photon resonant peak or double peaks due to inversion symmetry breaking. The peak splitting is determined by the chemical potential and tilt of the Weyl node. There is a nonmonotonic dependence of the nonlinear Hall current on the tilt of the Weyl node, and an optimal tilt for the maximum Hall current has been found. Moreover, with the help of quantum interference, the nonlinear Hall response can be effectively modulated by tuning the amplitude, phase, and polarization of the incident fields. In particular, in the presence of driving fields with frequencies ω0 and 3ω0, the interplay between the optical processes of second-harmonic generation and different frequency generation leads to the chirality-selective generation of nonlinear Hall current under suitable conditions.

关键词： Hall effect Optical conductivity Photoconductivity Weyl semimetal Linear response theory

Embedding and trajectories of temporal networks

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arXiv 2022年

作者： Thongprayoon, Chanon Livi, Lorenzo Masuda, Naoki Department of Mathematics State University of New York at Buffalo BuffaloNY United States Department of Computer Science University of Manitoba WinnipegMB Canada Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY United States Faculty of Science and Engineering Waseda University Shinjuku Tokyo Japan

Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to coarse grain temporal network data into a numeric trajectory embedded in a low-dimensional space. We refer to such a procedure as temporal network embedding, which is distinct from procedures that aim at embedding individual nodes. Temporal network embedding is a challenging task because we often have access only to discrete time-stamped events between node pairs, and, in general, the events occur with irregular intervals, making the construction of the network at a given time a nontrivial question already. We propose a method to generate trajectories of temporal networks embedded in a low-dimensional space given a sequence of time-stamped events as input. We realize this goal by combining the landmark multidimensional scaling, which is an out-of-sample extension of the well-known multidimensional scaling method, and the framework of tie-decay temporal networks. This combination enables us to obtain a continuous-time trajectory describing the evolution of temporal networks. We then study mathematical properties of the proposed temporal network embedding framework. Finally, we showcase the method with empirical data of social contacts to find temporal organization of contact events and loss of them over a single day and across different days. © 2022, CC BY.

关键词： Trajectories

Cell2Sentence: teaching large language models the language of biology 24

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Cell2Sentence: teaching large language models the language o...

Proceedings of the 41st International Conference on Machine Learning

作者： Daniel Levine Syed Asad Rizvi Sacha Lévy Nazreen Pallikkavaliyaveetil David Zhang Xingyu Chen Sina Ghadermarzi Ruiming Wu Zihe Zheng Ivan Vrkic Anna Zhong Daphne Raskin Insu Han Antonio Henrique De Oliveira Fonseca Josue Ortega Caro Amin Karbasi Rahul M. Dhodapkar David Van Dijk Department of Computer Science Yale University New Haven CT School of Engineering Applied Science University of Pennsylvania Philadelphia PA School of Computer and Communication Sciences Swiss Federal Institute of Technology Lausanne Lausanne Switzerland Department of Computer Science Yale University New Haven CT and Department of Neuroscience Yale School of Medicine New Haven CT Department of Computer Science Yale University New Haven CT and Department of Neuroscience Yale School of Medicine New Haven CT and Wu Tsai Institute Yale University New Haven CT Google and Yale Institute for Foundations of Data Science New Haven CT and Department of Computer Science Yale University New Haven CT and Yale School of Engineering and Applied Science New Haven CT Roski Eye Institute University of Southern California Los Angeles CA and Department of Internal Medicine (Cardiology) Yale School of Medicine New Haven CT Department of Computer Science Yale University New Haven CT and Yale Institute for Foundations of Data Science New Haven CT and Wu Tsai Institute Yale University New Haven CT and Cardiovascular Research Center Yale School of Medicine New Haven CT and Interdepartmental Program in Computational Biology & Bioinformatics Yale University New Haven CT and Department of Internal Medicine (Cardiology) Yale School of Medicine New Haven CT

We introduce Cell2Sentence (C2S), a novel method to directly adapt large language models to a biological context, specifically single-cell transcriptomics. By transforming gene expression data into "cell sentences," C2S bridges the gap between natural language processing and biology. We demonstrate cell sentences enable the fine-tuning of language models for diverse tasks in biology, including cell generation, complex cell-type annotation, and direct data-driven text generation. Our experiments reveal that GPT-2, when fine-tuned with C2S, can generate biologically valid cells based on cell type inputs, and accurately predict cell types from cell sentences. This illustrates that language models, through C2S fine-tuning, can acquire a significant understanding of single-cell biology while maintaining robust text generation capabilities. C2S offers a flexible, accessible framework to integrate natural language processing with transcriptomics, utilizing existing models and libraries for a wide range of biological applications.

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Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel

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arXiv 2022年

作者： Jiang, Ziyang Zheng, Tongshu Liu, Yiling Carlson, David Department of Civil and Environmental Engineering Duke University United States Division of Natural and Applied Science Duke Kunshan University China Program in Computational Biology and Bioinformatics Duke University School of Medicine United States Department of Civil and Environmental Engineering Department of Biostatistics and Bioinformatics Department of Computer Science Duke University United States

It is challenging to guide neural network (NN) learning with prior knowledge. In contrast, many known properties, such as spatial smoothness or seasonality, are straightforward to model by choosing an appropriate kernel in a Gaussian process (GP). Many deep learning applications could be enhanced by modeling such known properties. For example, convolutional neural networks (CNNs) are frequently used in remote sensing, which is subject to strong seasonal effects. We propose to blend the strengths of NNs and the clear modeling capabilities of GPs by using a composite kernel that combines a kernel implicitly defined by a neural network with a second kernel function chosen to model known properties (e.g., seasonality). We implement this idea by combining a deep network and an efficient mapping function based on either Nyström approximation or random Fourier features, which we call Implicit Composite Kernel (ICK). We then adopt a sample-then-optimize approach to approximate the full GP posterior distribution. We demonstrate that ICK has superior performance and flexibility on both synthetic and real-world datasets including a remote sensing dataset. The ICK framework can be used to include prior information into neural networks in many applications. © 2022, CC BY.

关键词： Remote sensing

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

Beyond trees: classification with sparse pairwise dependencies

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2020年第1期21卷 7728-7760页

作者： Yaniv Tenzer Amit Moscovich Mary Frances Dorn Boaz Nadler Clifford Spiegelman Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ Los Alamos National Laboratory Los Alamos NM Department of Statistics Texas A&M University College Station TX

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.

关键词： binary classification graphical model Bayesian network sparsity semi-parametric

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