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arXiv 2024年

作者： Jin, Xinghu Pang, Guodong Wang, Yu Xu, Lihu School of Mathematics Hefei University of Technology Anhui Hefei230601 China Department of Computational Applied Mathematics and Operations Research George R. Brown School of Engineering Rice University HoustonTX77005 United States Department of Mathematics Faculty of Science and Technology University of Macau Taipa999078 China UM Zhuhai Research Institute Guangdong Zhuhai519000 China

Piecewise α-stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Euler-Maruyama (EM) scheme more difficult to analyze. We develop an EM scheme with decreasing step size Λ = (ηn)n∈N to approximate their ergodic measures. This approximation does not have a bias and has a rate ηn1/α in Wasserstein-1 distance. We show by the classical OU process that our convergence rate is optimal. We further prove the central limit theorem (CLT) and moderate derivation principle (MDP) for the empirical measure of these piecewise α-stable Ornstein-Uhlenbeck processes. In addition, we use the Sinkhorn-Knopp algorithm to compute the Wasserstein-1 distance and conduct simulations for several concrete examples. Copyright © 2024, The Authors. All rights reserved.

关键词： Queueing networks

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Machine Learning for the edge energies of high symmetry Au nanoparticles

arXiv

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arXiv 2022年

作者： Pervolarakis, Emmanouil Tritsaris, Georgios A. Rosakis, Phoebus Remediakis, Ioannis N. Department of Materials Science and Technology University of Crete Heraklion70013 Greece John A. Paulson School of Engineering and Applied Sciences Harvard University MA Cambridge02138 United States Department of Mathematics and Applied Mathematics University of Crete Heraklion70013 Greece Institute of Applied & Computational Mathematics Foundation for Research and Technology Hellas Crete Heraklion71110 Greece Institute of Electronic Structure and Laser Foundation for Research and Technology Hellas Crete Heraklion71110 Greece

We present data-driven simulations for gold nanostructures, and develop a model that links total energy to geometrical features of the particle, with the ultimate goal of deriving reliable edge energies of gold. Assuming that the total energy can be decomposed into contributions from the bulk, surfaces, edges, and vertices, we use machine learning for reliable multi-variant fits of the associated coefficients. The proposed method of total energy calculations using machine learning produces almost ab-initio-like accuracy with minimal computational cost. Furthermore, a clear definition and metric for edge energy is introduced for edge-energy density calculations that avoid the troublesome definition of edge length in nanostructures. Our results for edge-energy density are 0.22 eV/Å for (100)/(100) edges and 0.20 eV/Å for (111)/(111) edges. Calculated vertex energies are about 1 eV/atom. The present method can be readily extended to other metals and edge orientations as well as arbitrary nanoparticle shapes. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning

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Harvesting random embedding for high-frequency change-point detection in temporal complex systems

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National Science Review 2022年第4期9卷 92-104页

作者： Jia-Wen Hou Huan-Fei Ma Dake He Jie Sun Qing Nie Wei Lin Research Institute of Intelligent Complex Systems Fudan University Centre for Computational Systems Biology Institute of Science and Technology for Brain-Inspired IntelligenceFudan University School of Mathematical Sciences Soochow University Xinhua Hospital Affiliated to Shanghai Jiao Tong University School of Medicine School of Mathematical Sciences and Shanghai Center for Mathematical Sciences Fudan University Department of Mathematics Department of Developmental and Cell Biologyand NSF-Simons Center for Multiscale Cell Fate ResearchUniversity of California Shanghai Key Laboratory for Contemporary Applied Mathematics LNMS (Fudan University)and LCNBI (Fudan University) State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain ScienceInstitutes of Brain ScienceFudan University

Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal structures has become a tremendously significant mission, beneficial to fully understanding the underlying mechanisms of evolving systems, and adequately modeling and predicting the dynamics of the systems as well. In real-world applications, due to a lack of prior knowledge on the explicit equations of evolving systems, an open challenge is how to develop a practical and model-free method to achieve the mission based merely on the time-series data recorded from real-world systems. Here, we develop such a model-free approach, named temporal change-point detection(TCD), and integrate both dynamical and statistical methods to address this important challenge in a novel way. The proposed TCD approach, basing on exploitation of spatial information of the observed time series of high dimensions, is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner, which cannot be directly achieved by using the existing methods and *** effectiveness is comprehensively demonstrated using the data from the representative complex dynamics and real-world systems from biology to geology and even to social science.

关键词： temporal systems time series change-point detection complex dynamical systems

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Determination of laser entrance hole size for ignition-scale octahedral spherical hohlraums

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Matter and Radiation at Extremes 2022年第6期7卷 41-49页

作者： Yao-Hua Chen Zhichao Li Hui Cao Kaiqiang Pan Sanwei Li Xufei Xie Bo Deng Qiangqiang Wang Zhurong Cao Lifei Hou Xingsen Che Pin Yang Yingjie Li Xiaoan He Tao Xu Yonggang Liu Yulong Li Xiangming Liu Haijun Zhang Wei Zhang Baibin Jiang Jun Xie Wei Zhou Xiaoxia Huang Wen Yi Huo Guoli Ren Kai Li Xudeng Hang Shu Li Chuanlei Zhai Jie Liu Shiyang Zou Yongkun Ding Ke Lan Institute of Applied Physics and Computational Mathematics Beijing 100094China Research Center of Laser Fusion China Academy of Engineering PhysicsMianyang 621900China Graduate School China Academy of Engineering PhysicsBeijingChina HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China

A recently proposed octahedral spherical hohlraum with six laser entrance holes(LEHs)is an attractive concept for an upgraded laser facility aiming at a predictable and reproducible fusion gain with a simple target ***,with the laser energies available at present,LEH size can be a critical *** to the uncertainties in simulation results,the LEH size should be determined on the basis of experimental ***,determination of LEH size of an ignition target at a small-scale laser facility poses *** this paper,we propose to use the prepulse of an ignition pulse to determine the LEH size for ignition-scale hohlraums via LEH closure behavior,and we present convincing evidence from multiple diagnostics at the SGIII facility with ignition-scale hohlraum,laser prepulse,and laser beam *** LEH closure observed in our experiment is in agreement with data from the National Ignition *** total LEH area of the octahedral hohlraum is found to be very close to that of a cylindrical hohlraum,thus successfully demonstrating the feasibility of the octahedral hohlraum in terms of laser energy,which is crucially important for sizing an ignition-scale octahedrally configured laser *** work provides a novel way to determine the LEH size of an ignition target at a small-scale laser facility,and it can be applied to other hohlraum configurations for the indirect drive approach.

关键词： laser size spherical

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Deformations of acid-mediated invasive tumors in a model with Allee effect

arXiv

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arXiv 2024年

作者： Carter, Paul Doelman, Arjen van Heijster, Peter Levy, Daniel Maini, Philip Okey, Erin Yeung, Paige Department of Mathematics University of California Irvine United States Mathematical Institute Leiden University Leiden Netherlands Mathematical and Statistical Methods—Biometris Wageningen University & Research Wageningen Netherlands Program in Applied and Computational Mathematics Princeton University Princeton United States Mathematical Institute University of Oxford Oxford United Kingdom Division of Applied Mathematics Brown University ProvidenceRI United States Massachusetts Institute of Technology Cambridge United States

We consider a Gatenby–Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds. © 2024, CC BY.

关键词： Perturbation techniques

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No Imputation Without Representation 35th

No Imputation Without Representation

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35th Benelux Conference on Artificial Intelligence and Machine Learning, BNAIC/Benelearn 2023

作者： Lenz, Oliver Urs Peralta, Daniel Cornelis, Chris Leiden Institute of Advanced Computer Science Leiden University Leiden Netherlands Research Group for Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium Department of Information Technology Ghent University Ghent Belgium

ISBN: (纸本)9783031746499

By filling in missing values in datasets, imputation allows these datasets to be used with algorithms that cannot handle missing values by themselves. However, missing values may in principle contribute useful information that is lost through imputation. The missing-indicator approach can be used in combination with imputation to instead represent this information as a part of the dataset. There are several theoretical considerations why missing-indicators may or may not be beneficial, but there has not been any large-scale practical experiment on real-life datasets to test this question for machine learning predictions. We perform this experiment for three imputation strategies and a range of different classification algorithms, on the basis of twenty real-life datasets. In a follow-up experiment, we determine attribute-specific missingness thresholds for each classifier above which missing-indicators are more likely than not to increase classification performance. And in a second follow-up experiment, we evaluate numerical imputation of one-hot encoded categorical attributes. We reach the following conclusions. Firstly, missing-indicators generally increase classification performance. Secondly, with missing-indicators, nearest neighbour and iterative imputation do not lead to better performance than simple mean/mode imputation. Thirdly, for decision trees, pruning is necessary to prevent overfitting. Fourthly, the thresholds above which missing-indicators are more likely than not to improve performance are lower for categorical attributes than for numerical attributes. Lastly, mean imputation of numerical attributes preserves some of the information from missing values. Consequently, when not using missing-indicators it can be advantageous to apply mean imputation to one-hot encoded categorical attributes instead of mode imputation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Adversarial machine learning

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Orthogonal Fourier Analysis on domains

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Expositiones Mathematicae 2024年

作者： Kolountzakis, Mihail N. Department of Mathematics and Applied Mathematics University of Crete Voutes Campus Heraklion 70013 Greece Institute of Computer Science Foundation of Research and Technology Hellas N. Plastira 100 Vassilika Vouton Heraklion 700 13 Greece

In this paper we go over the history of the Fuglede or Spectral Set Conjecture as it has developed over the last 30 years or so. We do not aim to be exhaustive and we do not cover important areas of development such as the results on the problem in classes of finite groups or the version of the problem that focuses on spectral measures instead of sets. The selection of the material has been strongly influenced by personal taste, history and capabilities. We are trying to be more descriptive than detailed and we point out several open questions. © 2024 Elsevier GmbH

关键词： Fuglede conjecture Spectral sets Tilings

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A One Dimensional (1D) computational Fluid Dynamics Study of Fontan-Associated Liver Disease (FALD)

arXiv

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arXiv 2025年

作者： Li, Yaqi Puelz, Charles Olufsen, Mette S. Taylor-Lapole, Alyssa Department of Brain and Cognitive Sciences Massachusetts Institute of Technology CambridgeMA02139 United States Mathematics University of Houston HoustonTX77204 United States Department of Mathematics North Carolina State University RaleighNC27695 United States Computational Applied Mathematics and Operations Research Rice University HoustonTX77251 United States

Fontan-Associated Liver Disease (FALD) is a disorder arising from hemodynamic changes and venous congestion in the liver. This disease is prominent in patients with hypoplastic left heart syndrome (HLHS). Although HLHS patients typically survive into adulthood, they have reduced cardiac output due to their univentricular physiology (i.e., a Fontan circuit). As a result, they have insufficient blood delivery to the liver. In comparison, patients with double outlet right ventricle (DORV), also having a univentricular circuit, have lower incidence of FALD. In this study, we use a patient-specific, one-dimensional computational fluid dynamics (1D-CFD) model to predict hemodynamics in the liver of an HLHS patient and compare predictions with an age- and size-matched DORV control patient. Additionally, we simulate FALD conditions in the HLHS patient to predict hemodynamic changes across various stages of disease progression. Our results show that the HLHS patient has a higher portal venous pressure compared to the DORV patient. This difference is exacerbated as FALD conditions progress. The wall shear stress (WSS) is also higher than normal for the HLHS patient, suggesting vascular remodeling. WSS decreases slightly under FALD conditions, consistent with the development of portal hypertension. Perfusion analysis gives insight into regions of liver tissue at risk for fibrosis development, showing increasing pressures and reduced flow throughout the liver tissue fed by the portal vein under FALD conditions. Our results provide insight into the specific hemodynamic changes in Fontan circulation that can cause FALD. © 2025, CC BY.

关键词： Shear stress

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(f,Γ)-Divergences: Interpolating between f-Divergences and Integral Probability Metrics

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Journal of Machine Learning research 2022年 23卷

作者： Birrell, Jeremiah Dupuis, Paul Katsoulakis, Markos A. Pantazis, Yannis Rey-Bellet, Luc TRIPODS Institute for Theoretical Foundations of Data Science University of Massachusetts Amherst AmherstMA01003 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Department of Mathematics and Statistics University of Massachusetts Amherst AmherstMA01003 United States Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas HeraklionGR-70013 Greece

We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both f-divergences and integral probability metrics (IPMs), such as the 1-Wasserstein distance. We prove under which assumptions these divergences, hereafter referred to as (f, Γ)-divergences, provide a notion of 'distance' between probability measures and show that they can be expressed as a two-stage mass-redistribution/mass-transport process. The (f, Γ)-divergences inherit features from IPMs, such as the ability to compare distributions which are not absolutely continuous, as well as from f-divergences, namely the strict concavity of their variational representations and the ability to control heavy-tailed distributions for particular choices of f. When combined, these features establish a divergence with improved properties for estimation, statistical learning, and uncertainty quantification applications. Using statistical learning as an example, we demonstrate their advantage in training generative adversarial networks (GANs) for heavy-tailed, not-absolutely continuous sample distributions. We also show improved performance and stability over gradient-penalized Wasserstein GAN in image generation. © 2022 Jeremiah Birrell, Paul Dupuis, Markos A. Katsoulakis, Yannis Pantazis, and Luc Rey-Bellet.

关键词： Generative adversarial networks

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Coherent enhancement of a frequency comb modulated by a terahertz laser field in high-order harmonic generation

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Physical Review A 2023年第4期108卷 043101-043101页

作者： Yuan-Yuan Wu Chang-Tong Liang Bao-Guang Zhao Peng-Cheng Li Research Center for Advanced Optics and Photoelectronics Department of Physics College of Science Shantou University Shantou Guangdong 515063 China Key Laboratory of Intelligent Manufacturing Technology of MOE Shantou University Shantou Guangdong 515063 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We present the coherent enhancement of the frequency comb via high-order harmonic generation (HHG) in a train of infrared laser pulses combined with terahertz (THz) laser fields. The HHG spectra are obtained by solving the three-dimensional time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. We find that the structure of the frequency comb via HHG becomes much smoother and more regular, and the yield of the comb is increased by nearly two orders of magnitude. By analyzing the phase coherence of HHG spectra, we demonstrate that the THz laser fields are responsible for the optimization of the structure and yield of the frequency comb since the constructive phase coherence of the HHG spectra is modulated by the THz field. The physical origin of the constructive phase coherence is thanks to the uniform ionization efficiency induced by the THz laser field for each laser pulse, which greatly improves the synchronization of the harmonic emission. Our finding provides a promising method for the enhancement of the frequency comb via HHG.

关键词： Atomic & molecular processes in external fields High-order harmonic generation Light-matter interaction Ultrafast phenomena

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