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Antithetic Multilevel Methods for Elliptic and Hypo-Elliptic Diffusions with Applications

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arXiv 2024年

作者： Iguchi, Yuga Jasra, Ajay Maama, Mohamed Beskos, Alexandros Department of Statistical Science University College London LondonWC1E 6BT United Kingdom School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Motivated by recent developments, we introduce a new MLMC estimator of expectations, which does not require simulation of intractable Lévy areas but has a weak error of order 2 and achieves the optimal computational complexity. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate with numerical simulations that our new approaches provide efficiency gains for several problems relative to some existing methods. © 2024, CC BY.

关键词： Diffusion

clotFoam: An Open-Source Framework to Simulate Blood Clot Formation Under Arterial Flow

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arXiv 2023年

作者： Montgomery, David Municchi, Federico Leiderman, Karin Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Department of Mechanical Engineering Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Department of Mathematics University of North Carolina at Chapel Hill 216 Lenoir Dr Chapel HillNC27599 United States Computational Medicine Program University of North Carolina at Chapel Hill 216 Lenoir Dr Chapel HillNC27599 United States

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain. © 2023, CC BY.

关键词： Coagulation

An Optimal Framework for SDN Based on Deep Neural Network

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Computers, Materials & Continua 2022年第10期73卷 1125-1140页

作者： Abdallah Abdallah Mohamad Khairi Ishak Nor Samsiah Sani Imran Khan Fahad RAlbogamy Hirofumi Amano Samih M.Mostafa Department of Industrial Engineering School of Applied Technical Sciences German Jordanian UniversityAmman35247Jordan School of Electrical and Electronic Engineering Universiti Sains MalaysiaNibong Tebal14300Malaysia Center for Artificial Intelligence Technology Faculty of Information Science and TechnologyThe National University of Malaysia(UKM)Bangi43600SelangorMalaysia Department of Electrical Engineering University of Engineering and TechnologyPeshawar814Pakistan Turabah University College Computer Sciences ProgramTaif UniversityTaif21944Saudi Arabia Research Institute for Information Technology Kyushu UniversityFukuoka819-0395Japan Computer Science-Mathematics Department Faculty of ScienceSouth Valley UniversityQena83523Egypt

Software-defined networking(SDN)is a new paradigm that promises to change by breaking vertical integration,decoupling network control logic from the underlying routers and switches,promoting(logical)network control centralization,and introducing network ***,the controller is similarly vulnerable to a“single point of failure”,an attacker can execute a distributed denial of service(DDoS)attack that invalidates the controller and compromises the network security in *** address the problem of DDoS traffic detection in SDN,a novel detection approach based on information entropy and deep neural network(DNN)is *** approach contains a DNN-based DDoS traffic detection module and an information-based entropy initial inspection *** initial inspection module detects the suspicious network traffic by computing the information entropy value of the data packet’s source and destination Internet Protocol(IP)addresses,and then identifies it using the DDoS detection module based on *** assaults were found when suspected irregular traffic was *** reveal that the algorithm recognizes DDoS activity at a rate of more than 99%,with a much better accuracy *** false alarm rate(FAR)is much lower than that of the information entropy-based detection ***,the proposed framework can shorten the detection time and improve the resource utilization efficiency.

关键词： Deep neural network computer networks data security optimization

IGA using Offset-based Overlapping Domain Parameterizations

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arXiv 2023年

作者： Kargaran, Somayeh Jüttler, Bert Takacs, Thomas Doctoral Program Computational Mathematics Johannes Kepler University Linz Altenberger Straße 69 Linz4040 Austria Hagenberg Austria Institute of Applied Geometry Johannes Kepler University Linz Altenberger Straße 69 Linz4040 Austria Austrian Academy of Sciences Altenberger Straße 69 Linz4040 Austria

Isogeometric analysis (IGA) is a numerical method, proposed in [1], that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a B-spline or NURBS parameterization of the domain, an isogeometric discretization is defined on the domain using the same B-spline or NURBS basis as for the domain parameterization. Ideally, such an isogeometric discretization allows an exact representation of the underlying CAD model. CAD models usually represent only the boundary of the object. For planar domains, the CAD model is given as a collection of curves representing the boundary. Finding a suitable parameterization of the interior is one of the major issues for IGA, similar to the mesh generation process in the FEA setting. The objective of this isogeometric parameterization problem is to obtain a set of patches, which exactly represent the boundary of the domain and which are parameterized regularly and without self-intersections. This can be achieved by segmenting the domain into patches which are matching along interfaces, or by covering the domain with overlapping patches. In this paper we follow the second approach. To construct from a given boundary curve a planar parameterization suitable for IGA, we propose an offset-based domain parameterization algorithm. Given a boundary curve, we obtain an inner curve by generalized offsetting. The inner curve, together with the boundary curve, naturally defines a ring-shaped patch with an associated parameterization. By definition, the ring-shaped patch has a hole, which can be covered by a multi-cell domain. Consequently, the domain is represented as a union of two overlapping subdomains which are regularly parameterized. On such a configuration, one can employ the overlapping multi-patch (OMP) method, as introduced in [2], to solve PDEs on the given domain. The performance of the proposed method is reported in several numer

关键词： Parameterization

Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

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Physical Review Materials 2022年第2期6卷 025603-025603页

作者： Charles Emmett Maher Frank H. Stillinger Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by |x1|2p+|x2|2p+|x3|2p≤1, where p∈(0,∞) is a deformation parameter indicating to what extent the shape deviates from a sphere. As p increases from the sphere point (p=1), the superball tends to a cuboidal shape and approaches a cube in the p→∞ limit. As p→0.5, it approaches an octahedron, becomes a concave body with octahedral symmetry for p<0.5, and approaches a three-dimensional cross in the limit p→0. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction ϕ, average contact number Z¯) vary nonanalytically as p diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with 0.85≤p≤1.50. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors S(Q) and spectral densities χ̃V(Q), as the wave number Q tends to zero, and find that these packings are effectively hyperuniform for all values of p examined. We show that the mean width w¯ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution F(δ) and find that the pore sizes tend to decrease as |1−p| increases. From F(δ), we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of p. Additionally, we compute the diffusion “spreadability” S(t) [Torquato, Phys. Rev. E 104, 054102 (2021)] of

关键词： Granular packing

Recent Methodological Advances in Federated Learning for Healthcare

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arXiv 2023年

作者： Zhang, Fan Kreuter, Daniel Chen, Yichen Dittmer, Sören Tull, Samuel Shadbahr, Tolou Preller, Jacobus Rudd, James H.F. Aston, John A.D. Schönlieb, Carola-Bibiane Gleadall, Nicholas Roberts, Michael Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom Department of Haematology University of Cambridge Cambridge United Kingdom

For healthcare datasets, it is often not possible to combine data samples from multiple sites due to ethical, privacy or logistical concerns. Federated learning allows for the utilisation of powerful machine learning algorithms without requiring the pooling of data. Healthcare data has many simultaneous challenges which require new methodologies to address, such as highly-siloed data, class imbalance, missing data, distribution shifts and non-standardised variables. Federated learning adds significant methodological complexity to conventional centralised machine learning, requiring distributed optimisation, communication between nodes, aggregation of models and redistribution of models. In this systematic review, we consider all papers on Scopus that were published between January 2015 and February 2023 and which describe new federated learning methodologies for addressing challenges with healthcare data. We performed a detailed review of the 89 papers which fulfilled these criteria. Significant systemic issues were identified throughout the literature which compromise the methodologies in many of the papers reviewed. We give detailed recommendations to help improve the quality of the methodology development for federated learning in healthcare. © 2023, CC BY.

关键词： Paper

Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium

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Physical Review E 2022年第4期106卷 044122-044122页

作者： Salvatore Torquato Haina Wang Department of Chemistry Department of Physics Princeton Institute of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g2(r) or corresponding structure factor S(k) in d-dimensional Euclidean space Rd is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)] conjectured that any realizable g2(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g2(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform “cloaked” uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accur

关键词： Nonequilibrium statistical mechanics Optimization problems Structural properties Complex materials

Designer Pair Statistics of Disordered Many-Particle Systems with Novel Properties

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arXiv 2023年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States

Knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing data base of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperature that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics. © 2023, CC BY.

关键词： Statistics

Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

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arXiv 2022年

作者： Maama, Mohamed Jasra, Ajay Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling;the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data. Copyright © 2022, The Authors. All rights reserved.

关键词： Mean square error