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Stroke classification using Virtual Hybrid Edge Detection from in silico electrical impedance tomography data

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arXiv 2025年

作者： Agnelli, Juan Pablo Moura, Fernando S. Rautio, Siiri Alsaker, Melody Murthy, Rashmi Lassas, Matti Siltanen, Samuli Argentina Engineering Modeling and Applied Social Sciences Center Federal University of ABC São Paulo Brazil Department of Mathematics and Statistics University of Helsinki Finland Department of Mathematics Gonzaga University Spokane United States Department of Mathematics Bangalore University India

Electrical impedance tomography (EIT) is a non-invasive imaging method for recovering the internal conductivity of a physical body from electric boundary measurements. EIT combined with machine learning has shown promise for the classification of strokes. However, most previous works have used raw EIT voltage data as network inputs. We build upon a recent development which suggested the use of special noise-robust Virtual Hybrid Edge Detection (VHED) functions as network inputs, although that work used only highly simplified and mathematically ideal models. In this work we strengthen the case for the use of EIT, and VHED functions especially, for stroke classification. We design models with high detail and mathematical realism to test the use of VHED functions as inputs. Virtual patients are created using a physically detailed 2D head model which includes features known to create challenges in real-world imaging scenarios. Conductivity values are drawn from statistically realistic distributions, and phantoms are afflicted with either hemorrhagic or ischemic strokes of various shapes and sizes. Simulated noisy EIT electrode data, generated using the realistic Complete Electrode Model (CEM) as opposed to the mathematically ideal continuum model, is processed to obtain VHED functions. We compare the use of VHED functions as inputs against the alternative paradigm of using raw EIT voltages. Our results show that (i) stroke classification can be performed with high accuracy using 2D EIT data from physically detailed and mathematically realistic models, and (ii) in the presence of noise, VHED functions outperform raw data as network inputs. © 2025, CC BY.

关键词： Electric impedance tomography

GLOBAL LINEARIZATION WITHOUT HYPERBOLICITY

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arXiv 2025年

作者： Kvalheim, Matthew D. Sontag, Eduardo D. Department of Mathematics and Statistics University of Maryland Baltimore CountyMD United States Departments of Electrical and Computer Engineering and Bioengineering Departments of Mathematics and Chemical Engineering Northeastern University BostonMA United States

We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjugacy is (i) defined on the entire basin of attraction if the vector field is complete, and (ii) a Ck≥1 diffeomorphism on the complement of the equilibrium if the vector field is Ck and the underlying space is not 5-dimensional. We also show that the Ck statement in the 5-dimensional case is equivalent to the 4-dimensional smooth Poincaré conjecture. Copyright © 2025, The Authors. All rights reserved.

关键词： Vector spaces

Connected domination in plane triangulations

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Involve 2025年第3期18卷 555-566页

作者： Bryant, Felicity Pavelescu, Elena Department of Mechanical Aerospace and Biomedical Engineering University of South Alabama Mobile AL United States Mathematics and Statistics Department University of South Alabama Mobile AL United States

A set of vertices of a graph G with the property that each vertex of G is either in the set or is adjacent to a vertex in the set is called a dominating set of G. If, additionally, the set of vertices induces a connected subgraph of G then the set is a connected dominating set of G. The domination number γ (G) of G is the smallest number of vertices in a dominating set of G, and the connected domination number γ_c (G) of G is the smallest number of vertices in a connected dominating set of G. We find the connected domination numbers for all triangulations of up to thirteen vertices. For n ≥ 15, n ≡ 0 (mod 3), we find graphs of order n and γ_c = n/3. We also show that the difference γ_c (G) − γ (G) can be arbitrarily large. © 2025 The Authors, under license to MSP (Mathematical Sciences Publishers).

关键词： connected domination domination triangulation

Local Reconstruction Analysis of Inverting the Radon Transform in the Plane from Noisy Discrete Data

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SIAM Journal on Imaging Sciences 2025年第2期18卷 936-962页

作者： Abhishek, Anuj Katsevich, Alexander Webber, James Applied Mathematics and Statistics Case Western Reserve University Cleveland 44106 OH United States Department of Mathematics University of Central Florida Orlando 32816-1364 FL United States Department of Biomedical Engineering Cleveland Clinic Cleveland 44196 OH United States

In this paper, we investigate the reconstruction error, Nϵrec (x), when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transform data with sampling step-size _ in two dimensions... 详细信息

In this paper, we investigate the reconstruction error, N_ϵ^rec (x), when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transform data with sampling step-size _ in two dimensions. Specifically, we analyze N_ϵ^rec (x) for x in small, O(ϵ)-sized neighborhoods around a generic fixed point, x0, in the plane, where the measurement noise values, η_k,j (i.e., the errors in the sinogram space), are random variables. The latter are independent, but not necessarily identically distributed. We show, under suitable assumptions on the first three moments of the η_k,j, that the following limit exists: (formula presenetd) for x in a bounded domain. Here, N_ϵ^rec and N^rec are viewed as continuous random variables, and the limit is understood in the sense of distributions. Once the limit is established, we prove that N^rec is a zero mean Gaussian random field and compute explicitly its covariance. In addition, we validate our theory using numerical simulations and pseudorandom noise. © 2025 Society for Industrial and Applied mathematics.

关键词： local reconstruction analysis noisy discrete data Radon inversion tomography

An Improved Exact Algorithm for the Euclidean $K$-Steiner Tree Problem

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SSRN

SSRN 2025年

作者： Lee, Jae Brazil, Marcus Ras, Charl Thomas, Doreen School of Mathematics and Statistics University of Melbourne Australia Department of Electrical and Electronic Engineering University of Melbourne Australia Department of Mechanical Engineering University of Melbourne Australia

In the classical geometric Steiner tree problem, we are given a set of points in the plane and our aim is to find the shortest network interconnecting the set of points. An unlimited number of additional vertices, called Steiner points, may be added to shorten the network. In the minimum k-Steiner tree problem, the number of Steiner points is limited to some nonnegative integer k, which creates additional complexity. This paper improves on the current algorithmic approach to solving the Euclidean k-Steiner tree problem. We introduce a novel pruning test and strengthen existing tests to allow more extensive elimination of sub-optimal topologies during the generation phase of the algorithm. We also introduce a new ILP model for the concatenation phase. Finally, we present experimental results that demonstrate the effectiveness of these novel components. © 2025, The Authors. All rights reserved.

关键词： Trees (mathematics)

A mathematical framework for analyzing co-infection of COVID-19 with lung cancer

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Partial Differential Equations in Applied mathematics 2025年 14卷

作者： Hye, Md. Abdul Biswas, Md. Haider Ali Uddin, Mohammed Forhad Department of Mathematics and Statistics Bangladesh University of Business and Technology (BUBT) Dhaka Bangladesh Mathematics Discipline Khulna University Khulna Bangladesh Department of Mathematics Bangladesh University of Engineering and Technology (BUET) Dhaka Bangladesh

This study introduces a novel mathematical framework to explore the complex relationship between COVID-19 and lung cancer, addressing a critical gap in the existing literature. While various co-infection models have been discussed, no prior work has focused explicitly on the mathematical modeling of COVID-19 and lung cancer co-infection, positioning this research as pioneering. The dynamical model incorporates sub-models to analyze two distinct scenarios: one focusing exclusively on lung cancer and the other on COVID-19. The basic reproduction number determines stability conditions for the disease-free and endemic equilibriums. The model also integrates intervention strategies, including lung cancer preventive measures and COVID-19-specific treatments, to evaluate their impact on co-infection dynamics. Stability analysis and numerical simulations identify critical factors influencing the severity and progression of the co-infection, highlighting the substantial role of lung cancer prevention in reducing COVID-19 co-infections. The results underscore the importance of targeted interventions in managing co-infections effectively. This framework provides valuable insights for researchers and healthcare professionals as a comprehensive tool for understanding co-infection dynamics. By addressing the complexities of COVID-19 and lung cancer co-infection, this study goes beyond previous efforts, offering actionable strategies and advancing the understanding of this critical public health issue. © 2025 The Author(s)

关键词： Basic reproduction number Compartmental modeling Epidemiological analysis Numerical simulations Sensitivity analysis

Real-Time Distributed Model Predictive Control with Limited Communication Data Rates

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IEEE Transactions on Automatic Control 2025年

作者： Yang, Yujia Wang, Ye Manzie, Chris Pu, Ye University of Melbourne Department of Electrical and Electronic Engineering ParkvilleVIC3010 Australia University of Melbourne School of Mathematics and Statistics ParkvilleVIC3010 Australia

The application of distributed model predictive controllers (DMPC) for multiagent systems (MASs) necessitates communication between agents, yet the consequence of communication data rates is typically overlooked. This work focuses on developing stability-guaranteed control methods for MASs with limited data rates. Initially, a distributed optimization algorithm with dynamic quantization is considered for solving the DMPC problem. Due to the limited data rate, the optimization process suffers from inexact iterations caused by quantization noise and premature termination, leading to suboptimal solutions. In response, we propose a novel real-time DMPC framework with a quantization refinement scheme that updates the quantization parameters on-line so that both the quantization noise and the optimization suboptimality decrease asymptotically. To facilitate the stability analysis, we treat the suboptimally controlled MAS, the quantization refinement scheme, and the optimization process as three interconnected subsystems. The cyclic-small-gain theorem is used to derive sufficient conditions on the quantization parameters for guaranteeing the stability of the system under a limited data rate. Finally, the proposed algorithm and theoretical findings are demonstrated in a multi-AUV formation control example. © 1963-2012 IEEE.

关键词： Predictive control systems

A SHORT PROOF OF ISSERLIS’ THEOREM

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arXiv 2025年

作者： Munthe-Kaas, Hans Z. Verdier, Olivier Vilmart, Gilles Department of Mathematics and Statistics UiT – The Arctic University of Norway Tromsø Norway Department of Mathematics University of Bergen Bergen Norway Department of Computing Electrical Engineering and Mathematical Sciences Western Norway Norway University of Applied Sciences Bergen Norway Section of Mathematics University of Geneva Switzerland

We show that Isserlis’ theorem follows as a corollary to the invariant tensor theorem for isotropic *** Codes Primary: 60C05, 15A72, Secondary: 41A58, 60H35 Copyright © 2025, The Authors. All rights reserved.

关键词： Tensors

Time parallelization for hyperbolic and parabolic problems

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arXiv 2025年

作者： Gander, Martin J. Wu, Shu-Lin Zhou, Tao Department of Mathematics University of Geneva CP64 Geneva 41211 Switzerland School of Mathematics and Statistics Northeast Normal University Changchun130024 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Time parallelization, also known as PinT (Parallel-in-Time) is a new research direction for the development of algorithms used for solving very large scale evolution problems on highly parallel computing architectures. Despite the fact that interesting theoretical work on PinT appeared as early 1964, it was not until 2004, when processor clock speeds reached their physical limit, that research in PinT took off. A distinctive characteristic of parallelization in time is that information flow only goes forward in time, meaning that time evolution processes seem necessarily to be sequential. Nevertheless, many algorithms have been developed over the last two decades to do PinT computations, and they are often grouped into four basic classes according to how the techniques work and are used: shooting-type methods;waveform relaxation methods based on domain decomposition;multigrid methods in space-time;and direct time parallel methods. However, over the past few years, it has been recognized that highly successful PinT algorithms for parabolic problems struggle when applied to hyperbolic problems. We focus in this survey therefore on this important aspect, by first providing a summary of the fundamental differences between parabolic and hyperbolic problems for time parallelization. We then group PinT algorithms into two basic groups: the first group contains four effective PinT techniques for hyperbolic problems, namely Schwarz Waveform Relaxation with its relation to Tent Pitching;Parallel Integral Deferred Correction;ParaExp;and ParaDiag. While the methods in the first group also work well for parabolic problems, we then present PinT methods especially designed for parabolic problems in the second group: Parareal: the Parallel Full Approximation Scheme in Space-Time;Multigrid Reduction in Time;and Space-Time Multigrid. We complement our analysis with numerical illustrations using four time-dependent PDEs: the heat equation;the advection-diffusion equation;Burgers’ equa

关键词： Wave equations