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丛书名： Lecture Notes on Mathematical Modelling in the Life sciences

2017年

作者： Takashi Suzuki

Structure-preserving interpolation for model reduction of parametric bilinear systems

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arXiv 2020年

作者： Benner, Peter Gugercin, Serkan Werner, Steffen W.R. Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Otto von Guericke University Faculty of Mathematics Universitätsplatz 2 Magdeburg39106 Germany Department of Mathematics and Computational Modeling and Data Analytics Division Academy of Integrated Science Virginia Tech BlacksburgVA24061 United States Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric bilinear systems, and then provide conditions on projection spaces for the interpolation of structured subsystem transfer functions such that the system structure and parameter dependencies are preserved in the reduced-order model. Two benchmark examples with different parameter dependencies are used to demonstrate the theoretical analysis. Copyright © 2020, The Authors. All rights reserved.

关键词： Interpolation

Weyl’s law for the eigenvalues of the Neumann–Poincaré operators in three dimensions: Willmore energy and surface geometry

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arXiv 2018年

作者： Miyanishi, Yoshihisa Center for Mathematical Modeling and Data Science Osaka University Osaka560-8531 Japan

We deduce eigenvalue asymptotics of the Neumann–Poincaré operators in three dimensions. The region Ω is C2,α (α > 0) bounded in R3 and the Neumann–Poincaré operator K∂Ω: L2(∂Ω) → L2(∂Ω) is defined by K∂Ω[ψ](x):= 4 1 π ∫ ∂Ω hy − x, n(y)iψ(y) dSy |x − y|3 where dSy is the surface element and n(y) is the outer normal vector on ∂Ω. Then the ordering eigenvalues of the Neumann–Poincaré operator λj(K∂Ω) satisfy |λj(K∂Ω)| ∼ {3W(∂Ω)128−π2πχ(∂Ω) }1/2j−1/2 as j → ∞. Here W(∂Ω) and χ(∂Ω) denote, respectively, the Willmore energy and the Euler charateristic of the boundary surface ∂Ω. This formula is the so-called Weyl’s law for eigenvalue problems of Neumann–Poincaré *** Codes 47A75 (primary), 58J50 (secondary) Copyright © 2018, The Authors. All rights reserved.

关键词： Mathematical operators

A K-shell improved method for the importance of complex network nodes 7

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A K-shell improved method for the importance of complex netw...

7th IEEE data Driven Control and Learning Systems Conference, DDCLS 2018

作者： Jianmin, Xing Jianqiang, Chen Xiuwen, Sun Xinli, Zhang Ruikun, Zhang School of Mathematics and Physics Qingdao University of Science and Technology Qingdao266061 China Institute of Intelligence Science and Data Technology School of Mathematics and Physics Qingdao University of Science and Technology Qingdao266061 China Research Center for Mathematical Modeling School of Mathematics and Physics Qingdao University of Science and Technology Qingdao266061 China

ISBN: (纸本)9781538626184

In this paper, a weighted k-shell method is proposed to further improve the distinction of node importance by taking advantage of the number of iterations and edge weights when the node is deleted. The weighted k-shell decomposition method is applied to simple networks and complex networks respectively. The simulation results show that the improved method has low computational complexity, high result resolution and high accuracy. © 2018 IEEE.

关键词： Complex networks

Spatiotemporal analysis of urban heatwaves using tukey g-and-h random field models

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arXiv 2020年

作者： Murakami, Daisuke Peters, Gareth W. Matsui, Tomoko Yamagata, Yoshiki Department of Data Science Institute of Statistical Mathematics 10-3 Midoricho Tokyo190-8562 Japan School of Mathematical and Computer Sciences Heriot-Watt University EdinburghEH14 4AS United Kingdom Department of Statistical Modeling Institute of Statistical Mathematics 10-3 Midoricho Tokyo190-8562 Japan Center for Global Environmental Research National Institute for Environmental Studies 16-2 Onogawa Ibaraki305-8506 Japan

The statistical quantification of temperature processes for the analysis of urban heat island (UHI) effects and local heat-waves is an increasingly important application domain in smart city dynamic modelling. This leads to the increased importance of real-time heatwave risk management on a fine grained spatial resolution. This study attempts to analyze and develop new methods for modelling the spatio-temporal behavior of ground temperatures. The developed models consider higher order stochastic spatial properties such as skewness and kurtosis, which are key components for understanding and describing local temperature uctuations and UHI's. The developed models are applied to the greater Tokyo metropolitan area for a detailed real world data case study. The analysis also demonstrates how to statistically incorporate a variety of real data sets. This includes remote sensed imagery and a variety of ground based monitoring site data to build models linking city and urban covariates to air temperature. The air temperature models are then used to capture high resolution spatial emulator outputs for ground surface temperature modelling. The main class of processes studied include the Tukey g-and-h processes for capturing spatial and temporal aspects of heat processes in urban environments. Copyright © 2020, The Authors. All rights reserved.

关键词： Atmospheric temperature

A tale of two countries: Optimal control and cost-effectiveness analysis of monkeypox disease in Germany and Nigeria

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Healthcare Analytics 2023年 4卷 100258-100258页

作者： Akinyemi, Samuel Tosin Idisi, Isaiah Oke Rabiu, Musa Okeowo, Victoria Iyabode Iheonu, Nneka Dansu, Emmanuel Jesuyon Abah, Roseline Toyin Mogbojuri, Oluwaseun Akinlo Audu, Alogla Monday Yahaya, Mukhtar Muhammed Ebimobowei, Johnny Samuel Akande, Kazeem Babatunde Ojoma, Atede Anne Adeniji, Adejimi Adesola Oshinubi, Kayode Department of Mathematics Sikiru Adetona College of Education Science and Technology Ogun State Nigeria Department of Mathematical Sciences Federal University of Technology Ondo State Akure Nigeria Technion Israel Institute of Technology Haifa Israel International Centre for Applied Mathematical Modelling and Data Analytics (ICAMMDA) in partnership with the West Africa Mathematical Modeling Capacity Development (WAMCAD) Nigeria Department of Mathematical Sciences Stellenbosch University South Africa Department of Mathematics Federal University of Technology Imo State Owerri Nigeria Graduate School of Life Sciences Tohoku University Sendai Japan Department of Mathematics University of Abuja FCT Nigeria Department of Mathematical Sciences Adekunle Ajasin University Ondo State Akungba-Akoko Nigeria Department of Mathematics Nasarawa State University Nasarawa State Keffi Nigeria Department of Mathematics Federal University of Technology Niger State Minna Nigeria Department of Mathematical Sciences Baze University Abuja FCT Nigeria Department of Mathematics and Statistics Tshwane University of Technology Pretoria South Africa School of Informatics Computing and Cyber Systems Northern Arizona University Flagstaff 86011 AZ United States

The Monkeypox (Mpox) virus started developing as potentially fatal in Spring 2022. Mpox is a zoonotic disease that can spread between animals and people. While the cases in Nigeria are on the rise, Germany has become one of Europe's most impacted nations. Mathematical modeling is useful for monitoring, managing, and predicting infectious disease epidemics. This study incorporates the transmission rate of human-to-animal and animal-to-animal in a compartmental mathematical model of Mpox to capture the current trend in transmission for wildlife and human preservation. Parameters were estimated while the model was fitted to reported case data of Mpox from Nigeria and Germany to capture the trend in Europe and West Africa. Analyses such as optimal control, sensitivity, and cost-effectiveness were carried out. The results show that the best strategy to combat the spread of the virus is through changing behavior and personal hygiene among humans. © 2023 The Author(s)

关键词： Case data Cost-effectiveness Mathematical model Model fitting Mpox Optimal control

Regional variation and epidemiological insights in malaria underestimation in Cameroon

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Infectious Disease Modelling 2025年第4期10卷 1103-1115页

作者： Sarafa A. Iyaniwura Qing Han Ngem Bede Yong Ghislain Rutayisire Agnes Adom-Konadu Okwen Patrick Mbah David Poumo Tchouassi Kingsley Badu Jude Dzevela Kong Theoretical Biology and Biophysics Theoretical Division Los Alamos National Laboratory Los Alamos NM 87545 USA Laboratory for Industrial and Applied Mathematics (LIAM) Department of Mathematics and Statistics York University Toronto M3J 1P3 Ontario Canada Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC) University of Toronto Toronto M5T 3M7 ON Canada Artificial Intelligence & Mathematical Modeling Lab (AIMMLab) Dalla Lana School of Public Health University of Toronto 155 College Street Toronto M5T 3M7 ON Canada Global South Artificial Intelligence for Pandemic and Epidemic Preparedness and Response Network (AI4PEP) University of Toronto Toronto M5T 3M7 ON Canada Department of Public Health Regional Delegation of Public Health North West Region Bamenda Cameroon Department of Mathematics and Statistics York University Toronto M3J 1P3 Ontario Canada Department of Mathematics University of Cape Coast Central Region Cape Coast Ghana Effective Basic Services Africa (eBASE) Research and Development Bamenda North West Region Cameroon International Centre of Insect Physiology and Ecology Nairobi Kenya Department of Theoretical and Applied Biology Kwame Nkrumah University of Science and Technology University Post Office Kumasi AK 039 Ghana Department of Mathematics University of Toronto Bahen Centre for Information Technology 40 St. George Street Toronto M5S 2E4 ON Canada

Background Despite significant global effort to control and eradicate malaria, many cases and deaths are still reported yearly. These efforts are hindered by several factors, including the severe underestimation of cases and deaths, especially in Africa. Methods We used a mathematical model, incorporating the underestimation of cases and seasonality in mosquito biting rate, to study the malaria dynamics in Cameroon. Using a Bayesian inference framework, we calibrated our model to the monthly reported malaria cases in ten regions of Cameroon from 2019 to 2021 to quantify the underestimation of cases and estimate other important epidemiological parameters. We performed Hierarchical Clustering on Principal Components analysis to understand regional disparities, looking at underestimation rates, population sizes, healthcare personnel, and healthcare facilities per 1000 people. Results We found varying levels of case underestimation across regions, with the East region having the lowest (14 %) and the Northwest having the highest (70 %). The mosquito biting rate peaks once every year in most regions, except in the Northwest where it peaks every 6.02 months and in Littoral every 15 months. We estimated a median mosquito biting rate of over 5 bites/day for most regions with Littoral having the highest (9.86 bites/day). Two regions have rates below five: Adamawa (4.78 bites/day) and East (4.64 bites/day). Conclusions The low case estimation underscores the pressing requirement to bolster reporting and surveillance systems. Regions in Cameroon display a range of unique features contributing to the differing levels of underestimation. These distinctions should be considered when evaluating the efficacy of community-based interventions.

关键词： Malaria Mathematical modeling Case under-estimation Vector-borne diseases Bayesian inference Hierarchical clustering on principal components analysis

HYBRID ESTIMATION FOR ERGODIC DIFFUSION PROCESSES BASED ON NOISY DISCRETE OBSERVATIONS

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arXiv 2018年

作者： Kaino, Yusuke Nakakita, Shogo H. Uchida, Masayuki Graduate School of Engineering Science Osaka University Center for Mathematical Modeling and Data Science Osaka University JST CREST

We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial values for optimisation of the quasi likelihood function of ergodic diffusion processes with noisy observations, we construct the initial Bayes type estimator based on the local means of the noisy observations. The asymptotic properties of the initial Bayes type estimators and the hybrid multi-step estimators with the initial Bayes type estimators are shown, and a concrete example and the simulation results are given. Copyright © 2018, The Authors. All rights reserved.

关键词： Diffusion

Revisiting IRKA: Connections with pole placement and backward stability

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arXiv 2019年

作者： Beattie, C. Drmač, Z. Gugercin, S. Department of Mathematics Virginia Tech BlacksburgVA24061 United States Faculty of Science Department of Mathematics University of Zagreb Zagreb10000 Croatia Department of Mathematics Division of Computational Modeling and Data Analytics Virginia Tech BlacksburgVA24061 United States

The iterative rational Krylov algorithm (IRKA) is a popular approach for producing locally optimal reduced-order H2-approximations to linear time-invariant (LTI) dynamical systems. Overall, IRKA has seen significant practical success in computing high fidelity (locally) optimal reduced models and has been successfully applied in a variety of large-scale settings. Moreover, IRKA has provided a foundation for recent extensions to the systematic model reduction of bilinear and nonlinear dynamical systems. Convergence of the basic IRKA iteration is generally observed to be rapid | but not always;and despite the simplicity of the iteration, its convergence behavior is remarkably complex and not well understood aside from a few special cases. The overall effectiveness and computational robustness of the basic IRKA iteration is surprising since its algorithmic goals are very similar to a pole assignment problem, which can be notoriously ill-conditioned. We investigate this connection here and discuss a variety of nice properties of the IRKA iteration that are revealed when the iteration is framed with respect to a primitive *** find that the connection with pole assignment suggests refinements to the basic algorithm that can improve convergence behavior, leading also to new choices for termination criteria that assure backward stability. Copyright © 2019, The Authors. All rights reserved.

关键词： Iterative methods

Recent advances in T-cell receptor repertoire analysis: Bridging the gap with multimodal single-cell RNA sequencing

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ImmunoInformatics 2022年 5卷

作者： Sebastiaan Valkiers Nicky de Vrij Sofie Gielis Sara Verbandt Benson Ogunjimi Kris Laukens Pieter Meysman Adrem Data Lab Department of Computer Science University of Antwerp Antwerp Belgium Antwerp Unit for Data Analysis and Computation in Immunology and Sequencing (AUDACIS) University of Antwerp Antwerp Belgium Clinical Immunology Unit Department of Clinical Sciences Institute of Tropical Medicine Antwerp Belgium Molecular Digestive Oncology Department of Oncology Katholieke Universiteit Leuven Leuven Belgium Centre for Health Economics Research & Modeling Infectious Diseases (CHERMID) Vaccine & Infectious Disease Institute (VAXINFECTIO) University of Antwerp Antwerp Belgium Antwerp Center for Translational Immunology and Virology (ACTIV) Vaccine and Infectious Disease Institute (VAXINFECTIO) University of Antwerp Antwerp Belgium Department of Paediatrics Antwerp University Hospital Antwerp Belgium

T cells exercise a multitude of functions such as cytotoxicity, secretion of immunomodulating cytokines or regulation of tolerance, collectively resulting in an effective control of immune-related disease. Through the unique mechanism of V(D)J recombination, T cells express a highly specific receptor complex known as the T-cell receptor (TCR). Single-cell sequencing technologies have paved the road for interrogating the transcriptome and the paired αβ TCR repertoire of a single T cell in tandem. In contrast, conventional bulk methods are restricted to only one layer of information. This combination of transcriptomic- and repertoire information can provide novel insight into the functional character of T cell immunity. Recently, single-cell technologies have gained in popularity due to improvements in throughput, decrease in cost and the ability for multimodal experiments that integrate different information layers. Consequently, this prompts the need for the development of novel computational tools that integrate transcriptomic profiles and corresponding features of the TCR repertoire. Here we discuss the current progress in the field of single-cell T cell sequencing, with a focus on the multimodality of new approaches that allow the paired profiling of cellular phenotype and clonotype information. In addition, this review provides detailed descriptions of recent computational developments for analyzing single-cell TCR sequencing data in an integrative manner using novel computational approaches. Finally, we present an overview of the available software tools that can be used to perform integrative analysis of gene expression and TCR profiles.

关键词： Single-cell sequencing Single-cell immune profiling Single-cell gene expression T-cell receptor repertoire Multi-omics