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arXiv 2022年

作者： Batko, Bogdan Gameiro, Marcio Hung, Ying Kalies, William Mischaikow, Konstantin Vieira, Ewerton Division of Computational Mathematics Faculty of Mathematics and Computer Science Jagiellonian University ul. St. Lojasiewicza 6 Kraków30-348 Poland Department of Mathematics Rutgers The State University of New Jersey PiscatawayNJ08854 United States Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo São Carlos São Paulo Brazil Department of Statistics Rutgers The State University of New Jersey PiscatawayNJ08854 United States Department of Mathematics and Statistics University of Toledo ToledoOH43606 United States DIMACS Rutgers The State University of New Jersey PiscatawayNJ08854 United States

We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More precisely, the sparse data is used to construct a statistical surrogate model based on a Gaussian process (GP). The dynamics of the surrogate model is interrogated using combinatorial methods and characterized using algebraic topological invariants (Conley index). The GP predictive distribution provides a lower bound on the confidence that these topological invariants, and hence the characterized dynamics, apply to the unknown dynamical system (assumed to be a sample path of the GP). The focus of this paper is on explaining the ideas, thus we restrict our examples to one-dimensional systems and show how to capture the existence of fixed points, periodic orbits, connecting orbits, bistability, and chaotic dynamics. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamics

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On the Derivation of Weights from Incomplete Pairwise Comparisons Matrices via Spanning Trees with Crisp and Fuzzy Confidence Levels

arXiv

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arXiv 2021年

作者： Mazurek, Jiri Kulakowski, Konrad Department of Informatics and Mathematics Silesian University in Opava School of Business Administration in Karvina Univerzitni namesti 1934/3 Czech Republic Department of Applied Computer Science Agh University of Science and Technology al. Mickiewicza 30 Kraków30-159 Poland

In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's confidence in a particular judgment. Then, from corresponding graph representations of a given PC matrix, all spanning trees are found. For each spanning tree, a unique priority vector is obtained with the weight corresponding to the confidence levels of entries that constitute this tree. At the end, the final priority vector is obtained through an aggregation of priority vectors achieved from all spanning trees. Confidence levels are modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical examples and comparisons with other methods are also provided. Last, but not least, we introduce a new formula for an upper bound of the number of spanning trees, so that a decision maker gains knowledge (in advance) on how computationally demanding the proposed method is for a given PC matrix. © 2021, CC BY-NC-ND.

关键词： Decision making

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Demonstration of a quantum-classical coprocessing protocol for simulating nuclear reactions

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Physical Review A 2023年第3期108卷 032417-032417页

作者： F. Turro T. Chistolini A. Hashim Y. Kim W. Livingston J. M. Kreikebaum K. A. Wendt J. L. Dubois F. Pederiva S. Quaglioni D. I. Santiago I. Siddiqi InQubator for Quantum Simulation (IQuS) Department of Physics University of Washington Seattle Washington 98195 USA Physics Department University of Trento Via Sommarive 14 I-38123 Trento Italy INFN-TIFPA Trento Institute of Fundamental Physics and Applications Trento Italy Quantum Nanoelectronics Laboratory Department of Physics University of California Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Materials Science Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Lawrence Livermore National Laboratory P.O. Box 808 L-414 Livermore California 94551 USA

Quantum computers hold great promise for exact simulations of nuclear dynamical processes (e.g., scattering and reactions), which are paramount to the study of nuclear matter at the limit of stability and in the formation of chemical elements in stars. However, quantum simulations of the unitary (real) time dynamics of fermionic many-body systems require a currently prohibitive number of reliable and long-lived qubits. We propose a co-processing algorithm for the simulation of real-time dynamics in which the time evolution of the spatial coordinates is carried out on a classical processor, while the evolution of the spin degrees of freedom is carried out on quantum hardware. We demonstrate this hybrid scheme with the simulation of two neutrons scattering at the Lawrence Berkeley National Laboratory's Advanced Quantum Testbed. After implementing error mitigation strategies to improve the accuracy of the algorithm in addition to a combination of circuit compression techniques and tomography as methods to elucidate the onset of decoherence, our results validate the principle of the proposed co-processing scheme. A generalization of this present scheme will open the way for (real-time) path integral simulations of nuclear scattering.

关键词： Nuclear reactions Quantum algorithms & computation Quantum computation Quantum error correction

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Symmetric Grothendieck Inequality

arXiv

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arXiv 2020年

作者： Friedland, Shmuel Lim, Lek-Heng Department of Mathematics Statistics and Computer Science University of Illinois ChicagoIL60607-7045 United States Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL60637-1514 United States

We establish an analogue of the Grothendieck inequality where the rectangular matrix is replaced by a symmetric (or Hermitian) matrix and the bilinear form by a quadratic form. We call this the symmetric Grothendieck inequality;despite its name, it is a generalization — the original Grothendieck inequality is a special case. While there are other proposals for such an inequality, ours differs in two important ways: (i) we have no additional requirement like positive semidefiniteness for the symmetric matrix;(ii) our symmetric Grothendieck constant is universal, i.e., independent of the matrix and its dimensions, like the original Grothendieck constant. A consequence of our symmetric Grothendieck inequality is a "conic Grothendieck inequality" for any family of cones of symmetric matrices: The original Grothendieck inequality is a special case;as is the Nesterov π/2-Theorem, which corresponds to the cones of positive semidefinite matrices;as well as the Goemans–Williamson inequality, which corresponds to the cones of weighted Laplacians. For yet other cones, e.g., of diagonally dominant matrices, we obtain new Grothendieck-like inequalities. With a slight extension, we obtain a unified framework that treats any Grothendieck-like inequality as an inequality between two norms within a family of "Grothendieck norms" restricted to an appropriate family of cones. This approach allows us to place on an equal footing the Goemans–Williamson inequality, Nesterov π/2-Theorem, Ben-Tal–Nemirovski–Roos 4/π-Theorem, generalized Grothendieck inequality, order-p Grothendieck inequality, rank-constrained positive semidefinite Grothendieck inequality, etc, and in turn allows us to simplify proofs, extend results from real to complex, obtain new bounds or establish sharpness of existing ones. Unsurprisingly, the symmetric Grothendieck inequality may also be applied to obtain uniform polynomial-time approximation bounds for various NP-hard combinatorial, integer, and nonconvex optimizat

关键词： Matrix algebra

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User Interaction Development for Radiotherapy Virtual Reality Training Application

User Interaction Development for Radiotherapy Virtual Realit...

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Computing (ICOCO), IEEE International Conference on

作者： Vei Siang Chan Andrés Iglesias Farhan Mohamed Faezah M. Salleh Habibollah Haron Najwa Ayuni Jamaludin Akemi Gálvez Pedro J. Prada Samuel Ruiz Lihua You Faculty of Computing Universiti Teknologi Malaysia Johor Bahru Malaysia Dept. of Applied Mathematics and Computational Sciences Universidad de Cantabria Santander Spain Faculty of Pharmaceutical Sciences Toho University Funabashi Japan Media and Game Innovation Center of Excellence Universiti Teknologi Malaysia Johor Bahru Malaysia Faculty of Science Universiti Teknologi Malaysia Johor Bahru Malaysia Hospital Universitario Marqués de Valdecilla Santander Spain National Center for Computer Animation Bournemouth University Poole United Kingdom

The advancement of virtual reality (VR) technology can enrich pedagogical approaches and information communication. In the oncology radiotherapy treatment, the medical practitioners revealed two main issues: the lack of training infrastructure and patient comprehension of the treatment process. Virtual simulation can assist in solving these complexities by offering an economical virtual embodiment of the medical facility. This study aims to improve the user interface and experience of VR training applications from previous work by conducting a domain expert intervention methodology. This paper discusses the main challenges and features of user interaction design for effective VR training systems and optimises the system based on feedback from domain experts. The authors anticipate that the key factors and design considerations proposed for this VR training application can benefit the development of related training systems in many other domains.

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Correction to: Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding

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Biological cybernetics 2021年第3期115卷 303-304页

作者： Shusen Pu Peter J Thomas Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University Cleveland OH USA. sxp600@case.edu. Department of Biomedical Engineering Vanderbilt University Nashville TN USA. sxp600@case.edu. Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University Cleveland OH USA. Department of Biology Case Western Reserve University Cleveland OH USA. Department of Cognitive Science Case Western Reserve University Cleveland OH USA. Department of Data and Computer Science Case Western Reserve University Cleveland OH USA. Department of Electrical Control and Systems Engineering Case Western Reserve University Cleveland OH USA.

A Correction to this paper has been published: https://***/10.1007/s00422-021-00877-7 .

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MODELING OF ASYMPTOTICALLY PERIODIC OUTBREAKS: A LONG-TERM SIRW2 DESCRIPTION OF COVID-19?

arXiv

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arXiv 2022年

作者： Viguerie, Alex Veneziani, Alessandro Carletti, Margherita Silvestri, Guido Division of Mathematics Gran Sasso Science Institute Viale Francesco Crispi 7 L'Aquila AQ 67100 Italy Department of Mathematics Department of Computer Science Emory University 400 Dowman Drive AtlantaGA30322 United States Department of Pure and Applied Sciences University of Urbino C. Bo Piazza della Repubblica 13 Pu Urbino61029 Italy Yerkes Division of Microbiology and Immunology Yerkes National Primate Research Center Yerkes Nonhuman Primate Genomics Core Emory University AtlantaGA30329 United States

As the outbreak of COVID-19 enters its third year, we have now enough data to analyse the behavior of the pandemic with mathematical models over a long period of time. The pandemic alternates periods of high and low infections, in a way that sheds a light on the nature of mathematical model that can be used for reliable predictions. The main hypothesis of the model presented here is that the oscillatory behavior is a structural feature of the outbreak, even without postulating a time-dependence of the coefficients. As such, it should be reflected by the presence of limit cycles as asymptotic solutions. This stems from the introduction of (i) a non-linear waning immunity based on the concept of immunity booster (already used for other pathologies);(ii) a fine description of the compartments with a discrimination between individuals infected/vaccinated for the first time, and individuals already infected/vaccinated, undergoing to new infections/doses. We provide a proof-of-concept that our novel model is capable of reproducing long-term oscillatory behavior of many infectious diseases, and, in particular, the periodic nature of the waves of infection. Periodic solutions are inherent to the model, and achieved without changing parameter values in time. This may represent an important step in the long-term modeling of COVID-19 and similar diseases, as the natural, unforced behavior of the solution shows the qualitative characteristics observed during the COVID-19 pandemic. © 2022, CC BY.

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Separating the contributions of electric and magnetic fields in deflecting the probes in proton radiography with multiple proton energies

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Matter and Radiation at Extremes 2021年第3期6卷 42-54页

作者： Bao Du Hong-Bo Cai Wen-Shuai Zhang Xiao-Fang Wang Dong-Guo Kang Luan Deng En-Hao Zhang Pei-Lin Yao Xin-Xin Yan Shi-Yang Zou Shao-Ping Zhu Institute of Applied Physics and Computational Mathematics Beijing 100094China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China IFSA Collaborative Innovation Center Shanghai Jiao Tong UniversityShanghai 200240China Department of Engineering and Applied Physics University of Science and Technology of ChinaHefei 230026China Graduate School China Academy of Engineering PhysicsBeijing 100088China Department of Engineering Physics Tsinghua UniversityBeijing 100084China STPPL Research Center of Laser FusionChina Academy of Engineering PhysicsMianyang 621900China

In proton radiography,degeneracy of electric and magnetic fields in deflecting the probe protons can prevent full interpretation of proton flux perturbations in the detection *** this paper,theoretical analyses and numerical simulations suggest that the contributions of the electric and magnetic fields can be separately obtained by analyzing the difference between the flux distributions of two discriminated proton energies in a single shot of proton *** eliminate the influence of field evolution on the separation,a strategy is proposed in which slow field evolution is assumed or an approximate estimate of field growth is *** could help achieve a clearer understanding of the radiographic process and allow further quantitative analysis.

关键词： magnetic fields assumed

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Redefining pandemic preparedness:Multidisciplinary insights from the CERP modelling workshop in infectious diseases,workshop report

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Infectious Disease Modelling 2024年第2期9卷 501-518页

作者： Marta C.Nunes Edward Thommes Holger Fröhlich Antoine Flahault Julien Arino Marc Baguelin Matthew Biggerstaff Gaston Bizel-Bizellot Rebecca Borchering Giacomo Cacciapaglia Simon Cauchemez Alex Barbier-Chebbah Carsten Claussen Christine Choirat Monica Cojocaru Catherine Commaille-Chapus Chitin Hon Jude Kong Nicolas Lambert Katharina B.Lauer Thorsten Lehr Cédric Mahe Vincent Marechal Adel Mebarki Seyed Moghadas Rene Niehus Lulla Opatowski Francesco Parino Gery Pruvost Andreas Schuppert Rodolphe Thiébaut Andrea Thomas-Bachli Cecile Viboud Jianhong Wu Pascal Crépey Laurent Coudeville Center of Excellence in Respiratory Pathogens(CERP) Hospices Civils de Lyon(HCL)and Centre International de Recherche en Infectiologie(CIRI)Équipe SantéPubliqueÉpidémiologie etÉcologieÉvolutive des Maladies Infectieuses(PHE3ID)Inserm U1111CNRS UMR5308ENS de LyonUniversitéClaude Bernard Lyon 1LyonFrance South African Medical Research Council Vaccines&Infectious Diseases Analytics Research UnitFaculty of Health SciencesUniversity of the WitwatersrandJohannesburgSouth Africa New Products and Innovation(NPI) Sanofi Vaccines(Global)TorontoOntarioCanada Department of Mathematics and Statistics University of GuelphGuelphOntarioCanada Fraunhofer Institute for Algorithms and Scientific Computing(SCAI) Department of BioinformaticsSchloss BirlinghovenSankt AugustinGermany University of Bonn Bonn-Aachen International Center for IT(b-it)BonnGermany Institute of Global Health Faculty of MedicineUniversity of GenevaGenevaSwitzerland and Swiss School of Public HealthZürichSwitzerland Department of Mathematics University of ManitobaWinnipegManitobaCanada MRC Centre for Global Infectious Disease Analysis School of Public HealthImperial College LondonLondonUK Centre for Mathematical Modelling of Infectious Diseases Department of Infectious Disease EpidemiologyLondon School of Hygiene&Tropical MedicineLondonUK National Center for Immunization and Respiratory Diseases(NCIRD) US Centers for Disease Control and Prevention(CDC)AtlantaGAUSA Departement of Computational Biology Departement of Global HealthInstitut PasteurParisFrance Institut de Physique des Deux Infinis de Lyon(IP2I) UMR5822IN2P3/CNRSUniversitéClaude Bernard Lyon 1VilleurbanneFrance Mathematical Modelling of Infectious Diseases Unit Institut PasteurUniversitéParis CitéUMR2000 CNRSParisFrance Decision and Bayesian Computation Institut PasteurUniversitéParis CitéCNRS UMR 3571France Fraunhofer-Institute for Translational Medicine and Pharmacology HamburgGermany Institute of Global Health Faculty of MedicineUniversity of

In July 2023,the Center of Excellence in Respiratory Pathogens organized a two-day workshop on infectious diseases modelling and the lessons learnt from the Covid-19 *** report summarizes the rich discussions that occurred during the *** workshop participants discussed multisource data integration and highlighted the benefits of combining traditional surveillance with more novel data sources like mobility data,social media,and wastewater *** advancements were noted in the development of predictive models,with examples from various countries showcasing the use of machine learning and artificial intelligence in detecting and monitoring disease *** role of open collaboration between various stakeholders in modelling was stressed,advocating for the continuation of such partnerships beyond the pandemic.A major gap identified was the absence of a common international framework for data sharing,which is crucial for global pandemic ***,the workshop underscored the need for robust,adaptable modelling frameworks and the integration of different data sources and collaboration across sectors,as key elements in enhancing future pandemic response and preparedness.

关键词： Modelling Covid-19 Infectious diseases Pandemic preparedness Workshop

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Correction: Image-Based Fracture Surface Defect Characterization Methods for Additively Manufactured Ti-6Al-4V Tested in Fatigue

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JOM 2024年第1期77卷 1-1页

作者： Ngo, Austin Hernandez, Kristen Olatunde, Ayorinde E. Ciardi, Thomas G. Harding, Alex Nihar, Arafath Mondal, Anirban French, Roger H. Bruckman, Laura S. Lewandowski, John J. Department of Materials Science and Engineering Case Western Reserve University Cleveland USA Materials Data Science for Stockpile Stewardship: Center of Excellence Case Western Reserve University Cleveland USA Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University Cleveland USA Department of Computer and Data Sciences Case Western Reserve University Cleveland USA

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