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arXiv 2020年

作者： Pang, Guodong Pardoux, Étienne Department of Computational Applied Mathematics and Operations Research George R. Brown College of Engineering Rice University HoustonTX77005 United States Aix Marseille Univ CNRS I2M Marseille France

In this paper, we prove a functional central limit theorem (FCLT) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in [9]. The infectivity process (total force of infection at each time) is composed of the independent infectivity random functions of each infectious individual, which starts at the time of infection. These infectivity random functions induce the infectious periods (as well as exposed, recovered or immune periods in full generality), whose probability distributions can be very general. The epidemic model includes the generalized non-Markovian SIR, SEIR, SIS, SIRS models with infection-age dependent infectivity. In the FCLTs for the generalized SIR and SEIR models, the limits of the diffusion-scaled fluctuations of the infectivity and susceptible processes are a unique solution to a two-dimensional Gaussian-driven stochastic Volterra integral equations, and then given these solutions, the limits for the infected (exposed/infectious) and recovered processes are Gaussian processes expressed in terms of the solutions to those stochastic Volterra integral equations. We also present the FCLTs for the generalized SIS and SIRS models. Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

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SCOUT: A fast Monte-Carlo modeling tool of scintillation camera output

SCOUT: A fast Monte-Carlo modeling tool of scintillation cam...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： William C. J. Hunter Harrison H. Barrett Thomas K. Lewellen Robert S. Miyaoka John P. Muzi Xiaoli Li Wendy McDougald Lawrence R. MacDonald Department of Radiology University of Washington Seattle WA USA Department of Radiology College of Optical Sciences the Applied Mathematics Program and the Biomedical Engineering Program University of Arizona Tucson Tucson AZ USA Departments of Radiology and Electrical Engineering University of Washington Seattle WA USA

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools.

关键词： Optical scattering Detectors Photonics Optical attenuators Crystals Photodetectors Cameras

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Long Term Monitoring of Air Pollution on Monuments and Cultural Heritage Sites in Cyprus Using Satellite Remote Sensing

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International Journal of Heritage in the Digital Era 2012年第1期1卷 145-167页

作者： K. Themistocleous A. Nisantzi A. Agapiou D. D. Alexakis D. G. Hadjimitsis V. Lysandrou S. Perdikou A. Retalis N. Chrysoulakis Department of Civil Engineering & Geomatics Cyprus University of Technology Lemesos Cyprus Restoration of Monuments and Sites Kykkos Museum Department of Civil Engineering Frederick University Nicosia Cyprus Institute of Environmental Research and Sustainable Development National Observatory of Athens Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology - Heraklion Crete Greece

Although cultural heritage sites are documented and preserved, to date there has been limited monitoring and documentation of how cultural heritage sites are affected by air pollution. This paper aims to introduce a new approach for monitoring air pollution for areas near cultural heritage sites by using satellite remotely sensed data. This approach provides a cost-effective tool for local authorities and government agencies to identify the most polluted cultural heritage sites and make decisions regarding the conservation of these sites. Archived data may be used in order to study long term the impact of air pollution to cultural heritage sites. The study area includes significant open air monuments of Cyprus located in the four main cities of the island. In this paper the Limassol Castle is used as a focused case study. Three years of MODIS satellite data was evaluated and analyzed in order to categorize high risk long-term areas. Ground measurements using sun-photometers, spectro-radiometers and particulate matter (PM10) laser photometer were also utilized in the study. The darkest pixel atmospheric correction in conjunction with the use of the radiative transfer equation was applied to retrieve the aerosol optical thickness (AOT) from Landsat TM/ETM+ satellite images in order also to cross-validate the AOT values found from MODIS and sun-photometers. The results of the study indicate that air pollution is high in all the major cities in Cyprus near cultural heritage sites. The results also found that the Limassol castle was most affected by air pollution, while the other cultural heritage sites exhibited similar results.

关键词： monitoring air pollution PM measurements MODIS AOT cultural heritage remote sensing GIS

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Relativistic dielectronic recombination process: Electron and H-like ions

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Physical Review A 1998年第2期57卷 1033-1033页

作者： Yi-Zhi Qu Jian-Guo Wang Jian-Kui Yuan Jia-Ming Li Institute of Physics Chinese Academy of Sciences P. O. Box 603 Beijing 100080 China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China Department of Physics Center of Atomic and Molecular Sciences Tsinghua University Beijing 100084 China

We have developed a simplified relativistic configuration-interaction method to calculate the dielectronic recombination (DR) cross sections and rate coefficients. In this method, the infinite resonant doubly excited states can be treated conveniently in the framework of quantum defect theory. Here we report a systematic study of DR rate coefficients of hydrogenlike isoelectronic sequence with atomic number 2<~Z<~79. The behavior of the DR rate coefficients along the isoelectronic sequence is studied. The results are compared with the Burgess formula and other theoretical works. Because of its relativistic treatment, our method can be applicable for arbitrary Z ions and the validity of the widely used Burgess formula can be examined, e.g., for the ion with Z>~36, the results calculated from Burgess formula would be larger by a factor of 2.

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Pseudospectral approximation of Hopf bifurcation for delay differential equations

arXiv

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arXiv 2020年

作者： de Wolff, Babette Scarabel, Francesca Lunel, Sjoerd Verduyn Diekmann, Odo Institut für Mathematik Freie Universität Berlin Arnimallee 3 BerlinD - 14195 Germany LIAM-Laboratory for Industrial and Applied Mathematics Department of Mathematics and Statistics York University 4700 Keele Street TorontoONM3J 1P3 Canada CDLab-Computational Dynamics Laboratory Department of Mathematics Computer Science and Physics University of Udine via delle scienze 206 Udine33100 Italy Department of Mathematics University of Utrecht Budapestlaan 6 P.O. Box 80010 TA Utrecht3508 Netherlands

Pseudospectral approximation reduces DDE (delay differential equations) to ODE (ordinary differential equations). Next one can use ODE tools to perform a numerical bifurcation analysis. By way of an example we show that this yields an efficient and reliable method to qualitatively as well as quantitatively analyse certain DDE. To substantiate the method, we next show that the structure of the approximating ODE is reminiscent of the structure of the generator of translation along solutions of the DDE. Concentrating on the Hopf bifurcation, we then exploit this similarity to reveal the connection between DDE and ODE bifurcation coefficients and to prove the convergence of the latter to the former when the dimension approaches *** Codes 34K18, 37M20, 65P30, 65L03, 92D25 Copyright © 2020, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Bootstrap Confidence Regions for Directional Data

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Journal of the American Statistical Association 1989年第408期84卷 996-996页

作者： Fisher, Nicholas I. Hall, Peter Program Leader Applied and Industrial Statistics Division of Mathematics and Statistics Commonwealth Scientific and Industrial Research Organisation Lindfield New South Wales 2070 Australia. Professor Department of Statistics Australian National University Canberra Australian Capital Territory 2601 Australia

Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions. It can readily be modified to incorporate extra assumptions about the underlying distribution, such as rotational symmetry. The general method leads to confidence pictures, which present information about the estimated posterior likelihood of mean orientation by shading spherical surfaces. An application is given to a sample of spherical cross-bed measurements. The methods extend to the case where X has random length, and to calculation of confidence regions for reference directions of axial bipolar or girdle distributions. [ABSTRACT FROM AUTHOR]

关键词： Axial data Circular data Confidence picture Gray-level image Pivotal statistic Studentization Weighted vectors.

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Tsi-Gcn: Translation and Scaling Invariant Gcn for 3d Point Cloud Analysis

SSRN

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SSRN 2024年

作者： Du, Zijin Liang, Jiye Yao, Kaixuan Cao, Feilong Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education School of Computer and Information Technology Shanxi University Shanxi Taiyuan030006 China Department of Applied Mathematics China Jiliang University Zhejiang Hangzhou310018 China

Point cloud is a crucial data format for 3D vision, but its irregularity makes it challenging to comprehend the associated geometric information. Although some previous research has attempted to improve deep learning on point cloud and achieved promising results, they often overlook the robust shape descriptors of 3D targets, making them susceptible to translation and scaling transformations. This paper proposes a novel framework for point cloud analysis, to achieve feature extraction with translation and scaling invariance. It mainly includes local adaptive kernel, translation and scaling invariant convolution (TSIConv), and graph attention pooling. The key component is the design of TSIConv, which extracts the shape information with translation and scaling invariance. Then it performs convolution with local adaptive kernels to capture the features in various shape structures. Following the convolution layer, we add the graph attention pooling to coarsen point cloud, thus achieving multi-scale analysis and computational overhead reduction. The proposed framework, consisting of two networks, completes point cloud classification and part segmentation tasks in an end-to-end manner. The property analysis and experiments demonstrate that our model strictly guarantees the translation and scaling invariance, meanwhile achieving comparable performance to previous methods. © 2024, The Authors. All rights reserved.

关键词： Convolutional neural networks

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Coulomb-enhanced dynamic localization and Bell-state generation in coupled quantum dots

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Physical Review A 2002年第2期66卷 022117-022117页

作者： Ping Zhang Qi-Kun Xue Xian-Geng Zhao X. C. Xie International Center of Quantum Structure and State Key Laboratory for Surface Physics Institute of Physics The Chinese Academy of Sciences Beijing 100080 People’s Republic of China Institute of Applied Physics and Computational Mathematics Beijing 100080 People’s Republic of China Department of Physics Oklahoma State University Stillwater Oklahoma 74078

We investigate the dynamics of two interacting electrons in coupled quantum dots driven by an ac field. We find that the two electrons can be trapped in one of the dots by the ac field, in spite of the strong Coulomb repulsion. In particular, we find that the interaction may enhance the localization effect. We also demonstrate the field excitation procedure to generate the maximally entangled Bell states. The generation time is determined by both analytic and numerical solutions of the time-dependent Schrödinger equation.

关键词： Semiconductor quantum dots

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Constraining the interaction between dark sectors with future HI intensity mapping observations

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Physical Review D 2018年第8期97卷 083504-083504页

作者： Xiaodong Xu Yin-Zhe Ma Amanda Weltman Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch 7701 Cape Town South Africa School of Chemistry and Physics University of KwaZulu-Natal Durban 4000 South Africa NAOC-UKZN Computational Astrophysics Centre (NUCAC) University of KwaZulu-Natal Durban 4000 South Africa School of Natural Sciences Institute for Advanced Study Olden Lane Princeton New Jersey 08540 USA

We study a model of interacting dark matter and dark energy, in which the two components are coupled. We calculate the predictions for the 21-cm intensity mapping power spectra, and forecast the detectability with future single-dish intensity mapping surveys (BINGO, FAST and SKA-I). Since dark energy is turned on at z∼1, which falls into the sensitivity range of these radio surveys, the HI intensity mapping technique is an efficient tool to constrain the interaction. By comparing with current constraints on dark sector interactions, we find that future radio surveys will produce tight and reliable constraints on the coupling parameters.

关键词： Cosmological parameters Dark energy Dark matter Radio, microwave, & sub-mm astronomy

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Extensibility of Hohenberg-Kohn Theorem to general quantum systems

arXiv

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arXiv 2022年

作者： Xu, Limin Mao, Jiahao Gao, Xingyu Liu, Zheng Department of Mathematical Sciences Tsinghua University Beijing100084 China State Key Laboratory of Low Dimensional Quantum Physics Department of Physics Tsinghua University Beijing100084 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Institute for Advanced Study Tsinghua University Beijing100084 China

Hohenberg-Kohn (HK) theorem is a cornerstone of modern electronic structure calculations. For interacting electrons, given that the internal part of the Hamiltonian (Ĥint), containing the kinetic energy and Couloumb interaction of electrons, has a fixed form, the theorem states that when the electrons are subject to an external electrostatic field, the ground-state density can inversely determine the field, and thus the full Hamiltonian completely. For a general quantum system, a HK-type Hamiltonian in the form of Ĥhk{gi} = Ĥint+Pi giÔi can always be defined, by grouping those terms with fixed or preknown coefficients into Ĥint, and factorizing the remaining as superposition of a set of Hermitian operators {Ôi}. We ask whether the HK theorem can be extended, so that the ground-state expectation values of {Ôi} as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. We show that the question can be addressed by introducing the concept of generalized density correlation matrix (GDCM) defined with respect to the {Ôi} operators. The invertibility of the GDCM represents a mathematically rigorous and practically useful criterion for the extension of HK theorem to be valid. We apply this criterion to several representative systems, including the quantum Ising dimer, the frustration-free systems, N-level quantum systems with fixed inter-level transition amplitude and tunable level energies, and a fermionic Hubbard chain with inhomogeneous on-site interactions. We suggest that for a finite-size system, finding an invertible GDCM under one single {gi} configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space. Copyright © 2022, The Authors. All rights reserved.

关键词： Hamiltonians

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