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International Conference on Sampling Theory and Applications (SampTA)

作者： Luís Daniel Abreu João M. Pereira Austrian Academy of Sciences Acoustics Research Institute Vienna Austria Program in Applied and Computational Mathematics Princeton University Princeton NJ USA

Let Dt and B Ω denote the operators which cut the time content outside T and the frequency content outside Ω, respectively. The prolate spheroidal functions are the eigen-functions of the operator Pτ, Ω = D t B Ω D t . With the aim of formulating in precise mathematical terms the notion of Nyquist rate, Landau and Pollack have shown that, asymptotically, the number of such functions with eigenvalue close to one is ≈ |T||Ω|/2π. We have recently revisited this problem with a new approach: instead of counting the number of eigenfunctions with eigenvalue close to one, we count the maximum number of orthogonal ε-pseudoeigenfunctions with ε-pseudoeigenvalue one. Precisely, we count how many orthogonal functions have a maximum of energy e outside the domain T x Ω, in the sense that ||P T, Ω f - f|| 2 ≤ ε. We have recently discovered that the sharp asymptotic number is ≈ (1 - ε) -1 |T||Ω|/2π. The proof involves an explicit construction of the pseudoeigenfunctions of P T, Ω . When T and Ω are intervals we call them pseudo prolate spheroidal functions. In this paper we explain how they are constructed.

关键词： Eigenvalues and eigenfunctions Time-frequency analysis Fourier transforms Linear approximation

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Planck intermediate results. LV. reliability and thermal properties of high-frequency sources in the second planck catalogue of compact sources

arXiv

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arXiv 2020年

作者： Akrami, Y. Ashdown, M. Aumont, J. Baccigalupi, C. Ballardini, M. Banday, A.J. Barreiro, R.B. Bartolo, N. Basak, S. Benabed, K. Bernard, J.-P. Bersanelli, M. Bielewicz, P. Bond, J.R. Borrill, J. Bouchet, F.R. Burigana, C. Calabrese, E. Carvalho, P. Chiang, H.C. Crill, B.P. Cuttaia, F. de Rosa, A. de Zotti, G. Delabrouille, J. Delouis, J.-M. Di Valentino, E. Diego, J.M. Dupac, X. Dusini, S. Efstathiou, G. Elsner, F. Enßlin, T.A. Eriksen, H.K. Fernandez-Cobos, R. Finelli, F. Fraisse, A.A. Franceschi, E. Frolov, A. Galeotta, S. Ganga, K. Gerbino, M. González-Nuevo, J. Górski, K.M. Gratton, S. Gruppuso, A. Gudmundsson, J.E. Handley, W. Hansen, F.K. Herranz, D. Hivon, E. Hobson, M. Huang, Z. Jones, W.C. Keihänen, E. Keskitalo, R. Kim, J. Kisner, T.S. Krachmalnicoff, N. Kunz, M. Kurki-Suonio, H. Lamarre, J.-M. Lasenby, A. Lattanzi, M. Lawrence, C.R. Le Jeune, M. Lilje, P.B. Lindholm, V. López-Caniego, M. Ma, Y.-Z. Macías-Pérez, J.F. Maggio, G. Mandolesi, N. Marcos-Caballero, A. Maris, M. Martin, P.G. Martínez-González, E. Matarrese, S. Mauri, N. McEwen, J.D. Migliaccio, M. Molinari, D. Moneti, A. Montier, L. Morgante, G. Natoli, P. Paoletti, D. Partridge, B. Perrotta, F. Pettorino, V. Piacentini, F. Polenta, G. Puget, J.-L. Rachen, J.P. Reinecke, M. Remazeilles, M. Renzi, A. Rocha, G. Roudier, G. Ruiz-Granados, B. Savelainen, M. Scott, D. Sirri, G. Spencer, L.D. Suur-Uski, A.-S. Tauber, J.A. Tavagnacco, D. Tenti, M. Toffolatti, L. Tomasi, M. Trombetti, T. Valiviita, J. van Tent, B. Vielva, P. Villa, F. Wehus, I.K. Zacchei, A. Zonca, A. AIM CEA CNRS Université Paris-Saclay Université Paris-Diderot Sorbonne Paris Cité Gif-sur-YvetteF-91191 France APC AstroParticule et Cosmologie Université Paris Diderot CNRS/IN2P3 CEA/lrfu Observatoire de Paris Sorbonne Paris Cité 10 rue Alice Domon et Léonie Duquet Paris Cedex 1375205 France African Institute for Mathematical Sciences 6-8 Melrose Road Muizenberg Cape Town South Africa Astrophysics Group Cavendish Laboratory University of Cambridge J J Thomson Avenue CambridgeCB3 0HE United Kingdom Astrophysics & Cosmology Research Unit School of Mathematics Statistics & Computer Science University of KwaZulu-Natal Westville Campus Private Bag X54001 Durban4000 South Africa CITA University of Toronto 60 St. George St. TorontoONM5S 3H8 Canada CMDLABS Cambridge Machines Deep Learning and Bayesian Systems Ltd 22 Wycombe End Beaconsfield BuckinghamshireHP9 1NB United Kingdom CNRS IRAP 9 Av. colonel Roche BP 44346 Toulouse cedex 4F-31028 France California Institute of Technology PasadenaCA United States Computational Cosmology Center Lawrence Berkeley National Laboratory BerkeleyCA United States Département de Physique Théorique Université de Genève 24 Quai E. Ansermet Genève 41211 Switzerland Département de Physique École normale supérieure PSL Research University CNRS 24 rue Lhomond Paris75005 France La Laguna TenerifeE-38206 Spain Departamento de Física Universidad de Oviedo C/ Federico García Lorca 18 Oviedo Spain Department of Astrophysics IMAPP Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Department of Physics & Astronomy University of British Columbia 6224 Agricultural Road VancouverBC Canada Department of Physics & Astronomy University of the Western Cape Cape Town7535 South Africa Department of Physics Gustaf Hällströmin katu 2a University of Helsinki Helsinki Finland Department of Physics Princeton University PrincetonNJ United States Dipartimento di Fisica e Astronomia G. Galilei Univ

We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution (SED), which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck’s three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP’s data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source;(b) SED-independent source flux densities at each frequency considered;and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. This parameter can be used to extract sub-samples of high-frequency sources with statistically well-understood properties. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1 % of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. We describe the characteristics of this specific high-quality subset of PCCS2 and its validation against other data sets, specifically for: the sub-sample of PCCS2 located in low-cirrus areas;the Planck Catalogue of Galactic Cold Clumps (GCC);the Herschel GAMA15-field catalogue;and the temperature- and spectral-index-reconstructed dust maps obtained with Planck’s Generalized Needlet Int

关键词： Extraction

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Reliability and Precision Are Optimal for Non-Uniform Distributions of Presynaptic Release Probability

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Journal of Biomedical Science and Engineering 2015年第3期8卷 170-183页

作者： Jean-Marc Fellous Nadia S. Corral-Frías Graduate Interdisciplinary Program in Neuroscience University of Arizona Tucson USA Department of Psychology and Applied Mathematics University of Arizona Tucson USA

Most conceptual and computational models assume that synaptic transmission is reliable, a simplification rarely substantiated by data. The functional consequences of the recruitment of high and low initial release probability synapses on the reliability and precision of their postsynaptic targets are studied in a multi-compartmental model of a hippocampal CA1 pyramidal cell. We show that changes in the firing rate of CA3 afferent inputs (rate remapping) are not reflected in the firing rate of the CA1 cell but in the reliability and precise timing of some of its action potentials, suggesting that a signature of remapping may be found in the precise spike timing of CA1. Our results suggest that about half of the action potentials produced by a CA1 cell can potentially carry reliable information in their precise timing with about 25 ms precision, a time scale on the order of the gamma cycle. We show further that reliable events were primarily elicited by CA3 synapses in a state of low probability of release. Overall, our results suggest that the non-uniform distribution of initial release probabilities observed experimentally achieves an optimum yielding simultaneously high precision and high reliability, and allows large populations of CA3 synapses to contribute to the production of reliable CA1 spiking events.

关键词： Spike Timing Hippocampus computational Model Synapses

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A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components

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Communications in Theoretical Physics 2014年第6期61卷 703-709页

作者：钱旭宋松和李伟斌 Department of Mathematics and Systems Science National University of Defense Technology Program in Applied and Computational Mathematics Princeton University State Key Laboratory of High Performance Computing National University of Defense Technology

Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time ***, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

关键词： conservative algorithm coupled nonlinear SchrSdinger equation multiply components unstablewave

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Digital Microfluidics: Paper-Based Digital Microfluidic Chip for Multiple Electrochemical Assay Operated by a Wireless Portable Control System (Adv. Mater. Technol. 3/2017)

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Advanced Materials Technologies 2017年第3期2卷

作者： Nipapan Ruecha Jumi Lee Heedo Chae Haena Cheong Veasna Soum Pattarachaya Preechakasedkit Orawon Chailapakul Georgi Tanev Jan Madsen Nadnudda Rodthongkum Oh-Sun Kwon Kwanwoo Shin Program in Macromolecular Science Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Department of Chemistry and Institute of Biological Interfaces Sogang University Seoul 04107 Republic of Korea Program in Biotechnology Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Electrochemistry and Optical Spectroscopy Research Unit (EOSRU) Department of Chemistry Faculty of Science Chulalongkorn University Bangkok 10330 Thailand Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby 2800 Denmark Metallurgy and Materials Science Research Institute Chulalongkorn University Bangkok 10330 Thailand

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Resonancelike enhancement in high-order above-threshold ionization of polyatomic molecules

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Physical Review A 2016年第4期93卷 043422-043422页

作者： C. Wang M. Okunishi X. Hao Y. Ito J. Chen Y. Yang R. R. Lucchese M. Zhang B. Yan W. D. Li D. Ding K. Ueda Institute of Atomic and Molecular Physics Jilin University Changchun 130012 PR China Institute of Multidisciplinary Research for Advanced Materials Tohoku University Sendai 980-8577 Japan Institute of Theoretical Physics and Department of Physics Shanxi University 030006 Taiyuan China CAPT HEDPS and IFSA Collaborative Innovation Center of MoE College of Engineering Peking University Beijing 100084 China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China Department of Chemistry Texas A&M University College Station Texas 77843-3255 USA

We investigate the resonance-like enhancement (RLE) in high-order above-threshold ionization (ATI) spectra of the polyatomic molecules C2H4 and C2H6. In the spectrum-intensity maps, strong and weak RLE areas emerge alternatively for both C2H4 and C2H6 but in different sequences. Theoretical calculations using the strong-field approximation reproduce the experimental observation and analysis shows that the different characteristics of the two molecules can be attributed to interference effects of molecular orbitals with different symmetries. For C2H4, the RLE structures are attributed to C–C centers of the highest occupied molecular orbital (HOMO) orbital. For C2H6, in contrast, the C–C centers of the HOMO and HOMO-1 orbitals do not contribute to the RLE due to destructive interference but the hydrogen centers of the bonding HOMO-1 orbital give rise to the multiple RLE regions. In addition, clear experimental evidence of the existence of two types of the RLE and their dependence on the parity of ground state is shown. Our result, which strongly supports the channel-closing mechanism of the RLE, for the first time reveals the important role of low-lying orbitals and the differing roles of different atomic centers in the high-order ATI spectrum of molecules.

关键词： High-order harmonic generation Multiphoton or tunneling ionization & excitation

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On ( γ ∗ , β ∗ )-almost-pre-continuous mappings in topological spaces

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Journal of the Egyptian Mathematical Society 2015年第1期23卷 180-189页

作者： D. Saravanakumar M. Ganster N. Kalaivani G. Sai Sundara Krishnan Department of Mathematics SNS College of Engineering Coimbatore India Graz University of Technology Steyrergasse 30 A-8010 Graz Austria Department of Mathematics Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College Chennai India Department of Applied Mathematics and Computational Sciences PSG College of Technology Coimbatore India

In this paper, we introduced the notion of γ ∗ -regular-open sets and γ ∗ - δ .open sets and studied some of their basic properties and investigated the relationship between them. Also we introduced the notion of γ ∗ - δ - T i i = 0 , 1 2 , 1 , 2 spaces and characterized them using γ ∗ - δ .open sets and γ ∗ - δ .closed sets. Finally the concepts of ( γ ∗ , β ∗ )-almost-pre-continuous mappings and ( γ ∗ , β ∗ )-almost-pre-open (closed) mappings and studied some of their basic properties.

关键词： 54A05 54A10 54D10 γ ∗ -regular-open (closed) γ ∗ - δ .open (closed) γ ∗ -pre-open (closed) ( γ ∗ , β ∗ )-almost-pre-continuous and ( γ ∗ , β ∗ )-almost-pre-open (closed)

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Kinetic Transition Networks for the Thomson Problem and Smale’s Seventh Problem

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Physical Review Letters 2016年第2期117卷 028301-028301页

作者： Dhagash Mehta Jianxu Chen Danny Z. Chen Halim Kusumaatmaja David J. Wales Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame Indiana 46556 USA Centre for the Subatomic Structure of Matter Department of Physics School of Physical Sciences University of Adelaide Adelaide South Australia 5005 Australia Department of Chemical and Biomolecular Engineering University of Notre Dame Notre Dame Indiana 46556 USA Department of Computer Science and Engineering University of Notre Dame Notre Dame Indiana 46556 USA Department of Physics Durham University South Road Durham DH1 3LE United Kingdom University Chemical Laboratories Lensfield Road Cambridge CB2 1EW United Kingdom

The Thomson problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here, we show that the energy landscape of the Thomson problem for N particles with N=132, 135, 138, 141, 144, 147, and 150 is single funneled, characteristic of a structure-seeking organization where the global minimum is easily accessible. Algorithmically, constructing starting points close to the global minimum of such a potential with spherical constraints is one of Smale’s 18 unsolved problems in mathematics for the 21st century because it is important in the solution of univariate and bivariate random polynomial equations. By analyzing the kinetic transition networks, we show that a randomly chosen minimum is, in fact, always “close” to the global minimum in terms of the number of transition states that separate them, a characteristic of small world networks.

关键词： Kinetic theory Mathematical physics Random graphs

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Second yield via dislocation-induced premelting in copper

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Physical Review B 2016年第17期93卷 174106-174106页

作者： L. Wang Y. Cai A. M. He S. N. Luo The Peac Institute of Multiscale Sciences Chengdu Sichuan 610031 People's Republic of China Key Laboratory of Advanced Technologies of Materials Ministry of Education Southwest Jiaotong University Chengdu Sichuan 610031 People's Republic of China CAS Key Laboratory of Materials Behavior and Design Department of Modern Mechanics University of Science and Technology of China Hefei Anhui 230027 People's Republic of China Institute of Applied Physics and Computational Mathematics Beijing 100094 People's Republic of China

Premelting or virtual melting was proposed previously as an important deformation mechanism for high strain-rate loading. However, two questions remain outstanding: how premelting occurs exactly, and whether it plays a role in plastic deformation independent of, parasitic on, or synergetic with, dislocation motion. By virtue of double-shock compression, our large-scale molecular dynamics simulations reveal two yields in single-crystal copper, with the first yield achieved via dislocation motion, and the second, via dislocation-induced premelting as well. The clean capture of melting during dislocation motion suggests that premelting occurs on slip planes and at their intersections, facilitating gliding and leading to yield together with dislocation motion.

关键词： Crystal melting Disclinations & dislocations Plastic deformation Molecular dynamics

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Thomas and Lindner Reply:

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Physical Review Letters 2015年第6期115卷 069402-069402页

作者： Peter J. Thomas Benjamin Lindner Department of Mathematics Applied Mathematics and Statistics. Case Western Reserve University Cleveland Ohio 44106 USA Bernstein Center for Computational Neuroscience 10115 Berlin Germany Department of Physics. Humboldt University 12489 Berlin Germany

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