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A general framework for quantum splines

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arXiv 2018年

作者： Abrunheiro, L. Camarinha, M. Clemente-Gallardo, J. Cuchí, J.C. Santos, P. CIDMA Center for Research and Development in Mathematics and Applications Higher Institute of Accounting and Administration University of Aveiro Aveiro3810-500 Portugal Centre for Mathematics University of Coimbra Department of Mathematics University of Coimbra Coimbra3001-454 Portugal University of Zaragoza Edificio I+D Mariano Esquillor s/n Zaragoza50018 Spain Department of Agricultural and Forest Engineering University of Lleida Av. Alcalde Rovira Roure 191 Lleida25198 Spain Polytechnic Institute of Coimbra ISEC Department of Physics and Mathematics Rua Pedro Nunes - Quinta da Nora Coimbra3030-199 Portugal

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on u∗(n) which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm.81Q93, 65D07, 81Q70 Copyright © 2018, The Authors. All rights reserved.

关键词： Quantum theory

Bounds for different spreads of line and total graphs

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arXiv 2018年

作者： Andrade, Enide Lenes, Eber Mallea-Zepeda, Exequiel Robbiano, Maria Jonnathan Rodrguez, Z. CIDMA-Center for Research and Development in Mathematics and Applications Departamento de Matemática Universidade de Aveiro Aveiro3810-193 Grupo de Investigación Deartica Universidad Del Sinú. Elýás Bechara Zainúm Cartagena Departamento de Matemática Universidad de Tarapacá Arica Departamento de Matemáticas Universidad Católica Del Norte Av. Angamos 0610 Antofagasta Chile

In this paper we explore some results concerning the spread of the line and the total graph of a given graph. In particular, it is proved that for an (n,m) connected graph G with m > n . 4 the spread of G is less than or equal to the spread of its line graph, where the equality holds if and only if G is regular bipartite. A sufficient condition for the spread of the graph not be greater than the signless Laplacian spread for a class of non bipartite and non regular graphs is proved. Additionally, we derive an upper bound for the spread of the line graph of graphs on n vertices having a vertex (edge) connectivity less than or equal to a positive integer k. Combining techniques of interlacing of eigenvalues, we derive lower bounds for the Laplacian and signless Laplacian spread of the total graph of a connected graph. Moreover, for a regular graph, an upper and lower bound for the spread of its total graph is given. Copyright © 2018, The Authors. All rights reserved.

关键词： Laplace transforms

Block matrices and Guo's Index for block circulant matrices with circulant blocks

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arXiv 2018年

作者： Andrade, Enide Manzaneda, Cristina Nina, Hans Robbiano, María CIDMA Center for Research and Development in Mathematics and Applications Departamento de Matemática Universidade de Aveiro Aveiro3810-193 Portugal Departamento de Matemáticas Facultad de Ciencias Universidad Católica del Norte Av. Angamos 0610 Antofagasta Chile Departamento de Matemáticas Facultad de Ciencias Básicas Universidad de Antofagasta Av. Angamos 601 Antofagasta Chile

In this paper we deal with circulant and partitioned into n-by-n circulant blocks matrices and introduce spectral results concerning this class of matrices. The problem of finding lists of complex numbers corresponding to a set of eigenvalues of a nonnegative block matrix with circulant blocks is treated. Along the paper we call realizable list if its elements are the eigenvalues of a nonnegative matrix. The Guo's index λ0 of a realizable list is the minimum spectral radius such that the list (up to the initial spectral radius) together with λ0 is realizable. The Guo's index of block circulant matrices with circulant blocks is obtained, and in consequence, necessary and sufficient conditions concerning the NIEP, Nonnegative Inverse Eigenvalue Problem, for the realizability of some spectra are given. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

First and second fundamental solutions of the time-fractional telegraph equation of order 2α

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AIP Conference Proceedings 2018年第1期2046卷

作者： M. Ferreira M. M. Rodrigues N. Vieira 1School of Technology and Management Polytechnic Institute of Leiria P-2411-901 Leiria Portugal and CIDMA - Center for Research and Development in Mathematics and Applications University of Aveiro Campus Universitário de Santiago 3810-193 Aveiro Portugal. 2CIDMA - Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Campus Universitário de Santiago 3810-193 Aveiro Portugal.

In this work we obtain the first and second fundamental solutions of the multidimensional time-fractional equation of order 2α, α ∈]0, 1], where the two time-fractional derivatives are in the Caputo sense. We obtain representations of the fundamental solutions in terms of Hankel transform, double Mellin-Barnes integral, and H-functions of two variables. As an application, the fundamental solutions are used to solve a Cauchy problem, and to study telegraph process with Brownian time.

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Compact objects and the swampland

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arXiv 2018年

作者： Herdeiro, Carlos A.R. Radu, Eugen Uzawa, Kunihito CENTRA Departamento de Física Instituto Superior Técnico Universidade de Lisboa Avenida Rovisco Pais 1 Lisboa1049 Portugal School of Theoretical Physics Dublin Institute for Advanced Studies 10 Burlington Road Dublin 4 Ireland Center for Research and Development in Mathematics and Applications Campus de Santiago Aveiro3810-183 Portugal Department of Physics School of Science and Technology Kwansei Gakuin University Sanda Hyogo669-1337 Japan

Recently, two simple criteria were proposed to assess if vacua emerging from an effective scalar field theory are part of the string "landscape" or "swampland". The former are the vacua that emerge from string compactifications;the latter are not obtained by any such compactification and hence may not survive in a UV completed theory of gravity. So far, these criteria have been applied to inflationary and dark energy models. Here we consider them in the context of solitonic compact objects made up of scalar fields: boson stars. Analysing several models (static, rotating, with and without self-interactions), we find that, in this context, the criteria are not independent. Furthermore, we find the universal behaviour that in the region wherein the boson stars are expected to be perturbatively stable, the compact objects may be part of the landscape. By contrast, in the region where they may be faithful black hole mimickers, in the sense they possess a light ring, the criteria fail (are obeyed) for static (rotating) ultracompact boson stars, which should thus be part of the swampland (landscape). We also consider hairy black holes interpolating between these boson stars and the Kerr solution and establish the part of the domain of existence where the swampland criteria are violated. In interpreting these results one should bear in mind, however, that the swampland criteria are not quantitatively strict. Copyright © 2018, The Authors. All rights reserved.

关键词： Stars

Relating bisimulations with attractors in boolean network models 3rd

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Relating bisimulations with attractors in boolean network mo...

3rd International Conference on Algorithms for Computational Biology, AlCoB 2016

作者： Figueiredo, Daniel Department of Mathematics CIDMA - Center for Research and Development in Mathematics and Applications University of Aveiro Campus Universitário de Santiago Aveiro3810-193 Portugal

ISBN: (纸本)9783319388267

When studying a biological regulatory network, it is usual to use boolean network models. In these models, boolean variables represent the behavior of each component of the biological system. Taking in account that the size of these state transition models grows exponentially along with the number of components considered, it becomes important to have tools to minimize such models. In this paper, we relate bisimulations, which are relations used in the study of automata (general state transition models) with attractors, which are an important feature of biological boolean models. Hence, we support the idea that bisimulations can be important tools in the study some main features of boolean network models. We also discuss the differences between using this approach and other well-known methodologies to study this kind of systems and we illustrate it with some examples. © Springer International Publishing Switzerland 2016.

关键词： Biological systems

The influence of inspiratory muscle training on lung function in female basketball players - a randomized controlled trial

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Porto biomedical journal 2017年第3期2卷 86-89页

作者： Tiago Vasconcelos Andreia Hall Rui Viana Faculty of Health Sciences University of Fernando Pessoa Porto Portugal. Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal. Physical Medicine and Rehabilitation Department Centro Hospitalar São João EPE Porto Portugal.

Inspiratory muscle fatigue may inhibit healthy athletes to achieve maximum performance, compromising blood flow and perfusion on locomotor muscles. Recent studies have showed irregular influence of inspiratory muscle training (IMT) on resting lung function. It was hypothesized that a 4-week IMT protocol would improve pulmonary function of basketball players. Twenty-one female basketball players were randomly assigned to an experimental group (EG) ( = 11) or a control group (CG) ( = 10). Pre- and post-forced expiratory volume in first second (FEV), forced vital capacity (FVC) and peak expiratory flow (PEF) were assessed with spirometry in the beginning of the sport's season, at the first day of protocol and four weeks after. The EG (22.00 ± 5.00 years) was submitted to IMT using a threshold, 5 times a week, for a 4-week protocol (30 maximal repetitions (RM) against a pressure threshold load equivalent to 50% of maximal inspiratory pressure), while the CG (18.50 ± 5.75 years) was not subjected to any intervention during the same period. Baseline sociodemographic and anthropometric characteristics were not significantly different with the exception of age ( = 0.036). No significant differences were found in baseline pulmonary volumes (0.173 ≤ 0.848) neither in predicted pulmonary variables (0.223 ≤ 0.654). Significant increase on FEV, FVC and PEF was found in the EG post-protocol ( < 0.001). In the CG, an improvement of PEF was found ( = 0.042). This type of specific inspiratory training appears to improve pulmonary function. Results suggest that the applied IMT protocol is effective. Further research is needed to assess the sustainability of the findings and to conclude the short and long term effects of IMT on basketball players.

关键词： Basketball Inspiratory muscle training Pulmonary function Spirometry

Dynamic Conditional Correlation between Electricity, Energy (Commodity) and Financial Markets during the Financial Crisis in Greece

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Journal of Mathematical Finance 2017年 7卷 990-1033页

作者： Panagiotis G. Papaioannou George P. Papaioannou Akylas Stratigakos Christos Dikaiakos Applied Mathematics and Physical Sciences National Technical University of Athens Athens Greece Research Technology & Development Department Independent Power Transmission Operator (IPTO) S.A. Athens Greece Center for Research and Applications in Nonlinear Systems (CRANS) Department of Mathematics University of Patras Patras Greece Department of Electrical and Computer Engineering University of Patras Patras Greece

Liberalization of electricity markets has increasingly created the need for understanding the volatility and correlation structure between electricity, financial and energy commodity markets. This work reveals the existence of structural changes in correlation patterns among these markets and links the changes to both fundamentals and regulatory conditions prevailing in the markets, as well as the current European financial crisis. We apply a Dynamic Conditional Correlation (DCC) GARCH model to a set of market’s fundamental variables, related commodity markets and Greece’s financial market and microeconomic indexes to study their interaction. Emphasis is given on the period of severe financial crisis of the Country to understand “contagion” and volatility spillover between these markets. This approach enables us to capture the changing co-movement of assets within and between markets (financial, commodity, electricity) as market conditions change. The main results are that there is strong evidence of volatility spillover (or co-volatility) between financial and commodity market, while the Greek electricity market seems to be almost “isolated” from these two markets.

关键词： Dynamic Conditional Correlation Garch Electricity & Financial Markets

Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3

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Physical Review X 2023年第1期13卷 011048-011048页

作者： R. Abbott T. D. Abbott F. Acernese K. Ackley C. Adams N. Adhikari R. X. Adhikari V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain P. Ajith T. Akutsu P. F. de Alarcón S. Akcay S. Albanesi A. Allocca P. A. Altin A. Amato C. Anand S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando T. Andrade N. Andres T. Andrić S. V. Angelova S. Ansoldi J. M. Antelis S. Antier F. Antonini S. Appert Koji Arai Koya Arai Y. Arai S. Araki A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud M. Arogeti S. M. Aronson K. G. Arun H. Asada Y. Asali G. Ashton Y. Aso M. Assiduo S. M. Aston P. Astone F. Aubin C. Austin S. Babak F. Badaracco M. K. M. Bader C. Badger S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai L. Baiotti J. Baird R. Bajpai M. Ball G. Ballardin S. W. Ballmer A. Balsamo G. Baltus S. Banagiri D. Bankar J. C. Barayoga C. Barbieri B. C. Barish D. Barker P. Barneo F. Barone B. Barr L. Barsotti M. Barsuglia D. Barta J. Bartlett M. A. Barton I. Bartos R. Bassiri A. Basti M. Bawaj J. C. Bayley A. C. Baylor M. Bazzan B. Bécsy V. M. Bedakihale M. Bejger I. Belahcene V. Benedetto D. Beniwal T. F. Bennett J. D. Bentley M. BenYaala F. Bergamin B. K. Berger S. Bernuzzi C. P. L. Berry D. Bersanetti A. Bertolini J. Betzwieser D. Beveridge R. Bhandare U. Bhardwaj D. Bhattacharjee S. Bhaumik I. A. Bilenko G. Billingsley S. Bini R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boer G. Bogaert M. Boldrini L. D. Bonavena F. Bondu E. Bonilla R. Bonnand P. Booker B. A. Boom R. Bork V. Boschi N. Bose S. Bose V. Bossilkov V. Boudart Y. Bouffanais A. Bozzi C. Bradaschia P. R. Brady A. Bramley A. Branch M. Branchesi J. Brandt J. E. Brau M. Breschi T. Briant J. H. Briggs A. Brillet M. Brinkmann P. Brockill A. F. Brooks J. Brooks D. D. Brown S. Brunett G. Bruno R. Bruntz J. Bryant T. Bulik H. J. Bulten A. Buonanno R. Buscicchio D. Buskulic C. Buy R. L. Byer L. Cadonati LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Louisiana State University Baton Rouge Louisiana 70803 USA Dipartimento di Farmacia Università di Salerno I-84084 Fisciano Salerno Italy INFN Sezione di Napoli Complesso Universitario di Monte S. Angelo I-80126 Napoli Italy OzGrav School of Physics & Astronomy Monash University Clayton 3800 Victoria Australia LIGO Livingston Observatory Livingston Louisiana 70754 USA University of Wisconsin-Milwaukee Milwaukee Wisconsin 53201 USA OzGrav Australian National University Canberra Australian Capital Territory 0200 Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-30167 Hannover Germany Leibniz Universität Hannover D-30167 Hannover Germany Inter-University Centre for Astronomy and Astrophysics Pune 411007 India University of Cambridge Cambridge CB2 1TN United Kingdom Theoretisch-Physikalisches Institut Friedrich-Schiller-Universität Jena D-07743 Jena Germany University of Birmingham Birmingham B15 2TT United Kingdom Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA) Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Gravity Exploration Institute Cardiff University Cardiff CF24 3AA United Kingdom INFN Sezione di Pisa I-56127 Pisa Italy International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Gravitational Wave Science Project National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan Universitat de les Illes Balears IAC3–IEEC E-07122 Palma de Mallorca Spain University College Dublin Dublin 4 Ireland INFN Sezione di Torino I-10125 Torino Italy Università di Napoli “Federico II” Complesso Universitario di Monte S. Angelo I-80126 Napoli

We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star–black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc−3 yr−1 and the neutron star–black hole merger rate to be between 7.8 and 140 Gpc−3 yr−1, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc−3 yr−1 at a fiducial redshift (z=0.2). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to (1+z)κ with κ=2.9−1.8+1.7 for z≲1. Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from 1.2−0.2+0.1 to 2.0−0.3+0.3M⊙. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of 8.3−0.5+0.3 and 27.9−1.8+1.9M⊙. While we continue to find that the mass distribution of a binary’s more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately 60M⊙, which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below χi≈0.25. While the majority of spins are preferentially aligned wi

关键词： Gravitational wave sources Gravitational waves Gravitational wave detection