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arXiv 2018年

作者： Almeida, P. Napp, D. CIDMA - Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Portugal

In this paper we present a new class of convolutional codes that admits an efficient algebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of the paper is devoted to investigate its use in a variant of the McEliece cryptosystem. In contrast to the classical McEliece cryptosystems, where block codes are used, we propose the use of a convolutional encoder to be part of the public key. In this setting the message is a sequence of messages instead of a single block message and the errors are added randomly throughout the sequence. We conclude the paper providing some comments on the security. Although there is no obvious security threats to this new scheme, we point out several possible adaptations of existing attacks and discuss the difficulties of such attacks to succeed in breaking this cryptosystem. Copyright © 2018, The Authors. All rights reserved.

关键词： Decoding

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Variational Calculus With Conformable Fractional Derivatives

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IEEE/CAA Journal of Automatica Sinica 2017年第2期4卷 340-352页

作者： Matheus J.Lazo Delfim F.M.Torres Instituto de Matemática Estatística e Física-FURG Center for Research and Development in Mathematics and Applications (CIDMA) Department of MathematicsUniversity of Aveiro

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

关键词： Conformable fractional derivative fractional calculus of variations fractional optimal control invariant variational conditions Noether’s theorem

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Theoretical simulation of solid polymer electrolytes based on poly(vinylidene fluoride) with lithium salts for lithium-ion battery application

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AIP Conference Proceedings 2024年第1期3094卷

作者： D. Miranda J. C. Barbosa R. Gonçalves F. Miranda J. Vilaça C. M. Costa S. Lanceros-Méndez 2Ai-Polytechnic Institute of Cávado and Ave Barcelos Portugal LASI – Associate Laboratory of Intelligent Systems Guimarães Portugal Physics Centre of Minho and Porto Universities (CF-UM-UP) University of Minho 4710-057 Braga Portugal Chemistry Centre of University of Minho 4710-057 Braga Portugal Instituto Politécnico de Viana do Castelo Rua Escola Industrial e Comercial de Nun’Álvares 4900-347 Viana do Castelo Portugal Center for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics University of Aveiro 3810-193 Aveiro Portugal proMetheus Instituto Politécnico de Viana do Castelo Rua Escola Industrial e Comercial de Nun’Álvares 4900-347 Viana do Castelo Portugal Institute of Science and Innovation for Bio-Sustainability (IB-S) University of Minho 4710-053 Braga Portugal BCMaterials Basque Center for Materials Applications and Nanostructures UPV/EHU Science Park 48940 Leioa Spain

Solid polymer electrolyte composited by poly(vinylidene fluoride) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) has been optimized for solid-state lithium-ion batteries taking into account the LiTFSI concentration. Computer simulations of battery systems was used to evaluate the influence of LiTFSI concentration at different battery operation temperatures (278.15 K, and 353.15 K) and different discharge rates (C/30 and 3C), evaluating also the dissipated ohmic heat. It is shown how battery performance depends on LiTFSI content, which is correlated with ionic mobility, diffusion and temperature. A minimum of 30% of LiTFSI content is essential to obtain suitable solid polymer electrolytes for battery operation.

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The importance of artificial intelligence in postprandial blood glucose prediction for insulin bolus calculation

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AIP Conference Proceedings 2024年第1期3094卷

作者： Francisco Miranda Débora Amorim Luís Ferreira Carlos Abreu Instituto Politécnico de Viana do Castelo Rua Escola Industrial e Comercial de Nun’Álvares 4900-347 Viana do Castelo Portugal Center for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics University of Aveiro 3810-193 Aveiro Portugal proMetheus Instituto Politécnico de Viana do Castelo Rua Escola Industrial e Comercial de Nun’Álvares 4900-347 Viana do Castelo Portugal ADiT-LAB Instituto Politécnico de Viana do Castelo Rua Escola Industrial e Comercial de Nun’Álvares 4900-347 Viana do Castelo Portugal 2Ai - School of Technology IPCA Barcelos Portugal LASI – Associate Laboratory of Intelligent Systems Guimarães Portugal

Many works are using artificial intelligence to forecast postprandial blood glucose. However, the following questions arise: is it necessary to develop artificial intelligence techniques to predict blood glucose? How important is artificial intelligence for this purpose? This work gives some insights seeking the answer to these questions in the context of using postprandial blood glucose predictions to optimize the prandial insulin bolus. Considering the bolus optimization model proposed in this work, the error in the postprandial glycemia due to an inaccurate postprandial blood glucose prediction is in the same amount as the error made in the prediction. Therefore, more accurate postprandial blood glucose predictions lead to postprandial blood glucose values closer to the predefined blood glucose target defined for that patient. In this way, it is possible to conclude that artificial intelligence could have a relevant role in helping patients control their blood glucose levels. In particular, regarding non-controlled patients with high glucose variability.

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Head-on collisions of ℓ-boson stars

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Physical Review D 2022年第10期105卷 104057-104057页

作者： Víctor Jaramillo Nicolas Sanchis-Gual Juan Barranco Argelia Bernal Juan Carlos Degollado Carlos Herdeiro Miguel Megevand Darío Núñez Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México Circuito Exterior C.U. A.P. 70-543 México D.F. 04510 México Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago 3810-183 Aveiro Portugal Departamento de Astronomía y Astrofísica Universitat de València Dr. Moliner 50 46100 Burjassot (València) Spain Departamento de Física División de Ciencias e Ingenierías Campus León Universidad de Guanajuato León 37150 México Instituto de Ciencias Físicas Universidad Nacional Autónoma de México Apdo. Postal 48-3 62251 Cuernavaca Morelos México Instituto de Física Enrique Gaviola CONICET. Ciudad Universitaria 5000 Córdoba Argentina

Fully nonlinear numerical evolutions of the Einstein-(multi)-Klein-Gordon equations are performed to study head-on collisions of ℓ-boson stars. Despite being spherically symmetric, ℓ-boson stars have a (hidden) frame of reference, used in defining their individual multipolar fields. To assess the impact of their relative orientation, we perform simulations with different angles between the axes of the two colliding stars. Additionally, two scenarios are considered for the colliding stars: that they are composites of either the same or different scalar fields. Despite some model-specific behaviors, the simulations generically indicate that (1) the collision of two sufficiently (and equally) massive stars leads to black hole formation; (2) below a certain mass threshold the end result of the evolution is a bound state of the composite scalar fields, that neither disperses nor collapses into a black hole within the simulation time; (3) this end product (generically) deviates from spherical symmetry and the equipartition of the number of bosonic particles between the different scalar fields composing the initial boson stars is lost, albeit not dramatically. This last observation indicates, albeit without being conclusive, that the end result of these collisions belongs to the previously reported larger family of equilibrium multifield boson stars, generically nonspherical, and of which ℓ-boson stars are a symmetry enhanced point. We also extract and discuss the waveforms from the collisions studied.

关键词： Fluids & classical fields in curved spacetime Gravitational wave sources Binary stars Numerical relativity

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Black hole scalarization from the breakdown of scale invariance

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Physical Review D 2019年第8期99卷 084039-084039页

作者： Carlos A. R. Herdeiro Eugen Radu Centro de Astrofísica e Gravitação—CENTRA Departamento de Física Instituto Superior Técnico—IST Universidade de Lisboa—UL Avenida Rovisco Pais 1 1049-001 Lisboa Portugal Center for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics Campus de Santiago 3810-183 Aveiro Portugal

Electrovacuum black holes are scale invariant; their energy-momentum tensor is traceless. Quantum corrections of various sorts, however, can often produce a trace anomaly and a breakdown of scale invariance. The (quantum-corrected) black hole solutions of the corresponding gravitational effective field theory (EFT) have a nonvanishing Ricci scalar. Then, the presence of a scalar field with the standard nonminimal coupling ξϕ2R naturally triggers a spontaneous scalarization of the corresponding black holes. This scalarization phenomenon occurs for an (infinite) discrete set of ξ. We illustrate the occurrence of this phenomenon for two examples of static, spherically symmetric, asymptotically flat black hole solution of EFTs. In one example the trace anomaly comes from the matter sector—a novel, closed form generalization of the Reissner-Nordström solution with an F4 correction—whereas in the other example it comes from the geometry sector—a noncommutative geometry generalization of the Schwarzschild black hole. For comparison, we also consider the scalarization of a black hole surrounded by (nonconformally invariant) classical matter (Einstein-Maxwell-dilaton black holes). We find that the scalarized solutions are, generically, entropically favored.

关键词： Alternative gravity theories Classical black holes General relativity equations & solutions

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Randomised benchmarking for characterizing and forecasting correlated processes

arXiv

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arXiv 2023年

作者： Zhang, Xinfang Wu, Zhihao White, Gregory A.L. Xiang, Zhongcheng Hu, Shun Peng, Zhihui Liu, Yong Zheng, Dongning Fu, Xiang Huang, Anqi Poletti, Dario Modi, Kavan Wu, Junjie Deng, Mingtang Guo, Chu Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China School of Physics and Astronomy Monash University VIC3800 Australia Dahlem Center for Complex Quantum Systems Freie Universität Berlin Berlin14195 Germany Institute of Physics Chinese Academy of Sciences Beijing100190 China Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education Department of Physics Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha410081 China Science Mathematics and Technology Cluster and Engineering Product Development Pillar Singapore University of Technology and Design 8 Somapah Road 487372 Singapore Centre for Quantum Technologies National University of Singapore 117543 Singapore MajuLab CNRS-UNS-NUS-NTU International Joint Research Unit UMI 3654 Singapore Quantum for NSW Sydney2000 Australia

The development of fault-tolerant quantum processors relies on the ability to control noise. A particularly insidious form of noise is temporally correlated or non-Markovian noise. By combining randomized benchmarking with supervised machine learning algorithms, we develop a method to learn the details of temporally correlated noise. In particular, we can learn the time-independent evolution operator of system plus bath and this leads to (i) the ability to characterize the degree of non-Markovianity of the dynamics and (ii) the ability to predict the dynamics of the system even beyond the times we have used to train our model. We exemplify this by implementing our method on a superconducting quantum processor. Our experimental results show a drastic change between the Markovian and non-Markovian regimes for the learning accuracies. Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

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Local boundedness for weak solutions to some quasilinear elliptic systems

arXiv

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arXiv 2019年

作者： Leonardi, Salvatore Leonetti, Francesco Pignotti, Cristina Rocha, Eugenio Staicu, Vasile DMI - Department of Mathematics and Informatics University of Catania Viale A. Doria 6 Catania95125 Italy DISIM Department of Information Engineering Computer Science and Mathematics University of L’Aquila Via Vetoio snc - Coppito L’Aquila67100 Italy CIDMA Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi’s counterexample. Here we assume a condition on the support of off-diagonal coefficients that"keeps away" the counterexample and allows us to prove local boundedness of weak solutions. Copyright © 2019, The Authors. All rights reserved.

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Kicks in charged black hole binaries

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Physical Review D 2022年第8期106卷 084017-084017页

作者： Raimon Luna Gabriele Bozzola Vitor Cardoso Vasileios Paschalidis Miguel Zilhão Departament d’Astronomia i Astrofísica Universitat de València Dr. Moliner 50 46100 Burjassot (València) Spain Departament de Física Quàntica i Astrofísica Institut de Ciències del Cosmos Universitat de Barcelona Martí i Franquès 1 E-08028 Barcelona Spain Centro de Astrofísica e Gravitação—CENTRA Departamento de Física Instituto Superior Técnico—IST Universidade de Lisboa—UL Avenida Rovisco Pais 1 1049-001 Lisboa Portugal Department of Astronomy University of Arizona Tucson Arizona 85721 USA Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 2100 Copenhagen Denmark Department of Physics University of Arizona Tucson Arizona 85721 USA Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago 3810-183 Aveiro Portugal

We compute the emission of linear momentum (kicks) by both gravitational and electromagnetic radiation in fully general-relativistic numerical evolutions of quasicircular charged black hole binaries. We derive analytical expressions for slowly moving bodies and explore numerically a variety of mass ratios and charge-to-mass ratios. We find that for the equal-mass case our analytical expression is in excellent agreement with the observed values, and, contrarily to what happens in the vacuum case, we find that in the presence of electromagnetic fields there is emission of momentum by gravitational waves. We also find that the strong gravitational kicks of binaries with unequal masses affect the electromagnetic kicks, causing them to strongly deviate from Keplerian predictions. For the values of charge-to-mass ratio considered in this work, we observe that magnitudes of the electromagnetic kicks are always smaller than the gravitational ones.

关键词： General relativity Gravitational waves Classical black holes Astrophysical electromagnetic fields Astrophysical & cosmological simulations Numerical relativity

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Hyers-Ulam stability of bessel equations

arXiv

引用

arXiv 2018年

作者： Castro, L.P. Simões, A.M. Cidma - Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Portugal CMA-UBI - Center of Mathematics and Applications Department of Mathematics University of Beira Interior Covilhã Portugal

We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, σ-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations. Those sufficient conditions are obtained based on the use of integral techniques and majorations. Copyright © 2018, The Authors. All rights reserved.

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