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Erratum to: Semigroups of max-plus linear operators

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Semigroup Forum 2017年第2期94卷 477-479页

作者： Andreianov, Boris Fijavž, Marjeta Kramar Peperko, Aljoša Sikolya, Eszter LMPT CNRS UMR7350 Université de Tours Tours France Faculty of Civil and Geodetic Engineering University of Ljubljana Ljubljana Slovenia Institute of Mathematics Physics and Mechanics Ljubljana Slovenia Faculty of Mechanical Engineering University of Ljubljana Ljubljana Slovenia Department of Applied Analysis and Computational Mathematics ELTE TTK Budapest Hungary

Application of fuzzy logic for the assessment of engineering students 8

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Application of fuzzy logic for the assessment of engineering...

8th IEEE Global Engineering Education Conference, EDUCON 2017

作者： Samarakou, Maria Prentakis, Pantelis Mitsoudis, Dimitrios Karolidis, Dimitrios Athinaios, Spyros Department of Energy Technology Engineering Technological Educational Institute of Athens Athens Greece Institute of Applied and Computational Mathematics FORTH Heraklian Greece Department of Electronics Engineering Technological Educational Institute of Athens Athens Greece

ISBN: (纸本)9781509054671

In this paper, we present a fuzzy-logic based model for the diagnosis of the so-called students' learning profile. The fuzzy logic module is coupled with an interactive open learning environment (StuDiAsE) that incorporates the text comprehension theory by Denhière and Baudet, the dialogue theory of Collins and Beranek, and the learning styles theory of Felder and Silverman. This intelligent learning environment is used for diagnosis, assistance and evaluation of engineering students. Preliminary tests for student assessment displayed high influence on the performance and motivation of its users. © 2017 IEEE.

关键词： Fuzzy logic

On the zero-stability of multistep methods on smooth nonuniform grids

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arXiv 2018年

作者： Söderlind, Gustaf Fekete, Imre Faragó, István Centre for Mathematical Sciences Lund University Box 118 LundSE-221 00 Sweden Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Pázmány P. s. 1/C BudapestH-1117 Hungary MTA-ELTE Numerical Analysis and Large Networks Research Group Pázmány P. s. 1/C BudapestH-1117 Hungary

In order to be convergent, linear multistep methods must be zero stable. While constant step size theorywas established in the 1950's, zero stability on nonuniform grids is less well understood. Here we investigate zero stability on compact intervals and smooth nonuniformgrids. In practical computations, step size control can be implemented using smooth (small) step size changes. The resulting grid {tn}Nn=0can be modeled as the image of an equidistant grid under a smooth deformationmap, i.e., tn= Φ(τn), where τn= n/N and the map Φ is monotonically increasing with Φ(0) = 0 and Φ(1) = 1. The model is justified for any fixed order method operating in its asymptotic regime when applied to smooth problems, since the step size is then determined by the (smooth) principal error function which determines Φ, and a tolerance requirement which determines N. Given any strongly stable multistep method, there is an N∗such that the method is zero stable for N > N∗, provided that Φ ϵ C2[0,1]. Thus zero stability holds on all nonuniform grids such that adjacent step sizes satisfy hn/hn-1= 1+O(N-1) as N →∞. The results are exemplified for BDF-type methods.65L04, 65L05, 65L06, 65L07 Copyright © 2018, The Authors. All rights reserved.

关键词： Initial value problems

Phase unwinding, or invariant subspace decompositions of hardy spaces

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arXiv 2017年

作者： Coifman, Ronald R. Peyrie, Jacques Department of Mathematics Program in Applied Mathematics Yale University New HavenCT06510 United States Laboratoire de Mathématiques d'Orsay Univ. Paris-Sud CNRS Université Paris-Saclay Orsay91405 France

We consider orthogonal decompositions of invariant subspaces of Hardy spaces, these relate to the Blaschke based phase unwinding decompositions [1, 2, 7]. We prove convergence in Lp. In particular we build an explicit multiscale wavelet basis. We also obtain an explicit unwindinig decomposition for the singular inner function, exp 2iπ/*** Codes 30B50, 30A10, 42C40, 65T99 Copyright © 2017, The Authors. All rights reserved.

关键词： Functions

Micromagnetic understanding of the skyrmion Hall angle current dependence in perpendicularly magnetized ferromagnets

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Physical Review B 2018年第22期98卷 224418-224418页

作者： Riccardo Tomasello Anna Giordano Stefano Chiappini Roberto Zivieri Giulio Siracusano Vito Puliafito Israa Medlej Aurelio La Corte Bruno Azzerboni Mario Carpentieri Zhongming Zeng Giovanni Finocchio Institute of Applied and Computational Mathematics FORTH GR-70013 Heraklion-Crete Greece Department of Mathematical and Computer Sciences Physical Sciences and Earth Sciences University of Messina I-98166 Messina Italy Istituto Nazionale di Geofisica e Vulcanologia Via di Vigna Murata 605 I-00143 Roma Italy Department of Electric Electronic and Computer Engineering University of Catania I-95125 Catania Italy Department of Engineering University of Messina I-98166 Messina Italy Department of Electrical and Information Engineering Politecnico di Bari I-70125 Bari Italy Key Laboratory of Nanodevices and Applications Suzhou Institute of Nano-tech and Nano-bionics Chinese Academy of Sciences Ruoshui Road 398 Suzhou 215123 People's Republic of China

The understanding of the dynamical properties of skyrmions is a fundamental aspect for the realization of a competitive skyrmion based technology beyond complementary metal-oxide semiconductors. Most of the theoretical approaches are based on the approximation of a rigid skyrmion. However, thermal fluctuations can drive a continuous change of the skyrmion size via the excitation of thermal modes. Here, by taking advantage of the Hilbert-Huang transform, we demonstrate that at least two thermal modes can be excited which are nonstationary in time. In addition, one limit of the rigid skyrmion approximation is that this hypothesis does not allow for correctly describing the recent experimental evidence of skyrmion Hall angle dependence on the amplitude of the driving force, which is proportional to the injected current. In this paper, we show that, in an ideal sample, the combined effect of fieldlike and dampinglike torques on a breathing skyrmion can indeed give rise to such a current dependent skyrmion Hall angle. While here we design and control the breathing mode of the skyrmion, our results can be linked to the experiments by considering that the thermal fluctuations and/or disorder can excite the breathing mode. We also develop a generalized Thiele equation and propose an experiment to validate our findings.

关键词： Skyrmions Spintronics Multilayer thin films Micromagnetic modeling

Global center stable manifold for the defocusing energy critical wave equation with potential

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arXiv 2017年

作者： JIA, HAO LIU, BAOPING SCHLAG, WILHELM XU, GUIXIANG School of Mathematics Institute of Advanced study 1 Einstein Drive PrincetonNJ08540 United States Beijing International Center for Mathematical Research Peking University Beijing China University of Chicago Department of Mathematics 5734 South University Avenue ChicagoIL60636 United States Institute of Applied Physics and Computational Mathematics Beijing China

In this paper we consider the defocusing energy critical wave equation with a trapping potential in dimension 3. We prove that the set of initial data for which solutions scatter to an unstable excited state (Ø, 0) forms a finite co-dimensional path connected C1 manifold in the energy space. This manifold is a global and unique center-stable manifold associated with (Ø, 0). It is constructed in a first step locally around any solution scattering to Ø, which might be very far away from Ø in the H 1 × L2(R3) norm. In a second crucial step a no-return property is proved for any solution which starts near, but not on the local manifolds. This ensures that the local manifolds form a global one. Scattering to an unstable steady state is therefore a non-generic behavior, in a strong topological sense in the energy space. This extends our previous result [19] to the nonradial case. The new ingredients here are (i) application of the reversed Strichartz estimate from [3] to construct a local center stable manifold near any solution that scatters to (Ø, 0). This is needed since the endpoint of the standard Strichartz estimates fails nonradially. (ii) The nonradial channel of energy estimate introduced by Duyckaerts-Kenig-Merle [15], which is used to show that solutions that start off but near the local manifolds associated with Ø emit some amount of energy into the far field in excess of the amount of energy beyond that of the steady state Ø. Copyright © 2017, The Authors. All rights reserved.

关键词： Wave equations

A constructive approach to L0 penalized regression

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2018年第1期19卷

作者： Jian Huang Yuling Jiao Yanyan Liu Xiliang Lu Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong China School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan China and Institute of Big Data of Zhongnan University of Economics and Law School of Mathematics and Statistics Wuhan University Wuhan China School of Mathematics and Statistics Wuhan University Wuhan China and Hubei Key Laboratory of Computational Science

We propose a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the l0-penalized least squares solutions. It generates a sequence of solutions iteratively, based on support detection using primal and dual information and root finding. We refer to the algorithm as SDAR for brevity. Under a sparse Riesz condition on the design matrix and certain other conditions, we show that with high probability, the l2 estimation error of the solution sequence decays exponentially to the minimax error bound in O(log(Rp√J)) iterations, where J is the number of important predictors and R is the relative magnitude of the nonzero target coefficients; and under a mutual coherence condition and certain other conditions, the l∞ estimation error decays to the optimal error bound in O(log(R)) iterations. Moreover the SDAR solution recovers the oracle least squares estimator within a finite number of iterations with high probability if the sparsity level is known. computational complexity analysis shows that the cost of SDAR is O(np) per iteration. We also consider an adaptive version of SDAR for use in practical applications where the true sparsity level is unknown. Simulation studies demonstrate that SDAR outperforms Lasso, MCP and two greedy methods in accuracy and efficiency.

关键词： KKT conditions geometrical convergence nonasymptotic error bounds oracle property root finding support detection

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric bayesian inverse problems

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arXiv 2017年

作者： Agapiou, Sergios Burger, Martin Dashti, Masoumeh Helin, Tapio Department of Mathematics and Statistics University of Cyprus 1 University Avenue Nicosia2109 Cyprus Institute for Computational and Applied Mathematics Westfälische Wilhelms-Universität Münster and Cells in Motion Cluster of Excellence Münster Germany Department of Mathematics University of Sussex BrightonBN1 5DJ United Kingdom Department of Mathematics and Statistics University of Helsinki Gustaf Hallströmin katu 2b HelsinkiFI-00014 Finland

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation y of its image through a known possibly non-linear ill-posed map G. The data y is finite-dimensional and the noise is Gaussian. We adopt a Bayesian approach to the problem and consider Besov space priors (see), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on nonparametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.49N45, 62C10, 62G05, 62G20 Copyright © 2017, The Authors. All rights reserved.

关键词： Banach spaces

Ion beam bunching via phase rotation in cascading laser-driven ion acceleration

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arXiv 2018年

作者： Wang, H.C. Weng, S.M. Liu, M. Chen, M. He, M.Q. Zhao, Q. Murakami, M. Sheng, Z.M. School of Physics and Astronomy Shanghai Jiao Tong University Shanghai200240 China Collaborative Innovation Center of IFSA Shanghai Jiao Tong University Shanghai200240 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Institute of Laser Engineering Osaka University Osaka565-0871 Japan Tsung-Dao Lee Institute Shanghai200240 China SUPA Department of Physics University of Strathclyde GlasgowG4 0NG United Kingdom

The ion beam bunching in a cascaded target normal sheath acceleration is investigated by theoretical analysis and particle-in-cell simulations. It is found that a proton beam can be accelerated and bunched simultaneously by injecting it into the rising sheath field at the rear side of a laser-irradiated foil target. In the rising sheath field, the ion phase rotation may take place since the back-end protons of the beam feels a stronger field than the front-end protons. Consequently, the injected proton beam can be compressed in the longitudinal direction. At last, the vital role of the ion beam bunching is illustrated by the integrated simulations of two successive stages in a cascaded acceleration. Copyright © 2018, The Authors. All rights reserved.

关键词： Ion beams