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A well-posedness result for an extended KdV equation

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Partial Differential Equations in applied math.matics 2024年 10卷

作者： Berjawi, M. El Arwadi, T. Israwi, S. Department of mathematics and Computer science Faculty of science Beirut Arab University Beirut Lebanon Laboratoire de mathématiques-EDST Faculté des sciences et EDST Université Libanaise Hadat Lebanon Arts Sciences and Technology University in Lebanon CRAMS: Center for Research in Applied Mathematics and Statistics Faculty of sciences Beirut Lebanon

Among the most interesting things Russell discovered was there is a math.matical relation between the height of the wave, the depth of the wave when water at rest and the speed at which the wave travels. KdV equation was the first math.matical unidimensional model describing the phenomenon observed by Scott-Russell. Despite its nonlinearity and dispersivity terms, KdV equation has being interesting because of its integrability, and specially being a soliton equation. In this paper, we aim to analyze an extended KdV equation. The construction of approximate solution of this equation will be done in H^s(R), for s>[Formula presented], using the modified energy method, its uniqueness and continuity with respect to the initial data is presented referring to a Bona–Smith technique. © 2024

关键词： KdV Model Well posedness

Crouzeix’s Conjecture and Related Problems

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arXiv 2020年

作者： Bickel, Kelly Gorkin, Pamela Greenbaum, Anne Ransford, Thomas Schwenninger, Felix Wegert, Elias Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Applied Mathematics University of Washington Département de mathématiques et de statistique Université Laval QuébecQCG1V 0A6 Canada Department of Mathematics Universität Hamburg Department of Applied Mathematics University of Twente Netherlands Department of Mathematics and Computer Science Technische Universität Bergakademie Freiberg Division of Mathematical Sciences National Science Foundation United States NSERC and the Canada Research Chairs program

In this paper, we establish several results related to Crouzeixs conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation constant, which is defined in terms of the pseudohyperbolic metric. Moreover, we study general properties of related extremal functions and associated vectors. Throughout, compressions of the shift serve as illustrating examples which also allow for refined *** Codes 47A25, 47A12, 15A60, 47A20, 30J10 Copyright © 2020, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Defining Protocols of Systematic Literature Reviews in Software Engineering: A Survey

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Defining Protocols of Systematic Literature Reviews in Softw...

Euromicro Conference on Software Engineering and Advanced Applications (SEAA)

作者： Katia Romero Felizardo Érica Ferreira de Souza Ricardo Almeida Falbo Nandamudi Lankalapalli Vijaykumar Emilia Mendes Elisa Yumi Nakagawa Department of Computer Federal University of Technology Cornélio Procópio/PR Brazil Federal University of Technology PR Brazil Depart. of Computer Science Federal University of Espírito Santo Vitória/ES Brazil Lab. of Comp. & Appl. Math. Nat. Inst. for Space Res. Sao Jose dos Campos SP BR University of Oulu Karlskrona Sweden Univ. of Sao Paulo São Carlos/SP Brazil

Context: Despite being defined during the first phase of the Systematic Literature Review (SLR) process, the protocol is usually refined when other phases are performed. Several researchers have reported their experiences in applying SLRs in Software Engineering (SE) however, there is still a lack of studies discussing the iterative nature of the protocol definition, especially how it should be perceived by researchers conducting SLRs. Objective: The main goal of this study is to perform a survey aiming to identify: (i) the perception of SE researchers related to protocol definition; (ii) the activities of the review process that typically lead to protocol refinements; and (iii) which protocol items are refined in those activities. Method: A survey was performed with 53 SE researchers. Results: Our results show that: (i) protocol definition and pilot test are the two activities that most lead to further protocol refinements; (ii) data extraction form is the most modified item. Besides that, this study confirmed the iterative nature of the protocol definition. Conclusions: An iterative pilot testcan facilitate refinements in the protocol.

关键词： Protocols Planning Electronic mail Data mining Software engineering Systematics Bibliographies

Applying an update method to a set of receivers (extended abstract) 95

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Applying an update method to a set of receivers (extended ab...

Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems

作者： Marc Andries Luca Cabibbo Jan Paredaens Jan Van den Bussche Department of Mathematics and Computer Science Leiden University Niels Bohrweg 1 2333 CA Leiden the Netherlands Dipartimento di Informatica e Sistemistica Università di Roma 'La Sapienza' Via Salaria 113 I-0019 Roma Italy Dept. Math. & Computer Sci. University of Antwerp (UIA) Universiteitsplein 1 B-2610 Antwerpen Belgium INRIA (Projet VERSO) Domaine de Voluceau Rocquencourt B.P. 105 F-78153 Le Chesnay Cedex France

Combinatorial algorithms enabling computational science: tales from the front

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Journal of Physics: Conference Series 2006年第1期46卷

作者： Sanjukta Bhowmick Erik G Boman Karen Devine Assefaw Gebremedhin Bruce Hendrickson Paul Hovland Todd Munson Alex Pothen Mathematics and Computer Science Division Argonne National Laboratory USA Department of Applied Physics and Applied Mathematics Columbia University USA Discrete Algorithms and Math Department Sandia National Laboratories USA Computer Science Department Old Dominion University USA

Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations. The importance of discrete algorithms continues to grow with the demands of new applications and advanced architectures. This paper surveys some recent developments in this rapidly changing and highly interdisciplinary field.

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A discontinuity of the energy of quantum walk in impurities

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arXiv 2021年

作者： Higuchi, Kenta Komatsu, Takashi Konno, Norio Morioka, Hisashi Segawa, Etsuo Department of Mathematical Sciences Ritsumeikan University Noji-Higashi Kusatsu525-8577 Japan Math. Research Institute Calc for Industry Minami Hiroshima732-0816 Japan Department of Applied Mathematics Yokohama National University Hodogaya Yokohama240-8501 Japan Graduate School of Science and Engineering Ehime University Bunkyo-cho 3 Ehime Matsuyama790-8577 Japan Graduate School of Environment Information Sciences Yokohama National University Hodogaya Yokohama240-8501 Japan

We consider the discrete-time quantum walk whose local dynamics is denoted by C at the perturbed region {0,1,·,M-1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωnat time n (|ω|=1). From this expression, we compute the scattering on the surface of -1 and M and also compute the quantity how quantum walker accumulates in the perturbed region;namely the energy of the quantum walk, in the long time limit. We find a discontinuity of the energy with respect to the frequency of the inflow. Copyright © 2021, The Authors. All rights reserved.

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Supervised multiple kernel learning approaches for multi-omics data integration

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arXiv 2024年

作者： Briscik, Mitja Tazza, Gabriele Vidács, László Dillies, Marie-Agnès Déjean, Sébastien Institut de Mathématiques de Toulouse UMR5219 CNRS UPS Université de Toulouse Cedex 9 Toulouse31062 France Department of Computer Science Applied Artificial Intelligence Group University of Szeged Szeged6720 Hungary Institut Pasteur Université Paris Cité Bioinformatics and Biostatistics Hub ParisF‑75015 France

Background: Advances in high‑throughput technologies have originated an ever‑ increasing availability of omics datasets. The integration of multiple heterogeneous data sources is currently an issue for biology and bioinformatics. Multiple kernel learn‑ ing (MKL) has shown to be a flexible and valid approach to consider the diverse nature of multi‑omics inputs, despite being an underused tool in genomic data mining. Results: We provide novel MKL approaches based on different kernel fusion strategies To learn from the meta‑kernel of input kernels, we adapted unsupervised integration algorithms for supervised tasks with support vector machines. We also tested deep learning architectures for kernel fusion and classification. The results show that MKL‑ based models can outperform more complex, state‑of‑the‑art, supervised multi‑omics integrative approaches. Conclusion: Multiple kernel learning offers a natural framework for predictive models in multi‑omics data. It proved to provide a fast and reliable solution that can compete with and outperform more complex architectures. Our results offer a direction for bio‑ data mining research, biomarker discovery and further development of methods for heterogeneous data integration. © 2024, CC BY.

关键词： Self-supervised learning

Artificial intelligence advances for de novo molecular structure modeling in cryo-EM

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arXiv 2021年

作者： Si, Dong Nakamura, Andrew Tang, Runbang Guan, Haowen Hou, Jie Firozi, Ammaar Cao, Renzhi Hippe, Kyle Zhao, Minglei Division of Computing and Software Systems University of Washington Bothell BothellWA98011 United States Molecular Engineering and Sciences Institute University of Washington Seattle SeattleWA98105 United States Applied and Computational Math Sciences University of Washington Seattle SeattleWA98195 United States Department of Computer Science Saint Louis University Saint. LouisMO63103 United States Department of Computer Science Pacific Lutheran University TacomaWA98447 United States Department of Biochemistry and Molecular Biology University of Chicago ChicagoIL60637 United States

Cryo-electron microscopy (cryo-EM) has become a major experimental technique to determine the structures of large protein complexes and molecular assemblies, as evidenced by the 2017 Nobel Prize. Although cryo-EM has been drastically improved to generate high-resolution three-dimensional (3D) maps that contain detailed structural information about macromolecules, the computational methods for using the data to automatically build structure models are lagging far behind. The traditional cryo-EM model building approach is template-based homology modeling. Manual de novo modeling is very time-consuming when no template model is found in the database. In recent years, de novo cryo-EM modeling using machine learning (ML) and deep learning (DL) has ranked among the top-performing methods in macromolecular structure modeling. Deep-learning-based de novo cryo-EM modeling is an important application of artificial intelligence, with impressive results and great potential for the next generation of molecular biomedicine. Accordingly, we systematically review the representative ML/DL-based de novo cryo-EM modeling methods. And their significances are discussed from both practical and methodological viewpoints. We also briefly describe the background of cryo-EM data processing workflow. Overall, this review provides an introductory guide to modern research on artificial intelligence (AI) for de novo molecular structure modeling and future directions in this emerging field. © 2021, CC BY-NC-ND.

关键词： Electron microscopes

FURSTENBERG SYSTEMS OF PRETENTIOUS AND MRT MULTIPLICATIVE FUNCTIONS

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arXiv 2023年

作者： Frantzikinakis, Nikos Lemańczyk, Mariusz de la Rue, Thierry University of Crete Department of Mathematics and Applied Mathematics Voutes University Campus Heraklion71003 Greece Faculty of Mathematics and Computer Science Nicolaus Copernicus University Toruń Poland Université de Rouen Normandie CNRS Laboratoire de Mathématiques Raphaël Salem Avenue de L’Université Saint Étienne du Rouvray76801 France

We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational discrete spectrum and, as a consequence, zero entropy. We obtain several other refined structural and spectral results, one consequence of which is that the Archimedean characters are the only pretentious multiplicative functions that have Furstenberg systems with trivial rational spectrum, another is that a pretentious multiplicative function has ergodic Furstenberg systems if and only if it pretends to be a Dirichlet character, and a last one is that for any fixed pretentious multiplicative function all its Furstenberg systems are isomorphic. We also study structural properties of Furstenberg systems of a class of multiplicative functions, introduced by Matomäki, Radziwill, and Tao, which lie in the intermediate zone between pretentiousness and strong aperiodicity. In a work of the last two authors and Gomilko, several examples of this class with exotic ergodic behavior were identified, and here we complement this study and discover some new unexpected phenomena. Lastly, we prove that Furstenberg systems of general bounded multiplicative functions have divisible spectrum. When these systems are obtained using logarithmic averages, we show that trivial rational spectrum implies a strong dilation invariance property, called strong stationarity, but, quite surprisingly, this property fails when the systems are obtained using Cesàro *** Codes Primary: 11N37, Secondary: 37A44, 11K65 © 2023, CC BY.

关键词： Rational functions