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MIXUP-BASED DEEP METRIC LEARNING APPROACHES FOR INCOMPLETE SUPERVISION

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arXiv 2022年

作者： Buris, Luiz H. Pedronette, Daniel C.G. Papa, Joao P. Almeida, Jurandy Carneiro, Gustavo Faria, Fabio Augusto Institute of Science and Technology Universidade Federal de São Paulo Brazil Depart. of Statistics Applied Math. and Computing São Paulo State University Brazil Department of Computing São Paulo State University Brazil Department of Computing Federal University of São Carlos Brazil Australian Institute for Machine Learning The University of Adelaide Australia

Deep learning architectures have achieved promising results in different areas (e.g., medicine, agriculture, and security). However, using those powerful techniques in many real applications becomes challenging due to the large labeled collections required during training. Several works have pursued solutions to overcome it by proposing strategies that can learn more for less, e.g., weakly and semi-supervised learning approaches. As these approaches do not usually address memorization and sensitivity to adversarial examples, this paper presents three deep metric learning approaches combined with Mixup for incomplete-supervision scenarios. We show that some state-of-the-art approaches in metric learning might not work well in such scenarios. Moreover, the proposed approaches outperform most of them in different datasets. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep learning

Analysis, circuit realization and controls of an autonomous Morse jerk oscillator

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SeMA Journal 2021年第3期78卷 415-433页

作者： Ainamon, Cyrille Tamba, Victor Kamdoum Pone, Justin Roger Mboupda Kingni, Sifeu Takougang Malwe, Hubert Boudoue Orou, Jean Bio Chabi Institut de Mathématiques et de Sciences Physiques Université d’Abomey-Calavi B.P. 613 Porto Novo Benin Department of Telecommunication and Network Engineering IUT-Fotso Victor of Bandjoun University of Dschang PO Box 134 Bandjoun Cameroon Electrical Engineering Department of IUT-Fotso Victor of Bandjoun Research Unit of Automation and Applied Computer (RU-AIA) University of Dschang PO Box 134 Bandjoun Cameroon Department of Mechanical Petroleum and Gas Engineering Faculty of Mines and Petroleum Industries University of Maroua PO Box 46 Maroua Cameroon Department of Physics Faculty of Science University of Maroua PO Box 814 Maroua Cameroon

In this paper, an autonomous Morse jerk oscillator which is designed by converting an autonomous two-dimensional Morse oscillator to a jerk oscillator, is analysed. The stability of its unique equilibrium point reveals the existence of Hopf bifurcation. Periodic and chaotic oscillations, antimonotonicity, chaotic bubbles and coexisting attractors are generated in the proposed jerk oscillator. Then, this proposed jerk oscillator is implemented in PSIM software and realized in a printed circuit board to verify the numerical results. The experimental/PSIM results agree well with the numerical simulations. Moreover, it is possible to control partially or totally the amplitude of its signals by introducing two additional parameters in the rate-equations describing the proposed jerk oscillator. Furthermore based on the Routh–Hurwitz conditions and using a single linear feedback controller, the proposed jerk oscillator is controlled to its unique equilibrium point. Finally, the coexistence between periodic and chaotic attractors is destroyed and controlled to a desired trajectory thank to the linear augmentation method. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.

关键词： Antimonotonicity Chaotic and coexisting attractors Control Electronic circuit realization Hopf bifurcation Morse jerk oscillator

A model for simulation of nuclear physics processes

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International Journal of Modelling and Simulation 1997年第4期17卷 276-282页

作者： Hartati, S. Nickerson, B.G. DeMille, G.R. Department of Physics Fac. of Math. and Natural Sciences Gajah Mada University Yogyakarta Indonesia Faculty of Computer Science University of New Brunswick Fredericton NB E3B 5A3 P.O. Box 4400 Canada Department of Physics University of New Brunswick Canada Fac. of Math. and Natural Sciences Gajah Mada University Yogyakarta Indonesia University of New Brunswick Canada Rensselaer Polytechnic Institute United States

A formal knowledge representation system for nuclear physics processes, called nuclear process theory (NPT), is introduced. NPT allows modelling and simulation of nuclear physics processes. Knowledge of these processes is expressed in terms of a basic nuclear physics model and an aggregate effects model. The basic nuclear physics model is used to express knowledge of many nuclear physics processes, including fission, radioactive capture, beta positive decay, and beta negative decay. The products of these processes are expressed in either deterministic or probabilistic values. The aggregate effects model coordinates basic nuclear physics processes expressed in the basic nuclear physics model. NPT, along with the NPT simulator, can be used to reason about nuclear physics processes for approximately 3,000 different nuclides. The approach was tested using a homogeneous thermal fission reactor model. The results of modelling fission and other nuclear physics processes in a pressurized heavy water reactor fueled with a mixture of 12% U235 and 88% U236 are presented.

关键词： Knowledge representation Nondeterministic process modelling Nuclear physics reasoning Simulation and modelling

On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates

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arXiv 2021年

作者： Garritano, James Kluger, Yuval Rokhlin, Vladimir Serkh, Kirill Program in Applied Mathematics Yale University New HavenCT06511 United States Yale School of Medicine New HavenCT06511 United States Dept. of Mathematics Yale University New HavenCT06511 United States Dept. of Math. and Computer Science University of Toronto TorontoONM5S 2E4 Canada

In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green's function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most state of the art methods cannot be easily parallelized. In this manuscript, we present an algorithm for evaluating the modal Green's function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as $O(m)$, where $m$ is the Fourier mode. Furthermore, our algorithm is embarrassingly parallelizable. © 2021, CC BY.

关键词： Bodies of revolution

A simple method to find all solutions to the functional equation of the smoothing transform

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arXiv 2019年

作者： Alsmeyer, Gerold Mallein, Bastien Inst. Math. Stochastics Department of Mathematics and Computer Science University of Münster Orléans-Ring 10 MünsterD-48149 Germany LAGA UMR 7539 Université Paris 13 - Sorbonne Paris Cité Université Paris 8 99 avenue Jean-Baptiste Clément Villetaneuse93430 France

Given a nonincreasing null sequence T = (Tj )j≽1 of nonnegative random variables satisfying some classical integrability assumptions and (Equation presented) for some α > 0, we characterize the solutions of the well-known functional equation (Equation presented), related to the so-called smoothing transform and its min-type variant. In order to do so within the class of nonnegative and nonincreasing functions, we provide a new three-step method whose merits are that (1) it simplifies earlier approaches in some relevant aspects, (2) it works under weaker, close to optimal conditions in the so-called boundary case when (Equation presented), (3) it can be expected to work as well in more general setups like random environment. At the end of this article, we also give a one-to-one correspondence between those solutions that are Laplace transforms and thus correspond to the fixed points of the smoothing transform and certain fractal random measures. The latter are defined on the boundary of a weighted tree related to an associated branching random *** Codes 39B22, 60E05, 60J85, 60G42 Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

Information retrieval from annotated texts

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Journal of the Association for Information science and Technology 1999年第10期50卷

作者： Aviezri S. Fraenkel Shmuel T. Klein Department of Applied Math & Computer Science The Weizmann Institute of Science Rehovot 76100 Israel Department of Math & Computer Science Bar-Ilan University Ramat-Gan 52900 Israel

Methods for the correct and efficient handling of annotations in a full-text retrieval system were investigated. The problem with annotations is that they cannot be treated as regular text, since this would disrupt proximity searches, but on the other hand, they cannot be ignored, as they may carry important information. Moreover, in some cases, a user may wish to restrict a search to prespecified subsets of annotations. We suggest a new way of processing the database to overcome the above dilemma.

关键词：

Mahler/Zeta Correspondence

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arXiv 2022年

作者： Komatsu, Takashi Konno, Norio Sato, Iwao Tamura, Shunya Math. Research Institute Calc for Industry Minami Hiroshima732-0816 Japan Department of Applied Mathematics Faculty of Engineering Yokohama National University Hodogaya Yokohama240-8501 Japan Oyama National College of Technology Oyama Tochigi323-0806 Japan Graduate School of Science and Engineering Yokohama National University Hodogaya Yokohama240-8501 Japan

The Mahler measure was introduced by Mahler in the study of number theory. It is known that the Mahler measure appears in different areas of math.matics and physics. On the other hand, we have been investigated a new class of zeta functions for various kinds of walks including quantum walks by a series of our previous work on "Zeta Correspondence". The quantum walk is a quantum counterpart of the random walk. In this paper, we present a new relation between the Mahler measure and our zeta function for quantum walks. Firstly we consider this relation in the case of one-dimensional quantum walks. Afterwards we deal with higher-dimensional quantum walks. For comparison with the case of the quantum walk, we also treat the case of higher-dimensional random walks. Our results bridge between the Mahler measure and the zeta function via quantum walks for the first time. Copyright © 2022, The Authors. All rights reserved.

关键词： Random processes

A generalized grover/zeta correspondence

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arXiv 2022年

We introduce a generalized Grover matrix of a graph and present an explicit formula for its characteristic polynomial. As a corollary, we give the spectra for the generalized Grover matrix of a regular graph. Next, we define a zeta function and a generalized zeta function of a graph G with respect to its generalized Grover matrix as an analog of the Ihara zeta function and present explicit formulas for their zeta functions for a vertex-transitive graph. As applications, we express the limit on the generalized zeta functions of a family of finite vertex-transitive regular graphs by an integral. Furthermore, we give the limit on the generalized zeta functions of a family of finite tori as an integral *** Codes 60F05, 05C50, 15A15, 05C25 © 2022, CC0.

关键词： Functions

Graph Fourier MMD for Signals on Graphs

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arXiv 2023年

作者： Leone, Samuel Venkat, Aarthi Huguet, Guillaume Tong, Alexander Wolf, Guy Krishnaswamy, Smita Applied Math Program New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Dept. of Math. & Stat Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Dept. of Comp. Sci. & Oper. Res. Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Department of Computer Science Department of Genetics Yale University New HavenCT United States

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization. Copyright © 2023, The Authors. All rights reserved.

关键词： Genes