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Median matrix completion: From embarrassment to optimality 37

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Median matrix completion: From embarrassment to optimality

37th International Conference on Machine Learning, ICML 2020

作者： Liu, Weidong Mao, Xiaojun Wong, Raymond K.W. Sch. of Math. Sciences and MoE Key Lab of Artificial Intelligence Shanghai Jiao Tong University Shanghai200240 China School of Data Science Fudan University Shanghai200433 China Department of Statistics Texas AandM University College StationTX77843 United States

ISBN: (纸本)9781713821120

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge for large-scale data sets which are increasingly common among matrix completion problems. A simple solution to large-scale problems is parallel computing. However, embarrassingly parallel fashion often leads to inefficient estimators. Based on the idea of pseudo data, we propose a novel refinement step, which turns such inefficient estimators into a rate (near-)optimal matrix completion procedure. The refined estimator is an approximation of a regularized least median estimator, and therefore not an ordinary regularized empirical risk estimator. This leads to a nonstandard analysis of asymptotic behaviors. Empirical results are also provided to confirm the effectiveness of the proposed method. © 2020 37th International Conference on Machine Learning, ICML 2020. All rights reserved.

关键词： Matrix algebra

PRIMITIVE WEAKLY DISTANCE-REGULAR CIRCULANT DIGRAPHS

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arXiv 2019年

作者： Munemasa, Akihiro Wang, Kaishun Yang, Yuefeng Research Center for Pure and Applied Mathematics Graduate School of Information Sciences Tohoku University Sendai980–8579 Japan Sch. Math. Sci. & Lab. Math. Com. Sys Beijing Normal University Beijing100875 China School of Science China University of Geosciences Beijing100083 China

We classify certain non-symmetric commutative association sch.mes. As an application, we determine all the primitive weakly distance-regular circulant *** Codes 05E30 Copyright © 2019, The Authors. All rights res... 详细信息

关键词： Directed graphs

The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal cahn-hilliard equation

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arXiv 2019年

作者： Liu, Zhengguang Cheng, Aijie Li, Xiaoli School of Mathematics and Statistics Shandong Normal University Jinan School of Mathematics Shandong University Jinan250100 Fujian Prov. Key Lab. on Math. Modeling and High Perf. Sci. Comp. and Sch. of Mathematical Sciences Xiamen University Xiamen Fujian361005

Comparing with the classical local gradient ow and phase field models, the non-local models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase transitions. In this paper, we construct an accurate and effcient scalar auxiliary variable approach for the nonlocal Cahn-Hilliard equation with general nonlinear potential. The first contribution is that we have proved the unconditional energy stability for nonlocal Cahn-Hilliard model and its semi-discrete sch.mes carefully and rigor-ously. Secondly, what we need to focus on is that the non-locality of the nonlocal difiusion term will lead the stifiness matrix to be almost full matrix which generates huge computational work and memory requirement. For spatial discretizaion by finite difierence method, we find that the discretizaition for nonlocal operator will lead to a block-Toeplitz-Toeplitz-block (BTTB) matrix by applying four transformation operators. Based on this special structure, we present a fast procedure to reduce the computational work and memory requirement. Finally, several numerical simulations are demonstrated to verify the accuracy and effciency of our proposed sch.mes. Copyright © 2019, The Authors. All rights reserved.

关键词： Numerical models

High order residual distribution for steady state problems for hyperbolic conservation laws

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arXiv 2018年

作者： Lin, Jianfang Abgrall, Remi Qiu, Jianxian School of Mathematical Sciences Xiamen University Xiamen Fujian361005 Institute of Mathematics University of Zurich Zurich8057 Sch. of Math. Sci. and Fujian Prov. Key Lab. of Math. Modeling and High-Perf. Scientific Computing Xiamen University Xiamen Fujian361005

In this paper, we propose a high order residual distribution conservative finite difference sch.me for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution sch.mes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Physical properties

A fully discrete energy stable sch.me for a phase-field moving contact line model with variabledensities and viscosities

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arXiv 2018年

作者： Zhu, Guangpu Chen, Huangxin Sun, Shuyu Yao, Jun Qingdao266580 China Sch. of Math. Sci. and Fujian Prov. Key Lab. on Math. Modeling and High Perf. Scientific Computing Xiamen University Xiamen361005 China Computational Transport Phenomena Laboratory Division of Physical Science and Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this work, we propose a fully discrete energy stable sch.me for the phase-field moving contact line model with variable densities and viscosities. The math.matical model consists of a Cahn-Hilliard equation, a Navier-Stokes equation and the generalized Navier boundary condition. A scalar auxiliary variable is introduced to transform the nonlinear potential into an equivalent form, allowing the nonlinear potential to be treated effectively and semi-explicitly. A pressure stabilization method is used to decouple the computation of velocity and pressure. Some subtle implicit-explicit treatments are adopted to deal with convention and stress terms. An artificial term is added to balance the explicit nonlinear term originating from the surface energy at fluid-solid interface. We establisharigorous proof of energy stability for the proposed time-marching *** a finite difference methodon staggered grids isusedto spatially discretize the constructed time-marchingsch.me. We prove that the fully discrete sch.me satisfiesthe discrete energy dissipationlaw. Numerical results demonstrate accuracy and energy stability of the proposed sch.me. Using our numerical sch.me, we analyze theevolution of kinetic energy, mixing energy and surface energy at fluid-solid interfaceduring the bubble rising process. Three-dimensional droplet spreading is also investigated onachemically patterned surface. Our numerical simulation accurately predicts the expected energy evolutions and it successfully reproduces expected phenomenathat an oil droplet contractsinwardson a hydrophobiczone and spreadsoutwards quickly on a hydrophiliczone. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite difference method

A stochastic generalized Ginzburg-Landau equation driven by jump noise

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arXiv 2017年

作者： Lin, Lin Gao, Hongjun Jiangsu Provincial Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China Sch. of Math. Sci. and Jiangsu Ctr. for Collab. Innov. in Geogr. Info. Rsrc. Devmt. and Application Nanjing Normal University Nanjing210023 China

This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of an initial- boundary value problem with homogeneous Dirichlet boundary condition. However, for the generalized Ginzburg-Landau equation, such a locally monotonic condition of the nonlinear term can not be satisfied in a straight way. For this, we utilize the characteristic structure of nonlinear term and refined analysis to overcome this *** Codes 60H15, 35Q99 Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

Global Software Engineering Experience through International Capstone Project Exchanges

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Global Software Engineering Experience through International...

International Conference on Global Software Engineering (ICGSE)

作者： Dean Knudson Stavros Kalafatis Carsten Kleiner Stephen Zahos Barbara Seegebarth Jonas Deeterfelt Iman Avazpour Kristian Sandahl Peter Gorder Jeewani Ginige Alex Radermacher Hugo Caballero Humberto Gomez Mikael Roos Computer Science Dept. North Dakota State University Fargo ND USA ECE Department Texas A& M University College Station TX USA Computer Science Dept. Hannover University of Applied Sciences & Arts Hannover Germany Agricultural and Biological Eng. University of Illinois at Urbana-Champaign Urbana IL USA Institute of Marketing Technische Universitat Braunschweig Braunschweig Germany Linkopings universitet Linkoping SE School of IT Deakin University Burwood Australia Department of Computer and Information Science Linkoping University Linkoping SE Sweden Department of Mechanical and Aerospace Engineering Univ. of Colorado Colorado Springs CO USA Sch. of Comput. Eng. & Math. Western Sydney Univ. Sydney NSW Australia Departamento de Ingenieria Mecanica Universidad del Norte Barranquilla Colombia Department of Computer Science and Engineering Blekinge Institute of Technology (BTH) Karlskrona Sweden

Today it is very common for software systems to be built by teams located in more than one country. For example, a project team may be located in the US while the team lead resides in Sweden. How then should students be trained for this kind of work? Senior design or capstone projects offer students real-world hands-on experience but rarely while working internationally. One reason is that most instructors do not have international business contacts that allow them to find project sponsors in other countries. Another reason is the fear of having to invest a huge amount of time managing an international project. In this paper we present the general concepts related to "International Capstone Project Exchanges", the basic model behind the exchanges (student teams are led by an industry sponsor residing in a different country) and several alternate models that have been used in practice. We will give examples from projects in the US, Germany, Sweden, Australia, and Colombia. We have extended the model beyond software projects to include engineering projects as well as marketing, and journalism. We conclude with a description of an International Capstone Project Exchange website that we have developed to aid any university in establishing their own international project exchange.

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A Novel Dynamic Hidden Semi-Markov Model (D-HSMM) for Occupancy Pattern Detection from Sensor Data Stream

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A Novel Dynamic Hidden Semi-Markov Model (D-HSMM) for Occupa...

New Technologies, Mobility and Security (NTMS)

作者： Jose Luis Gomez Ortega Liangxiu Han Nicholas Bowring Sch. of Comput. Math. & Digital Technol. Manchester Metropolitan University Manchester Greater Manchester GB School of Computing Mathematics and Digital Technology Manchester Metropolitan University Manchester UK School of Computing Mathematics and Digital Technology Manchester Metropolitan University Manchester UK

ISBN: (纸本)9781509029150

Occupant presence and behaviour have a large impact on building energy performance. With the availability of low cost and affordable sensors, accurate occupancy detection by combining sensor stream data with machine learning approaches becomes possible. In this paper, we propose a novel dynamical hidden semi-Markov model (D-HSMM) which can accurately detect occupancy pattern from sensor data stream in real time. Our approach extends traditional hidden Markov (HMM) and hidden semi-Markov models (HSMM). The novelty of the proposed approach consists in 1) a new dynamic duration modelling way in which the duration is dynamically changing, instead of using fixed duration in traditional HSMM based models; 2) a new approach to state prediction (i.e. occupant presence or absence in this case) based on a weighted function with partially available observations instead of using the whole set of observations. In order to evaluate the performance of our model, we have compared our results with traditional HMM and HSMM approaches. The experimental evaluation shows that our D-HSMM model outperforms the conventional HMM and HSMM-based approaches with very high accuracy.

关键词： Hidden Markov models Data models Predictive models Probability Buildings Adaptation models Heuristic algorithms

Topological characterization of housekeeping genes in human protein-protein interaction network 8

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Topological characterization of housekeeping genes in human ...

8th International Conference on Systems Biology, ISB 2014

作者： Wang, Pei Zhang, Yuhuan Lü, Jinhu Yu, Xinghuo Sch. Math. Inf. Sci. Henan University Kaifeng475004 China Acad. Math. Syst. Sci. Chinese Academy of Sciences Beijing100190 China Sch. Elect. Comput. Eng. RMIT University MelbourneVIC3001 Australia

ISBN: (纸本)9781479972944

Human housekeeping genes (HKGs) are widely expressed in various tissues, which involve in cell maintenance or sustaining cell function, and are often taken as experimental control and normalization references in gene expression experiments. Based on literature curation and up-to-date databases, we construct a large-scale human protein-protein interaction network (HPIN) and a HKGs subnetwork. Through the topological features of HKGs in the HPIN, we characterize the topological features of human HKGs. Our results indicate HKGs are with very large average degree, k-shell, betweeness, semilocal and eigenvector centralities, clustering coefficient, closeness, PageRank and motif centrality, which are all higher than that of the HPIN. Among the nine indexes, HKGs are with the average betweeness about 7 times larger than that for the HPIN, but they are also with the largest coefficient of variant (CV). The closeness of HKGs is with the smallest CV and very large median. Based on ROC analysis, we find most of the indexes and their compositions can be used to predict HKGs, with prediction accuracy around 80%. Especially, the prediction accuracy of the closeness can achieve as high as 82.36%. The investigations shed some lights on the characterization and identification of human functional genes, which have potential implications in systems biology and networked medicine. © 2014 IEEE.

关键词： Gene expression