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Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

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arXiv 2017年

作者： Alessandrini, Giovanni de Hoop, Maarten V. Gaburro, Romina Sincich, Eva Dipartimento di Matematica e Geoscienze Università di Trieste Italy Departments of Computational and Applied Mathematics Earth Science Rice University HoustonTX United States Department of Mathematics and Statistics University of Limerick Ireland Dipartimento di Matematica e Geoscienze Università di Trieste Italy

We consider the inverse boundary value problem of determining the potential q in the equation ∆u + qu = 0 in Ω ⊂ Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n ≥ 3 for potentials that are piecewise linear on a given partition of Ω. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation ∆u + k2c−2u = 0 at fixed frequency k.35R30, 86A22 Copyright © 2017, The Authors. All rights reserved.

关键词： Piecewise linear techniques

Bayesian modelling of skull conductivity uncertainties in EEG source imaging

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arXiv 2017年

作者： Rimpiläinen, Ville Koulouri, A. Lucka, F. Kaipio, J.P. Wolters, C.H. Institute for Biomagnetism and Biosignalanalysis University of Münster Münster Germany Institute for Computational and Applied Mathematics University of Münster Münster Germany Centre for Medical Image Computing University College London London United Kingdom Department of Mathematics University of Auckland Auckland New Zealand

Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors related to erronous skull conductivity. We demonstrate the potential of the approach by simulating EEG data of focal source activity and using the dipole scan algorithm and a sparsity promoting prior to reconstruct the underlying sources. The results suggest that the greatest improvements with the proposed method can be achieved when the focal sources are close to the skull. Copyright © 2017, The Authors. All rights reserved.

关键词： Electroencephalography

Babuška-Osborn techniques in discontinuous Galerkin methods: L2-norm error estimates for unstructured meshes

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arXiv 2017年

作者： Georgoulis, Emmanuil H. Makridakis, Charalambos G. Pryer, Tristan Department of Mathematics University of Leicester University Road LeicesterLE1 7RH United Kingdom School of Applied Mathematical and Physical Sciences National Technical University of Athens Zografou15780 Greece Institute for Applied and Computational Mathematics-FORTH and DMAM University of Crete Heraklion-CreteGR 70013 Greece Department of Mathematics University of Sussex BrightonBN1 9QH United Kingdom Department of Mathematics and Statistics University of Reading Whiteknights PO Box 220 ReadingRG6 6AX United Kingdom

We prove the inf-sup stability of the interior penalty class of discontinuous Galerkin schemes in unbalanced mesh-dependent norms, under a mesh condition allowing for a general class of meshes, which includes many examples of geometrically graded element neighbourhoods. The inf-sup condition results in the stability of the interior penalty Ritz projection in a mesh dependent L2-norm, which allows for the proof of novel a priori error estimates that do not depend on the global maximum meshsize in L2. Quasi-optimality results are also derived and some numerical experiments are given. Copyright © 2017, The Authors. All rights reserved.

关键词： Mesh generation

de Haas–van Alphen study on three-dimensional topological semimetal pyrite PtBi2

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arXiv 2018年

作者： Gao, Wenshuai Zhu, Xiangde Zhang, Hongwei Wu, Min Hu, Jin Zheng, Fawei Zheng, Guolin Hao, Ning Ning, Wei Tian, Mingliang Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions High Magnetic Field Laboratory Chinese Academy of Sciences Hefei Anhui230031 China Department of physics University of Science and Technology of China Hefei230026 China Department of Physics School of Physics and Materials Science Anhui University Hefei230601 China Collaborative Innovation Center of Advanced Microstructures Nanjing University Nanjing210093 China Department of Physics Institute for Nanoscience and Engineering University of Arkansas FayettevilleAR72701 United States Institute of Applied Physics and Computational Mathematics Beijing100088 China

We present the systematic de Haas–van Alphen (dHvA) quantum oscillations studies on the recently discovered topological Dirac semimetal pyrite PtBi2 single crystals. Remarkable dHvA oscillations were observed at field as low as 1.5 T. From the analyses of dHvA oscillations, we have extracted high quantum mobility, light effective mass and phase shift factor for Dirac fermions in pyrite PtBi2. From the angular dependence of dHvA oscillations, we have mapped out the topology of the Fermi surface and identified additional oscillation frequencies which were not probed by SdH oscillations. Copyright © 2018, The Authors. All rights reserved.

关键词： Pyrites

Imprints of Chameleon f(R) Gravity on galaxy rotation curves

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arXiv 2018年

作者： Naik, Aneesh P. Puchwein, Ewald Davis, Anne-Christine Arnold, Christian Institute of Astronomy University of Cambridge Madingley Road CambridgeCB3 0HA United Kingdom Kavli Institute for Cosmology University of Cambridge CambridgeCB3 0HA United Kingdom Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences CambridgeCB3 0HA United Kingdom Department of Physics Institute for Computational Cosmology Durham University South Roa DurhamDH1 3LE United Kingdom

Current constraints on gravity are relatively weak on galactic and intergalactic scales. Screened modified gravity models can exhibit complex behaviour there without violating stringent tests of gravity within our Solar System. They might hence provide viable extensions of the theory of gravity. Here, we use galaxy kinematics to constrain screened modified gravity models. We focus on chameleon f(R) gravity and predict its impact on galaxy rotation curves and radial acceleration relations. This is achieved by post-processing state-of-the-art galaxy formation simulations from the \textsc{auriga project}, using the \textsc{mg-gadget} code. For a given galaxy, the surface dividing screened and un-screened regions adopts an oblate shape, reflecting the disc morphology of the galaxy's mass distribution. At the 'screening radius'-the radius at which screening is triggered in the disc plane-characteristic ùpturns' are present in both rotation curves and radial acceleration relations. The locations of these features depend on various factors, such as the galaxy mass, the concentration of the density profile and the value of the background field amplitude fR0. Self-screening of stars and environmental screening also play a role. For Milky Way-size galaxies, we find that a model with |fR0|=10-7results in rotation curves that are indistinguishable from ΛCDM, while for |fR0|≥2×10-6 the simulated galaxies are entirely unscreened, violating Solar System constraints. For intermediate values, distinct upturns are present. With a careful statistical analysis of existing samples of observed rotation curves, including lower mass objects, constraints on f(R) gravity with a sensitivity down to |fR0|∼10-7 should be possible. Copyright © 2018, The Authors. All rights reserved.

关键词： Gravitation

Community detection and stochastic block models: recent developments

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2017年第1期18卷

作者： Emmanuel Abbe Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Princeton NJ

The stochastic block model (SBM) is a random graph model with planted clusters. It is widely employed as a canonical model to study clustering and community detection, and provides generally a fertile ground to study the statistical and computational tradeoffs that arise in network and data *** note surveys the recent developments that establish the fundamental limits for community detection in the SBM, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery (a.k.a., detection). The main results discussed are the phase transitions for exact recovery at the Chernoff-Hellinger threshold, the phase transition for weak recovery at the Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial recovery, the learning of the SBM parameters and the gap between information-theoretic and computational *** note also covers some of the algorithms developed in the quest of achieving the limits, in particular two-round algorithms via graph-splitting, semi-definite programming, linearized belief propagation, classical and nonbacktracking spectral methods. A few open problems are also discussed.

关键词： clustering community detection computational gaps network data analysis random graphs spectral algorithms stochastic block models unsupervised learning

computational intelligence, cyber security and computational models: Proceedings of ICC3 2015

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International Conference on computational Intelligence, Cyber Security and computational Models, ICC3 2015

作者： Senthilkumar, Muthukrishnan Ramasamy, Vijayalakshmi Sheen, Shina Veeramani, C. Bonato, Anthony Batten, Lynn Applied Mathematics and Computational Sciences PSG College of Technology Coimbatore Tamil Nadu India Department of Mathematics Ryerson University TorontoON Canada School of Information Technology Deakin University Melbourne Australia

computational Intelligence, Cyber Security and computational Models 1

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丛书名： Advances in Intelligent Systems and Computing

2016年

作者： Muthukrishnan Senthilkumar Vijayalakshmi Ramasamy Shina Sheen C. Veeramani Anthony Bonato Lynn Batten

PairClone: A Bayesian subclone caller based on mutation Pairs

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arXiv 2017年

作者： Zhou, Tianjian Müller, Peter Sengupta, Subhajit Ji, Yuan Department of Statistics and Data Sciences University of Texas Austin United States Department of Mathematics University of Texas Austin United States Program for Computational Genomics and Medicine NorthShore University HealthSystem Department of Public Health Sciences University of Chicago

Tumor cell populations can be thought of as being composed of homogeneous cell subpopulations, with each subpopulation being characterized by overlapping sets of single nucleotide variants (SNVs). Such subpopulations are known as subclones and are an important target for precision medicine. Reconstructing such subclones from next-generation sequencing (NGS) data is one of the major challenges in precision medicine. We present PairClone as a new tool to implement this reconstruction. The main idea of PairClone is to model short reads mapped to pairs of proximal SNVs. In contrast, most existing methods use only marginal reads for unpaired SNVs. Using Bayesian nonparametric models, we estimate posterior probabilities of the number, genotypes and population frequencies of subclones in one or more tumor sample. We use the categorical Indian buffet process (cIBP) as a prior probability model for subclones that are represented as vectors of categorical matrices that record the corresponding sets of mutation pairs. Performance of PairClone is assessed using simulated and real datasets. An open source software package can be obtained at http://***/pairclone. Copyright © 2017, The Authors. All rights reserved.

关键词： Matrix algebra