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15th International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2019, held in conjunction with the 12th International Conference on Frontiers of Information Technology, Applications and Tools, FITAT 2019

作者： Lin, Meng-Ju Zhao, Ming Chen, Shuo-Tsung Chen, Ching-Ju Department of Applied Mathematics Tunghai University No. 1727 Sec.4 Taiwan Boulevard Taichung Taiwan40704 Taiwan School of Computer Science Yangtze University Jingzhou CityHubei Province China College of Future Bachelor Program in Interdisciplinary Studies National Yunlin University of Science and Technology TaiwanYunlin64002 Taiwan National Yunlin University of Science and Technology TaiwanYunlin64002 Taiwan

ISBN: (纸本)9789811397134

This paper proposed an amplitude embedding system for digital audio watermarking in the wavelet domain. In this paper, the relationship between the watermarked coefficients and the original coefficients is first presented and then amplitude-based embedding rules are combined into an amplitude-based embedding system that incorporates a system state. For the embedding in this system, the information includes synchronization codes and the watermarks are embedded into the DWT lowest frequency sub-band coefficients which can be described by a matrix form. Moreover, the SNR is rewritten as a performance index which is a quadratic form. Then, a nonlinear function connecting the performance index and the embedding system is derived. Accordingly, an optimization-based embedding system is proposed. Finally, the Karush–Kuhn–Tucker (KKT) Theorem is used to obtain the optimal solution, which is an important formula for watermarking. In addition, the hidden information can be extracted without knowledge of the original audio. In the experiments, the performance of the proposed system is tested and the results verify the high SNR and strong robustness against multimedia signal processing or malicious attacks. © 2020, Springer Nature Singapore Pte Ltd.

关键词： Embeddings

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Parsimonious reconstruction of network evolution

Parsimonious reconstruction of network evolution

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Lecture Notes in computer science

作者： Patro, Rob Sefer, Emre Malin, Justin Marçais, Guillaume Navlakha, Saket Kingsford, Carl Center for Bioinformatics and Computational Biology University of Maryland College Park MD 20742 United States Department of Computer Science University of Maryland College Park MD 20742 United States Computational Biology Bioinformatics and Genomics Concentration Biological Sciences Graduate Program University of Maryland College Park MD 20742 United States Program in Applied Mathematics Statistics and Scientific Computation University of Maryland College Park MD 20742 United States School of Computer Science Carnegie Mellon University Pittsburgh PA 15213 United States

ISBN: (纸本)9783642230370

We consider the problem of reconstructing a maximally parsimonious history of network evolution under models that support gene duplication and loss and independent interaction gain and loss. We introduce a combinatorial framework for encoding network histories, and we give a fast procedure that, given a set of duplication histories, in practice finds network histories with close to the minimum number of interaction gain or loss events. In contrast to previous studies, our method does not require knowing the relative ordering of unrelated duplication events. Results on simulated histories suggest that common ancestral networks can be accurately reconstructed using this parsimony approach. © 2011 Springer-Verlag.

关键词： Genes

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Digital Audio Watermarking by Quantization Embedding System 15th

Digital Audio Watermarking by Quantization Embedding System

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作者： Chen, Ching-Ju Zhao, Ming Chen, Shuo-Tsung Lin, Meng-Ju College of Future Bachelor Program in Interdisciplinary Studies National Yunlin University of Science and Technology DouliuYunlin Taiwan64002 Taiwan School of Computer Science Yangtze University Jingzhou CityHubei Province China Department of Applied Mathematics Tunghai University No. 1727 Sec. 4 Taiwan Boulevard TaichungTaiwan40704 Taiwan National Yunlin University of Science and Technology DouliuYunlin Taiwan64002 Taiwan

ISBN: (纸本)9789811397134

This paper designs a digital audio watermarking scheme using a quantization embedding system in the wavelet domain. In this paper, the relationship between the watermarked coefficients and the original coefficients is first presented and then the quantization-based embedding rules are combined into a quantization-based embedding system that incorporates a system state. For the embedding in this system, the information includes synchronization codes and the watermarks are embedded into the DWT lowest frequency sub-band coefficients, which can be described by a matrix form. Moreover, the SNR is rewritten as a performance index which is a quadratic form. Then, a nonlinear function connecting the performance index and the embedding system is derived. Accordingly, an optimization-based embedding system is proposed. Finally, the Lagrange Principle is used to obtain the optimal solution which is an important formula for watermarking. In addition, the hidden information can be extracted without knowledge of the original audio. In the experiments, the performance of the proposed system is tested and the results verify the high SNR and strong robustness against multimedia signal processing or malicious attacks. © 2020, Springer Nature Singapore Pte Ltd.

关键词： Audio watermarking

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Limited angle acousto-electrical tomography

arXiv

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arXiv 2017年

作者： Hubmer, Simon Knudsen, Kim Li, Changyou Sherina, Ekaterina Johannes Kepler University Linz Doctoral Program Computational Mathematics Altenbergerstraße 69 LinzA-4040 Austria Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark School of Electronics and Information Northwestern Polytechnical University Xian China Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.65J22, 35R30, 65M32 Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary conditions

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Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

arXiv

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arXiv 2022年

作者： Maama, Mohamed Jasra, Ajay Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling;the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data. Copyright © 2022, The Authors. All rights reserved.

关键词： Mean square error

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Geometry based data generation 18

Geometry based data generation

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Proceedings of the 32nd International Conference on Neural Information Processing Systems

作者： Ofir Lindenbaum Jay S. Stanley, III Guy Wolf Smita Krishnaswamy Applied Mathematics Program Yale University New Haven CT Computational Biology & Bioinformatics Program Yale University New Haven CT Departments of Genetics & Computer Science Yale University New Haven CT

We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis.

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A Flow Artist for High-Dimensional Cellular Data

A Flow Artist for High-Dimensional Cellular Data

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IEEE Workshop on Machine Learning for Signal Processing

作者： Kincaid MacDonald Dhananjay Bhaskar Guy Thampakkul Nhi Nguyen Joia Zhang Michael Perlmutter Ian Adelstein Smita Krishnaswamy Department of Mathematics Yale University Department of Genetics Yale School of Medicine Department of Computer Science Yale University Department of Mathematics Pomona College Applied Mathematics Program Yale University Department of Statistics University of Washington Department of Mathematics Boise State University Computational Biology and Bioinformatics Program Yale University

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data.

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Multilevel Monte Carlo Methods for the Grad-Shafranov Free Boundary Problem

SSRN

引用

SSRN 2023年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Department of Mathematics The University of Arizona United States

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costsby performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductionstypically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the model. © 2023, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

arXiv

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arXiv 2023年

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 © 2023, CC BY.

关键词： Monte Carlo methods

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Optimal control for reconstruction of curves without cusps

Optimal control for reconstruction of curves without cusps

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IEEE Conference on Decision and Control

作者： Ugo Boscain Remco Duits Francesco Rossi Yuri Sachkov Center for Applied Mathematics Ecole Polytechnique France Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands LSIS Aix-Marseille Universite Marseilles France Program Systems Institute Pereslavl-Zalessky Russia

ISBN: (纸本)9781467320658

We consider the problem of minimizing ∫ 0 ℓ √(ξ 2 +K 2 (s)ds) for a planar curve having fixed initial and final positions and directions. The total length ℓ is free. Here s is the variable of arclength parametrization, K(s) is the curvature of the curve and ξ >; 0 a parameter. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem. We prove that if for a certain choice of boundary conditions there is no global minimizer, then there is neither a local minimizer nor a stationary curve (geodesic). Our main tool is the construction of the optimal synthesis for the Reed and Shepp car with quadratic cost.

关键词： Brain modeling Boundary conditions Visualization Trajectory Aerospace electronics Optimal control Biological system modeling

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