The Experts below are selected from a list of 40092 Experts worldwide ranked by ideXlab platform
Salakhudinov R. - One of the best experts on this subject based on the ideXlab platform.
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Integral properties of the classical Warping function of a simply connected domain
2020Co-Authors: Salakhudinov R.Abstract:Let u(z,G) be the classical Warping function of a simply connected domain G. We prove that the L p-norms of the Warping function with different exponents are related by a sharp isoperimetric inequality, including the functional u(G) = sup x∈Gu(x, G). A particular case of our result is the classical Payne inequality for the torsional rigidity of a domain. On the basis of the Warping function, we construct a new physical functional possessing the isoperimetric monotonicity property. For a class of integrals depending on the Warping function, we also obtain a priori estimates in terms of the L p-norms of the Warping function as well as the functional u(G). In the proof, we use the estimation technique on level lines proposed by Payne. © 2012 Pleiades Publishing, Ltd
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Isoperimetric monotony of the L p -norm of the Warping function of a plane simply connected domain
2020Co-Authors: Salakhudinov R.Abstract:Let G be a simply connected domain and let u(x,G) be its Warping function. We prove that L p -norms of functions u and u -1 are monotone with respect to the parameter p. This monotony also gives isoperimetric inequalities for norms that correspond to different values of the parameter p. The main result of this paper is a generalization of classical isoperimetric inequalities of St.Venant-Pólya and the Payne inequalities. © 2010 Allerton Press, Inc
Gendro Germai - One of the best experts on this subject based on the ideXlab platform.
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Stability estimates for an inverse Steklov problem in a class of hollow spheres
2020Co-Authors: Gendro GermaiAbstract:In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. Precisely, we aim at studying the continuous dependence of the Warping function dening the warped product with respect to the Steklov spectrum. We first show that the knowledge of the Steklov spectrum up to an exponential decreasing error is enough to determine uniquely the Warping function in a neighbourhood of the boundary. Second, when the Warping functions are symmetric with respect to 1/2, we prove a log-type stability estimate in the inverse Steklov problem. As a last result, we prove a log-type stability estimate for the corresponding Calder{\'o}n problem
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Uniqueness results in the inverse spectral Steklov problem
2020Co-Authors: Gendro GermaiAbstract:This paper is devoted to an inverse Steklov problem for a particular class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. We prove that the knowledge of the Steklov spectrum determines uniquely the associated Warping function up to a natural invariance
Froese Vince - One of the best experts on this subject based on the ideXlab platform.
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Comparing Temporal Graphs Using Dynamic Time Warping
'Springer Science and Business Media LLC', 2020Co-Authors: Froese Vince, Jai Ijnesh, Niedermeie Rolf, Renke MalteAbstract:Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different temporal graphs. To this end, we propose to study dynamic time Warping on temporal graphs. We define the dynamic temporal graph Warping distance (dtgw) to determine the dissimilarity of two temporal graphs. Our novel measure is flexible and can be applied in various application domains. We show that computing the dtgw-distance is a challenging (in general) NP-hard optimization problem and identify some polynomial-time solvable special cases. Moreover, we develop a quadratic programming formulation and an efficient heuristic. In experiments on real-word data we show that the heuristic performs very well and that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches
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Fast Exact Dynamic Time Warping on Run-Length Encoded Time Series
2020Co-Authors: Froese Vince, Jai Ijnesh, Ryma Maciej, Welle MathiasAbstract:Dynamic Time Warping (DTW) is a well-known similarity measure for time series. The standard dynamic programming approach to compute the DTW distance of two length-$n$ time series, however, requires~$O(n^2)$ time, which is often too slow for real-world applications. Therefore, many heuristics have been proposed to speed up the DTW computation. These are often based on lower bounding techniques, approximating the DTW distance, or considering special input data such as binary or piecewise constant time series. In this paper, we present a first exact algorithm to compute the DTW distance of two run-length encoded time series whose running time only depends on the encoding lengths of the inputs. The worst-case running time is cubic in the encoding length. In experiments we show that our algorithm is indeed fast for time series with short encoding lengths
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An Average-Compress Algorithm for the Sample Mean Problem under Dynamic Time Warping
2020Co-Authors: Jai Ijnesh, Froese Vince, Schultz DavidAbstract:Computing a sample mean of time series under dynamic time Warping (DTW) is NP-hard. Consequently, there is an ongoing research effort to devise efficient heuristics. The majority of heuristics have been developed for the constrained sample mean problem that assumes a solution of predefined length. In contrast, research on the unconstrained sample mean problem is underdeveloped. In this article, we propose a generic average-compress (AC) algorithm for solving the unconstrained problem. The algorithm alternates between averaging (A-step) and compression (C-step). The A-step takes an initial guess as input and returns an approximation of a sample mean. Then the C-step reduces the length of the approximate solution. The compressed approximation serves as initial guess of the A-step in the next iteration. The purpose of the C-step is to direct the algorithm to more promising solutions of shorter length. The proposed algorithm is generic in the sense that any averaging and any compression method can be used. Experimental results show that the AC algorithm substantially outperforms current state-of-the-art algorithms for time series averaging
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Faster Binary Mean Computation Under Dynamic Time Warping
2020Co-Authors: Schaa Natha, Froese Vince, Niedermeie RolfAbstract:Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time Warping distance, best known from applications in time series mining. Doing so, we study the problem of finding a mean string that minimizes the sum of (squared) dynamic time Warping distances to a given set of input strings. While this problem is known to be NP-hard (even for strings over a three-element alphabet), we address the binary alphabet case which is known to be polynomial-time solvable. We significantly improve on a previously known algorithm in terms of worst-case running time. Moreover, we also show the practical usefulness of one of our algorithms in experiments with real-world and synthetic data. Finally, we identify special cases solvable in linear time (e.g., finding a mean of only two binary input strings) and report some empirical findings concerning combinatorial properties of optimal means
Thomas Wiemann - One of the best experts on this subject based on the ideXlab platform.
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Intertemporal Similarity of Economic Time Series: An Application of Dynamic Time Warping
Computational Economics, 2020Co-Authors: Philip Hans Franses, Thomas WiemannAbstract:This paper adapts the non-parametric dynamic time Warping (DTW) technique in an application to examine the temporal alignment and similarity across economic time series. DTW has important advantages over existing measures in economics as it alleviates concerns regarding a pre-defined fixed temporal alignment of series. For example, in contrast to current methods, DTW can capture alternations between leading and lagging relationships of series. We illustrate DTW in a study of US states’ business cycles around the Great Recession, and find considerable evidence that temporal alignments across states dynamic. Trough cluster analysis, we further document state-varying recoveries from the recession.
Kpalma K. - One of the best experts on this subject based on the ideXlab platform.
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A semantics-guided Warping for semi-supervised video object instance segmentation
'Springer Science and Business Media LLC', 2020Co-Authors: Wang Q.f., Lu Zhang, Kpalma K.Abstract:International audienceIn the semi-supervised video object instance segmentation domain, the mask Warping technique, which warps the mask of the target object to flow vectors frame by frame, is widely used to extract target object. The big issue with this approach is that the generated warped map is not always of high accuracy, where the background or other objects may be wrongly detected as the target object. To cope with this problem, we propose to use the semantics of the target object as a guidance during the Warping process. The Warping confidence computation firstly judges the confidence of the generated warped map. Then a semantic selection is introduced to optimize the warped map with low confidence, where the target object is re-identified using the semantics-labels of the target object. The proposed method is assessed on the recently published large-scale Youtube-VOS dataset and compared to some state-of-the-art methods. The experimental results show that the proposed approach has a promising performance. © Springer Nature Switzerland AG 2020
