The Experts below are selected from a list of 14658 Experts worldwide ranked by ideXlab platform
Gunther Uhlmann - One of the best experts on this subject based on the ideXlab platform.
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inverse problems with partial data for a magnetic schrodinger operator in an infinite slab and on a bounded domain
Communications in Mathematical Physics, 2012Co-Authors: Katsiaryna Krupchyk, Matti Lassas, Gunther UhlmannAbstract:In this paper we study inverse boundary value problems with partial data for the magnetic Schrodinger operator. In the case of an infinite slab in \({\mathbb{R}^n}\) , n ≥ 3, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary Hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of Li and Uhlmann (Inverse Probl Imaging 4(3):449–462, 2010), obtained for the Schrodinger operator without magnetic potentials.
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inverse problems with partial data for a magnetic schr odinger operator in an infinite slab and on a bounded domain
arXiv: Analysis of PDEs, 2011Co-Authors: Katsiaryna Krupchyk, Matti Lassas, Gunther UhlmannAbstract:In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary Hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane.
Naiyang Deng - One of the best experts on this subject based on the ideXlab platform.
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nonparallel hyperplane support vector machine for binary classification problems
Information Sciences, 2014Co-Authors: Yuanhai Shao, Weijie Chen, Naiyang DengAbstract:In this paper, we propose a nonparallel hyperplane support vector machine (NHSVM) for binary classification problems. Our proposed NHSVM is formulated by clustering the training points according to the similarity between classes. It constructs two nonparallel Hyperplanes simultaneously by solving a single quadratic programming problem, and is consistent between its predicting and training processes - an essential difference that distinguishes it from other nonparallel SVMs. This proposed NHSVM has been analyzed theoretically and implemented experimentally. The results of experiments conducted using it on both artificial and publicly available benchmark datasets confirm its feasibility and efficacy, especially for ''Cross Planes'' datasets and datasets with heteroscedastic noise.
Hiroaki Terao - One of the best experts on this subject based on the ideXlab platform.
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the characteristic quasi polynomials of the arrangements of root systems and mid hyperplane arrangements
arXiv: Combinatorics, 2009Co-Authors: Hidehiko Kamiya, Akimichi Takemura, Hiroaki TeraoAbstract:Let q be a positive integer. In [8], we proved that the cardinality of the complement of an integral arrangement, after the modulo q reduction, is a quasi-polynomial of q, which we call the characteristic quasi-polynomial. In this paper, we study general properties of the characteristic quasi-polynomial as well as discuss two important examples: the arrangements of reflecting Hyperplanes arising from irreducible root systems and the mid-hyperplane arrangements. In the root system case, we present a beautiful formula for the generating function of the characteristic quasi-polynomial which has been essentially obtained by Ch. Athanasiadis [2] and by A. Blass and B. Sagan [3]. On the other hand, it is hard to find the generating function of the characteristic quasi-polynomial in the mid-hyperplane arrangement case. We determine them when the dimension is less than six.
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the characteristic quasi polynomials of the arrangements of root systems
2007Co-Authors: Hidehiko Kamiya, Akimichi Takemura, Hiroaki TeraoAbstract:Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic quasi-polynomial. In this paper, we study general properties of the characteristic quasi-polynomial as well as discuss two important examples: the arrangements of reflecting Hyperplanes arising from irreducible root systems and the mid-hyperplane arrangements. In the root system case, we present a beautiful formula for the generating function of the characteristic quasi-polynomial which has been essentially obtained by Ch. Athanasiadis and by A. Blass and B. Sagan. On the other hand, it is hard to find the generating function of the characteristic quasi-polynomial in the mid-hyperplane arrangement case. We determine them when the dimension is less than six.
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periodicity of hyperplane arrangements with integral coefficients modulo positive integers
arXiv: Combinatorics, 2007Co-Authors: Hidehiko Kamiya, Akimichi Takemura, Hiroaki TeraoAbstract:We study central hyperplane arrangements with integral coefficients modulo positive integers $q$. We prove that the cardinality of the complement of the Hyperplanes is a quasi-polynomial in two ways, first via the theory of elementary divisors and then via the theory of the Ehrhart quasi-polynomials. This result is useful for determining the characteristic polynomial of the corresponding real arrangement. With the former approach, we also prove that intersection lattices modulo $q$ are periodic except for a finite number of $q$'s.
Soumyabrata Pal - One of the best experts on this subject based on the ideXlab platform.
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recovery of sparse linear classifiers from mixture of responses
Neural Information Processing Systems, 2020Co-Authors: Venkata Gandikota, Arya Mazumdar, Soumyabrata PalAbstract:In the problem of learning a mixture of linear classifiers, the aim is to learn a collection of Hyperplanes from a sequence of binary responses. Each response is a result of querying with a vector and indicates the side of a randomly chosen hyperplane from the collection the query vector belongs to. This model provides a rich representation of heterogeneous data with categorical labels and has only been studied in some special settings. We look at a hitherto unstudied problem of query complexity upper bound of recovering all the Hyperplanes, especially for the case when the Hyperplanes are sparse. This setting is a natural generalization of the extreme quantization problem known as 1-bit compressed sensing. Suppose we have a set of $\ell$ unknown $k$-sparse vectors. We can query the set with another vector $\boldsymbol{a}$, to obtain the sign of the inner product of $\boldsymbol{a}$ and a randomly chosen vector from the $\ell$-set. How many queries are sufficient to identify all the $\ell$ unknown vectors? This question is significantly more challenging than both the basic 1-bit compressed sensing problem (i.e., $\ell=1$ case) and the analogous regression problem (where the value instead of the sign is provided). We provide rigorous query complexity results (with efficient algorithms) for this problem.
Yuanhai Shao - One of the best experts on this subject based on the ideXlab platform.
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nonparallel hyperplane support vector machine for binary classification problems
Information Sciences, 2014Co-Authors: Yuanhai Shao, Weijie Chen, Naiyang DengAbstract:In this paper, we propose a nonparallel hyperplane support vector machine (NHSVM) for binary classification problems. Our proposed NHSVM is formulated by clustering the training points according to the similarity between classes. It constructs two nonparallel Hyperplanes simultaneously by solving a single quadratic programming problem, and is consistent between its predicting and training processes - an essential difference that distinguishes it from other nonparallel SVMs. This proposed NHSVM has been analyzed theoretically and implemented experimentally. The results of experiments conducted using it on both artificial and publicly available benchmark datasets confirm its feasibility and efficacy, especially for ''Cross Planes'' datasets and datasets with heteroscedastic noise.
