We consider an overdetermined elliptic problem known as the hollow vortex problem. We prove that the solutions to this problem are in 1:1 correspondence with minimal graphs bounded by horizontal symmetry lines. We use this correspondence to give various examples of domains with hollow vortices.
Under the additional assumption that @math in @math and @math on @math , solutions to the hollow vortex problem are called exceptional domains. Hauswirth, H 'elein and Pacard studied the problem in @cite_15 and discovered an exceptional domain which, as it turns out, corresponds to the horizontal catenoid. Partial classification results were obtained by Khavinson, Lundberg and Teodorescu in @cite_5 . A complete classification is given in @cite_10 .
@cite_5 @cite_15 @cite_10
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . We investigate a problem posed by L. Hauswirth, F. H 'elein, and F. Pacard, namely, to characterize all the domains in the plane that admit a "roof function", i.e., a positive harmonic function which solves simultaneously a Dirichlet problem with null boundary data, and a Neumann problem with constant boundary data. Under some a priori assumptions, we show that the only three examples are the exterior of a disk, a halfplane, and a nontrivial example. We show that in four dimensions the nontrivial simply connected example does not have any axially symmetric analog containing its own axis of symmetry. This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function @math in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. Our work makes the following assumption: there exists a non-linear transformation between the joint feature label space distributions of the two domain @math and @math . We propose a solution of this problem with optimal transport, that allows to recover an estimated target @math by optimizing simultaneously the optimal coupling and @math . We show that our method corresponds to the minimization of a bound on the target error, and provide an efficient algorithmic solution, for which convergence is proved. The versatility of our approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification and regression problems, for which we reach or surpass state-of-the-art results. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc. New analytical solutions are presented for steadily translating von Karman vortex streets made up of two infinite rows of hollow vortices. First, the solution for a single row of hollow vortices due to ["Structure of a linear array of hollow vortices of finite cross-section," J. Fluid Mech. 74, 469 (1976)] is rederived, in a modified form, and using a new mathematical approach. This approach is then generalized to find relative equilibria for both unstaggered and staggered double hollow vortex streets. The method employs a combination of free streamline theory and conformal mapping ideas. The staggered hollow vortex streets are compared with analogous numerical solutions for double streets of vortex patches due to Saffman and Schatzman [“Properties of a vortex street of finite vortices,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 2, 285 (1981)] and several common features are found. In particular, within the two different inviscid vortex models, the same street aspect ratio of approxi... We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the partial information models of the so-called "semi-bandit", and "bandit" problems. We consider both @math -, and @math -type of restrictions for the losses assigned by the adversary. We formulate a general strategy using Bregman projections on top of a potential-based gradient descent, which generalizes the ones studied in the series of papers (2007), (2008), (2008), Cesa-Bianchi and Lugosi (2009), Helmbold and Warmuth (2009), (2010), (2010), (2010) and Audibert and Bubeck (2010). We provide simple proofs that recover most of the previous results. We propose new upper bounds for the semi-bandit game. Moreover we derive lower bounds for all three feedback assumptions. With the only exception of the bandit game, the upper and lower bounds are tight, up to a constant factor. Finally, we answer a question asked by (2010) by showing that the exponentially weighted average forecaster is suboptimal against @math adversaries. Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically property testers, to understand local properties of the data. We focus on the natural local problem of testing pattern freeness: given a large @math -dimensional array @math and a fixed @math -dimensional pattern @math over a finite alphabet, we say that @math is @math -free if it does not contain a copy of the forbidden pattern @math as a consecutive subarray. The distance of @math to @math -freeness is the fraction of entries of @math that need to be modified to make it @math -free. For any @math and any large enough pattern @math over any alphabet, other than a very small set of exceptional patterns, we design a tolerant tester that distinguishes between the case that the distance is at least @math and the case that it is at most @math , with query complexity and running time @math , where @math and @math depend only on @math . To analyze the testers we establish several combinatorial results, including the following @math -dimensional modification lemma, which might be of independent interest: for any large enough pattern @math over any alphabet (excluding a small set of exceptional patterns for the binary case), and any array @math containing a copy of @math , one can delete this copy by modifying one of its locations without creating new @math -copies in @math . Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data. They serve as a first step towards a general understanding of local properties of multi-dimensional arrays, as any such property can be characterized by a fixed family of forbidden patterns. Abstract Irregular sampling and “stable sampling” of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52]. We prove that quasicrystals are sets of stable sampling. To cite this article: B. Matei, Y. Meyer, C. R. Acad. Sci. Paris, Ser. I 346 (2008). All nonabelian finite simple groups of rank @math over a field of size @math , with the possible exception of the Ree groups @math , have presentations with at most @math relations and bit-length @math . Moreover, @math and @math have presentations with 3 generators @math 7 relations and bit-length @math , while @math has a presentation with 7 generators, @math relations and bit-length @math Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . Given a set of @math @math -dimensional Boolean vectors with the promise that the vectors are chosen uniformly at random with the exception of two vectors that have Pearson -- correlation @math (Hamming distance @math ), how quickly can one find the two correlated vectors? We present an algorithm which, for any constants @math and @math finds the correlated pair with high probability, and runs in time @math given @math vectors in @math , our algorithm returns a pair of vectors whose Euclidean distance differs from that of the closest pair by a factor of at most @math and runs in time @math . The best previous algorithms (including LSH) have runtime @math Learning Sparse Parity with Noise: Given samples from an instance of the learning parity with noise problem where each example has length @math , the true parity set has size at most @math . Learning @math -Juntas without Noise: Our results for learning sparse parities with noise imply an algorithm for learning juntas without noise with runtime $n^ + 4 k poly(n) which improves on the runtime n !+1 ! poly(n) n0:7kpoly(n) of [13]. Several polynomial time approximation algorithms for some @math -complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined. A mixed-strategy heuristic with a bound of 9 5 is presented for the stacker-crane problem (a modified traveling salesman problem). A tour-splitting heuristic is given for k-person variants of the traveling salesman problem, the Chinese postman problem, and the stacker-crane problem, for which a minimax solution is sought. This heuristic has a bound of @math , where e is the bound for the corresponding 1-person algorithm. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively investigated during the last decades. Several nonlinear reconstruction methods have been proposed, and it is by now well-established that the "classical" convergence order can be completely restored up to the discontinuities. Still, the maximal accuracy of determining the positions of these discontinuities remains an open question. In this paper we prove that the locations of the jumps (and subsequently the pointwise values of the function) can be reconstructed with at least "half the classical accuracy". In particular, we develop a constructive approximation procedure which, given the first @math Fourier coefficients of a piecewise- @math function, recovers the locations of the jumps with accuracy @math , and the values of the function between the jumps with accuracy @math (similar estimates are obtained for the associated jump magnitudes). A key ingredient of the algorithm is to start with the case of a single discontinuity, where a modified version of one of the existing algebraic methods (due to K.Eckhoff) may be applied. It turns out that the additional orders of smoothness produce a highly correlated error terms in the Fourier coefficients, which eventually cancel out in the corresponding algebraic equations. To handle more than one jump, we propose to apply a localization procedure via a convolution in the Fourier domain. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... In the three-dimensional (3D) strip packing problem, we are given a set of 3D rectangular items and a 3D box @math . The goal is to pack all the items in @math such that the height of the packing is minimized. We consider the most basic version of the problem, where the items must be packed with their edges parallel to the edges of @math and cannot be rotated. Building upon Caprara's work for the two-dimensional (2D) bin packing problem, we obtain an algorithm that, given any @math , achieves an approximation of @math , where @math is the well-known number that occurs naturally in the context of bin packing. Our key idea is to establish a connection between bin packing solutions for an arbitrary instance @math and the strip packing solutions for the corresponding instance obtained from @math by applying the harmonic transformation to certain dimensions. Based on this connection, we also give a simple alternate proof of the @math approximation for 2D ... We consider @math -median clustering in finite metric spaces and @math -means clustering in Euclidean spaces, in the setting where @math is part of the input (not a constant). For the @math -means problem, show that if the optimal @math -means clustering of the input is more expensive than the optimal @math -means clustering by a factor of @math , then one can achieve a @math -approximation to the @math -means optimal in time polynomial in @math and @math by using a variant of Lloyd's algorithm. In this work we substantially improve this approximation guarantee. We show that given only the condition that the @math -means optimal is more expensive than the @math -means optimal by a factor @math for some constant @math , we can obtain a PTAS. In particular, under this assumption, for any @math we achieve a @math -approximation to the @math -means optimal in time polynomial in @math and @math , and exponential in @math and @math . We thus decouple the strength of the assumption from the quality of the approximation ratio. We also give a PTAS for the @math -median problem in finite metrics under the analogous assumption as well. For @math -means, we in addition give a randomized algorithm with improved running time of @math . Our technique also obtains a PTAS under the assumption of that all @math approximations are @math -close to a desired target clustering, in the case that all target clusters have size greater than @math and @math is constant. Note that the motivation of is that for many clustering problems, the objective function is only a proxy for the true goal of getting close to the target. From this perspective, our improvement is that for @math -means in Euclidean spaces we reduce the distance of the clustering found to the target from @math to @math when all target clusters are large, and for @math -median we improve the largeness'' condition needed in the work of to get exactly @math -close from @math to @math . Our results are based on a new notion of clustering stability.