We introduce a space of stable meromorphic differentials with poles of prescribed orders and define its tautological cohomology ring. This space, just as the space of holomorphic differentials, is stratified according to the set of multiplicities of zeros of the differential. The main goal of this paper is to compute the Poincar 'e-dual cohomology classes of all strata. We prove that all these classes are tautological and give an algorithm to compute them. In a second part of the paper we study the Picard group of the strata. We use the tools introduced in the first part to deduce several relations in these Picard groups.
* Incidence variety compactification. The problem of the compactification of the strata is extensively studied from different approaches in a joint work of Bainbridge, Chen, Gendron, Grushevsky, and Moeller (see @cite_13 and @cite_26 ). Their compactification (called incidence variety compactification ) is slightly different from the one that we use here. We will recall their definitions in since we will make use of some of their results.
@cite_26 @cite_13
1743277569 2342521385
The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian differentials. The main ingredients to study the compactifications of the strata are a version of the plumbing cylinder construction for differential forms and an extension of the parity of the connected components of the strata to the differentials on curves of compact type. We study in detail the compactifications of the hyperelliptic minimal strata and of the odd minimal stratum in genus three. Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian differentials. The open strata can have up to three connected components, due to spin and hyperelliptic structures. We prove that the spin parity can be distinguished on the boundary of the log compactification. Moreover, combining the techniques of log geometry and admissible covers, we introduce log twisted hyperelliptic differentials, and prove that their moduli stack provides a toroidal compactification of the hyperelliptic loci in the open strata. It was shown by Connes, Douglas, Schwarz [hep-th 9711162] that one can compactify M(atrix) theory on a non-commutative torus To. We prove that compactifications on Morita equivalent tori are in some sense physically equivalent. This statement can be considered as a generalization of non-classical SL(2,Z)N duality conjectured by Connes, Douglas and Schwarz for compactifications on two-dimensional non-commutative tori. Abstract The effective action for type II string theory compactified on a six-torus is N = 8 supergravity, which is known to have an E7 duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, E 7 ( Z ) , which contains both the T-duality group O(6, 6; Z ) and the S-duality group SL(2; Z ). We present evidence for the conjecture that E 7 ( Z ) is an exact ‘U-duality’ symmetry of type II string theory. This conjecture requires certain extreme black hole states to be identified with massive modes of the fundamental string. The gauge bosons from the Ramond-Ramond sector couple not to string excitations but to solitons. We discuss similar issues in the context of toroidal string compactifications to other dimensions, compactifications of the type II string on K3 × T2 and compactifications of 11-dimensional supermembrane theory. We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recently, roughly by extending the problem across the boundary of the compactification of the asymptotically hyperbolic space in a suitable manner. The main novelty is that the non-scalar nature of the operator is dealt with by relating it to a problem on an asymptotically Minkowski space to motivate the choice of the extension across the conformal boundary. In the 80's H. Masur and W. Veech defined two numerical invariants of strata of abelian differentials: the volume and the Siegel-Veech constant. Based on numerical experiments, A. Eskin and A. Zorich proposed a series of conjectures for the large genus asymptotics of these invariants. By a careful analysis of the asymptotic behavior of quasi-modular forms, D. Chen, M. Moeller, and D. Zagier proved this conjecture for strata of differentials with simple zeros. Here, we prove that the conjecture holds for the other extreme case, i.e. for strata of differentials with a unique zero. Our main ingredient is the expression of the numerical invariants of these strata in terms of Hodge integrals on moduli spaces of curves. 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. Abstract We present non-extreme generalisations of intersecting p -brane solutions of eleven-dimensional supergravity which upon toroidal compactification reduce to non-extreme static black holes in dimensions D = 4, D = 5 and 6 ⩽ D ⩽ 9, parameterised by four, three and two charges, respectively. The D = 4 black holes are obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The D = 5 black holes arise from three intersecting two-branes or from a system of an intersecting two-brane and five-brane with a boost along the common string. The five-brane and two-brane with a boost along one direction reduce to black holes in D = 6 and D = 9, respectively, while a D = 7 black hole can be interpreted in terms of a non-extreme configuration of two intersecting two-branes. We discuss the expressions for the corresponding masses and entropies. 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 . In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. In this paper we consider the large genus asymptotics for Masur-Veech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by Eskin-Okounkov to exactly evaluate these quantities, we show that the volume @math of a stratum indexed by a partition @math is @math as @math tends to @math . This confirms a prediction of Eskin-Zorich and generalizes some of the recent results of Chen-Moeller-Zagier and Sauvaget, who established these limiting statements in the special cases @math and @math , respectively. We also include an Appendix by Anton Zorich that uses our main result to deduce the large genus asymptotics for Siegel-Veech constants that count certain types of saddle connections. 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. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Let H0, …, H n be m x m matrices with entries in Q and Hankel structure, i.e. constant skew diagonals. We consider the linear Hankel matrix H(x) = H0+x1H_1+…+xnHn and the problem of computing sample points in each connected component of the real algebraic set defined by the rank constraint rank (H(x))≤ r, for a given integer r ≤ m-1. Computing sample points in real algebraic sets defined by rank defects in linear matrices is a general problem that finds applications in many areas such as control theory, computational geometry, optimization, etc. Moreover, Hankel matrices appear in many areas of engineering sciences. Also, since Hankel matrices are symmetric, any algorithmic development for this problem can be seen as a first step towards a dedicated exact algorithm for solving semi-definite programming problems, i.e. linear matrix inequalities. Under some genericity assumptions on the input (such as smoothness of an incidence variety), we design a probabilistic algorithm for tackling this problem. It is an adaptation of the so-called critical point method that takes advantage of the special structure of the problem. Its complexity reflects this: it is essentially quadratic in specific degree bounds on an incidence variety. We report on practical experiments and analyze how the algorithm takes advantage of this special structure. A first implementation outperforms existing implementations for computing sample points in general real algebraic sets: it tackles examples that are out of reach of the state-of-the-art. 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. The concept of a perfect equilibrium point has been introduced in order to exclude the possibility that disequilibrium behavior is prescribed on unreached subgames. (Selten 1965 and 1973). Unfortunately this definition of perfectness does not remove all difficulties which may arise with respect to unreached parts of the game. It is necessary to reexamine the problem of defining a satisfactory non-cooperative equilibrium concept for games in extensive form. Therefore a new concept of a perfect equilibrium point will be introduced in this paper. In retrospect the earlier use of the word "perfect" was premature. Therefore a perfect equilibrium point in the old Sense will be called "subgame perfect". The new definition of perfectness has the property that a perfect equilibrium point is always subgame perfect but a subgame perfect equilibrium point may not be perfect. It will be shown that every finite extensive game with perfect recall has at least one perfect equilibrium point. Since subgame perfectness cannot be detected in the normal form, it is clear that for the purpose of the investigation of the problem of perfectness, the normal form is an inadequate representation of the extensive form. It will be convenient to introduce an "agent normal form" as a more adequate representation of games with perfect recall. 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] With the tremendous amount of research publications, recommending relevant papers to researchers to fulfill their information need becomes a significant problem. The major challenge to be tackled by our work is that given a target paper, how to effectively recommend a set of relevant papers from an existing citation network. In this paper, we propose a novel method to address the problem by incorporating various citation relations for a proper set of papers, which are more relevant but with a very limited size. The proposed method has two unique properties. Firstly, a metric called Local Relation Strength is defined to measure the dependency between cited and citing papers. Secondly, a model called Global Relation Strength is proposed to capture the relevance between two papers in the whole citation graph. We evaluate our proposed model on a real-world publication dataset and conduct an extensive comparison with the state-of-the-art baseline methods. The experimental results demonstrate that our method can have a promising improvement over the state-of-the-art techniques. 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. Citations are important in academic dissemination. To help researchers check the completeness of citations while authoring a paper, we introduce a citation recommendation system called RefSeer. Researchers can use it to find related works to cited while authoring papers. It can also be used by reviewers to check the completeness of a paper's references. RefSeer presents both topic based global recommendation and also citation-context based local recommendation. By evaluating the quality of recommendation, we show that such recommendation system can recommend citations with good precision and recall. We also show that our recommendation system is very efficient and scalable.