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18,956
Transverse Subjectivity Classification
"... In this paper, we consider the problem of building models that have high subjectivity classification accuracy across domains. For that purpose, we present and evaluate new methods based on multiview learning using both highlevel (i.e. linguistic features for subjectivity detection) and lowlevel ..."
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In this paper, we consider the problem of building models that have high subjectivity classification accuracy across domains. For that purpose, we present and evaluate new methods based on multiview learning using both highlevel (i.e. linguistic features for subjectivity detection) and low
Assessing agreement on classification tasks: the kappa statistic
 Computational Linguistics
, 1996
"... Currently, computational linguists and cognitive scientists working in the area of discourse and dialogue argue that their subjective judgments are reliable using several different statistics, none of which are easily interpretable or comparable to each other. Meanwhile, researchers in content analy ..."
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Cited by 846 (9 self)
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Currently, computational linguists and cognitive scientists working in the area of discourse and dialogue argue that their subjective judgments are reliable using several different statistics, none of which are easily interpretable or comparable to each other. Meanwhile, researchers in content
Mathematics Subject Classification
"... Abstract. It is shown that every noncompact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with nonempty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncat ..."
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Abstract. It is shown that every noncompact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with nonempty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups. Epstein and Penner [2] used a convex hull construction in Lorentzian space to show that every noncompact hyperbolic manifold of finite volume has a canonical subdivision into convex geodesic polyhedra all of whose vertices lie on the sphere at infinity of hyperbolic space. In general, one cannot expect to further subdivide these polyhedra into ideal geodesic simplices such that the result is an ideal triangulation. That this is possible after lifting the cell decomposition to an appropriate finite cover is the first main result of this paper. A cell decomposition of a hyperbolic nmanifold into ideal geodesic nsimplices all of which are embedded will be referred to as an embedded geodesic ideal triangulation. Theorem 1. Any noncompact hyperbolic manifold of finite volume has a finite regular cover which admits an embedded geodesic ideal triangulation. The study of geodesic ideal triangulations of hyperbolic 3manifolds goes back to Thurston
Mathematics Subject Classification
"... Abstract. For any set S let seq 11 (S) denote the cardinality of the set of all finite onetoone sequences that can be formed from S, and for positive integers a let a S denote the cardinality of all functions from S to a. Using a result from combinatorial number theory, Halbeisen and Shelah have ..."
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Abstract. For any set S let seq 11 (S) denote the cardinality of the set of all finite onetoone sequences that can be formed from S, and for positive integers a let a S denote the cardinality of all functions from S to a. Using a result from combinatorial number theory, Halbeisen and Shelah have shown that even in the absence of the axiom of choice, for infinite sets S one always has seq 11 (S) = 2 S (but nothing more can be proved without the aid of the axiom of choice). Combining stronger numbertheoretic results with the combinatorial proof for a = 2, it will be shown that for most positive integers a one can prove the inequality seq 11 (S) = a S without using any form of the axiom of choice. Moreover, it is shown that a very probable numbertheoretic conjecture implies that this inequality holds for every positive integer a in any model of set theory. Motivation It was proved in [3, Theorem 4] that for any set S with more than one element, the cardinality seq 11 (S) of the set of all finite onetoone sequences that can be formed from S can never be equal to the cardinality of the power set of S, denoted by 2 S . The proof does not make use of any form of the axiom of choice and hence, the result also holds in models of set theory where the axiom of choice fails. Moreover, in the absence of the axiom of choice, seq 11 (S) = 2 S is all one can prove about the relation between these two cardinalities. In other words, for each of the statements seq 11 (S) < 2 S , seq 11 (S) > 2 S , and seq 11 (S) incomparable to 2 S , there are models of ZermeloFraenkel's set theory without the axiom of choice in which the statement is true (cf. [4, §9]). However, in the presence of the axiom of choice, for any infinite set S we always have seq 11 (S) < 2 S . Now,
Mathematics Subject Classification
"... Abstract Spatial point processes are stochastic models for point patterns, systems of points scattered in R d . A point process can be used as a generating stochastic mechanism for additional spatial random systems such as random tessellations, random fields and random graphs, which are collectivel ..."
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Abstract Spatial point processes are stochastic models for point patterns, systems of points scattered in R d . A point process can be used as a generating stochastic mechanism for additional spatial random systems such as random tessellations, random fields and random graphs, which are collectively called secondary structures of point processes. Secondary structures have a role in the statistical analysis of point processes, e.g. in the form of statistical summaries based on tessellations, and in a method called regionalisation which bridges point pattern statistics with geostatistics. In this study the objective is to use geometric graphs together with graphbased summaries in the statistical analysis of smallscale properties of point patterns. The functional summaries of this study are connectivity function, cumulative connectivity function and clustering function. The concepts and their estimators are given, their properties are discussed, and a simulation study is conducted. The simulation experiment gives evidence that the graphtheoretical summaries are able to detect differences between point patterns where the secondorder statistics such as Ripley's K or paircorrelation function fail. An R library has been developed for the computation of the graphbased summaries.
Mathematics Subject Classification
"... Abstract. Let G be a classical complex Lie group, P any parabolic subgroup of G, and G/P the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in H * (G/P ) as a polynomial in certain special Schubert class generator ..."
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Abstract. Let G be a classical complex Lie group, P any parabolic subgroup of G, and G/P the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in H * (G/P ) as a polynomial in certain special Schubert class generators. Our formula extends to one that applies to the torusequivariant cohomology ring of G/P and to the setting of symplectic and orthogonal degeneracy loci. Introduction The Giambelli formula [G] is one of the fundamental results concerning Schubert calculus in the cohomology ring of the Grassmannian X. The variety X has a decomposition into Schubert cells, which gives an additive basis of Schubert classes for the cohomology of X. On the other hand, the ring H * (X, Z) is generated by certain special Schubert classes, which are the Chern classes of the universal quotient bundle over X. The formula of Giambelli expresses a general Schubert class as a determinant of a JacobiTrudi matrix with entries given by special classes. One can show that this formula is equivalent to the Pieri rule [P]; see for instance [T4]. The Schubert calculus on X can be generalized to any homogeneous space G/P , where G is a complex reductive Lie group and P a parabolic subgroup of G. However, more than a century since the theorems of Pieri and Giambelli were discovered, no combinatorially explicit analogues of these results are known in this generality, unless the Lie group G is of type A. One reason for this is that there is no uniform way to extend the notion of a special Schubert class over all possible Lie types and parabolics. Another serious concern is the more difficult algebrocombinatorial questions that arise in the other Lie types, about which more below. When G is a classical Lie group, one can define special Schubert class generators for the cohomology ring H * (G/P ) uniformly, as follows. In this situation, the variety G/P parametrizes partial flags of subspaces of a vector space, which in types B, C, and D are required to be isotropic with respect to an orthogonal or symplectic form. First, the special Schubert varieties on any Grassmannian are defined as the locus of (isotropic) linear subspaces which meet a given (isotropic or coisotropic) linear subspace nontrivially, following [BKT1]. The special Schubert classes are the cohomology classes determined by these Schubert varieties. Finally, the special Schubert classes on a partial flag variety G/P are the pullbacks of special Schubert classes on Grassmannians, in agreement with the convention in type A. In most cases, these special classes are equal to the Chern classes of the universal quotient
Mathematics Subject Classifications (2000):
"... The Berezin transform for complex multivariable domains D ⊂ Cn is important to harmonic analysis because of its covariance with respect to holomorphic transformations. It can be regarded as an analogue of the Poisson transform, replacing the boundary integration by integrating over the domain itself ..."
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The Berezin transform for complex multivariable domains D ⊂ Cn is important to harmonic analysis because of its covariance with respect to holomorphic transformations. It can be regarded as an analogue of the Poisson transform, replacing the boundary integration by integrating over the domain itself. This applies in particular
Convergence Properties of the NelderMead Simplex Method in Low Dimensions
 SIAM Journal of Optimization
, 1998
"... Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper pr ..."
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Cited by 598 (3 self)
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methods, Nelder–Mead simplex methods, nonderivative optimization AMS subject classifications. 49D30, 65K05
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A
A Shallow Approach To Subjectivity Classification
 in Proc. of ICWSM‟08
, 2008
"... We present a shallow linguistic approach to subjectivity classification. Using multinomial kernel machines, we demonstrate that a data representation based on counting character ngrams is able to improve on results previously attained on the MPQA corpus using wordbased ngrams and syntactic inform ..."
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Cited by 8 (2 self)
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We present a shallow linguistic approach to subjectivity classification. Using multinomial kernel machines, we demonstrate that a data representation based on counting character ngrams is able to improve on results previously attained on the MPQA corpus using wordbased ngrams and syntactic
Results 1  10
of
18,956