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NonCritical Pure Spinor Superstrings
, 2006
"... We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spi ..."
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Cited by 15 (3 self)
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We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure
The Theory of Hybrid Automata
, 1996
"... A hybrid automaton is a formal model for a mixed discretecontinuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discretecontinuous state spaces that was previously studied on pur ..."
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Cited by 685 (12 self)
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on purely discrete state spaces only. In particular, various classes of hybrid automata induce finitary trace equivalence (or similarity, or bisimilarity) relations on an uncountable state space, thus permitting the application of various modelchecking techniques that were originally developed for finite
Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose learner. Some transductive graph learning al ..."
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Cited by 578 (16 self)
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algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 958 (9 self)
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is the case when the code is overcompletei.e., when the number of code elements is greater than the effective dimensionality of the input space. Because the basis functions are nonorthogonal and not linearly independent of each other, sparsifying the code will recruit only those basis functions necessary
A new maximally supersymmetric background of IIB superstring theory
, 2001
"... We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous fiveform flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry supe ..."
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Cited by 405 (27 self)
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We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous fiveform flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry
Character of pure spinors
"... The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simp ..."
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Cited by 29 (2 self)
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The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a
Pure Spinors and D=6 SuperYang–Mills
, 2008
"... Abstract: Pure spinor cohomology has been used to describe maximally supersymmetric theories, like D = 10 superYang–Mills and D = 11 supergravity. Supersymmetry closes onshell in such theories, and the fields in the cohomology automatically satisfy the equations of motion. In this paper, we invest ..."
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Cited by 4 (4 self)
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investigate the corresponding structure in a model with offshell supersymmetry, N = 1 superYang–Mills theory in D = 6. Here, fields and antifields are obtained as cohomologies in different complexes with respect to the BRST operator Q. It turns out to be natural to enlarge the pure spinor space
Pure Spinors on Lie groups
, 2007
"... For any manifold M, the direct sum TM = TM ⊕T ∗ M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there is a notion of pure spinor. In this paper, we study pure ..."
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Cited by 4 (1 self)
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For any manifold M, the direct sum TM = TM ⊕T ∗ M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there is a notion of pure spinor. In this paper, we study pure
Results 1  10
of
6,670