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87,212
Cartier isomorphism and Hodge theory in the noncommutative case
 in Arithmetic geometry, Clay Math. Proc. 8, AMS
, 2009
"... ..."
MValgebras with operators (the commutative and the noncommutative case)
"... In the present paper we define the (pseudo) MValgebras with nary operators, generalizing MVmodules and product MValgebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MValgebra and the operators defined on the corresponding ℓgroup. ..."
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Cited by 3 (1 self)
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In the present paper we define the (pseudo) MValgebras with nary operators, generalizing MVmodules and product MValgebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MValgebra and the operators defined on the corresponding ℓgroup. We also provide a categorical framework and we prove the analogue of Mundici’s categorical equivalence between MValgebras
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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is the Dirac operator. We extend these simple relations to the non commutative case using Tomita’s involution J. We then write a spectral action, the trace of a function of the length element in Planck units, which when applied to the non commutative geometry of the Standard Model will be shown (in a joint
A Classification of the Projective Lines over Small Rings II. NonCommutative Case
"... A list of different types of a projective line over noncommutative rings with unity of order up to thirtyone inclusive is given. Eight different types of such a line are found. With a single exception, the basic characteristics of the lines are identical to those of their commutative counterparts. ..."
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Cited by 11 (7 self)
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A list of different types of a projective line over noncommutative rings with unity of order up to thirtyone inclusive is given. Eight different types of such a line are found. With a single exception, the basic characteristics of the lines are identical to those of their commutative counterparts
QUANTUM SYMMETRIES OF HIGHER COXETERDYNKIN GRAPHS. A Noncommutative Case: The D3 Graph of SU(3) System
"... The purpose of this contribution is to show how quantum geometry of higher Coxeter graphs of SU(N) type gives a common algebraic formulation for both RCFT and quantum groupoı̈ds. These apparently two different fields are hardly studied by wide communities of physicists and mathematicians. To carry o ..."
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out this formulation we determine all Nimreps describing CFT and weak Hopf algebra structures based on combinatorial data of graphs. We will pay attention to a particular case: the D 3 orbifold graph of SU(3) system for which the algebra of quantum symmetries is noncommutative.
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 633 (38 self)
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considered the special case where D is an overcomplete system consisting of exactly two orthobases, and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex
SupportVector Networks
 Machine Learning
, 1995
"... The supportvector network is a new learning machine for twogroup classification problems. The machine conceptually implements the following idea: input vectors are nonlinearly mapped to a very highdimension feature space. In this feature space a linear decision surface is constructed. Special pr ..."
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Cited by 3703 (35 self)
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properties of the decision surface ensures high generalization ability of the learning machine. The idea behind the supportvector network was previously implemented for the restricted case where the training data can be separated without errors. We here extend this result to nonseparable training data.
Monads for functional programming
, 1995
"... The use of monads to structure functional programs is described. Monads provide a convenient framework for simulating effects found in other languages, such as global state, exception handling, output, or nondeterminism. Three case studies are looked at in detail: how monads ease the modification o ..."
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Cited by 1487 (43 self)
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The use of monads to structure functional programs is described. Monads provide a convenient framework for simulating effects found in other languages, such as global state, exception handling, output, or nondeterminism. Three case studies are looked at in detail: how monads ease the modification
Large N field theories, string theory and gravity
, 2001
"... We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evide ..."
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Cited by 1443 (45 self)
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and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field
The Skill Content of Recent Technological Change: An Empirical Exploration
, 2000
"... Recent empirical and case study evidence documents a strong association between the adoption of computers and increased use of college educated or nonproduction workers. With few exceptions, the conceptual link explaining how computer technology complements skilled labor or substitutes for unskille ..."
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Cited by 643 (28 self)
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Recent empirical and case study evidence documents a strong association between the adoption of computers and increased use of college educated or nonproduction workers. With few exceptions, the conceptual link explaining how computer technology complements skilled labor or substitutes
Results 1  10
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87,212