Results 1  10
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27
Complex interpolation between Hilbert, Banach and operator spaces
, 2008
"... Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆X(ε) tending to zero with ε> 0 such that every operator T: L2 → L2 with ‖T ‖ ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L1 and on L ∞ must be of ..."
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Cited by 9 (0 self)
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Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆X(ε) tending to zero with ε> 0 such that every operator T: L2 → L2 with ‖T ‖ ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L1 and on L ∞ must be of norm ≤ ∆X(ε) on L2(X). We show that ∆X(ε) ∈ O(ε α) for some α> 0 iff X is isomorphic to a quotient of a subspace of an ultraproduct of θHilbertian spaces for some θ> 0 (see Corollary 6.7), where θHilbertian is meant in a slightly more general sense than in our previous paper [43]. Let Br(L2(µ)) be the space of all regular operators on L2(µ). We are able to describe the complex interpolation space (Br(L2(µ)),B(L2(µ))) θ. We show that T: L2(µ) → L2(µ) belongs to this space iff T ⊗ idX is bounded on L2(X) for any θHilbertian space X. More generally, we are able to describe the spaces (B(ℓp0),B(ℓp1))θ or (B(Lp0),B(Lp1))θ for any pair 1 ≤ p0,p1 ≤ ∞ and 0 < θ < 1. In the same vein, given a locally compact Abelian group G, let M(G) (resp. PM(G)) be the space of complex measures (resp. pseudomeasures) on
Activized Learning: Transforming Passive to Active with Improved Label Complexity
"... Active learning methods often achieve improved performance using fewer labels compared to passive learning methods. A variety of practically successful active learning algorithms use a passive learning algorithm as a subroutine, and the essential role of the active component is to construct data set ..."
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Cited by 8 (4 self)
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Active learning methods often achieve improved performance using fewer labels compared to passive learning methods. A variety of practically successful active learning algorithms use a passive learning algorithm as a subroutine, and the essential role of the active component is to construct data sets to feed into the passive subroutine. This general idea is appealing for a variety of reasons, as it may be able
Random complex zeroes, II. Perturbed lattice
, 2005
"... We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function ψ(z) = ∑∞ zk k=0 ζk √ where ζ0,ζ1,... are indek! pendent standard complexvalued Gaussian variables) can be regarded as a random perturbation of a lattice in the plane. The distribution of the distances bet ..."
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Cited by 6 (2 self)
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We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function ψ(z) = ∑∞ zk k=0 ζk √ where ζ0,ζ1,... are indek! pendent standard complexvalued Gaussian variables) can be regarded as a random perturbation of a lattice in the plane. The distribution of the distances between the zeroes and the corresponding lattice points is shiftinvariant and has a Gaussiantype decay of the tails.
THE MONGE PROBLEM FOR DISTANCE COST IN GEODESIC SPACES
"... Abstract. We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are dcontinuous and locally compact, we can reduce the ..."
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Cited by 6 (2 self)
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Abstract. We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are dcontinuous and locally compact, we can reduce the transport problem to 1dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show
A Characterization of the Core of Convex Games Through Gateaux Derivatives
, 2002
"... We establish a calculus characterization of the core of supermodular games, which reduces the description of the core to the computation of suitable Gateaux derivatives of the Choquet integrals associated with the game. Our result generalizes to infinite games a classic result of Shapley (1971). As ..."
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Cited by 4 (4 self)
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We establish a calculus characterization of the core of supermodular games, which reduces the description of the core to the computation of suitable Gateaux derivatives of the Choquet integrals associated with the game. Our result generalizes to infinite games a classic result of Shapley (1971). As a secondary contribution, we provide a fairly complete analysis of the Gateaux and Frechet differentiability of the Choquet integrals of supermodular measure games.
ContextDependent ForwardInduction Reasoning
, 2008
"... This paper studies the case where a game is played in a particular context. The context in uences what beliefs players hold. As such, it may a ect forward induction (FI) reasoning: If players rule out speci c beliefs, they may not be able to rationalize observed behavior. The e ects are not obvious. ..."
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Cited by 4 (1 self)
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This paper studies the case where a game is played in a particular context. The context in uences what beliefs players hold. As such, it may a ect forward induction (FI) reasoning: If players rule out speci c beliefs, they may not be able to rationalize observed behavior. The e ects are not obvious. Contextladen FI may allow di erent outcomes than contextfree FI. At the formal level, contextual reasoning is de ned within an epistemic structure. In particular, we represent contextual FI reasoning as "rationality and common strong belief of rationality" (RCSBR) within an arbitrary type structure. (The concept of RCSBR is due to BattigalliSiniscalchi [2002].) What strategies are consistent with RCSBR (de ned on an arbitrary type structure)? We show that the RCSBR is characterized by a new solution concept we call Extensive Form Best Response Sets (EFBRS's). We go on to study the EFBRS concept in games of interest. In particular, we establish a relationship between EFBRS's and Nash outcomes, in perfectinformation games satisfying a `no ties' condition. We also show how to compute EFBRS's in certain cases of interest.
The Demonic Product of Probabilistic Relations
, 2001
"... The demonic product of two probabilistic relations is defined and investigated. It is shown that the product is stable under bisimulations when the mediating object is probabilistic, and that under some mild conditions the nondeterministic fringe of the probabilistic relations behaves properly: the ..."
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Cited by 3 (1 self)
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The demonic product of two probabilistic relations is defined and investigated. It is shown that the product is stable under bisimulations when the mediating object is probabilistic, and that under some mild conditions the nondeterministic fringe of the probabilistic relations behaves properly: the fringe of the product equals the demonic product of the fringes.
Stochastic relations of random variables and processes
, 2010
"... This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes ..."
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Cited by 3 (3 self)
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This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes preserve some, not necessarily reflexive or transitive, subrelation of the order relation. The main contributions of the paper are: a functional characterization of stochastic relations, necessary and sufficient conditions for the preservation of stochastic relations, and an algorithm for finding subrelations preserved by probability kernels. The theory is illustrated with applications to hidden Markov processes, population processes, and queueing systems.
MORSE DESCRIPTION AND MORPHOLOGICAL ENCODING OF CONTINUOUS DATA
"... A geometric representation for images is studied in this work. This is based on two complementary geometric structures for the topographic representation of an image. The first one computes a description of the Morse structure, while the second one computes a simplified version of drainage structure ..."
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Cited by 2 (1 self)
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A geometric representation for images is studied in this work. This is based on two complementary geometric structures for the topographic representation of an image. The first one computes a description of the Morse structure, while the second one computes a simplified version of drainage structures. The topographic significance of the Morse and drainage structures of Digital Elevation Maps (DEM) suggests that they can been used as the basis of an efficient encoding scheme. As an application we then combine this geometric representation with a consistent interpolation algorithm and lossless data compression schemes to develop an efficient compression algorithm for DEM. This coding scheme controls the L ∞ error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEM. We present the underlying theory and some compression results for standard DEM data.
CONCERNING THE DUAL GROUP OF A DENSE SUBGROUP
, 2002
"... Abstract. Throughout this Abstract, G is a topological Abelian group and ̂G is the space of continuous homomorphisms from G into T in the compactopen topology. A dense subgroup D of G determines G if the (necessarily continuous) surjective isomorphism ̂G ։ ̂D given by h ↦ → hD is a homeomorphism, ..."
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Cited by 2 (0 self)
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Abstract. Throughout this Abstract, G is a topological Abelian group and ̂G is the space of continuous homomorphisms from G into T in the compactopen topology. A dense subgroup D of G determines G if the (necessarily continuous) surjective isomorphism ̂G ։ ̂D given by h ↦ → hD is a homeomorphism, and G is determined if each dense subgroup of G determines G. The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is determined. The authors offer several related results, including these. (1) There are (many) nonmetrizable, noncompact, determined groups. (2) If the dense subgroup Di determines Gi with Gi compact, then ⊕i Di determines Πi Gi. In particular, if each Gi is compact then ⊕i Gi determines Πi Gi. (3) Let G be a locally bounded group and let G + denote G with its Bohr topology. Then G is determined if and only if G + is determined. (4) Let non(N) be the least cardinal κ such that some X ⊆ T of cardinality κ has positive outer measure. No compact G with w(G) ≥ non(N) is determined; thus if non(N) = ℵ1 (in particular if CH holds), an infinite compact group G is determined if and only if w(G) = ω. Question. Is there in ZFC a cardinal κ such that a compact group G is determined if and only if w(G) < κ? Is κ = non(N)? κ = ℵ1?