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Equivalent formulation
"... Let F̂n be the empirical CDF of n draws from U [0, 1] w.l.o.g. Given two ..."
SOME EQUIVALENT FORMULATIONS OF UNIVERSALITY LIMITS IN THE BULK
"... Abstract. We present some equivalences for universality limits in the bulk, involving partial derivatives of reproducing kernels, and spacing of zeros of reproducing kernels. ..."
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Cited by 2 (0 self)
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Abstract. We present some equivalences for universality limits in the bulk, involving partial derivatives of reproducing kernels, and spacing of zeros of reproducing kernels.
Training Linear SVMs in Linear Time
, 2006
"... Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for highdimensional sparse data commonly encountered in applications like text classification, wordsense disambiguation, and drug design. These applications involve a large number of examples n ..."
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Cited by 549 (6 self)
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is based on an alternative, but equivalent formulation of the SVM optimization problem. Empirically, the CuttingPlane Algorithm is several orders of magnitude faster than decomposition methods like SVMLight for large datasets.
The Coordination of Arm Movements: An Experimentally Confirmed Mathematical Model
 Journal of neuroscience
, 1985
"... This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematic ..."
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Cited by 688 (18 self)
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This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled
Equivalent formulation and numerical analysis of a fire confinement problem, preprint 2008
"... We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion ˙x ∈ F(x), starting from an initial set R0. To block the fire, a barrier can be con ..."
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Cited by 10 (7 self)
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We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion ˙x ∈ F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ IR 2. In this paper we show that the search for blocking strategies and for optimal strategies can be reduced to a problem involving one single admissible rectifiable set Γ ⊂ IR 2, rather than the multifunction t ↦ → γ(t) ⊂ IR 2. Relying on this result, we then develop a numerical algorithm for the computation of optimal strategies, minimizing the total area burned by the fire. 1
En route to the logrank conjecture: New reductions and equivalent formulations
 In Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP
, 2014
"... Abstract We prove that several measures in communication complexity are equivalent, up to polynomial factors in the logarithm of the rank of the associated matrix: deterministic communication complexity, randomized communication complexity, information cost and zerocommunication cost. This shows t ..."
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Cited by 8 (3 self)
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Abstract We prove that several measures in communication complexity are equivalent, up to polynomial factors in the logarithm of the rank of the associated matrix: deterministic communication complexity, randomized communication complexity, information cost and zerocommunication cost. This shows
Equivalent formulations of the Müntz–Szász completeness condition for systems of complex exponentials
"... New results pertaining to the completeness of a system of complex exponentials in Lp spaces are presented. It is shown that the wellknown MüntzSzász condition can be interpreted in terms of an equivalence relation, thereby proving that the standard MüntzSzász formulation is equivalent with certa ..."
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New results pertaining to the completeness of a system of complex exponentials in Lp spaces are presented. It is shown that the wellknown MüntzSzász condition can be interpreted in terms of an equivalence relation, thereby proving that the standard MüntzSzász formulation is equivalent
A NOTE ON NYMAN’S EQUIVALENT FORMULATION OF THE RIEMANN HYPOTHESIS
, 1999
"... A certain subspace of L²((0,1),dt) has been considered by Nyman, Beurling, and others, with the result that the constant function 1 belongs to it if and only if the Riemann Hypothesis holds. I show that the product 1 − ρ ∣ ρ ∣ ζ(ρ)=0,Re(ρ)> 1 2 is the norm of the projection of 1 to this subspace. ..."
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Cited by 3 (1 self)
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A certain subspace of L²((0,1),dt) has been considered by Nyman, Beurling, and others, with the result that the constant function 1 belongs to it if and only if the Riemann Hypothesis holds. I show that the product 1 − ρ ∣ ρ ∣ ζ(ρ)=0,Re(ρ)> 1 2 is the norm of the projection of 1 to this subspace. This provides a quantitative refinement to Nyman’s theorem.
Results 1  10
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