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174
4 PROPAGATION OF CHAOS FOR THE SPATIALLY HOMOGENEOUS LANDAU EQUATION FOR MAXWELLIAN MOLECULES
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1On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD
, 2013
"... This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion ..."
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it is further demonstrated that given a finite number of training samples N, such that N / logN = O(K3d), except with probability O(N−Kd) there is a local minimum of the K-SVD criterion within distance O(KN−1/4) to the generating dictionary. Index Terms dictionary learning, sparse coding, K-SVD, finite sample
unknown title
, 1999
"... hy st o. dk Atoms in strong magnetic fields: The high field limit at fixed nuclear charge ..."
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hy st o. dk Atoms in strong magnetic fields: The high field limit at fixed nuclear charge
J. London Math. Soc. (2) 75 (2007) 545–562 C2007 London Mathematical Society doi:10.1112/jlms/jdm033 ON BASE SIZES FOR ACTIONS OF FINITE CLASSICAL GROUPS
"... Let G be a finite almost simple classical group and let Ω be a faithful primitive non-standard G-set. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. Let b(G) be the minimal size of a base for G. A well-known conjecture of Cameron and Kantor asserts that there exists an ab ..."
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an absolute constant c such that b(G) c for all such groups G, and the existence of such an undetermined constant has been established by Liebeck and Shalev. In this paper we prove that either b(G) 4, or G = U6(2) · 2, Gω = U4(3) · 22 and b(G) = 5. The proof is probabilistic, using bounds on fixed
UNITU–THEP–3/1998 FAU–TP3–98/2 Solving a Coupled Set of Truncated QCD Dyson–Schwinger Equations
, 1998
"... Truncated Dyson–Schwinger equations represent finite subsets of the equations of motion for Green’s functions. Solutions to these non–linear integral equations can account for non–perturbative correlations. A closed set of coupled Dyson–Schwinger equations for the propagators of gluons and ghosts in ..."
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in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4–point correlations and by implementing the Slavnov–Taylor identities for the 3–point vertex functions. We solve this coupled set in an one–dimensional approximation which allows for an analytic infrared expansion necessary
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