Comment on "Hole-Burning Experiments within Glassy Models with Infinite Range Interactions"

Comment on: L.F. Cugliandolo and J.L. Iguain; Phys. Rev. Lett. {\bf 85} 3448 (2000)Comment: 1 page, RevTe

Regression with Linear Factored Functions

Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties that allow to analytically solve certain integrals and to calculate point-wise products. Applications like belief propagation and reinforcement learning can exploit these properties to break the curse and speed up computation. We derive a regularized greedy optimization scheme, that learns factored basis functions during training. The novel regression algorithm performs competitively to Gaussian processes on benchmark tasks, and the learned LFF functions are with 4-9 factored basis functions on average very compact.Comment: Under review as conference paper at ECML/PKDD 201

A new two-sphere singularity in general relativity

The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.Comment: 17 pages, 3 figure

Debye relaxation and 250 K anomaly in glass forming monohydroxy alcohols

A previous dielectric, near-infrared (NIR), and nuclear magnetic resonance study on the hydrogen-bonded liquid 2-ethyl-1-hexanol [C. Gainaru et al., Phys. Rev. Lett. 107, 118304 (2011)] revealed anomalous behavior in various static quantities near 250 K. To check whether corresponding observations can be made for other monohydroxy alcohols as well, these experimental methods were applied to such substances with 5, 6, 7, 8, and 10 carbon atoms in their molecular backbone. All studied liquids exhibit a change of behavior near 250 K which is tentatively ascribed to effects of hydrogen bond cooperativity. By analyzing the NIR band intensities, a linear cluster size is derived that agrees with estimates from dielectric spectroscopy. All studied alcohols, except 4-methyl-3-heptanol, display a dominant Debye-like peak. Furthermore, neat 2-ethyl-1-butanol exhibits a well resolved structural relaxation in its dielectric loss spectrum which so far has only been observed for diluted monohydroxy alcohols.Comment: 39 pages including 12 figure

A note on dilaton gravity with non-smooth potentials

Recent interest in brane world models motivates the investigation of generic first order dilaton gravity actions, with potentials having some non-smoothness. We consider two different types of \delta-like contributions in the action and analyse their effects on the solutions. Furthermore a second source of non-smoothness arises due to the remaining ambiguities in the solutions in the separated smooth patches, after fixing all other constants by matching and asymptotic conditions. If moreover staticity is assumed, we explicitly construct exact solutions. With the methods described, for example models with point like sources or brane world models (where the second source of non-smoothness becomes crucial), can now be treated as non-smooth dilaton gravity theories.Comment: 10 pages, 1 table; two new references, some typos corrected, Dedicated to Wolfgang Kummer at the occasion of his Emeritierun