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

Physics of dark energy particles

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the ``quanta'' of the cosmological constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 10^55 g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of `classical' fundamental constants.Comment: 10 pages, no figures; typos corrected, 4 references added; 1 reference added; reference added; entirely revised version, contains new parts, now 14 page

NMR evidence for static local nematicity and its cooperative interplay with low-energy magnetic fluctuations in FeSe under pressure

We present $^{77}$Se-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\rm s}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperation between magnetism and local nematicity in FeSe.Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. B rapid communicatio

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

Chirality in the plane

It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be restored by adding appropriate two-dimensional chiral terms. In this paper we show how to construct a three-dimensional chiral energy function which can achieve two-dimensional chirality induced already by a chiral three-dimensional model. The key ingredient to this approach is the consideration of a nonlinear chiral energy containing only rotational parts. After formulating an appropriate energy functional, we study the equations of motion and find explicit soliton solutions displaying two-dimensional chiral properties