Discussed are two numerical packages for computing equilibrium structures of liquid crystals. The first uses Frank elasticity in a rectangular geometry in two spatial dimensions. The second uses a tensor order parameter and Landau-deGennes free energy in the geometry of a finite circular cylinder. The Frank code is being used to study the phenomenon of the “stripe phase” in thin nematic films i...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

bearing capacity prediction of axially loaded piles is one of the most important problems in geotechnical engineering practices, with a wide variety range of methods which have been introduced to forecast it accurately. machine learning methods have been reported by many contemporary researches with some degree of success in modeling geotechnical phenomena. in this study, a fairly new machine l...

We investigate thermodynamic geometries of two families of asymptotically Anti-de Sitter black holes, i.e. the Reissner-Nordström Anti-de Sitter in four dimensions and the BTZ black hole. It is found that the Anti-de Sitter space renders the geometry nontrivial (cf. the ReissnerNordström black hole in asymptotically flat background). The BTZ black hole’s thermodynamic geometry is trivial despit...

The dependence of vegetation attenuation on propagation geometry has been experimentally investigated at SHF band for isolated single trees. Two measurement heights (Trunk and Canopy) have been used in these experiments that involve three fully foliated trees, Common Whitebeam (Sorbus aria), Silver Maple (Acer Saccharinum) and Common Hazel (Corylus Avellana). Result shows that apart from freque...

We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier (Dix54) and fragments of linear logic. We expose for this purpose a modified construction of Girard’s hyperfinite geometry of interaction (Gir11). The expressivity of the logic soundly interpreted in this model is dependent on properties of a MASA which is a parameter of the int...

We investigate the parameter-space geometry of recurrent neural networks (RNNs), and develop an adaptation of path-SGD optimization method, attuned to this geometry, that can learn plain RNNs with ReLU activations. On several datasets that require capturing long-term dependency structure, we show that path-SGD can significantly improve trainability of ReLU RNNs compared to RNNs trained with SGD...

Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and dep...

We argue that the optimization plays a crucial role in generalization of deep learning models through implicit regularization. We do this by demonstrating that generalization ability is not controlled by network size but rather by some other implicit control. We then demonstrate how changing the empirical optimization procedure can improve generalization, even if actual optimization quality is ...

In the title compound, C(23)H(22)ClN(3)O, the benzene ring of the 4-chorobenzyl group makes a dihedral angle of 78.56 (6)° with the best plane of the indole ring. The double bond connecting the aza-bicyclic and indole groups adopts a Z geometry. The geometry adopted by the C=N bond with respect to the N-OH bond is trans. The absolute configuration of the compound was determined from refinement ...