In [Ch1], Chern gives a generalization of projective geometry by considering foliations on the Grassman bundle of p-planes Gr(p, R) → R by p-dimensional submanifolds that are integrals of the canonical contact differential system. The equivalence method yields an sl(n + 1, R)valued Cartan connection whose curvature captures the geometry of such foliation. In the flat case, the space of leaves o...

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space, as found recently in some ferromagnetic crystals while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect. cond-mat/0606472,...

Imitation learning is a powerful approach to humanoid behavior generation, however, the most existing methods assume the availability of the information on the internal state of a demonstrator such as joint angles, while humans usually cannot directly access to imitate the observed behavior. This paper presents a method of imitation learning based on visuosomatic mapping from observing the demo...

Mobile computing environments are characterised by significant and rapid changes in their supporting infrastructure and, in particular, in the quality-of-service (QoS) available from their underlying communications channels. Applications which can operate in these environments and take advantage of changing QoS require distributed systems support platforms. The current state-of-the-art in such ...

An example of homogeneous space which has no metric but has a connection with non–vanishing curvature suggests that " spacetime " should be not defined as a pair (M, g), a manifold plus a metric, but as a pair (M, Γ) — a differentiable manifold plus a connection. The general theory of homogeneous spaces ensures the existence of a certain well–defined connection independently of the existence of...

In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its curvature is not and, t...

As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically speaking, we define the tangent (velocity) space of the embedded space imposing non-holonomic constraints upon the tangent space of the embedding space. Paralle...

In many applications of color technology such as spectral color reproduction it is of interest to represent the spectral data with lower dimensions than spectral space’s dimensions. It is more than half of a century that Principal Component Analysis PCA method has been applied to find the number of independent basis vectors of spectral dataset and representing spectral reflectance with lower di...

Tourism is a progressively major part of economies of urban areas. Urban regeneration as a subcategory of urban tourism has been the center of many urban projects. This study addresses the role of space syntax theory as an analytical tool and design aided tool in urban regeneration. For this purpose, we examined the development of a square in the Kuala Lumpur City Center (KLCC) using space synt...

At the present work we consider infinitesimal deformations f : x → x + εz(x) of a space LN with non-symmetric affine connection L i jk . Based on the non-symmetry of the connection, we use four kinds of covariant derivative to express the Lie derivative and the deformations. Rigidity of geometric objects (connection, tensors, curvature) is defined by virtue of Lie derivative. AMS Subj. Class.: ...