At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...

We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of Poincaré-Birkhoff normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in h...

In this paper, we present local image descriptor using VQ-SIFT for more effective and efficient image retrieval. Instead of SIFT's weighted orientation histograms, we apply vector quantization (VQ) histogram as an alternate representation for SIFT features. Experimental results show that SIFT features using VQ-based local descriptors can achieve better image retrieval accuracy than the conventi...

We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra ŝl2 on a Maxwell-Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show t...

A Wiener-regularized path integral is presented as an alternative way to formulate Berezin-Toeplitz quantization on a toroidal phase space. Essential to the result is that this quantization prescription for the torus can be constructed as an induced representation from anti-Wick quantization on its covering space, the plane. When this construction is expressed in the form of a Wiener-regularize...

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...