Abstract We study a class of inhomogeneous and anisotropic G2 string cosmological models. In the case of separable G2 models we show that the governing equations reduce to a system of ordinary differential equations. We focus on a class of separable G2 M-theory cosmological models, and study their qualitative behaviour (a class of models with time-reversed dynamics is also possible). We find th...

We present new exact inhomogeneous vacuum cosmological solutions of Einstein’s equations. They provide new information about the nature of general cosmological solutions to Einstein’s equations. PACS 04.20.Jb, 98.80H, 04.30.-w Inhomogeneous and anisotropic solutions of Einstein’s equations are of great interest because of the subtleties of their non-linearity and the clues they offer about the ...

All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.

We study the motion of long polymers (eg DNA) in a gel under the influence of an external force acting locally on small segments of the polymer. In particular, we examine the dependence of the drift velocity on the position where the force acts and the length of the polymer. As an application, we discuss the possibility of gel magnetophoresis the size-separation of long polymers by the attachme...

Automated detection of touching cells in images with inhomogeneous illumination is a challenging problem. A detection framework using a stack of two conditional random fields is proposed to detect touching elongated cells in scanning electron microscopy images with inhomogeneous illumination. The first conditional random field employs shading information to segment the cells where the effect of...

In metric Diophantine approximation there are two main types of approximations: simultaneous and dual for both homogeneous and inhomogeneous settings. The well known measure-theoretic theorems of Khintchine and Jarník are fundamental in these settings. Recently, there has been substantial progress towards establishing a metric theory of Diophantine approximations on manifolds. In particular, bo...

We determine the relationship between the depolarization properties of inhomogeneous particles and the statistical parameters of their internal refractive-index distributions. Our analysis demonstrates that the linear depolarization ratio of backscattered light by an inhomogeneous particle is approximately proportional to both the squared standard deviation and the squared correlation length of...

Helical configurations of inhomogeneous symmetric rods with non-constant bending and twisting stiffness are studied within the framework of the Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of differential equations for the curvature and torsion of the centerline of the rod and the Lancret’s theorem is used to find helical solutions. We obtain a free standing helical...

We describe an algorithm for locally-adaptive parameter estimation of spatially inhomogeneous Markov random elds (MRFs). In particular, we establish that there is a unique solution which maximizes the local pseudo-likelihood in the inhomogeneous MRF model. Subsequently we demonstrate how Besag's iterative conditional mode (ICM) procedure can be generalized from homogeneous MRFs to inhomogeneous...

Statistical dynamical closures for inhomogeneous turbulence described by multi-field equations are derived based on renormalized perturbation theory. Generalizations of the computationally tractable quasi-diagonal direct interaction approximation for inhomogeneous barotropic turbulent flows over topography are developed. Statistical closures are also formulated for large eddy simulations includ...