My work focuses on the geometry and differential equations invariant under groups of affine and projective motions (in R and RP respectively). In particular, affine differential geometry, the study of properties of hypersurfaces in R which are invariant under affine volume-preserving motions, informs most of my work. Affine differential geometry is an old subfield of geometry, with Blaschke mak...

We introduce the discrete affine group of a regular tree as finitely generated subgroup group. describe Poisson boundary random walks on it space configurations. compute isoperimetric profile and Hilbert compression exponent also discuss metric relationship with some lamplighter groups graphs.

In this paper we propose a new geometric interpretation for General Relativity (GR). It has always been presumed that the gravitational field is described in GR by a Levi-Civita connection. We suggest that this may not necessarily be the case. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine ...

A formula is derived that links the coefficients of the monetary policy rule for the shortterm interest rate to the coefficients of the implied affine equations for long-term interest rates. The formula predicts that an increase in the coefficients in the monetary policy rule will lead to an increase in the coefficients in the affine equations. Empirical evidence for such a prediction is provid...

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the gene...

Non-polynomial baxterized solutions of reflection equations associated with affine Hecke and affine Birman-Murakami-Wenzl algebras are found. Relations to integrable spin chain models with nontrivial boundary conditions are discussed.

We extend the classical empirical interpolation method [1] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [13]. ...

The analytical form of general affine transform families with givenmaximum likelihood estimators for the affine parameters is determined. In this context, the simultaneous maximum likelihood equations of the affine parameters in the generalised Pareto distribution cannot have a common solution. This pathological situation is removed by extending it to a four parameter family, called Pareto type...