We address the distribution regression problem (DRP): regressing on the (possibly infinite dimensional) domain of probability measures, in the two-stage sampled setup when only samples from the distributions are observable. The DRP formulation offers a unified framework for several important tasks in statistics and machine learning including for example, drug activity prediction, aerosol optica...

We prove sharp convergence rates for a class of domain embedding methods for elliptic boundary value problems. The theory is established for Dirichlet, Neumann, and Robin boundary conditions, and is unified in a new formulation for mixed boundary condition. On the continuous level, the methods for these boundary value problems perform equally well.

The classical problem of self-energy divergence was studied in the framework of Lagrangian formulation of Relativistic Mechanics. The conclusion was made that a revision of mass-energy concept is needed for the development of singularity-free gravitational and electromagnetic field theory. Perspectives of the development of unified field theory are

Object recognition under partial occlusion is an important problem that arises in many remote sensing and surveillance applications. Occlusion is often caused by objects with significant spatial extent, thereby resulting in spatial correlation as to which parts of objects are visible. In this paper, we develop a unified formulation for occluded object recognition using spatially correlated occl...

In this paper we propose an adaptation of the static eikonal equation over weighted graphs of arbitrary structure using a framework of discrete operators. Based on this formulation, we provide explicit solutions for the L1,L2 and L∞ norms. Efficient algorithms to compute the explicit solution of the eikonal equation on graphs are also described. We then present several applications of our metho...

Universality has always played a major role in every branch of science. Since the advent of cellular automata (CAs), this type of model has been widely applicable to the modeling of physical phenomena. On the other hand, the way the evolution rules were described lacked a unified formulation in terms of mathematical functions. In the present paper, a general formulation that is able to describe...

A general multiband formulation of the linear and nonlinear optical response functions for realistic models of correlated crystals is presented. Dipole-forbidden d-d optical transitions originate from vertex functions, which we consider assuming the locality of an irreducible four-leg vertex. The unified formulation for second- and third-order response functions in terms of the three-leg vertex...

the paper presents a possibility formulation of oneparameter estimation that unifies some usual probability formulations. Point and confidence interval estimation are unified in a single theoretical formulation and incorporated into estimators of an omnibus form: a possibility distribution. New relationships between continuous possibility distribution and probability concepts are established. T...

String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many “miracles” exhibited by the string...

The paper proposes a new formulation of the output feedback pole assignment problem. In this formulation, a unified approach is presented for solving the pole assignment problem with various additional objectives. These objectives include optimizing a variety of performance indices, and imposing constraints on the output feedback matrix structure, e.g. decentralized structure. Conditions for th...