Related papers: The derivative expansion approach to the interacti…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
We extend our previous work on a derivative expansion for the Casimir energy, to the case of the electromagnetic field coupled to two thin, imperfect mirrors. The latter are described by means of vacuum polarization tensors localized on the…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis.…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
We consider higher-derivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and short-distance expansions of Feynman diagrams. In the case of single…
We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Pad\'e approximants to meromorphic functions. However, only recently this…
We extend density-matrix expansions in nuclei to higher orders in derivatives of densities and test their convergence properties. The expansions allow for converting the interaction energies characteristic to finite- and short-range nuclear…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on $C^0$-discretizations -- piece-wise linear or polynomial surfaces -- suffer from…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…