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We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various…
We device a new method to calculate a large number of Mellin moments of single scale quantities using the systems of differential and/or difference equations obtained by integration-by-parts identities between the corresponding Feynman…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
Refining raw disparity maps from different algorithms to exploit their complementary advantages is still challenging. Uncertainty estimation and complex disparity relationships among pixels limit the accuracy and robustness of existing…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…
A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale…
An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To…
We develop a systematic and fully explicit approach to the evaluation of binomial sums involving reciprocals of binomial coefficients based on Beta integral techniques. Starting from a simple integral representation, we provide a derivation…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for theevaluation of Feynman diagrams. We describe the operational rules and illustrate the method…
By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory…
Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of…