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A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…
Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…
Enumerating the extremal submodular functions defined on subsets of a fixed base set has only been done for base sets up to five elements. This paper reports the results of attempting to generate all such functions on a six-element base…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are…
The theory of self-reciprocal functions is applied to the study Mordell type integrals. We find two particular eigenfunctions of the double cosine Fourier transform and then use them to evaluate certain one- and two-dimensional Mordell type…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively. In particular we generalize the known…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…