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We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
We study a two-dimensional Coulomb gas consisting of a mixture of particles carrying various positive multiple integer charges, confined on a unit circle. We consider the system in the canonical and grand canonical ensembles, and attempt to…
This paper addresses different aspects of "coupled" model descriptions in computational electromagnetics. This includes domain decomposition, multiscale problems, multiple or hybrid discrete field formulation and multi-physics problems.…
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…
It is known a method for converting a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we show a formula for systems of Boolean polynomial equations which is based on the…
We use radial basis functions to model the input--output response of an electronic device. A new methodology for producing models that accuratly describe the response of the device over a wide range of operating points is introduced. A key…
The increasing complexity of control systems necessitates control laws that guarantee safety w.r.t. complex combinations of constraints. In this letter, we propose a framework to describe compositional safety specifications with control…
Particle-in-Cell (PIC) methods are widely used computational tools for fluid and kinetic plasma modeling. While both the fluid and kinetic PIC approaches have been successfully used to target either kinetic or fluid simulations, little was…
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…
Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial / topological argument. These functions are then extended into a larger family of…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
We propose a unified view of the polarity of functions, that encompasses all specific definitions, generalizes several well-known properties and provides new results. We show that bipolar sets and bipolar functions are isomorphic lattices.…
By the method of discrete Morse flows, we construct an energy reducing multiple-valued function flow. The flow we get is Holder continuous with respect to the L-2 norm. We also give another way of constructing flows in some special cases,…
We construct a three dimensional toy systems with two types of fermions forming a composite boson. They are hold in a harmonic potential. The basis functions are constructed from an internal and an external Gauss function. All integrals…
We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of…