Related papers: A Simplification Method of Polymorphic Boolean Fun…
The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional…
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…
A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piece-wise linear model which exhibits various…
Linear operations on coefficients in the spherical harmonics (SH) transform domain that again yield SH-domain coefficients are an important toolset in many disciplines of research and engineering. They comprise rotations, spatially…
We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we…
This paper describes a simplified model of an electric circuit with a DC-DC converter and a PID-regulator as a system of integral differential equations with an identically singular matrix multiplying the higher derivative of the desired…
We study the properties of convex functionals which have been proposed for the simulation of charged molecular systems within the Poisson-Boltzmann approximation. We consider the extent to which the functionals reproduce the true…
The concept of a nested canalizing Boolean function has been studied over the course of the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such functions…
A coarse-grained multi-blob description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and non-bonded blobs. The number of blobs is chosen such that the blob density does not exceed…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
The purpose of this paper is to provide some properties of maximal plurisubharmonic functions in a bounded domain of \mathbb{C}^n
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple polylogarithms to calculate Feynman periods. For the zig-zag and two more families…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…