Related papers: All 4-variable functions can be perfectly quadrati…
Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice…
We construct new smallest parts partition functions and smallest parts crank functions by considering variations of Bailey's Lemma and conjugate Bailey pairs. The functions we introduce satisfy simple linear congruences modulo $3$ and $5$.…
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a…
We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with four variables over rational function fields of characteristic 2. We apply these results to find prescribed quadratic subfields of quaternion…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
For a fixed quadratic irreducible polynomial $f$ with no fixed prime factors at prime arguments, we prove that there exist infinitely many primes $p$ such that $f(p)$ has at most 4 prime factors, improving a classical result of Richert who…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
A fast new algorithm is used compute the zeros of the quadratic character L-functions for all negative fundamental discriminants with absolute value 10^12<d<10^12+10^7. These are compared to the 1-level density, including various lower…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
A (positive definite and integral) quadratic form $f$ is called regular if it represents all integers that are locally represented. It is known that there are only finitely many regular ternary quadratic forms up to isometry. However, there…
This work presents a formalization of analogy on numbers that relies on generalized means. It is motivated by recent advances in artificial intelligence and applications of machine learning, where the notion of analogy is used to infer…
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\infty$-variate functions. Such $\infty$-variate integrals occur for example as expectations in uncertainty…
Statistical inferences for quadratic functionals of linear regression parameter have found wide applications including signal detection, global testing, inferences of error variance and fraction of variance explained. Classical theory based…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…