Related papers: Power-free values of binary forms and the global d…
We formulate the planar `large N limit' of matrix models with a continuously infinite number of matrices directly in terms of U(N) invariant variables. Non-commutative probability theory, is found to be a good language to describe this…
A Baker-type linear independece measure is obtained for the values of generalized Heine series at non-zero points of an imaginary quadratic number field. This kind of estimate depends on the individual coefficients of the linear form, not…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only…
We present a fast and memory efficient algorithm for the estimation of generalized linear models with an additive separable k-way error component. The brute force approach uses dummy variables to account for the unobserved heterogeneity,…
This paper is concerned with the density of rational points of bounded height lying on a variety defined by an integral quadratic form Q. In the case of four variables, we give an estimate that does not depend on the coefficients of Q. For…
The binary sum-of-digits function $\mathsf{s}$ returns the number of ones in the binary expansion of a nonnegative integer. Cusick's Hamming weight conjecture states that, for all integers $t\geq 0$, the set of nonnegative integers $n$ such…
This paper re-examines the density for sums of independent exponential, Erlang and gamma random variables. By using a divided difference perspective, the paper provides a unified approach to finding closed-form formulae for such…
We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $\nu\ne 0$, we also obtain new bounds on exponential sums with $\nu$-th powers of such…
For irreducible integer polynomials $f(n)=n^d+c$ we prove an asymptotic formula for the number of $k$-th power free values taken by $f(n)$, for $n$ running up to $x$, subject to the condition $k\ge (5d+3)/9$. This improves earlier results…
We determine the Hilbert series of some classes of ideals generated by generic forms of degree two and three, and investigate the difference to the Hilbert series of ideals generated by powers of linear generic forms of the corresponding…
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
We begin by proving that any Presburger-definable image of one or more sets of powers has zero natural density. Then, by adapting the proof of a dichotomy result on o-minimal structures by Friedman and Miller, we produce a similar dichotomy…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
Given $A\subseteq \mathbb{Z}$, the ratio set or the quotient set of $A$ is defined by $R(A):=\{a/b: a, b\in A, b\neq 0\}$. It is an open problem to study the denseness of $R(A)$ in the $p$-adic numbers when $A$ is the set of values attained…
In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distribution and unlike classical autoregressive…
A key feature of determinantal sampling designs is their capacity to provide known and parametrisable inclusion probabilities at any order. This paper aims to demonstrate how to effectively leverage this characteristic, highlighting its…
We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given $k$ and a target density $\rho$, there exist potentials having $k^{\text{th}}$ bound mixed states which densities…
Starting from a general material system of $N$ particles coupled to a cavity, we use a coherent-state path integral formulation to produce a non-perturbative effective theory for the material degrees of freedom. We tackle the effects of…
Scattering amplitudes connect theoretical descriptions to experimental predictions. Low energy terms of the scattering amplitude tend to factorize from the high energy. Different methods have already been established to understand the…