Related papers: Pseudorandom Numbers and Hash Functions from Itera…
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…
We study skew-orthogonal polynomials with respect to the weight function $\exp[-2V(x)]$, with $V(x)=\sum_{K=1}^{2d}(u_{K}/{K})x^{K}$, $u_{2d} > 0$, $d > 0$. A finite subsequence of such skew-orthogonal polynomials arising in the study of…
The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…
We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of…
Humans can leverage hierarchical structures to split a task into sub-tasks and solve problems efficiently. Both imitation and reinforcement learning or a combination of them with hierarchical structures have been proven to be an efficient…
The quantum Haar random oracle model is an idealized model where every party has access to a single Haar random unitary and its inverse. We construct strong pseudorandom unitaries in the quantum Haar random oracle model. This strictly…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
Template abstract domains allow to express more interesting properties than classical abstract domains. However, template generation is a challenging problem when one uses template abstract domains for program analysis. In this paper, we…
The library \emph{fast\_polynomial} for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as H\"orner, divide and conquer and new ones can be added easily. Notably, a new…
In this paper, it is shown that every polynomial function is mixed monotone globally with a polynomial decomposition function. For univariate polynomials, the decomposition functions can be constructed from the Gram matrix representation of…
In this paper we introduce a novel hash learning framework that has two main distinguishing features, when compared to past approaches. First, it utilizes codewords in the Hamming space as ancillary means to accomplish its hash learning…
We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
The main purpose of this paper is to establish some new properties of Horadam numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between Horadam and…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
We introduce and study modular truncations of the Ackermann function viewed as self-maps on finite rings. These maps form a hierarchy of rapidly increasing compositional complexity indexed by recursion depth. We investigate their structural…
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
The iterative conditional branchings appear in various sensitive algorithms, like the modular exponentiation in the RSA cryptosystem or the scalar multiplication in ellipticcurve cryptography. In this paper, we abstract away the desirable…