Related papers: On generalizing cryptographic results to Sidon set…

In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in $\mathbb{R}_+$. Here we show that by generalizing the classical definition of…

In the ElGamal signature and encryption schemes, an element $x$ of the underlying group $G = \mathbb{Z}_p^\times = \{1, \ldots, p-1 \}$ for a prime $p$ is also considered as an exponent, for example in $g^x$, where $g$ is a generator of G.…

We give a construction of a set $A \subset \mathbb N$ such that any subset $A' \subset A$ with $|A'| \gg |A|^{2/3}$ is neither an additive nor multiplicative Sidon set. In doing so, we refute a conjecture of Klurman and Pohoata.

Overparameterised deep neural networks (DNNs) are highly expressive and so can, in principle, generate almost any function that fits a training dataset with zero error. The vast majority of these functions will perform poorly on unseen…

A subset $S$ of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of elements of $S$ are distinct. Imre Ruzsa asked the following…

In this paper, we propose a unified framework to analyze the performance of dense small cell networks (SCNs) in terms of the coverage probability and the area spectral efficiency (ASE). In our analysis, we consider a practical path loss…

It is well-known that an algorithm exists which approximates the NP-complete problem of Set Cover within a factor of ln(n), and it was recently proven that this approximation ratio is optimal unless P = NP. This optimality result is the…

The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…

Let $S\subset \mathbb{C}^n$ be a non-singular algebraic set and $f \colon \mathbb{C}^n \to \mathbb{C}$ be a polynomial function. It is well-known that the restriction $f|_S \colon S \to \mathbb{C}$ of $f$ on $S$ is a locally trivial…

We study a list-constrained extension of modular equation deletion over powers of two, called Coset-List Min-2-Lin$^{\pm}$ over $\mathbb{Z}/2^d\mathbb{Z}$. Each variable is restricted to a dyadic coset…

Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…

Cylindrical Algebraic Decomposition (CAD) algorithms typically produce a decomposition adapted to a finite family of semi-algebraic sets $\mathcal{F}$ (i.e. every member of $\mathcal{F}$ is a union of cells). Different algorithms may…

Let $G$ be a connected semisimple algebraic group of adjoint type defined over an algebraically closed field $K$ of positive characteristic. The characteristic $p$ is very good for $G$ when $p$ is suitably large and, if $G$ is of type…

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be…

Sidon spaces have been introduced by Bachoc, Serra and Z\'emor in 2017 as the $q$-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth, Raviv and Tamo in 2018, in which they…

Let G be a finite abelian group. This paper is concerned with nonnegative functions on G that are sparse with respect to the Fourier basis. We establish combinatorial conditions on subsets S and T of Fourier basis elements under which…

The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero…

In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$…

The Radon transform Rf of functions f on SO(3) has recently been applied extensively in texture analysis, i.e. the analysis of preferred crystallographic orientation. In practice one has to determine the orientation probability density…

Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al.…