In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasipolynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. Using these developments, Adj, Menezes, Oliveira and Rodŕıguez-Henŕıquez analysed the concrete security of the DLP, as it arises from pairings ...

A skew brace is a triplet $(A,\cdot,\circ)$, where $(A,\cdot)$ and $(A,\circ)$ are groups such that the relation $x\circ (y\cdot z) = (x\circ y)\cdot x^{-1}\cdot z)$ holds for all $x,y,z\in A$. In this paper, we study number of finite braces up to isomorphism, both isomorphic $T^n$ with $T$ non-abelian simple $n\in\mathbb{N}$. We prove it equal unlabeled directed graphs on $n+1$ vertices, one d...

‎We show that for all normalized Hecke eigenforms $f$‎ ‎with weight one and of CM type‎, ‎the number $(f,f)$ where $(cdot‎, ‎cdot )$ denotes‎ ‎the Petersson inner product‎, ‎is a linear form in logarithms and‎ ‎hence transcendental‎.

Abstract For a skew left brace ( G , rspace="4.2pt">? ? stretchy="false">) {(G,\cdot\,,\circ)} , the map ? : ? Aut ? {\lambda:(G,\circ)\to\operatorname{Aut}(G,\cdot\,...

This paper concerns the chemotaxis-Navier-Stokes system \begin{document}$\begin{equation} \begin{cases} n_t+u\cdot {\nabla } n = \Delta - {{\nabla }\cdot}(n\chi(c) c),\\ c_t+u\cdot c -nf(c),\\ u_t+\kappa (u\cdot }) u + P +n }\Phi, \quad }\cdot} 0 \end{cases} \end{equation} \;\;\;\;\;\;\;\;\;\;\;\;(\star)$ \end{document} in a smoothly convex bounded domain under Neumann/Neumann/Dirichlet boundar...

The massive 3-loop fermion-loop corrections $\propto C_A N_f T_F^2$ and $C_F N_f T_F^2$ to the massive operator matrix elements $A_{Qg}$, $A_{Qq}^{\rm{PS}}$, $A_{qq,Q}^{\rm{PS}}$, $A_{qq,Q}^{\rm{NS}}$ and $A_{qq,Q}^{\rm{NS,TR}} have been obtained for general values of $N$. Thereby the corresponding contributions to the asymptotic heavy flavor Wilson coefficients of the structure function $F_2(x...

We give a maximal independent set (MIS) algorithm that runs in $O(\log \log \Delta)$ rounds in the congested clique model, where $\Delta$ is the maximum degree of the input graph. This improves upon the $O(\frac{\log(\Delta) \cdot \log \log \Delta}{\sqrt{\log n}} + \log \log \Delta )$ rounds algorithm of [Ghaffari, PODC '17], where $n$ is the number of vertices of the input graph. In the first ...

Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in diverse fields of science, from abstract mathematics to physics, biology chemistry. For centuries, new formulas relating fundamental have been scarce usually discovered sporadically. Here we propose a novel systematic approach that leverages algorithms for deriving help reveal their underlying structure. Our find dozens wel...