Research
Research
Research
Research
1,545+ open-access research outputs.
Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct. In this short note, we give the negative answe…
The SVOM mission (Space-based multi-band astronomical Variable Objects Monitor) is a Franco-Chinese mission dedicated to the study of the most distant explosions of stars, the gamma-ray bursts. Here, …
In low-depth implementations of the Quantum Approximate Optimization Algorithm (QAOA), the dominant cost is often the number of objective evaluations rather than circuit depth. We introduce a graph-co…
We study a fixed-core absorption problem for regular induced subgraphs. A set is q-modular if all induced degrees are congruent modulo q. Given a q-modular witness A and a retained core U subset A, we…
In 1965 Kraichnan pointed out that a sufficiently strong background magnetic field, i.e. the case of small Alfv\'en number, will reduce the nonlinear interaction and inhibit the formation of strong gr…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric a…
Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error …
We establish an exact identity among four dimensionless invariants accessible by standard polarimetric and interferometric measurements in a polarized double-slit experiment: the in-phase and quadratu…
Designing optimizers that remain effective under tight evaluation budgets is critical in expensive black-box settings such as cardiac digital twinning. We propose Frenetic Cat-inspired Particle Optimi…
A tournament has Schuttes property $S_k$ if for every set of $k$ vertices, there is a vertex which dominates the set. In 1963, Erdos provided bounds for $f(k)$, the smallest order of an $S_k$ tourname…
For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivari…
In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of complete synchronization in the Sakaguchi-Kuramoto (SK) model. In this study, we propose an anal…
We show that a family of extremely thin sets satisfy the Erd\H{o}s similarity conjecture. These examples lie outside the range covered by recent work of Shmerkin and Yavicoli \cite{ShmerkinYavicoli202…
This paper addresses the security allocation problem within networked control systems, which consist of multiple interconnected control systems under the influence of two opposing agents: a defender a…
Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, asso…
Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own righ…
We study the typical structure of oriented graphs and digraphs that do not contain a blow-up T_{r+1}^t of a transitive tournament. For any integers r >= 2, t >= 1 and any real a in (3/2,2], we prove t…
In previous joint work with Tenenbaum, the truncation step $f \mapsto f_R$ in the conditional effective Erdos-Wintner theorem on the fibre $\omega(n)=k$ yields, in the continuous case for real strongl…
Advanced AI reasoning systems route tasks through dynamic execution graphs of specialized agents. We identify a structural blind spot in this architecture: schedulers optimize load and fitness but lac…
For a graph $G$ with $m$ edges, let $\rho(G)$ be its spectral radius, and let $N_F(G)$ denote the number of copies of $F$ in $G$. Nikiforov [Combin. Probab.\,Comput., 2002] proved that for $r\geq 2$, …
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