Research
Research
Research
Research
3,523+ open-access research outputs.
In 1967 Hajnal and Juh{\'a}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most $\mathfrak{c}$, the cardinality of the real li…
Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some d…
Many Multi-Agent Reinforcement Learning (MARL) agents fail to adapt properly to cooperating with agents trained with the same objectives but different seeds, algorithms, or other training differences.…
The Ramsey number $r_k(s,n)$ is the smallest integer $N$ such that every $N$-vertex $k$-graph contains either a copy of $K_s^{(k)}$ or an independent set of size $n$. We prove that $r_4(5,n)\ge 2^{2^{…
We generalise the reparameterization trick applied in variational autoencoders (VAEs) letting these have latent spaces of non-trivial topology - i.e. that of base manifolds covered with other ones, on…
We investigate whether explicit belief graphs improve LLM performance in cooperative multi-agent reasoning. Through 3,000+ controlled trials across four LLM families in the cooperative card game Hanab…
Graphs whose maximum clique size exceeds half of the total number of vertices satisfy a classical property: the family of their maximum sized cliques can be pierced by a single vertex. This result dat…
We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switching to a potential var…
In astronomical imaging, the low photon count of exposures necessitates extensive post-processing steps, including contamination removal and denoising. This paper evaluates deep-learning denoising met…
This paper proposes a novel method that incorporates empowerment when reasoning actions in reinforcement learning (RL), thereby achieving the flexibility of exploration-exploitation dilemma (EED). In …
We take a close look at a classical magic trick performed with a string, where a trivial knot is seemingly isotoped into a trefoil, and generalize it to a family of magic tricks for transforming the u…
Let $k \in \mathbb{N}$ and let $G$ be a simple graph with maximum degree $\Delta$. A $k$-colouring $\varphi$ of $G$ is an assignment of colours from $\{1,2,\ldots,k\}$ to the vertices of $G$. We call …
User behavior sequence modeling plays a significant role in Click-Through Rate (CTR) prediction on e-commerce platforms. Except for the interacted items, user behaviors contain rich interaction inform…
Addressing a question posed by Erd\H{o}s and Hajnal, Chen and Ma proved that, for all $n \ge 600$, the complete bipartite graph $K_{n,n+1}$ is the unique graph on $2n+1$ vertices with at least $n^2+n$…
In 1956 John Kelly wrote a paper at Bell Labs describing the relationship between gambling and Information Theory. What came to be known as the Kelly Criterion is both an objective and a closed-form s…
The Koopman operator is a powerful approach to global stability analysis of nonlinear systems, which provides a systematic procedure for Lyapunov function design. In this framework, Lyapunov functions…
To elucidate how land surface state and soil moisture dynamics regulate moist convection, and how convective rainfall subsequently reshapes surface and root-zone hydrology, we develop a stochastic dyn…
Meteor clusters are typically defined as groups of meteors that appear close together in both space and time. To date, only a handful of such events have been recorded instrumentally and analysed in d…
The systematics of energies and the contribution of pygmy dipole resonance (PDR) to the energy-weighted sum rule of dipole gamma transitions in medium-heavy and heavy nuclei with an excess of neutrons…
The Ethereum state database uses Merkle Patricia Trie (MPT), which suffers from large witness proof sizes and high storage overhead. Verkle Tries have been proposed as a replacement, offering witness …
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