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Research
Research
222,847+ open-access research outputs.
Reinforcement learning (RL) has become essential to the post-training of large language models (LLMs) for reasoning, agentic capabilities and alignment. Successful RL relies on sufficient exploration …
The RPO4 orthophosphates (R = rare earth element) have recently attracted a wide interest due to the strong coupling between their electronic, orbital and structural ordering parameters resulting in a…
Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, sho…
This paper investigates the existence and uniqueness of solutions for a nonlinear evolution equation governed by an m-accretive operator A in a Banach space, presenting a perturbation term that does n…
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
Fast radio bursts (FRBs), thought to originate from magnetars, exhibit diverse polarization properties that constrain their emission physics and local magneto-ionic environments. The polarization posi…
Type Ia supernova (SN Ia) standardisation parameters exhibit evidence for systematic variation across the host galaxy star-formation rate - stellar mass (SFR$-M_\star$) plane, motivating the incorpora…
Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial se…
We study the Liouville equation $\triangle u+e^{2u} =0$ in a Riemannian surface $(M, g)$ with nonnegative $Ricci$ curvature. Under some asymptotic lower bound assumptions, we classify all the soluti…
In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of o…
The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and…
Galaxy physical properties are influenced by their environments, but the processes responsible for mass and environmental quenching and structural transformations remain debated. Galaxy clusters are i…
Degenerate spinor Bose gases with repulsive density-density interaction and anti-ferromagnetic spin-spin coupling in one spatial dimension are shown to be described by a quantum integrable matrix exte…
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. Howeve…
The 'Species Scale' has proved to be an important concept when studying consistent effective actions in Quantum Gravity. This is a short summary of my contribution to the Corfu Summer Institute in Sep…
We study hypergeometric functions of nilpotent operators in finite-dimensional settings, motivated by the algebraic structure of exceptional points in non-Hermitian quantum mechanics. Our starting poi…
Open clusters are fundamental laboratories for investigating stellar and Galactic evolution, and serve as important benchmarks for asteroseismic analyses. Using a boutique method to analyze TESS photo…
We give a self-contained, modern exposition of \'Edouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic po…
The excitation of plasma wakefields driven by chirped laser pulses is investigated using a reduced relativistic fluid Poisson model supported by fully relativistic particle in cell (PIC) simulations. …
Let $X_1,\ldots,X_n$ be independent random points in the closed unit ball of $\mathbb{R}^d$. Assume that each $X_i$ has a beta distribution with parameter $\beta_i \ge -1$: if $\beta_i>-1$, then $X_i$…
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