Research
Research
Research
Research
129+ open-access research outputs.
We prove the congruence $\sum_{1 \leq k < \sqrt{N}} \sigma_0 (N - k^2) \equiv 0 \pmod 4$, where $\sigma_0(m)$ denotes the number of positive divisors of $m$, for $N = An + B$ with $(A,B) \in \{ (16,14…
This performance presents a duet between two intelligent musical instruments, S\`u (to trace back; to go upstream) and Agentier (playing on agentic clavier), and their human performers, connected thro…
In this work, we extend a classical theorem of Keith Ball on integrals of log-concave functions along rays against the weight $r^{p-1}$ to the previously inaccessible regime $p\in (-1,0)$: if $g:\math…
We prove that if $K$ is a symmetric and isotropic convex body in $\mathbb{R}^n$, then $$\int_K\langle x,u\rangle^2\,dx\int_{K^\circ}\langle x,u\rangle^2\,dx\leq \left(\int_{B_2^n}\langle x,u\rangle^2\…
Underwater photography presents significant inherent challenges including reduced contrast, spatial blur, and wavelength-dependent color distortions. These effects can obscure the vibrancy of marine l…
We investigate the combinatorial structure of unrefinable partitions through their correspondence with numerical sets and Young diagrams. Building on the bijection introduced by Keith and Nath, we app…
We present a new approach to formulating and solving heterogeneous agent models with aggregate risk. We replace the cross-sectional distribution with low-dimensional prices as state variables and let …
We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep lear…
Recently, Keith investigated arithmetic properties for the reciprocals of some false theta functions and posed several conjectures. In this paper, we prove some parity results for the reciprocals of…
Understanding household behaviour is essential for modelling macroeconomic dynamics and designing effective policy. While heterogeneous agent models offer a more realistic alternative to representativ…
We study a model of the Fiscal Theory of the Price Level (FTPL) in a Bewley-Huggett-Aiyagari framework with heterogeneous agents. The model is set in continuous time, and ex post heterogeneity arises …
We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for individual optimization…
Moons tidally interact with their host planets and stars. A close moon is quickly synchronised by the planet, or becomes captured in a higher spin-orbit resonance. However, the planet requires much mo…
We develop a general comparison result for inf convolution operators related to rearrangement. As a consequence we derive comparison results under spherically symmetric rearrangement for Laplace and p…
Numerical turbulence simulations typically involve parameterizations such as Large Eddy Simulations (LES). Applications to geophysical flows, especially ocean flows, are further complicated by the pre…
Recently, Keith investigated reciprocals of false theta functions and proved some interesting results such as congruences, asymptotic bounds, and combinatorial identities. At the end of his paper, Kei…
Nick Huggett, James Ladyman, and Karim Thebault (HLT) have presented a comprehensive article examining the Born-Oppenheimer Approximation (BOA). Their central objective is to challenge our position on…
In 2017, Keith presented a comprehensive survey on integer partitions into parts that are simultaneously regular, distinct, and/or flat. Recently, the authors initiated a study of partitions into part…
This paper introduces DeeCLIP, a novel framework for detecting AI-generated images using CLIP-ViT and fusion learning. Despite significant advancements in generative models capable of creating highly …
Physics-based closures such as eddy-viscosity and backscattering models are widely used for large-eddy simulation (LES) of geophysical turbulence for applications including weather and climate predict…
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