Research
Research
Research
Research
229+ open-access research outputs.
We prove that the theory of the Farey graph is pseudofinite by constructing a sequence of finite structures that satisfy increasingly large subsets of its first-order axiomatization. This graph is an …
Let $\Gamma < G := \operatorname{SO}(d+1, 1)$ for $d \geq 1$ be a Zariski dense, geometrically finite, discrete subgroup with critical exponent strictly greater than $d/2$. We show that $L^2(\Gamma\ba…
Recent advancements of the Artificial Intelligence (AI) have led to the development of large language models (LLMs) that are capable of understanding, analysing, and creating textual data. These langu…
Can LLM agents explore codebases and reason about code semantics without executing the code? We study this capability, which we call agentic code reasoning, and introduce semi-formal reasoning: a stru…
In this paper, we establish the strong well-posedness of SDEs with merely integrable time-dependent drifts driven by fractional Brownian motions with Hurst parameter H<1/2. Our result holds over the e…
Let $k\geq2$. Then the $k$-th order Fibonacci cube $\Gamma^{(k)}_{n}$ is the subgraph of the hypercube $Q_{n}$ induced by vertices without $k$ consecutive $1$s. The case $k=2$ corresponds to the class…
In a recent letter [T. D. K\"uhne, M. Krack, F. Mohamed and M. Parrinello, Phys. Rev. Lett. 98, 066401 (2007)], we outlined a new Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics. H…
Mathematicians have long been fascinated by the resolution of algebraic and Diophantine equations in search of integer or rational solutions. This article presents a list of thirty-three open problems…
The rapid expansion of artificial intelligence (AI) in the Gulf Cooperation Council (GCC) raises a central question: are investments in compute infrastructure matched by an equally robust build-out of…
Manual peripheral blood smear (PBS) analysis is labor intensive and subjective. While deep learning offers a promising alternative, a systematic evaluation of state of the art models such as YOLOv11 f…
This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagona…
We establish dimensional thresholds for dot product sets associated with compact subsets of translated paraboloids. Specifically, we prove that when the dimension of such a subset exceeds $ \frac{5}{4…
George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions. In particular, they studied the connection between two-colored partitions and overpartitions. Their proof…
We study point-line configurations and their associated matroid and circuit varieties. We aim to find a finite set of defining equations for matroid varieties and an irreducible decomposition for circ…
Misinformation is a growing concern in a decade involving critical global events. While social media regulation is mainly dedicated towards the detection and prevention of fake news and political misi…
We introduce the cave polynomial of a polymatroid and show that it yields a valuative function on polymatroids. The support of this polynomial after homogenization is again a polymatroid. The cave pol…
This paper empirically examines the extent to which a favorable view of a firm, shaped by its social contributions, influences consumer choices and firm sales. Using a favorability rating that reflect…
We determine weak asymptotics of counting functions on generic surfaces in a component of a stratum of $k$-differentials when $k$ is prime and genus is greater than $2$. In order to do so, we classify…
In offline reinforcement learning, agents are trained using only a fixed set of stored transitions derived from a source policy. However, this requires that the dataset be labeled by a reward function…
Text-based hyperbole and metaphor detection are of great significance for natural language processing (NLP) tasks. However, due to their semantic obscurity and expressive diversity, it is rather chall…
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