Research
Research
Research
Research
2,435+ open-access research outputs.
We study scale-invariant geometric quantities associated with embedded closed curves in Euclidean three-space, with an emphasis on their behavior under optimization within a fixed knot type. Given a E…
The "Turner window" corresponds to axions with masses $\gtrsim$ 1 eV that have sufficiently strong couplings to matter to evade limits from the cooling of SN1987A. This window, through which the traje…
Motivated by entanglement-assisted quantum error-correcting codes, where the hull dimension determines the number of required pre-shared entangled pairs, we study hulls of two families of $\mathbb{F}_…
Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new graph parameters: st…
We study composition operators acting on the weighted Bergman spaces on the bidisc, i.e. $C_{\Phi}:A^2_{\beta}(\mathbb{D}^2)\to A^2_{\beta}(\mathbb{D}^2)$ where $\Phi$ is induced by rational inner fun…
We establish a fractal transference principle for continued fraction expansions over the field of Laurent series. Let $S$ be an infinite subset of the set of all polynomials over a finite field of $q$…
We present a framework for evaluating adaptive personalization of educational reading materials with theory-grounded simulated learners. The system builds a learning-objective and knowledge-component …
Erd\H{o}s asked whether every $n$-point set in Euclidean space whose $\binom{n}{2}$ pairwise distances are mutually at least $1$ apart must have diameter at least $(1+o(1))n^2$. We disprove this state…
We prove a strong general-purpose bound for the diameter of a finite group depending only on the diameters of its composition factors and the maximal exponent of a normal abelian section. There are a …
Abusive speech detection is becoming increasingly important as social media shifts towards voice-based interaction, particularly in multilingual and low-resource settings. Most current systems rely on…
Assume $n=2m\geq 2$ and let $F(x)=x^{d_1}+x^{d_2}$ be a binomial vectorial function over $\F_{2^n}$ possessing the maximal number (i.e. $2^n-2^m$) of bent components. Suppose the $2$-adic Hamming weig…
Content creation for major video-sharing platforms demands significant manual labor, particularly for long-form documentary videos spanning one to two hours. In this work, we introduce Sima 1.0, a mul…
Harmful content detectors-particularly disinformation classifiers-are predominantly developed and evaluated on Standard American English (SAE), leaving their robustness to dialectal variation unexplor…
Board games have shown promise as educational tools, but their use in engaging learners with the complex, long-term trade-offs of forest management remains strikingly underdeveloped. Addressing this g…
Medical imaging techniques, especially Magnetic Resonance Imaging (MRI), are accepted as the gold standard in the diagnosis and treatment planning of neurological diseases. However, the manual analysi…
For the partition graph $G_n$ on the set of partitions of $n$, we study the stratification induced by the local simplex dimension $\dim_{\mathrm{loc}}(\lambda)$, defined as the maximal dimension of a …
Social and personal decisions in relational domains such as matchmaking are deeply entwined with cultural norms and historical hierarchies, and can potentially be shaped by algorithmic and AI-mediated…
Visual food recognition in real-world dietary logging scenarios naturally exhibits severe data imbalance, where a small number of food categories appear frequently while many others occur rarely, resu…
We prove that no cyclic division algebra (in the sense of Dickson) admits an abelian maximal subgroup in its multiplicative group. This settles a special case of a long-standing conjecture of Akbari--…
For each positive integer $n$, let $G_n$ be the graph whose vertices are the partitions of $n$, with edges given by elementary transfers of one unit between parts, followed by reordering. We study the…
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