Research
Research
Research
Research
9,950+ open-access research outputs.
We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of t…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Max…
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit exceptions when k < 4, ther…
Wurtzite ferroelectrics such as scandium-doped aluminum nitride (AlScN) are promising for next-generation memory because of their compatibility with semiconductor processes and strong spontaneous pola…
This article presents a partial differential equation (PDE) of Keller-Segel (KS) type that reproduces patterns commonly observed during the growth of brain microvasculature. We provide mathematical in…
For a fixed integer $k \ge 0$, consider representations of positive integers as sums of binomial coefficients of the form $\binom{n}{k}$. While exact minimal bounds for the number of required summands…
ULLER (Unified Language for LEarning and Reasoning) offers a unified first-order logic (FOL) syntax, enabling its knowledge bases to be used directly across a wide range of neurosymbolic systems. The …
The Hanoi Omega-Automata (HOA) format has established itself as the definitive standard for encoding $\omega$-regular automata in modern synthesis tools. While HOA is widely adopted due to its succinc…
Negative permittivity metamaterial is a scientifically rich avenue due to its tremendous application in several arena of materials research including novel superlens, band-gap materials, invisibility …
Modern retrieval pipelines increasingly serve downstream consumers like retrieval-augmented generation (RAG) and autonomous agents that need more than a scalar relevance score. A reranker that only te…
From the onset of observations of JWST we have discovered unexpectedly luminous galaxies at redshifts $z>10$ and as high as $z=14$. With their discovery, the question immediately followed as to where …
This paper studies the transmission of productivity shocks in general equilibrium production networks, when firms in different sectors operate under informational rigidity and rely on external debt. R…
Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfr…
Numerical simulations have established that star clusters with densities comparable to the high redshift ($z>6$-$10$) James Webb Space Telescope (JWST) proto globular clusters may build up extremely m…
Stars embedded in the accretion disks of active galactic nuclei (AGN) can accrete rapidly from their surroundings, dramatically altering their structure and evolution. However, feedback from the relea…
Accurate characterization of polarization dependent light matter interactions in nanostructured systems is paramount for the development of chiral metasurfaces. It is also often challenging, because m…
Mueller matrix (MM) polarimetry is an effective, non-invasive tool for retrieving information from complex media. However, the finite dynamic range of optical detectors poses a significant challenge w…
Most clinical prediction studies are developed from retrospective cohorts and reported as if all patient information were observed at once. In practice, clinicians face a more consequential question: …
Large language models (LLMs) have recently shown strong potential for generating project-level unit tests. However, existing state-of-the-art approaches primarily rely on execution-path information to…
For a nonnegative integer $r$ and a positive integer $v$ satisfying \[ \frac{r(q-1)}{2}<v<\frac{(r+1)(q-1)}{2}, \] we define the combinatorial numbers \[ A_r(v)= \begin{cases} \display…
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