Research
Research
Research
Research
4,004+ open-access research outputs.
We study the problem of online coloring for graphs with large odd girth. The best previously known algorithm uses $O(n^{1/2})$ colors, which was discovered by Kierstead in 1998. This algorithm works w…
Recommendation algorithms have become the dominant mechanism for information distribution on digital platforms, profoundly shaping personalized information consumption environments. However, gender bi…
Large Language Models (LLMs) have been widely applied to student-facing educational tools, this work explores their use in supporting instructors by presenting a practical adaptation of the Framework …
Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wis…
Coded caching is a technique that leverages locally cached contents at the end users to reduce the network's peak-time communication load. Coded caching has been shown to achieve significant performan…
We introduce a generalized family of $\left( 2\cdot \left\lfloor \frac{k}{2} \right\rfloor-1, 2\cdot \left\lceil \frac{k}{2} \right\rceil \cdot W_{1} +\max\left\{0,2\cdot\left(\left\lceil\frac{k}{2}\r…
We introduce Flashback, a reversible string decomposition that repeatedly peels the maximal leading and trailing character runs from a sentinel-wrapped input, recording each pair as one bilateral toke…
Mount Washington is home to extreme, and extremely volatile, weather conditions. Consulting a weather forecast of conditions at the summit is vital for making one's visit as safe as possible. Using th…
We study the rainbow matching (RM) problem: given an edge-colored graph, find a maximum matching with at most one edge of each color. Rainbow matchings correspond to stable sets in the \emph{augmented…
Goppa codes form an important class of alternant codes with wide applications in algebraic coding theory and code-based cryptography. Determining the true minimum distance of a Goppa code is a difficu…
This paper uncovers an exact $\chi^2$ dissipation identity for the Blahut--Arimoto (BA) flow and establishes its fundamental information-geometric structure. While prior works have analyzed BA converg…
Injecting artificial noise (AN) along the tangent space of a curved constellation makes each transmitted symbol induce a Gaussian observation with a symbol-dependent rank-one covariance, so the matche…
What do recurrent neural networks, polynomial ODEs, and discrete polynomial maps each bring to computation, and what do they lack? All three operate over the continuum--real-valued states evolved by r…
The challenge of programming classical computers to play traditional, competitive games against human players has helped to advance classical hardware and software. Quantum computers have the potentia…
BCH codes form an important class of cyclic codes, which have applications in communication and data storage systems. Although the BCH bound provides a lower bound on the minimum distance of BCH codes…
Research shows that dialogue, the interactive process through which participants articulate their thinking, plays a central role in constructing shared understanding, coordinating action, and shaping …
We present a deterministic linear-time algorithm for finding an odd cycle through two specified vertices in an undirected graph. This is shown in a generalized form as follows: Let $\Gamma$ be any gro…
Despite steady global advances, maternal mortality remains alarmingly high in Pakistan (155 deaths per 100,000 live births in 2023); largely as a consequence of fragmented paper records, low literacy,…
Classical robot ethics is often framed around obedience, including Asimov's laws. This framing is insufficient for contemporary AI systems, which are increasingly adaptive, generative, embodied, and e…
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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