Research
Research
Research
Research
221+ open-access research outputs.
We study the topological structure of random geometric forests $G$ in the Euclidean plane under mild assumptions: non-crossing edges, stationarity, and finite edge intensity. The framework covers a br…
In the celebrated paper of Henzinger, Klein, Rao and Subramanian (1997), it was shown that planar graphs admit a linear time single-source shortest path algorithm. Their algorithm unfortunately does n…
As Spoken Language Models (SLMs) integrate speech and text modalities, they inherit the safety vulnerabilities of their LLM backbone and an expanded attack surface. SLMs have been previously shown to …
The Teissier distribution, originally proposed by Teissier [31], was designed to model mortality due to aging in domestic animals. More recently, Krishna et al. [19] introduced the Unit Teissier (UT) …
Given a digraph $D$, we denote by $\vec{\alpha}(D)$ the maximum size of an acyclic set of $D$ (i.e. a set of vertices which induces a subdigraph with no directed cycles), and by $\vec\chi(D)$ the mini…
Background: Accurate glottal segmentation in high-speed videoendoscopy (HSV) is essential for extracting kinematic biomarkers of laryngeal function. However, existing deep learning models often produc…
Many cloud infrastructure organizations increasingly rely on third-party eBPF-based network functions for use cases like security, observability, and load balancing, so that not everyone requires a te…
Vector similarity search is an essential primitive in modern AI and ML applications. Most vector databases adopt graph-based approximate nearest neighbor (ANN) search algorithms, such as DiskANN (Subr…
Magic state distillation is a leading but costly approach to fault-tolerant quantum computation, and it is important to explore all possible ways of minimizing its overhead cost. The number of ancilla…
The enumeration of small steps walks confined to the first quadrant of the plane has attracted a lot of attention over the past fifteen years. The associated generating functions are trivariate formal…
The ray transform $I_m$ integrates a symmetric $m$ rank tensor field $f$ on $\mathbb{R}^n$ over lines. In the case of $n\ge3$, the range characterization of the operator $I_m$ on weighted Sobolev spac…
We prove that the random Schrodinger operators on $\mathbb{R}^3$ with independent, identically distributed random variables and single-site potentials given by $\delta$-functions on $\mathbb{Z}^3$, ex…
In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Morton, we prove that th…
Indian farmers often lack timely, accessible, and language-friendly agricultural advice, especially in rural areas with low literacy. To address this gap in accessibility, this paper presents a novel …
Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of …
In this paper, I investigate gravitational thermodynamics of the Einstein-Maxwell-scalar system in three dimensions without a cosmological constant. In the previous work by Krishnan,Shekhar, and Bala …
The knot Floer order $\operatorname{Ord}(K)$ is a knot invariant derived from knot Floer homology that provides bounds on many other invariants, such as the bridge index $\operatorname{br}(K)$ for whi…
Silverman showed that, assuming the $abc$ conjecture, there are $\gg \log x$ non-Wieferich primes base $a$ less than $x$ \cite{silverman}, for all non-zero $a$. This inspired Graves and Murty \cite{Gr…
In the context of orbitronics, the rising of the orbital angular momentum generated at light metal interfaces from orbital textures via orbital Rashba-Edelstein effects nowadays represent extraordinar…
For a tree $T$ and a function $f \colon E(T)\to \mathbb{S}^d$, the imbalance of a subtree $T'\subseteq T$ is given by $|\sum_{e \in E(T')} f(e)|$. The $d$-dimensional discrepancy of the tree $T$ is th…
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