Research
Research
Research
Research
289+ open-access research outputs.
Reliable automated analysis of Optical Coherence Tomography (OCT) imaging is crucial for diagnosing retinal disorders but faces a critical barrier: the need for expensive, labor-intensive expert annot…
Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a…
We prove a conjecture of Kumbhakar, Roy, and Srinivasan (2024) on the classification of order one differential equations, and a conjecture of Kumbhakar and Srinivasan (2025) on higher order equations.…
Machine learning and high-throughput screening approaches to superconductor discovery require physically meaningful descriptors that capture essential physics while remaining computationally tractable…
It is well known that there is no closed form analytic expression for the perimeter of an ellipse. In 1927, Srinivasa Ramanujan provides two approximations to the perimeter of an ellipse that are amaz…
Rajagopal and Srinivasa's thermodynamic framework derives constitutive relations in continuum mechanics from two scalar functions describing energy storage and entropy production via a constrained opt…
Bimetallic catalysts provide new routes toward sustainable ammonia synthesis, but the structural dynamics controlling their performance under real-world conditions remain poorly understood. Here, we c…
In this work, we establish separation theorems for several subsystems of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM, 2018). Separation theorems a…
This paper explores the perfect reconstruction property of filter banks based on Ramanujan sums and their applications in signal recovery. Originally introduced by Srinivasa Ramanujan, Ramanujan sums …
We report the experimental discovery of bulk superconductivity in two kagome lattice compounds, YRu$_3$B$_2$ and LuRu$_3$B$_2$, which were predicted through machine learning-accelerated high-throughpu…
A graph $G = (V, E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that, for any two distinct vertices $x, y \in V$, $xy \in E$ if and only if $x$ and $y$ alternate in $w…
This paper presents a formal framework for sequencing instructions in AI agents, inspired by the Indian philosophical system of Mimamsa. The framework formalizes sequencing mechanisms through action o…
We study explicit constructions of min-wise hash families and their extension to $k$-min-wise hash families. Informally, a min-wise hash family guarantees that for any fixed subset $X\subseteq[N]$, ev…
This paper investigates Srinivasa Ramanujan's initial intuitive methodology for assigning the finite value -1/12 to the sum of the divergent infinite series of all positive integers. We systematically…
We use the formalism of Poincar\'e $ \infty $-categories, as developed by Calm\`es-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus-Steimle, to define and study moduli stacks of line bundles with $ \l…
A connected graph is called \emph{geodetic} if there is a unique shortest path between each pair of vertices. We introduce a systematic method for constructing new presentations of free products that …
We study whether lower bounds against constant-depth algebraic circuits computing the Permanent over finite fields (Limaye-Srinivasan-Tavenas, J. ACM 2025; Forbes, CCC 2024) are hard to prove in certa…
A rounding scheme for set cover has served as an important component in design of approximation algorithms for the problem, and there exists an H_s-approximate rounding scheme, where s denotes the max…
We give new lower bounds for the fragments of the Ideal Proof System (IPS) introduced by Grochow and Pitassi (JACM 2018). The Ideal Proof System is a central topic in algebraic proof complexity develo…
The celebrated Ore-DeMillo-Lipton-Schwartz-Zippel (ODLSZ) lemma asserts that n-variate non-zero polynomial functions of degree d over a field $\mathbb{F}$ are non-zero over any "grid" $S^n$ for finite…
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