Research
Research
Research
Research
118+ open-access research outputs.
Grover's algorithm is a cornerstone of quantum algorithms and is strictly optimal in oracle-query complexity. While the full search problem admits no further improvement, one may trade accuracy for sp…
Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, …
The third Gaia data release includes 33.8 million radial velocity measurements, extending to a magnitude of G_RVS = 14. To reach this magnitude limit, spectra were processed down to a signal-to-noise …
Grover's algorithm provides a quadratic speedup over classical algorithms for searching unstructured databases and is known to be strictly optimal in oracle query complexity, with tight bounds on its …
The study by Jung et al. (Jung H, Covino R, Arjun A, et al., Nat Comput Sci. 3:334-345 (2023)) introduced Artificial Intelligence for Molecular Mechanism Discovery (AIMMD), a novel sampling algorithm …
By extending the notion of spin of prime ideals, we show that a short character sum conjecture implies that the set of primes raising the level of a certain even Galois representation has density 2/3,…
Understanding feature learning is an important open question in establishing a mathematical foundation for deep neural networks. The Neural Feature Ansatz (NFA) states that after training, the Gram ma…
We present a new method for identifying Galactic halo substructures accreted from dwarf galaxies by combining metallicity distribution functions (MDFs) with orbital parameters. Using apogalactic dista…
In this work, we show that given a finite p-group G, a number field K having a trivial p-class group Cl K , and a finite set of primes S of K, there exists a finite extension F/K such that the S-split…
Using the WZ method to prove supercongruences critically depends on an inspired WZ pair choice. This paper demonstrates a procedure for finding WZ pair candidates to prove a given supercongruence. Whe…
It is a central challenge in deep learning to understand how neural networks learn representations. A leading approach is the Neural Feature Ansatz (NFA) (Radhakrishnan et al. 2024), a conjectured mec…
We describe a class of Lie superalgebras in characteristic $3$, containing the Elduque-Cunha superalgebras $\mathfrak{g}(3,3), \mathfrak{g}(6,6)$ and the Elduque superalgebra $\mathfrak{el}(5,3)$, usi…
Let $p\geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$-torsion in the Bloch-Kato Selmer group can be made …
This paper presents a novel AI-powered framework designed to streamline database management and query optimization for PostgreSQL systems. Structured in three phases: Natural Language to SQL Translati…
By the FKG inequality for FK-percolation, the probability of the alternating two-arm event is smaller than the product of the probabilities of having a primal arm and a dual arm, respectively. In this…
This is an expository paper intended to introduce the polynomial time lattice basis reduction algorithm first described by Arjen Lenstra, Hendrik Lenstra, and L\'aszl\'o Lov\'asz in 1982. We begin by …
Using kinematic data from the Gaia Data Release 3 catalog, along with metallicity estimates robustly derived from Gaia XP spectra, we have explored the Galactic stellar halo in search of both known an…
In this paper we generalize the forcing ramification argument of Khare-Ramakrishna to the setting of the lifting result by Fakhruddin-Khare-Patrikis. In particular, we show that in the relative deform…
Our understanding of the assembly timeline of the Milky Way has been transforming along with the dramatic increase in astrometric and spectroscopic data available over the past several years. Many sub…
In [1], we calibrated a one-factor Cheyette SLV model with a local volatility that is linear in the benchmark forward rate and an uncorrelated CIR stochastic variance to 3M caplets of various maturiti…
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