Research
Research
Research
Research
929+ open-access research outputs.
We study enumeration problems for multi-operator monomials generated from one indeterminate by an associative multiplication together with finitely many unary operators. We consider four regimes, acco…
Under-resourced languages remain underrepresented in quantitative rhythm research,particularly in systematic intra-branch analysis of acoustic differentiation within closely related linguistic groups.…
This work investigates the role of the $U(N) \times U(\tilde{N})$ global symmetry in tree-level scattering amplitudes of the bi-adjoint $\phi^3$ theory from three perspectives: combinatorics, correlat…
The generating functions of some sequences of Catalan numbers and Narayana polynomials have simple expansions as continued fractions of Jacobi type. We give an overview of these facts and prove analog…
In the FDR-controlling literature, mirror statistics offer a flexible alternative to $p$-value based procedures. When prior information is available, however, it is unclear how to incorporate mirror s…
This manuscript investigates channel capacity under mismatched stochastic likelihood decoding. We derive Feinstein- and Verd\'u-Han-style bounds on the error probability coded communication. These are…
Inversion sequences, also known as subexcedant sequences, form a fundamental class of objects in enumerative combinatorics. In this paper, we study the joint distribution of five statistics on inversi…
In this paper, we study the quasinormal modes of the generalized Joshi-Malafarina-Narayan (JMN) naked singularity spacetime using the exact Wentzel-Kramers-Brillouin (WKB) method. Working in the compl…
We present the first three-dimensional general relativistic magnetohydrodynamic simulation of sustained accretion onto a horizonless singularity in which matter reaches the central object rather than …
The Cohn-Elkies linear programming (LP) bound for sphere packing is known to be sharp in dimensions 8 and 24 but in no other dimension above 2. We investigate why by examining three independent necess…
We develop a systematic classification of asymmetric $\mathbb{Z}_2$ orbifold actions in Pati--Salam heterotic string vacua constructed in the free fermionic formulation. Starting from symmetric $\math…
Motivated by the recently proposed geometric descriptions of 0A and 0B in M-theory and F-theory, we propose a web of duality among non-supersymmetric strings. In particular we argue that the distinct …
We analyze a weighted convolution of Catalan numbers $$ \sum_{k=0}^{n} \binom{2k}{k}\binom{2(n-k)}{n-k} a^k = \sum_{k=0}^{n} (k+1)(n-k+1) C_k C_{n-k} a^k, $$ emphasizing its combinatorial, analytic, a…
Weighted Catalan numbers are a class of weighted sums over Dyck paths. Well-studied for their arithmetic properties and applications to enumerative combinatorics, these numbers were recently generaliz…
Following a systematic analysis of existing results, we investigate when complete interlacing between the zeros of distinct polynomial sequences, $\{\mathcal{P}_n\}$ and $\{\mathcal{G}_n\}$ can be ach…
Outpatient departments (OPDs) in Indian public hospitals face severe overcrowding, with daily volumes reaching 200--8,000 patients~\cite{aiims2020annual}. The prevailing First-Come-First-Served (FCFS)…
We study a new class of palindromic descent polynomials. Given a Dyck path $d$ of semilength $n$ and a permutation $\sigma$ of size $n$, one can label the up-steps and down-steps of $d$ with the eleme…
Vision-language models score well on mathematical, scientific, and spatial reasoning benchmarks, yet these evaluations are overwhelmingly English. I present the first cross-lingual visual reasoning au…
We analyze the causal structure of horizonless compact objects via the light-cone geometry and conformal compactification of the Joshi-Malafarina-Narayan (JMN-1) and Janis-Newman-Winicour (JNW) spacet…
We construct a generalized class of Joshi-Malafarina-Narayan (JMN) naked singularity spacetimes that arise as equilibrium end states of gravitational collapse with non-vanishing tangential pressure. T…
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