Research
Research
Research
Research
978+ open-access research outputs.
Let $G=PSL(n,\mathbb{C})$. Let $T$ be a maximal torus of $G$. Let $\omega_{r}$ denote the $r^{th}$ fundamental weight. Let $\mathcal{L}(n\omega_{r})$ denote the line bundle on the Grassmannian $G_{r,n…
Standard text-to-speech (TTS) evaluation measures intelligibility (WER, CER) and overall naturalness (MOS, UTMOS) but does not quantify accent. A synthesiser may score well on all four yet sound non-n…
Commercial TTS systems produce near-native Indic audio, but the best open-source bases (Chatterbox, Indic Parler-TTS, IndicF5) trail them on measured phonological dimensions, and the most widely adopt…
Motivated by recent theoretical and experimental studies on the role of flatbands in the thermoelectric properties of Ni$_3$In$_{1-x}$Sn$_x$ compounds, we investigate electron transport in two minimal…
For a simple graph $G$ with $n$ vertices, let $A_G$ denote the adjacency matrix of $G$, and let $\lambda_1(G) \geq \lambda_2(G) \geq \dots \geq \lambda_n(G)$ be its eigenvalues. For an integer $p \geq…
A proper orientation $D$ of an undirected graph $G$ is an orientation of $G$ such that $d_D^+(u)\not=d_D^+(v)$ for any edge $uv\in E(G)$. Denote the proper orientation number $\vec{\chi}(G)$ of an und…
Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative fr…
In this paper we study the range of possible almost sure dimensions of random measures arising from a natural model of random Moran measures. Specifically, we consider the Assouad-like ``large'' $\Phi…
I prove that the Borel directed graphs whose vertex set admits a partition into two Borel acyclic sets form a $\mathbf\Sigma^1_2$-complete set; equivalently, that deciding whether a Borel directed gra…
Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. In a sample compression scheme, we are given a large s…
For a graph $G$ of order $n$, the spectral sum of $G$ is defined to be the sum $\lambda_1(G) + \lambda_2(G)$, where $\lambda_1(G)$ (resp. $\lambda_2(G)$) is the largest (resp. second largest) adjacenc…
We prove that for every integer $d \ge 3$, the median eigenvalues of any graph of maximum degree $d$ are bounded above by $\sqrt{d-1}$. We also prove that, in three separate cases, the median eigenval…
Identifying the causal effects of socioeconomic determinants on population health is of many great interests - from statistical methodology development to public health practitioners and policy develo…
Lipshitz-Sarkar defined a stable homotopy type refining Khovanov homology, producing cohomology operations $\text{Sq}^i$ on the Khovanov homology $Kh(L)$ of a link $L$. Later, Mor\'an proposed a seque…
The development of robust language models for low-resource languages is frequently bottlenecked by the scarcity of high-quality, coherent, and domain-appropriate training corpora. In this paper, we in…
What is a diffusion model actually doing when it turns noise into a photograph? We show that the deterministic DDIM reverse chain operates as a Partitioned Iterated Function System (PIFS) and that t…
Collective modes in Fermi liquids are usually regarded as dissipation channels that relax electronic excitations through Landau damping. Whether such modes can instead mediate the formation of correla…
AI memory systems increasingly organize knowledge into graph structures -- knowledge graphs, entity relations, community hierarchies -- yet lack a principled mechanism for continuous resolution contro…
We study the Dirichlet problem for a class of fractional $p$-Laplacian operators of order $s \in (0,1)$ defined through the Riesz fractional gradient, which differs fundamentally from the standard fra…
This paper develops a comprehensive Markov-based framework for modelling reservoir behaviour and assessing key performance measures such as reliability and resilience. We first formulate a stochastic …
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