Research
Research
Research
Research
202+ open-access research outputs.
On the flag variety $ \mathcal{F}l_s(E)$ associated to a vector bundle $E,$ , a sequence $s$ and a partition $a,$ there is a line bundle $\it Q^a_s$ on $ \mathcal{F}l_s(E).$ The aim of this pape…
Loading high dimensional distributions is an important task for utilizing quantum computers on applications ranging from machine learning to finance. The high dimensionality leads to a curse of dimens…
We provide a complete characterization of those graphons $W$ for which the inhomogeneous random graph $G(n,W)$ is asymptotically almost surely Hamiltonian. The characterization involves three conditio…
Large Language Models (LLMs) are increasingly deployed in domains such as education, mental health and customer support, where stable and consistent personas are critical for reliability. Yet, existin…
We study the optimal design of additive mechanisms for vector-valued queries under $\epsilon$-differential privacy (DP). Given only the sensitivity of a query and a norm-monotone cost function measuri…
As a consequence of the Littlewood-Richardson (LR) commuters coincidence and the Kumar-Torres branching model via Kushwaha-Raghavan-Viswanath flagged hives, we have solved the Lecouvey- -Lenart conjec…
We study the relation between semipositivity, nefness, and bigness of line bundles on compact K\"ahler manifolds. Every nef and big line bundle on a compact K\"ahler manifold $X$ is positive when ${\r…
Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the …
In this paper, we prove similar results for odd and even cycle lengths. Let $L_o(G)$ denote the set of odd cycle lengths of $G$ and $\ell_o(G)$ denote the longest odd cycle length. In 1992, Gy\'arf\'a…
The increasing use of vine copulas in high-dimensional settings, where the number of parameters is often of the same order as the sample size, calls for asymptotic theory beyond the traditional fixed-…
Nanoscale topologically non-trivial magnetization configurations generate significant interest due to both the fundamental properties of their knotted structures and their potential applications in ul…
Given an $n$-dimensional compact K\"ahler manifold, we continue our study of $m$-positivity in two ways. We first propose generalisations of the notions of pseudo-effective and big Bott-Chern cohomolo…
Classical studies of the Fibonacci sequence focus on its periodicity modulo $m$ (the Pisano periods) with canonical initialization. We investigate instead the complete periodic structure arising from …
Sign languages play a crucial role in the communication of deaf communities, but they are often marginalized, limiting access to essential services such as healthcare and education. This study propose…
Vine copulas offer flexible multivariate dependence modeling and have become widely used in machine learning. Yet, structure learning remains a key challenge. Early heuristics, such as Dissmann's gree…
Betel leaf is an important crop because of its economic advantages and widespread use. Its betel vines are susceptible to a number of illnesses that are commonly referred to as betel leaf disease. Pla…
Psychometric tests, traditionally used to assess humans, are now being applied to Large Language Models (LLMs) to evaluate their behavioral traits. However, existing studies follow a context-free appr…
Vine copulas are sophisticated models for multivariate distributions and are increasingly used in machine learning. To facilitate their integration into modern ML pipelines, we introduce the vine comp…
Simplified vine copulas are flexible tools over standard multivariate distributions for modeling and understanding different dependence properties in high-dimensional data. Their conditional distribut…
This study investigates the nonlinear dynamics of a symmetric vibro-impact nonlinear energy sink (VI-NES) subjected to dry friction, a crucial factor that remains insufficiently explored in previous r…
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