arXiv subjects

Avik Das

Publications and source records attributed to Avik Das.

3 recordsLinked to original sources

arXiv2026

Coarse Embeddability Ratios of Banach Spaces

Given two Banach spaces $X$ and $E$, one can associate a numerical invariant $\mathcal{CR}(X, E)$, called the coarse embeddability ratio, which provides a criterion for coarse and uniform embeddability. We compute the coarse embeddability ratio for several important classes of Banach spaces, using various tools from the nonlinear theory of Banach spaces. Finally, we find pairs of Banach spaces with arbitrarily large coarse embeddability ratio, resolving an open problem of Rosendal in the negative.

math.FA↗

arXiv2026

3D Spatial Pattern Matching

Spatial pattern matching is the process of matching query entities and constraints with database entities and relations. It has many applications, including similar region search, housing market search, landmark search, and road network matching. To our knowledge, all existing spatial pattern matching approaches frame the problem in a 2 dimensional space, where entities lie in a cartesian plane and relationships defined between them are contained in 2 dimensions. However, this problem framing has significant limitations when searching for real world entities that have height in addition to position. To address this limitation, we extend spatial pattern matching to 3 dimensions and provide a generalized definition of the problem. We describe a subgraph matching algorithm capable of resolving 3D spatial patterns over distance relations and release two 3D spatial pattern matching datasets, one synthetic and one containing real 3D building data from the city of Hamburg, Germany. We test our subgraph matching algorithm on both datasets and present results as a baseline for future methods to build upon.

cs.DB↗

arXiv2022

Understanding Volatility Spillover Relationship Among G7 Nations And India During Covid-19

Purpose: In the context of a COVID pandemic in 2020-21, this paper attempts to capture the interconnectedness and volatility transmission dynamics. The nature of change in volatility spillover effects and time-varying conditional correlation among the G7 countries and India is investigated. Methodology: To assess the volatility spillover effects, the bivariate BEKK and t- DCC (1,1) GARCH (1,1) models have been used. Our research shows how the dynamics of volatility spillover between India and the G7 countries shift before and during COVID-19. Findings: The findings reveal that the extent of volatility spillover has altered during COVID compared to the pre-COVID environment. During this pandemic, a sharp increase in conditional correlation indicates an increase in systematic risk between countries. Originality: The study contributes to a better understanding of the dynamics of volatility spillover between G7 countries and India. Asset managers and foreign corporations can use the changing spillover dynamics to improve investment decisions and implement effective hedging measures to protect their interests. Furthermore, this research will assist financial regulators in assessing market risk in the future owing to crises like as COVID-19.

econ.EM↗