96 citations · 491 across the 80 of their papers we have counts for
8 papers · 1 filter
On Ideal Lattices, Gröbner Bases and Generalized Hash Functions
Maria Francis, Ambedkar Dukkipati
In this paper, we draw connections between ideal lattices and multivariate polynomial rings over integers using Gröbner bases. Ideal lattices are ideals in the residue class ring,…
On Ideal Lattices and Gröbner Bases
Maria Francis, Ambedkar Dukkipati
In this paper, we draw a connection between ideal lattices and Gröbner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in $\mathbb{Z}…
Border Bases for Polynomial Rings over Noetherian Rings
Ambedkar Dukkipati, Nithish Pai, Maria Francis
The theory of border bases for zero-dimensional ideals has attracted several researchers in symbolic computation due to their numerical stability and mathematical elegance. As show…
Gröbner Basis Theory for Modules over Polynomial Rings over Fields with Valuation
Aritra Sen, Ambedkar Dukkipati
A motivation to study Gröbner theory for fields with valuations comes from tropical geometry, for example, they can be used to compute tropicalization of varieties \citep{maclagan2…
Spectral Clustering with Jensen-type kernels and their multi-point extensions
Debarghya Ghoshdastidar, Ambedkar Dukkipati, Ajay P. Adsul +1
Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multi-point' kernels, and study their applications. We study a class of…
To go deep or wide in learning?
Gaurav Pandey, Ambedkar Dukkipati
To achieve acceptable performance for AI tasks, one can either use sophisticated feature extraction methods as the first layer in a two-layered supervised learning model, or learn…