Ishan Banerjee
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View article: Slicing Correspondences with High Degree Hypersurfaces
Slicing Correspondences with High Degree Hypersurfaces Open
We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product $Y \times Y'$ an…
View article: Survey of Large Multimodal Model Datasets, Application Categories and Taxonomy
Survey of Large Multimodal Model Datasets, Application Categories and Taxonomy Open
Multimodal learning, a rapidly evolving field in artificial intelligence, seeks to construct more versatile and robust systems by integrating and analyzing diverse types of data, including text, images, audio, and video. Inspired by the hu…
View article: Number of Hamiltonian Cycles in Certain Bipartite Graphs of Size 4k+2
Number of Hamiltonian Cycles in Certain Bipartite Graphs of Size 4k+2 Open
We will try to use the approach of labeled cycle cover sum to count the number of hamiltonian cycles in a special type of bipartite graphs, with 4k + 2 vertices which can also be considered as an alternative method to check hamiltonicity i…
View article: Error terms for the motives of discriminant complements and a Cayley-Bacharach theorem
Error terms for the motives of discriminant complements and a Cayley-Bacharach theorem Open
In this paper we prove under some simplifying hypotheses questions of Picoco and Levinson-Ullery on Cayley-Bacharach sets. Our results imply that, under suitable hypotheses Cayley-Bacharach sets lie on curves of low degree. We then use the…
View article: Review of Some Prey-Predator Models Relevant to the Lynx-Snowshoe Hare Relation
Review of Some Prey-Predator Models Relevant to the Lynx-Snowshoe Hare Relation Open
The paper focuses on the different dynamical systems for the prey-predator model for different cases which includes greater depth of the food chain and varying number of preys and predators. We simulate the different postulated models and …
View article: Brief Discussion on the Mathematics Behind Extinctions A Detailed Statistical Assay on the Population Density of Northern White Rhinoceros
Brief Discussion on the Mathematics Behind Extinctions A Detailed Statistical Assay on the Population Density of Northern White Rhinoceros Open
Species extinctions have been a significant part in disturbing the biodiversity. This creates an importance in trying to simulate the populations of the species of interest to get an idea when its population looks threateningly low. We wil…
View article: Sums of Two Squares Visualized
Sums of Two Squares Visualized Open
We provide a geometric interpretation of Brillhart's celebrated algorithm for expressing a prime $p\equiv 1\pmod 4$ as the sum of two squares.
View article: A Short Review on Fast Ways to Multiply Two Matrices
A Short Review on Fast Ways to Multiply Two Matrices Open
Matrix multiplication is probably one of the most basic and important operations having a wide range of applications in studying Linear algebra. We will be primarily focused on reviewing different algorithms for the multiplication of two n…
View article: Stable Cohomology of Discriminant Complements for an algebraic curve
Stable Cohomology of Discriminant Complements for an algebraic curve Open
In this paper we show that in a stable range the cohomology of the space of regular algebraic sections of a line bundle $\mathscr{L}$on a curve $X$ is isomorphic to the cohomology of the space of regular $C^{\infty}$sections of the same li…
View article: Stable cohomology of the universal degree $d$ hypersurface in\n $\\mathbb{P}^n$
Stable cohomology of the universal degree $d$ hypersurface in\n $\\mathbb{P}^n$ Open
Let $U_{d,n}^*$ be the universal degree $d$ hypersurface in $\\mathbb{P}^n$.\nIn this paper we compute the stable (with respect to $d$) cohomology of\n$U_{d,n}^*$ and give a geometric description of the stable classes. This builds\non work…
View article: Event-Code Interaction Directed Test Cases
Event-Code Interaction Directed Test Cases Open
The Graphical User Interface (GUI) is an integral component of contemporary computer software. A stable and reliable GUI is necessary for correct functioning of software applications. Comprehensive verification of the GUI is a routine part…