In this thesis,we study combinatorial batch codes (CBCs) and permutation binomials (PBs) over �nite �elds of even characteristic. Our primary motivation for considering these problems comes from their importance in ...

An arrangement of a set of non-self-intersecting curves is their embedding in the Euclidean plane such that at each intersection point the curves involved cross each other. Arrangements are well-studied both in Discrete ...

Cops and Robber is a two-player pursuit-evasion game played on graphs. Here, one player controls a set of k cops, and the other player controls a single robber. The game starts with k cops placing themselves on the vertices ...

Query complexity, both classical and quantum, are important and well-established notions of computation. In this thesis, we will investigate query complexity in both classical and quantum worlds and study their relationship ...

Symmetric key cryptography refers to the encryption methods in which the same key is used by both the sender and the receiver. Cryptanalysis is a process of finding vulnerabilities in cryptographic algorithms in order to ...

Single-cell transcriptome data provide us with an enormous scope of studying biological systems at the cellular level. We aim to address different problems involving the statistical analysis of single-cell RNA-seq data. ...

Nowadays, cloud computing and storage services have become crucial in everyone’s life either directly or indirectly. However, data stored in untrusted cloud servers is prone to attacks by the server itself. In case, the ...

Quantum key distribution (QKD) has raised some promise for more secured communica- tion than its classical counterpart. It allows the legitimate parties to detect eavesdropping which introduces error in the channel. If ...