6 papers
A primer on the closure of algebraic complexity classes under factoring
C. S. Bhargav, Prateek Dwivedi, Nitin Saxena
Polynomial factorisation is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different…
Lower Bounds in Algebraic Complexity via Symmetry and Homomorphism Polynomials
Prateek Dwivedi, Benedikt Pago, Tim Seppelt
Valiant's conjecture asserts that the circuit complexity classes VP and VNP are distinct, meaning that the permanent does not admit polynomial-size algebraic circuits. As it is the…
On Closure Properties of Read-Once Oblivious Algebraic Branching Programs
Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen +3
We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following. - Non-closure…
Monotone Bounded-Depth Complexity of Homomorphism Polynomials
C. S. Bhargav, Shiteng Chen, Radu Curticapean +1
For every fixed graph , it is known that homomorphism counts from and colorful -subgraph counts can be determined in time on -vertex input graphs , whe…
Emergence of Order in Chemically Active Droplets: Temporal Dynamics and Collective Behavior
Sobiya Ashraf, Pawan Kumar, Prateek Dwivedi +3
Collective behaviors such as swarming, chemical signaling, and clustering are fundamental to biological microorganisms, enabling hierarchical colony formation, coordinated motion,…
Chemical interactions in active droplets
Prateek Dwivedi, Sobiya Ashraf, Pawan Kumar +2
Interactions among biologically active agents is facilitated by their self-generated chemical and hydrodynamic fields. In order to elucidate the pair-wise interactions between such…