35 citations · 107 across the 11 of their papers we have counts for
13 papers
Tight Lower Bounds for Algebraic Communication and Applications
Manon Blanc, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen +2
Communication complexity studies how much information must be exchanged to solve a problem whose input is split among two or more parties. In this work, we study an algebraic varia…
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…
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…
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…
Motility and pair-wise interactions of chemically active droplets in 1-D confinement
Pawan Kumar, Prateek Dwivedi, Sobiya Ashraf +2
Self-propelled droplets serve as ideal model systems to delve deeper into understanding of the motion of biological micro-swimmers by simulating their motility. Biological microorg…
Deforming Active Droplets in Viscoelastic Media
Prateek Dwivedi, Atishay Shrivastava, Naveen Tiwari +2
To mimic the motion of biological swimmers in bodily fluids, a novel experimental system of micellar solubilization driven active droplets in a visco-elastic polymeric solution is…
Mode-Switching of Active Droplets in Macromolecular Solutions
Prateek Dwivedi, Atishay Shrivastava, Dipin Pillai +1
Typical bodily and environmental fluids encountered by biological swimmers consist of dissolved macromolecules such as proteins and polymers, often rendering them non Newtonian. To…
Interaction of Active Janus Particles with Passive Tracers
Karnika Singh, Ankit Yadav, Prateek Dwivedi +1
In this study, we investigated the motion of active SiO2-Pt Janus particles in the 2D bath of smaller silica tracers dispersed in varying areal densities. The effect on the organiz…
Rheotaxis of Active Droplets
Prateek Dwivedi, Atishay Shrivastava, Dipin Pillai +1
Rheotaxis is a well-known phenomenon among microbial organisms and artificial active colloids, wherein the swimmers respond to an imposed flow. We report the first experimental evi…
Solute Induced Jittery Motion of Self-Propelled Droplets
Prateek Dwivedi, Bishwa Ranjan Si, Dipin S. Pillai +1
The intriguing role of the presence of solutes in the activity of a self-propelling droplet is investigated. A system of self-propelling micron sized 4-pentyl-4-biphenylcarbonitril…