23 citations · 37 across the 9 of their papers we have counts for
12 papers
Minimal invariant regions and minimal globally attracting regions for variable-k reaction systems
Yida Ding, Abhishek Deshpande, Gheorghe Craciun
The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit cons…
Homeostasis and injectivity: a reaction network perspective
Gheorghe Craciun, Abhishek Deshpande
Homeostasis is a mechanism by which a feature can remain invariant with change in external parameters. We adopt the definition of homeostasis in the context of singularity theory.…
Autocatalytic systems and recombination: a reaction network perspective
Gheorghe Craciun, Abhishek Deshpande, Badal Joshi +1
Autocatalytic systems are very often incorporated in the "origin of life" models, a connection that has been analyzed in the context of the classical hypercycles introduced by Manf…
On reaction network implementations of neural networks
David F. Anderson, Badal Joshi, Abhishek Deshpande
This paper is concerned with the utilization of deterministically modeled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general…
Minimal invariant regions and minimal globally attracting regions for toric differential inclusions
Yida Ding, Abhishek Deshpande, Gheorghe Craciun
Toric differential inclusions occur as key dynamical systems in the context of the Global Attractor Conjecture. We introduce the notions of minimal invariant regions and minimal gl…
Quasi-Toric Differential Inclusions
Gheorghe Craciun, Abhishek Deshpande, Hyejin Jenny Yeon
Toric differential inclusions play a pivotal role in providing a rigorous interpretation of the connection between weak reversibility and the persistence of mass-action systems and…
Endotactic Networks and Toric Differential Inclusions
Gheorghe Craciun, Abhishek Deshpande
An important dynamical property of biological interaction networks is persistence, which intuitively means that "no species goes extinct". It has been conjectured that dynamical sy…
Optimizing enzymatic catalysts for rapid turnover of substrates with low enzyme sequestration
Abhishek Deshpande, Thomas E. Ouldridge
We analyse the mechanism of enzyme-substrate catalysis from the perspective of minimizing the load on the enzymes through sequestration, whilst maintaining at least a minimum react…
Designing the Optimal Bit: Balancing Energetic Cost, Speed and Reliability
Abhishek Deshpande, Manoj Gopalkrishnan, Thomas E. Ouldridge +1
We consider the technologically relevant costs of operating a reliable bit that can be erased rapidly. We find that both erasing and reliability times are non-monotonic in the unde…
A Bayesian view of Single-Qubit Clocks, and an Energy versus Accuracy tradeoff
Manoj Gopalkrishnan, Varshith Kandula, Praveen Sriram +2
We bring a Bayesian approach to the analysis of clocks. Using exponential distributions as priors for clocks, we analyze how well one can keep time with a single qubit freely prece…
Measurement Induced Randomness and State Merging
Indranil Chakrabarty, Abhishek Deshpande, Sourav Chatterjee
In this work we introduce the randomness which is truly quantum mechanical in nature arising as an act of measurement. For a composite classical system we have the joint entropy to…
Autocatalysis in Reaction Networks
Abhishek Deshpande, Manoj Gopalkrishnan
The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applyin…