1 citations · 1 across the 14 of their papers we have counts for
16 papers
On Measures of Dissimilarity on the Majorization Simplex
Tarun Hariharan, Prasad Krishnan, Abhishek Deshpande
The majorization simplex is the set of probability vectors of length whose entries are arranged in non-increasing order. Under the majorization order, $\mathcal…
Implementation of Linear Regression and Linear Interpolation using Reaction Networks
Aryan Kumar, Amey Choudhary, Jiaxin Jin +2
Statistical inference is a fundamental component of data science. In this work, we focus on two classical inference techniques: regression and interpolation. We propose a reaction-…
Mean-Field and Pairwise Approaches for the SIRI Model on Poisson Networks
Akshara Bhat, Abhishek Deshpande, Chittaranjan Hens +1
Compartmental epidemic models, grounded in mass-action kinetics, often assume homogeneous mixing. Although this neglects network structure, recent results show that for Poisson ran…
Extinction in Reaction Network Models
Pranav Agarwal, Gheorghe Craciun, Abhishek Deshpande +1
In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the stru…
The Computation of the Disguised Toric Locus of Reaction Networks
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Mathematical models of reaction networks can exhibit very complex dynamics, including multistability, oscillations, and chaotic dynamics. On the other hand, under some additional a…
Implementation of Support Vector Machines using Reaction Networks
Amey Choudhary, Jiaxin Jin, Abhishek Deshpande
Can machine learning algorithms be implemented using chemistry? We demonstrate that this is possible in the case of support vector machines (SVMs). SVMs are powerful tools for data…
Weakly reversible deficiency zero realizations of reaction networks
Neal Buxton, Gheorghe Craciun, Abhishek Deshpande +1
We prove that if a given reaction network has a weakly reversible deficiency zero realization for all choice of rate constants, then there exists a …
The Dimension of the Disguised Toric Locus of a Reaction Network
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Under mass-action kinetics, complex-balanced systems emerge from biochemical reaction networks and exhibit stable and predictable dynamics. For a reaction network , the associat…
Realizations through Weakly Reversible Networks and the Globally Attracting Locus
Samay Kothari, Jiaxin Jin, Abhishek Deshpande
We investigate the possibility that for any given reaction rate vector associated with a network , there exists another network with a corresponding reaction rate vecto…
On the Connectivity of the Disguised Toric Locus of a Reaction Network
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Complex-balanced mass-action systems are some of the most important types of mathematical models of reaction networks, due to their widespread use in applications, as well as their…
A Lower Bound on the Dimension of the -Disguised Toric Locus of a Reaction Network
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Polynomial dynamical systems (i.e. dynamical systems with polynomial right hand side) are ubiquitous in applications, especially as models of reaction networks and interaction netw…
Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Given a dynamical system with polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some netwo…
Endotactic and strongly endotactic networks with infinitely many positive steady states
Samay Kothari, Abhishek Deshpande
We show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess infinitely many steady states. We provide a few examples i…
Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Systems of differential equations with polynomial right-hand sides are very common in applications. In particular, when restricted to the positive orthant, they appear naturally (a…
Source-only realizations, weakly reversible deficiency one networks and dynamical equivalence
Abhishek Deshpande
Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical eq…
High rates of fuel consumption are not required by insulating motifs to suppress retroactivity in biochemical circuits
Abhishek Deshpande, Thomas E. Ouldridge
Retroactivity arises when the coupling of a molecular network to a downstream network results in signal propagation back from to $\mathcal…