4 citations · 16 across the 23 of their papers we have counts for
23 papers
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…
A flux-based approach for analyzing the disguised toric locus of reaction networks
Balázs Boros, Gheorghe Craciun, Oskar Henriksson +2
Dynamical systems with polynomial right-hand sides are very important in various applications, e.g., in biochemistry and population dynamics. The mathematical study of these dynami…
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…
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…
Infinitesimal Homeostasis in Mass-Action Systems
Jiaxin Jin, Grzegorz A. Rempala
Homeostasis occurs in a biological system when a chosen output variable remains approximately constant despite changes in an input variable. In this work we specifically focus on b…
The toric locus of a reaction network is a smooth manifold
Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea
We show that the toric locus of a reaction network is a smoothly embedded submanifold of the Euclidean space. More precisely, we prove that the toric locus of a reaction network is…
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…
Homeostasis Patterns
William Duncan, Fernando Antoneli, Janet Best +5
Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when…
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…
The structure of the moduli spaces of toric dynamical systems
Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea
We consider complex-balanced mass-action systems, or toric dynamical systems. They are remarkably stable polynomial dynamical systems arising from reaction networks seen as Euclide…
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…
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…
Exponential Mixing of Vlasov equations under the effect of Gravity and Boundary
Jiaxin Jin, Chanwoo Kim
In this paper, we study exponentially fast mixing induced/enhanced by gravity and stochastic boundary in the kinetic theory of Vlasov equations. We consider the Vlasov equations wi…
An algorithm for finding weakly reversible deficiency zero realizations of polynomial dynamical systems
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
Systems of differential equations with polynomial right-hand sides are very common in applications. On the other hand, their mathematical analysis is very challenging in general, d…
Damping of kinetic transport equation with diffuse boundary condition
Jiaxin Jin, Chanwoo Kim
We prove that exponential moments of a fluctuation of the pure transport equation decay pointwisely almost as fast as when the domain is any general strictly convex subset…
Uniqueness of weakly reversible and deficiency zero realizations of dynamical systems
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
A reaction network together with a choice of rate constants uniquely gives rise to a system of differential equations, according to the law of mass-action kinetics. On the other ha…
The structure of the moduli space of toric dynamical systems of a reaction network
Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea
We consider toric dynamical systems, which are also called complex-balanced mass-action systems. These are remarkably stable polynomial dynamical systems that arise from the analys…
Single-Target Networks
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
We characterize the dynamics of all single-target networks under mass-action kinetics: either the system is (i) globally stable for all choice of rate constants (in fact, dynamical…
Instability of boundary equilibrium for Reaction-Diffusion system of a complex-balanced reaction network
Jiaxin Jin
In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first an…
Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria
Gheorghe Craciun, Jiaxin Jin, Casian Pantea +1
In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-s…
An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dyn…