27 problems

A stochastic mass-action reaction system (SMART) is a continuous-time Markov chain describing molecule counts in a mass-action reaction network, and it is weakly reversible when ev…

Let $N$ be the model described in the preceding proposition, with parameters $\alpha$ and $p$ satisfying $\alpha=\log(1/p)$. Boundary-case nonexplosivity conjecture. The model $N$…

Let $N$ be the coarse-grained model associated to the general content-dependent fragmentation reaction network, and let $\mathcal I_\mathcal K$ denote its chemistry. Nonexplosivity…

A $D$-unstable core is a $D$-unstable Child-Selection matrix $\mathbb{S}[\pmb{\kappa}]$ such that none of its principal submatrices are $D$-unstable. A network is said to admit ins…

Example transience conjecture. There exists $\alpha>0$ such that the mixed process from Example is transient for all sufficiently small values of $\kappa$.

An endotactic mass-action system is a mass-action system whose reaction network is endotactic, and a system is permanent when its trajectories remain uniformly separated from the b…

Let $G$ be a reaction network containing the motif … where $Y$ appears in no other complex. Let $p_{(h,\ell)}$ and $p'_{(h,\ell')}$ be the reduced characteristic polynomials of $G$…

Let $G$ be a reaction network with $n$ species containing a motif … such that the species $Y$ does not appear in any other complex of the network. Let $G'$ be obtained from $G$ by…

A mass-action system $(G,\boldsymbol{\kappa})$ has associated ODEs and is permanent if, on every compatibility class, all solutions eventually enter a compact set that remains attr…

Joshi–Shiu's conjecture. A reaction network with one-dimensional stoichiometric subspace and more than one source complex has the capacity for multistationarity if and only if it h…

Nondegeneracy conjecture. Given a network $G$, if

Consider the minimally bistable ERK subnetwork, and let a compatibility class be determined by the conserved quantities of the reaction system. Three-steady-state conjecture. For e…

Bistability at all processivity levels. For every choice of $p_k,p_{\ell}\in(0,1)$, there is such a rate-constant vector for which the resulting system admits multiple exponentiall…

A reaction network is a directed network of complexes whose mass-action kinetics induces a kinetic differential equation; it is weakly reversible when every reaction lies in a stro…

Let a kinetic differential equation be represented by a polynomial vector field, and consider the heuristic that repeatedly pairs monomial reactant vectors with reaction vectors to…

Product-form Poisson conjecture. If $B(u(t))=0$, then the distribution of the process $X_t$ is a product of Poisson distributions for all time.

Consider the full ERK network and the same network with $k_{\mathrm{on}}=0$, and let a positive steady state mean a steady state with all relevant concentrations positive; call a s…

Let $G$ be a reaction network consisting of one reversible-reaction pair $y\leftrightarrows y'$ and one irreversible reaction $\widetilde y\to\widetilde y'$. The reaction vectors a…

Let $G$ be a reaction network, and suppose that $G$ does not admit infinitely many positive steady states in any stoichiometric compatibility class. Recall that $G$ admits $k$ posi…

Nondegeneracy conjecture. Every network with finitely many positive steady states has the same capacity when capacity is counted using all positive steady states or only nondegener…

Let $K_{m,n}$ be the sequestration network with $n$ reactions and $n$ species, and let $\widetilde K_{m,n}$ denote its fully open extension. A steady state is nondegenerate when it…

A weakly reversible mass-action kinetics ODE system is a system whose reaction network is weakly reversible and whose dynamics follow mass-action kinetics. Boundedness conjecture.…

An endotactic reaction network is a reaction network satisfying the endotactic geometric condition, and a network is permanent when its mass-action differential inclusion is perman…

A weakly reversible mass-action kinetics ODE system is a system whose reaction network is weakly reversible, with dynamics governed by mass-action kinetics. A system is persistent…

Let $X_0\in\mathbb{R}_+^{mN}$ be an initial condition for the closed compartmental reaction-diffusion system, with trajectories denoted by $t\mapsto X(t)$. Global persistency conje…