68 problems

Consider a reaction-network dynamical system with a positive complex-balanced equilibrium, meaning an equilibrium at which the total flow into and out of each complex agrees. The a…

A reaction network consists of chemical species and directed reactions between complexes, and it is weakly reversible when every reaction lies in a strongly connected component of…

A complex balanced mass-action dynamical system evolves on a positive stoichiometric compatibility class, meaning the set of positive states compatible with the system's conservati…

Let a dynamical system be generated by a weakly reversible reaction network, and call a solution $\boldsymbol{x}(t)$ persistent if, for every initial condition…

An endotactic reaction network is a reaction network whose embedded reaction graph has the endotacticity property; a $\kappa$-variable mass-action system is one whose reaction rate…

Global stability conjecture. The equilibria of $\WR0$ systems are globally stable with respect to their compatibility classes.

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…

Consider a mass-action reaction network with stoichiometric compatibility classes determined by its reaction vectors. A system is complex balanced if there is a nonnegative state a…

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…

Let $(\mathcal{X},\mathcal{C},\mathcal{R},\kappa(\tau))$ be a mass-action system with bounded kinetics, governed by … where $0<\varepsilon<1$ and…

Consider a stochastic regulatory network with components $X_1,\dots,X_N$, linear degradation, and arbitrary cross-regulatory production rates. For each component, let $F_{X_i}$ den…

Hartmanis–Stearns conjecture. No irrational algebraic number is real-time computable by a Turing machine.

Cis-reaction conjecture. This reaction does not lead to the type of Notch activation described above.

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 stochastic compartment model with reaction-rate parameters $\kappa_b$, $\kappa_F$, $\kappa_E$, and $\kappa_d$. Transience conjecture. If … then $N$ is transient. Thi…

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 $\kappa$.

Common-support evanescence conjecture. If

Let $F_{\boldsymbol{\boldsymbol{\kappa}},\boldsymbol{b}}$ be the steady-state system of a reaction network, and let $\mathbb{V}_{>0}(F_{\boldsymbol{\kappa},\boldsymbol{b}})$ denote…

Let $\varphi$ be the map associated with the vertically parametrized system and its intermediates, and suppose that all intermediates are single-input. Surjectivity conjecture. The…

Let $G$ be a reaction network containing the motif … with $Y$ absent from every other complex. Let $p_{(h,\ell)}$ and $p'_{(h,\ell')}$ be the corresponding reduced characteristic p…

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 $G$…

A phosphorylation network may contain reverse reactions in motifs of the form … where $y$ and $y'$ are complexes not containing the intermediate species $Y$. Reverse-reaction irrel…