56 problems

Product-form characterization conjecture. The network $(\mathcal{G},\kappa)$ has a product-form stationary distribution if and only if it is complex balanced.

Consider an endotactic variable-$k$ dynamical system, together with its stoichiometric subspace $S$ and stoichiometric compatibility classes … It is persistent if, for every initia…

Let $x(t)$ be a solution of the balanced reaction-network system … with positive initial condition $x_0\in \mathbb{R}_{+}^m$, where $x(t)\in\mathbb{R}_{+}^m$ is the concentration v…

Stability conjecture. The property also holds for arbitrary $\alpha_i^-$ and $\beta_i^-$, for $i=1,2$.

Siphon–precluster duality conjecture. Given the close relation between maximal invariant polyhedral supports and siphons, there is a duality relation between siphons and precluster…

Precluster–support duality conjecture. For conservative mass-action networks that do not have two species with exactly the same rates and have at least one positive steady state, t…

Consider the Michaelis–Menten reaction network with species $ES$, $S$, and $P$, and reactions $ES\rightleftarrows S$ with rates $k_-$ and $k_+$ together with slower reactions…

Regular-splitting definition. The existence of a regular splitting for the $x$-$y$ partition induced by the DFE could be taken as a definition of a multistrain epidemic (ME) model.

Sensitivity vanishing and sign-change conjecture. The sensitivity $\alpha_4$ vanishes for $c(x)=\beta^{-1}$ and becomes negative for $c(x)>\beta^{-1}$, irrespective of the value of…

Consider an idealized chemical reservoir computer whose governing equation is modeled as a chemical reaction network, with reaction rates spanning a wide range of scales. Relaxatio…

Consider a chemical reaction network (CRN) whose steady-state ideal satisfies Assumptions 1–3: mass-action kinetics, inclusion of conservation laws, and absence of independent subn…

Kaihnsa's attainable-region conjecture. For this class of networks, the attainable region and the convex hull of a trajectory are equal.

ERK steady-state conjecture. The maximum number of positive steady states of the ERK network is $3$.

Global attractor conjecture. Every trajectory beginning in the relative interior of $\mathcal{P}$ converges to $x^*$.

Let $(G,\kappa^*)$ be a mass-action system with $n$ species and rational-number rate constants, and let $I$ be its steady-state ideal. For each species $X_i$, Algorithm computes a…

Consider an $n$-futile cycle, constructed iteratively by adding distributive and sequential phosphorylation steps. Let $S[\pmb{\kappa}]$ denote an invertible Child-Selection matrix…

Let $\mathbf{\Gamma}$ be a chemical reaction network with Jacobian $G(\mathbf{r'})$. A D-unstable core is a minimal Child-Selection matrix that is D-unstable, meaning that it becom…

Consider the network operation introduced by Cappelletti, Feliu, and Wiuf that generalizes E2 for chemical reaction networks. Cappelletti–Feliu–Wiuf conjecture. This operation pres…

Let $\mathcal N'$ be obtained from a chemical reaction network $\mathcal N$ by an E5$'$ operation, where E5$'$ generalizes E5 by requiring that the columns corresponding to new rea…

Global Asymptotic Stability conjecture. All complex balanced systems are persistent.

A chemical reaction network (CRN) is a mathematical model of chemical reactions and their species concentrations; a CRN is formally autocatalytic when it satisfies the formal autoc…

Functional-module specificity conjecture. Then this chemical, or set of chemicals, is specific for the respective functional module.

A complex-balanced system is a mass-action dynamical system admitting a positive steady state at which the total reaction flow into each complex equals the total reaction flow out.…

A conservative reaction network is a chemical reaction network in which each species occurs in at least one nonnegative conservation law. Let the mixed-volume bound be the upper bo…

A chemical reaction network is a system of chemical species and reactions whose steady states are solutions of its associated mass-action equations; a steady state is positive when…