14 problems

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 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…

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…

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…

Non-product-form conjecture. Then $\mathcal{G}$ has a non-product-form stationary distribution independently of the reaction rate; equivalently, it belongs to class N.

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

The CRC-CRN is the colorectal-cancer-cell chemical reaction network described in the paper. The global stability condition is the condition introduced in Definition. Global stabili…

Let a weakly reversible chemical reaction network have linkage class one, meaning that its underlying graph has only one strongly connected component. Consider a trajectory that re…

Jacobian nonresonance conjecture. If, for all $x\in\mathbb{R}^n_{\gg 0}$ and all $v\in\mathcal{K}$, the Jacobian matrix $\Gamma Dv(x)$ has no purely imaginary eigenvalues, then…

Persistence Conjecture. Every weakly reversible mass action system is persistent.

Global Attractor Conjecture. The unique complex-balanced steady state in each positive stoichiometric compatibility class of a complex-balanced mass action system is a global attra…

Global attractor conjecture. The rate equation has exactly one equilibrium solution in each positive stoichiometric compatibility class, and any positive solution that starts in th…

Consider a reversible reaction system and a detailed balanced equilibrium, meaning an equilibrium satisfying detailed balance for every reversible reaction. A trajectory is a solut…

Let $G$ be a weakly-reversible chemical reaction network (CRN). A critical siphon is a siphon that is stoichiometrically compatible with a positive point, and $G$ is autocatalytic…