13 problems

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…

For each $m\geq 2$, consider the weakly and strongly irreversible $m$-site phosphorylation networks and their parameter regions of multistationarity. Connectedness conjecture. The…

For a fixed $m\in\mathbb{N}$, consider the $m$-site phosphorylation cycle with Michaelis–Menten phosphorylation steps, reaction-rate constants $\kappa$, and parameters $c$. The ful…

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…

Let $G$ be a reaction network with $r$ reactions and conservation-law matrix $W$. Let $\Sigma$ and $\widetilde \Sigma$ be, respectively, the multistationarity-allowing and multista…

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…

Let $p_k$ and $p_{\ell}$ be the two processivity levels, and let the multistationarity interval be the interval of parameter values for which multistationarity occurs. Vanishing-in…

Let $p_k$ and $p_{\ell}$ denote the kinase and phosphatase processivity levels, respectively, and let the multistationarity interval be the interval of values of the relative total…

Let $m\geq 2$ and $n\geq 3$ be integers, and let $\widetilde{K}_{m,n}$ denote the fully open extension of the sequestration network $K_{m,n}$. A steady state is nondegenerate when…

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 $\widetilde{K}_{m,n}$ be the fully open extension of the sequestration network, with $m\geq 2$ and odd $n$. In the determinant optimization method, choose parameters…

For positive integers $m\geq 2$ and $n\geq 2$, let $K_{m,n}$ be the sequestration network … and let $\widetilde{K}_{m,n}$ be its fully open extension, obtained by adjoining all inf…

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…