19 problems

Feinberg's persistence conjecture for weakly reversible reaction networks
arXiv@arxiv
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…
Conjecturesolveddynamical-systems persistence reaction-networks
0
The Persistence Conjecture for weakly reversible reaction networks
arXiv@arxiv
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…
Conjectureopendynamical-systems persistence reaction-networks
0
Extended persistence conjecture for endotactic variable- $k$ dynamical systems
arXiv@arxiv
Consider an endotactic variable- $k$ dynamical system, together with its stoichiometric subspace $S$ and stoichiometric compatibility classes … It is persistent if, for every initia…
Conjectureopenchemical-reaction-networks dynamical-systems persistence
0
Conjecture on convergence in the non-mutual invasion scenario
arXiv@arxiv
Let $u(t,x)$ and $v(t,x)$ denote the densities of species $u$ and $v$ at time $t$ and location $x\in\Omega$ , and let $u_0,v_0$ be initial conditions satisfying $u_0+v_0\leq 1$ . Wri…
Conjectureopenmetacommunity-dynamics persistence spatial-ecology
0
Conjecture on complex monodromy over depth posets
arXiv@arxiv
Persistence diagrams can be augmented to depth posets, which equip their points with a partial ordering and can be applied to the radial transform of a loop around a singularity. C…
Conjectureopenmonodromy persistence topological-data-analysis
1
Persistence above threshold for models with several minimal siphons
arXiv@arxiv
Let a balanced bilinear epidemic model have possibly several minimal siphons, and consider the boundary faces supported by these siphons. A boundary face is repelling when the rest…
Conjectureopenmathematical-epidemiology persistence reaction-network-theory
0
Universality of entropic repulsion for strongly correlated fields
arXiv@arxiv
Let $f$ be a continuous centred non-degenerate stationary Gaussian field on either $\mathbb{R}^d$ or $\mathbb{Z}^d$ . A persistence, or hard wall event, is an event of the form…
Conjectureopenentropic-repulsion persistence stationary-gaussian-fields
1
Persistence and lack of persistence in the PAVD model without higher-order assumptions
arXiv@arxiv
Let the PAVD model be the preferential attachment model with vertex death from Definition. Suppose that the attachment and death-rate sequences $b$ and $d$ satisfy Assumptions and.…
Conjectureopenpersistence preferential-attachment random-trees
1
Poonen–Stoll universality conjecture for random-polynomial persistence exponents
arXiv@arxiv
Let $Q_n(x)=\sum_{i=0}^{n}a_i x^i$ be a random polynomial with i.i.d. coefficients, and let the persistence exponent be the limiting value of $\log p_n^{(0)}/\log n$ when it exists…
Conjectureopenpersistence random-polynomials universality
0
Global Asymptotic Stability conjecture for complex balanced systems
arXiv@arxiv
Global Asymptotic Stability conjecture. All complex balanced systems are persistent.
Conjectureopenchemical-reaction-networks complex-balanced-systems persistence
0
Extension of the main theorem to constructible functions up to infinity
arXiv@arxiv
Theorem concerns constructible functions with compact support and a distance controlled by the convolution distance. Extension conjecture. Theorem should continue to hold when the…
Conjectureopenconstructible-functions persistence sheaf-function-correspondence
0
Finite-size scaling conjecture for the persistence probability
arXiv@arxiv
Let $Q_0(\tau,N)$ denote the persistence probability at time $\tau$ for matrices of finite size $N$ , and let $\mu$ be the persistence exponent from the large- $N$ asymptotic…
Conjectureopenfinite-size-scaling persistence random-matrices
0
The persistence conjecture for weakly reversible reaction networks
arXiv@arxiv
A reaction network is weakly reversible if every reaction lies on a directed cycle of the reaction graph. For a solution $\boldsymbol{x}(t)$ of the associated dynamics on…
Conjectureopendynamical-systems persistence reaction-networks
0
Persistence for structured population models without monotonicity
arXiv@arxiv
Consider the structured stochastic difference equation … is almost surely persistent and persistent in probability. A theorem establishes this conclusion under the stronger monoton…
Conjectureopenpersistence stochastic-dynamics structured-populations
0
Almost-sure persistence under mutual invasibility
arXiv@arxiv
Consider the two-species Markov chain … is almost surely persistent. Mutual invasibility is known to imply persistence in probability under the monotonicity assumptions; the conjec…
Conjectureopenecology persistence stochastic-dynamics
0
The bounded-trajectory persistence conjecture for weakly reversible reaction networks
arXiv@arxiv
Persistence conjecture, bounded-trajectory version. Any weakly reversible reaction network with mass-action kinetics and bounded trajectories is persistent.
Conjectureopenchemical-reaction-network-theory mass-action-kinetics persistence
0
Craciun–Nazarov–Pantea persistence conjecture
arXiv@arxiv
Persistence conjecture. Any weakly reversible mass-action system is persistent.
Conjectureopenchemical-reaction-network-theory mass-action-systems persistence
0
The persistence conjecture for weakly reversible mass-action systems
arXiv@arxiv
Persistence conjecture. Any weakly reversible mass-action system is persistent.
Conjectureopenchemical-reaction-network-theory mass-action-systems persistence
0
Non-persistence under the reversed rock-paper-scissors criterion
arXiv@arxiv
Non-persistence conjecture. If the opposite inequality to the persistence condition holds, namely $I(m)\leq 0$ , then persistence does not occur.
Conjectureopenecology persistence stochastic-dynamics
0