Related papers: Flexible stability and nonsoficity

A graph $X$ is said to be unstable if the direct product $X \times K_2$ (also called the canonical double cover of $X$) has automorphisms that do not come from automorphisms of its factors $X$ and $K_2$. It is nontrivially unstable if it is…

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…

In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may…

A graph $\Gamma$ is said to be unstable if for the direct product $\Gamma \times K_2$, $Aut(\Gamma \times K_2)$ is not isomorphic to $Aut(\Gamma) \times \mathbb{Z}_2$. In this paper we show that a connected and non-bipartite Cayley graph…

A new proof of a result of Lutz Weis is given, that states that the stability of a positive strongly continuous semigroup $(e^{tA})_{t \ge 0}$ on $L_p$ may be determined by the quantity $s(A)$. We also give an example to show that the…

We define the notion of $\varepsilon$-flexible periodic point: it is a periodic point with stable index equal to two whose dynamics restricted to the stable direction admits $\varepsilon$-perturbations both to a homothety and a saddle…

We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…

In this short note we prove that a definable set $X$ over $\mathbb F_n$ is superstable only if $X(\mathbb F_n)=X(\mathbb F_{\omega})$.

Let $A$ be a (not necessarily unital) separable non-elementary simple amenable C*-algebra whose tracial basis may not have finite covering dimension and may not be compact but satisfies certain condition (C). We show that $A$ is ${\cal…

A C*-algebra is said to be K-stable if its nonstable K-groups are naturally isomorphic to the usual K-theory groups. We study continuous $C(X)$-algebras, each of whose fibers are K-stable. We show that such an algebra is itself K-stable…

Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the…

Let $G$ be a finite group. The solubility graph associated with the finite group $G$, denoted by $\Gamma_{\cal S}(G)$, is a simple graph whose vertices are the non-trivial elements of $G$, and there is an edge between two distinct elements…

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.

Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…

We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a group is simulated by a suitable sofic approximation. The…

Let $S$ be an algebraic semigroup (not necessarily linear) defined over a field $F$. We show that there exists a positive integer $n$ such that $x^n$ belongs to a subgroup of $S(F)$ for any $x \in S(F)$. In particular, the semigroup $S(F)$…

We associate a graph $\mathcal{C}_G$ to a non locally cyclic group $G$ (called the non-cyclic graph of $G$) as follows: take $G\backslash Cyc(G)$ as vertex set, where $Cyc(G)=\{x\in G | < x,y> \text{is cyclic for all} y\in G\}$ is called…

This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…

We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also…

We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $\mathbb{P}^r$ is semistable if $g=1$ or $g\geq \left \lceil \frac{5r}{2}\right\rceil r(r-1)$, or $d$ is larger than an explicit function…