Related papers: Stability Theorems for Forbidden Configurations

We study the stability problem for a non-relativistic quantum system in dimension three composed by $ N \geq 2 $ identical fermions, with unit mass, interacting with a different particle, with mass $ m $, via a zero-range interaction of…

Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…

Let $t\ge 1$ be a given integer. Let ${\cal F}$ be a family of subsets of $[m]=\{1,2,\ldots,m\}$. Assume that for every pair of disjoint sets $S,T\subset [m]$ with $|S|=|T|=k$, there do not exist $2t$ sets in ${\cal F}$ where $t$ subsets of…

If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable. Here "almost" and "close" are in terms of the Hilbert-Schmidt norm. Using tracial 2-norm…

We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and…

This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping…

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…

Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…

We consider the problems of characterizing and testing the stability of cellular automata configurations that evolve on a two-dimensional torus according to threshold rules with respect to the von-Neumann neighborhood. While stable…

Good frames were suggested in [Sh:h] as the (bare-bones) parallel, in the context of AECs, to superstable (among elementary classes). Here we consider $(\mu,\lambda,\kappa)$-frames as candidates for being (in the context of AECs) the…

It is well known that, contrary to the autonomous case, the stability/instability of solutions of nonautonomous linear ordinary differential equations $x' = A(t) x$ is in no relation to the sign of the real parts of the eigenvalues of…

In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set $\fc$ of $m$ vectors in the complex Hilbert space of dimension n allows for…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…

If $D$ is a partially filled-in $(0,1)$-matrix with a unique completion to a $(0,1)$-matrix $M$ (with prescribed row and column sums), we say that $D$ is a {\em defining set} for $M$. A {\em critical set} is a minimal defining set (the…

We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…

Proper modeling of inverter-based microgrids is crucial for accurate assessment of stability boundaries. It has been recently realized that the stability conditions for such microgrids are significantly different from those known for large-…

Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover…

This chapter investigates the cone of copositive matrices, with a focus on the design and analysis of conic inner approximations for it. These approximations are based on various sufficient conditions for matrix copositivity, relying on…

The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…