Related papers: A homotopy theorem for incremental stability

In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of…

We provide a partially affirmative answer to the following question on robustness of polynomial stability with respect to sampling: ``Suppose that a continuous-time state-feedback controller achieves the polynomial stability of the…

We characterise asymptotic stability of port-Hamiltonian systems by means of matrix conditions using well-known resolvent criteria from $C_0$-semigroup theory. The idea of proof is based on a recent characterisation of exponential stability…

We develop local stable group theory directly from topological dynamics, and extend the main results in this subject to the setting of stability "in a model". Specifically, given a group $G$, we analyze the structure of sets $A\subseteq G$…

We prove that every endomorphism which satisfies Axiom A and the strong transversality conditions is $C^1$-inverse limit structurally stable. These conditions were conjectured to be necessary and sufficient. This result is applied to the…

We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture…

There is a well studied notion of GIT-stability for coherent systems over curves, which depends on a real parameter $\alpha$. For generated coherent systems, there is a further notion of stability derived from Mumford's definition of linear…

We obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be L^{p}-integrable for p>3. We show that, under this condition (which depends only on the…

The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, if and only if homotopy finite limit functors have right adjoints, and if and only if homotopy finite colimit functors have left…

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…

In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…

We prove that homological stability holds for configuration spaces of orbifolds. This builds on the work of Bailes' thesis where he proves that the stabilisation maps are injective.

This paper is about the surprising interaction of a foundational result from model theory, about stability of theories, with algorithmic stability in learning. First, in response to gaps in existing learning models, we introduce a new…

In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…

Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…

The stability conditions of a relativistic hydrodynamic theory can be derived directly from the requirement that the entropy should be maximised in equilibrium. Here we use a simple geometrical argument to prove that, if the hydrodynamic…

We prove the well-posedness of a linear closed-loop system with an explicit (already known) feedback leading to arbitrarily large decay rates. We define a mild solution of the closed-loop problem using a dual equation and we prove that the…

In this paper we obtain an almost sure invariance principle for convergent sequences of either Anosov diffeomorphisms or expanding maps on compact Riemannian manifolds and prove an ergodic stability result for such sequences. The sequences…