Related papers: The rank invariant stability via interleavings
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
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…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
We derive robust long-time a-priori estimates for the Navier-Stokes equation in a two-dimensional infinite strip which are uniform in the Reynolds number. These estimates provide several new scale invariant upper bounds for the size of the…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all…
A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…
The purpose of this paper is to show stability of order preserving/reversing transforms on the class of non-negative convex functions in ${\mathbb R}^n$, and its subclass, the class of non-negative convex functions attaining $0$ at the…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
This article provides a characterization of stability for switched nonlinear systems under average dwell-time constraints, in terms of necessary and sufficient conditions involving multiple Lyapunov functions. Earlier converse results focus…
In this paper, we first explore exponential stability by using Monotonicity inequality and use this information to obtain the existence of Invariant measure for linear Stochastic PDEs with potential in the space of tempered distributions.…
We examine the robustness of bottleneck assignment problems to perturbations in the assignment weights. We derive two algorithms that provide uncertainty bounds for robust assignment. We prove that the bottleneck assignment is guaranteed to…
In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
Conditions for the existence and stability of de Sitter space in modified gravity are derived by considering inhomogeneous perturbations in a gauge-invariant formalism. The stability condition coincides with the corresponding condition for…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…
A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…
The purpose of this note is to describe of a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for…