Related papers: Stability Theory for Local Iterated Function Syste…
In this article we develop a new approach to the problem of the stability of locally conformally K\"ahler structures (l.c.k structures) under small deformations of complex structures and deformations of flat line bundles. We show that under…
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and…
On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these…
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering…
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
The recent proof by Madsen and Weiss of Mumford's conjecture on the stable cohomology of moduli spaces of Riemann surfaces, was a dramatic example of an important stability theorem about the topology of moduli spaces. In this article we…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
This paper is in the form of an essay. It defines fractal tops and code space structures associated with set-attractors of hyperbolic iterated function systems (IFSs). The fractal top of an IFS is associated with a certain shift invariant…
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
We analyze a criterion which guarantees that the ground states of certain many body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…
This paper provides conditions to ensure contractive behavior of Filippov solutions generated by multi-modal piecewise smooth (PWS) systems. These conditions are instrumental in analyzing the asymptotic behavior of PWS systems, such as…
This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the tensors Z-eigenvalues and Z-eigenvectors. Firstly, for a…
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles,…
Planning accurate manipulation for deformable objects requires prediction of their state. The prediction is often complicated by a loss of stability that may result in collapse of the deformable object. In this work, stability of a fabric…
We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the…
This paper addresses the problem of reaching consensus under input saturation and intermittent communication, which can hinder the convergence of the system. We propose a method that translates the consensus into an equivalent stability…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS.…