Related papers: Representation Stability
In this paper we consider BIBO stability of systems described by infinite-dimensional linear state-space representations, filling the so far unattended gap of a formal definition and characterization of BIBO stability in this general case.…
In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
We prove that the dual rational homotopy groups of the configuration spaces of a 1-connected manifold of dimension at least 3 are uniformly representation stable in the sense of Church, and that their derived dual integral homotopy groups…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
Stability conditions play an important role in the study of representations of a quiver. In the present paper, we study semistable representations of quivers. In particular, we describe the slopes of semistable representations of a tame…
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.…
Recently, continuous representation methods emerge as novel paradigms that characterize the intrinsic structures of real-world data through function representations that map positional coordinates to their corresponding values in the…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
We prove that the irreducible decomposition of the permutation representation of GL(n,q) on GL(n,q)/GL(n-m,q) stabilizes for large n. We deduce, as a consequence, a representation stability theorem for finitely generated VIC-modules.
Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we…
In this paper we develop machinery for studying sequences of representations of any of the three families of classical Weyl groups, extending work of Church, Ellenberg, Farb, and Nagpal on the symmetric groups S_n to the signed permutation…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts…
In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…
We introduce the persistence heatmap, a parametrized summary based on representative cycles in persistence diagrams, designed to enhance stability and explainability in topological data analysis. Algorithms to compute persistence diagrams…
We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…
A stochastically continuous process $\xi(t)$, $t\geq0$, is said to be time-stable if the sum of $n$ i.i.d. copies of $\xi$ equals in distribution to the time-scaled stochastic process $\xi(nt)$, $t\geq0$. The paper advances the…