Related papers: Representation Stability
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$…
In this paper we study the integral cohomology of pure mapping class groups of surfaces, and other related groups and spaces, as FI-modules. We use recent results from Church, Miller, Nagpal and Reinhold to obtain explicit linear bounds for…
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…
The aim of this paper is to study foliations that remain invariant by parallel transports along the integral curves of vector fields of another foliations. According to this idea, we define a new concept of stability between foliations. A…
A matching queue is described via a graph $G$ together with a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items which can either be queued, or matched with queued items in neighboring…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We investigate the stability of the holographic description of the universe. By treating the perturbation globally, we discover that this description is stable, which is support for the holographic description of the universe.
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…
We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
The Representation Theorem by Zomorodian and Carlsson has been the starting point of the study of persistent homology under the lens of algebraic representation theory. In this work, we give a more accurate statement of the original theorem…
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…
This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group $S_n$ on the cohomology of the configuration space of $n$ ordered points in $\mathbf{R}^d$. This cohomology is known to…
We consider in parallel pointed homotopy automorphisms of iterated wedge sums of topological spaces and boundary relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces…
Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…