Related papers: Stirling complexes

We consider "Thurston maps": branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence problem between them (continuous deformation of maps along with their critical orbits) is…

Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice…

Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…

There has been renewed interest in $\mathbb{S}^3$-bundles over $\mathbb{S}^4$ since K. Grove and W. Ziller constructed metrics on nonnegative curvature on the total spaces of these bundles. In this paper we write down necessary and…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…

Using the theory of Properly Embedded Graphs developed in an earlier work we define an involutory duality on the set labeled non-crossing trees that lifts the obvious duality in the set of unlabeled non-crossing trees. The set of…

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…

We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength $g$ is varied. We primarily…

Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…

We define decorated $\alpha$-stable trees which are informally obtained from an $\alpha$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $\alpha$-stable looptrees of Curien and Kortchemski, where…

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…

An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…

We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…

We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…

We revisit the classical problem of searching in a binary search tree (BST) using rotations, and present novel connections of this problem to a number of geometric and combinatorial structures. In particular, we show that the execution…

We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kaehler manifolds. As a consequence of this structure, there are no unexpected relations among the Hodge numbers, and no essential…

We prove that every stable, combinatorial model category has a natural enrichment by symmetric spectra (or more precisely, a natural equivalence class of enrichments). This in some sense generalizes the simplicial enrichments of model…

Given a simplicial complex $X$, we construct a simplicial complex $\Omega X$ that may be regarded as a combinatorial version of the based loop space of a topological space. Our construction explicitly describes the simplices of $\Omega X$…

The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…