## Graph Alignment Exploiting the Spatial Organisation Improves the Similarity of Brain Networks

Consider a closed surface $M$ with negative Euler characteristic, and an admissible probability measure on the fundamental group of $M$ with finite first moment. Corresponding to each point in the Teichm\"uller space of $M$, there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function o...

By using motivic homotopy theory, we introduce an analogue in algebraic geometry of oriented links and their linking numbers. After constructing the quadratic linking degree --- our analogue of the linking number which takes values in the Witt group of the ground field --- and exploring some of its properties, we give a method to explicitly compute...

The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures ...

Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.

In this paper, we prove that discrete Morse functions are equivalent to simplicial stacks under reasonable constraints. We also show that, as in Discrete Morse Theory, we can see the GVF of a simplicial stack (seen as a discrete Morse function) as the only relevant information we should consider. Last, but not least, we prove that the Minimum Spann...

In this article, we enrich the framework of morphological hierarchies with new acyclic graphs and trees.These structures lie at the convergence of hierarchical models and topological descriptors.We define them in the context of digital grey-level imaging.We discuss their links with component-trees, trees of shapes and adjacency trees.This analysis ...

We show that, for $\varepsilon=\dfrac{1}{4000}$, any action of a finite cyclic group by $(1+\varepsilon)$-bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.

We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support of the uniform distribution depends on the state of the Hidden Markov Model. Such models generalise the more ...

In this paper we prove that the problem of deciding contractibility of an arbitrary closed curve on the boundary of a 3-manifold is in NP. We emphasize that the manifold and the curve are both inputs to the problem. Moreover, our algorithm also works if the curve is given as a compressed word. Previously, such an algorithm was known for simple (non...