We completely describe the structure of the connected components of transversals to a collection of n arbitrary line segments in R. We show that n 3 line segments in R admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.

We prove that the non-ordinary component is connected in the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This was conjectured by Kisin. As an application to global Galois representations, we prove a theorem on the modularity comparing a deformation ring and a Hecke ring.

On the prime-top part of the groups of connected components of Néron models.

We prove orthogonality formulas for the characteristic functions of certain complexes on a connected component of a reductive group.

The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we investigate the categori...

The problematic of automatically searching series of broad patterns in technical documents is studied. Such series can be assumed to ordered information useful for the understanding of documents. The proposed methodology is able to extract successive patterns of different natures without a priori information about the shape. To make this, we consider the spatial location of triplets of similar ...

Wepropose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set ...

We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors’ opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updat...