It is known that non-isomorphic coupled cell networks can have equivalent dynamics. Such networks are said to be ODE-equivalent and are related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE-equivalence class is said to be minimal if it has a minimum number of edges. When studying a given network in an ODE-class it can be of great value to study inst...

We study geodesics on planar Riemann surfaces of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these geodesics and relate them to the structure of the boundary of a Dirichlet polygon for a Fuchsian group representing the surface.

We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we characterize the set of all points that are connected to the root by more than one geodesic. We also prove that points of the Brownian map can be connected to ...

The scattering data of a Riemannian manifold with boundary record the incoming and outgoing directions of each geodesic passing through. We show that the scattering data of a generic Riemannian surface with no trapped geodesics and no conjugate points determine the lengths of geodesics. Counterexamples exists when trapped geodesics are allowed.

We present a homogeneous space geometry for the manifold of symmetric positive semidefinite matrices of fixed rank. The total space is the general linear group endowed with its natural rightinvariant metric, and the metric on the homogeneous space is chosen such that the quotient space is the image of a Riemannian submersion from the total space. As a result, we obtain complete geodesics that a...

Let S be a surface and let P be a pair of pants. Geodesics on surfaces, and on pairs of pants specifically, have been studied extensively over the years. In this paper, we focus on getting a lower bound on the number of closed geodesics on P with given upper bounds on length and self-intersection number. As a direct consequence, we get a lower bound for the number of such closed geodesics on an...

Der ständig zunehmende Einsatz verteilter DV-Systeme führt zu einem stark steigenden Bedarf an verteilten Anwendungen. Deren Entwicklung in den verschiedensten Anwendungsfeldern wie Fabrikund Büroautomatisierung ist für die Anwender bislang kaum zu handhaben. Neue Konzepte des Software Engineering sind daher notwendig, und zwar in den drei Bereichen ‘Sprachen’, ‘Werkzeuge’ und ‘Umgebungen’. Obj...

The relationships existing between MP graphs, metabolic P systems, and ODE systems are investigated. Formal results show that every MP system, once derived by its MP graph, results in an ODE system whose solution equals, in the limit, the solution obtained by a non-cooperative MP system that is ODE equivalent to the original one. The freedom of choice of the ODE equivalent from the original MP ...

Let X be a compact Riemannian manifold with conic singularities, i.e. a Riemannian manifold whose metric has a conic degeneracy at the boundary. Let ∆ be the Friedrichs extension of the Laplace-Beltrami operator on X. There are two natural ways to define geodesics passing through the boundary: as “diffractive” geodesics which may emanate from ∂X in any direction, or as “geometric” geodesics whi...

*Correspondence: Valter Moretti, Dipartimento di Matematica, Università di Trento and Istituto Nazionale di Fisica Nucleare Gruppo Collegato di Trento, via Sommarive 14 I-38050 Povo, Italy e-mail: [email protected] A spacetime is locally flat if and only if no geodesical deviation exists for congruences of all kinds of geodesics. However, while for causal geodesics the deviation can be m...