The multiplex structure of interbank networks

The interbank market has a natural multiplex network representation. We employ a unique database of supervisory reports of Italian banks to the Banca d'Italia that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract. We find that layers have different topological properties and persistence over time. The presence of a link in a layer is not a good predictor of the presence of the same link in other layers. Maximum entropy models reveal different unexpected substructures, such as network motifs, in different layers. Using the total interbank network or focusing on a specific layer as representative of the other layers provides a poor representation of interlinkages in the interbank market and could lead to biased estimation of systemic risk.Comment: 41 pages, 8 figures, 10 table

The Goldman bracket determines intersection numbers for surfaces and orbifolds

In the mid eighties Goldman proved an embedded curve could be isotoped to not intersect a closed geodesic if and only if their Lie bracket (as defined in that work) vanished. Goldman asked for a topological proof and about extensions of the conclusion to curves with self-intersection. Turaev, in the late eighties, asked about characterizing simple closed curves algebraically, in terms of the same Lie structure. We show how the Goldman bracket answers these questions for all finite type surfaces. In fact we count self-intersection numbers and mutual intersection numbers for all finite type orientable orbifolds in terms of a new Lie bracket operation, extending Goldman's. The arguments are purely topological, or based on elementary ideas from hyperbolic geometry. These results are intended to be used to recognize hyperbolic and Seifert vertices and the gluing graph in the geometrization of three manifolds. The recognition is based on the structure of the String Topology bracket of three manifolds

Space-time extensions II

The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $\gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is shown that it is always possible to select a synchronised family of causal geodesics $\Gamma$ and an open neighbourhood $\mathcal{U}$ of a final segment of $\gamma$ in $M$ such that $\mathcal{U}$ is comprised by members of $\Gamma$, and suitable local coordinates can be defined everywhere on $\mathcal{U}$ provided that $\gamma$ does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime, $(M,g_{ab})$, is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order $k-1$ are bounded on $\mathcal{U}$, and also the line integrals of the components of the $k^{th}$-order covariant derivatives are finite along the members of $\Gamma$---where all the components are meant to be registered with respect to a synchronised frame field on $\mathcal{U}$---then there exists a $C^{k-}$ extension $\Phi: (M,g_{ab}) \rightarrow (\widehat{M},\widehat{g}_{ab})$ so that for each $\bar\gamma\in\Gamma$, which is inextendible in $(M,g_{ab})$, the image, $\Phi\circ\bar\gamma$, is extendible in $(\widehat{M},\widehat{g}_{ab})$. Finally, it is also proved that whenever $\gamma$ does terminate on a topological singularity $(M,g_{ab})$ cannot be generic.Comment: 42 pages, no figures, small changes to match the published versio

Enhanced Place Name Search Using Semantic Gazetteers

With the increased availability of geospatial data and efficient geo-referencing services, people are now more likely to engage in geospatial searches for information on the Web. Searching by address is supported by geocoding which converts an address to a geographic coordinate. Addresses are one form of geospatial referencing that are relatively well understood and easy for people to use, but place names are generally the most intuitive natural language expressions that people use for locations. This thesis presents an approach, for enhancing place name searches with a geo-ontology and a semantically enabled gazetteer. This approach investigates the extension of general spatial relationships to domain specific semantically rich concepts and spatial relationships. Hydrography is selected as the domain, and the thesis investigates the specification of semantic relationships between hydrographic features as functions of spatial relationships between their footprints. A Gazetteer Ontology (GazOntology) based on ISO Standards is developed to associate a feature with a Spatial Reference. The Spatial Reference can be a GeoIdentifier which is a text based representation of a feature usually a place name or zip code or the spatial reference can be a Geometry representation which is a spatial footprint of the feature. A Hydrological Features Ontology (HydroOntology) is developed to model canonical forms of hydrological features and their hydrological relationships. The classes modelled are endurant classes modelled in foundational ontologies such as DOLCE. Semantics of these relationships in a hydrological context are specified in a HydroOntology. The HydroOntology and GazOntology can be viewed as the semantic schema for the HydroGazetteer. The HydroGazetteer was developed as an RDF triplestore and populated with instances of named hydrographic features from the National Hydrography Dataset (NHD) for several watersheds in the state of Maine. In order to determine what instances of surface hydrology features participate in the specified semantic relationships, information was obtained through spatial analysis of the National Hydrography Dataset (NHD), the NHDPlus data set and the Geographic Names Information System (GNIS). The 9 intersection model between point, line, directed line, and region geometries which identifies sets of relationship between geometries independent of what these geometries represent in the world provided the basis for identifying semantic relationships between the canonical hydrographic feature types. The developed ontologies enable the HydroGazetteer to answer different categories of queries, namely place name queries involving the taxonomy of feature types, queries on relations between named places, and place name queries with reasoning. A simple user interface to select a hydrological relationship and a hydrological feature name was developed and the results are displayed on a USGS topographic base map. The approach demonstrates that spatial semantics can provide effective query disambiguation and more targeted spatial queries between named places based on relationships such as upstream, downstream, or flows through

Local geometry of random geodesics on negatively curved surfaces

It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation -- for instance, the fraction of triangles -- approach those of the limiting Poisson line process.Comment: This version extends the results of the previous version to surfaces with possibly variable negative curvatur

On Infinite EPR-like Correlations

The paper investigates, in the framework of branching space-times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible.Comment: 42 pages, no figure