NOTE ON CROSSING CHANGES

For any pair of knots of Gordian distance two, we construct an infinite family of knots which are ‘between' these two knots, that is, which differ from the given two knots by one crossing change. In particular, we prove that every knot of unknotting number two can be unknotted via infinitely many different knots of unknotting number on

Rings and spirals in barred galaxies. I Building blocks

In this paper we present building blocks which can explain the formation and properties both of spirals and of inner and outer rings in barred galaxies. We first briefly summarise the main results of the full theoretical description we have given elsewhere, presenting them in a more physical way, aimed to an understanding without the requirement of extended knowledge of dynamical systems or of orbital structure. We introduce in this manner the notion of manifolds, which can be thought of as tubes guiding the orbits. The dynamics of these manifolds can govern the properties of spirals and of inner and outer rings in barred galaxies. We find that the bar strength affects how unstable the L1 and L2 Lagrangian points are, the motion within the 5A5A5Amanifold tubes and the time necessary for particles in a manifold to make a complete turn around the galactic centre. We also show that the strength of the bar, or, to be more precise, of the non-axisymmetric forcing at and somewhat beyond the corotation region, determines the resulting morphology. Thus, less strong bars give rise to R1 rings or pseudorings, while stronger bars drive R2, R1R2 and spiral morphologies. We examine the morphology as a function of the main parameters of the bar and present descriptive two dimensional plots to that avail. We also derive how the manifold morphologies and properties are modified if the L1 and L2 Lagrangian points become stable. Finally, we discuss how dissipation affects the manifold properties and compare the manifolds in gas-like and in stellar cases. Comparison with observations, as well as clear predictions to be tested by observations will be given in an accompanying paper.Comment: Typos corrected to match the version in press in MNRA

Existence of Monetary Steady States in a Matching Model: Indivisible Money

Existence of a monetary steady state is established for a random matching model with divisible goods, indivisible money, and take-it-or-leave-it offers by consumers. There is no restriction on individual money holdings. The background environment is that in papers by Shi and by Trejos and Wright. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is increasing and strictly concave, and the measure over money holdings has full support.

Knotted holomorphic discs in

We construct knotted proper holomorphic embeddings of the unit disc i

Average four-genus of two-bridge knots

We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity

A Graphical User Interface for Formal Proofs in Geometry.

International audienceWe present in this paper the design of a graphical user interface to deal with proofs in geometry. The software developed combines three tools: a dynamic geometry software to explore, measure and invent conjectures, an automatic theorem prover to check facts and an interactive proof system (Coq) to mechanically check proofs built interactively by the user

Computing Compliant Anonymisations of Quantified ABoxes w.r.t. EL Policies

We adapt existing approaches for privacy-preserving publishing of linked data to a setting where the data are given as Description Logic (DL) ABoxes with possibly anonymised (formally: existentially quantified) individuals and the privacy policies are expressed using sets of concepts of the DL EL. We provide a chacterization of compliance of such ABoxes w.r.t. EL policies, and show how optimal compliant anonymisations of ABoxes that are non-compliant can be computed. This work extends previous work on privacy-preserving ontology publishing, in which a very restricted form of ABoxes, called instance stores, had been considered, but restricts the attention to compliance. The approach developed here can easily be adapted to the problem of computing optimal repairs of quantified ABoxes

Get my pizza right: Repairing missing is-a relations in ALC ontologies (extended version)

With the increased use of ontologies in semantically-enabled applications, the issue of debugging defects in ontologies has become increasingly important. These defects can lead to wrong or incomplete results for the applications. Debugging consists of the phases of detection and repairing. In this paper we focus on the repairing phase of a particular kind of defects, i.e. the missing relations in the is-a hierarchy. Previous work has dealt with the case of taxonomies. In this work we extend the scope to deal with ALC ontologies that can be represented using acyclic terminologies. We present algorithms and discuss a system