Thin presentation of knots and lens spaces

This paper concerns thin presentations of knots K in closed 3-manifolds M^3 which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a lens space as a connected summand, we first prove that all such thin presentations, with respect to any spine of M have only local maxima. If M is a lens space and K has an essential thin presentation with respect to a given standard spine (of lens space M) with only local maxima, then we show that K is a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal intersection between K and such spines to be at least three, and finally, if the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the following inequality: |r| <= 2g, where g is the genus of K_gamma.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.htm

Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

Numerical bifurcation of predator-prey fractional differential equations with a constant rate harvesting

In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system

A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control

Many boundary controlled and observed Partial Differential Equations can be represented as port-Hamiltonian systems with dissipation, involving a Stokes-Dirac geometrical structure together with constitutive relations. The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE). Different types of dissipation are examined: internal damping, boundary damping and also diffusion models

Scaling up strategies of the chronic respiratory disease programme of the European innovation partnership on active and healthy ageing (Action Plan B3: Area 5)

Action Plan B3 of the European Innovation Partnership on Active and Healthy Ageing (EIP on AHA) focuses on the integrated care of chronic diseases. Area 5 (Care Pathways) was initiated using chronic respiratory diseases as a model. The chronic respiratory disease action plan includes (1) AIRWAYS integrated care pathways (ICPs), (2) the joint initiative between the Reference site MACVIA-LR (Contre les MAladies Chroniques pour un VIeillissement Actif) and ARIA (Allergic Rhinitis and its Impact on Asthma), (3) Commitments for Action to the European Innovation Partnership on Active and Healthy Ageing and the AIRWAYS ICPs network. It is deployed in collaboration with the World Health Organization Global Alliance against Chronic Respiratory Diseases (GARD). The European Innovation Partnership on Active and Healthy Ageing has proposed a 5-step framework for developing an individual scaling up strategy: (1) what to scale up: (1-a) databases of good practices, (1-b) assessment of viability of the scaling up of good practices, (1-c) classification of good practices for local replication and (2) how to scale up: (2-a) facilitating partnerships for scaling up, (2-b) implementation of key success factors and lessons learnt, including emerging technologies for individualised and predictive medicine. This strategy has already been applied to the chronic respiratory disease action plan of the European Innovation Partnership on Active and Healthy Ageing