Extinction in lower Hessenberg branching processes with countably many types

We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton-Watson processes with typeset $\mathcal{X}=\{0,1,2,\dots\}$, in which individuals of type $i$ may give birth to offspring of type $j\leq i+1$ only. For this class of processes, we study the set $S$ of fixed points of the progeny generating function. In particular, we highlight the existence of a continuum of fixed points whose minimum is the global extinction probability vector $\boldsymbol{q}$ and whose maximum is the partial extinction probability vector $\boldsymbol{\tilde{q}}$. In the case where $\boldsymbol{\tilde{q}}=\boldsymbol{1}$, we derive a global extinction criterion which holds under second moment conditions, and when $\boldsymbol{\tilde{q}}<\boldsymbol{1}$ we develop necessary and sufficient conditions for $\boldsymbol{q}=\boldsymbol{\tilde{q}}$

Symmetry & Controllability for Spin Networks with a Single-Node Control

We consider the relation of symmetries and subspace controllability for spin networks with XXZ coupling subject to control of a single node by a local potential (Z-control). Such networks decompose into excitation subspaces. Focusing on the single excitation subspace it is shown that for single-node Z-controls external symmetries are characterized by eigenstates of the system Hamiltonian that have zero overlap with the control node, and there are no internal symmetries. It is further shown that there are symmetries that persist even in the presence of random perturbations. For uniformly coupled XXZ chains a characterization of all possible symmetries is given, which shows a strong dependence on the position of the node we control. Finally, it is shown rigorously for uniform Heisenberg and XX chains subject to single-node Z-control that the lack of symmetry is not only necessary but sufficient for subspace controllability. The latter approach is then generalized to establish controllability results for simple branched networks.Comment: 11 pages, some figures. 3 tables, minor revisio

Evidence for Partial Taylor Relaxation from Changes in Magnetic Geometry and Energy during a Solar Flare

Solar flares are powered by energy stored in the coronal magnetic field, a portion of which is released when the field reconfigures into a lower energy state. Investigation of sunspot magnetic field topology during flare activity is useful to improve our understanding of flaring processes. Here we investigate the deviation of the non-linear field configuration from that of the linear and potential configurations, and study the free energy available leading up to and after a flare. The evolution of the magnetic field in NOAA region 10953 was examined using data from Hinode/SOT-SP, over a period of 12 hours leading up to and after a GOES B1.0 flare. Previous work on this region found pre- and post-flare changes in photospheric vector magnetic field parameters of flux elements outside the primary sunspot. 3D geometry was thus investigated using potential, linear force-free, and non-linear force-free field extrapolations in order to fully understand the evolution of the field lines. Traced field line geometrical and footpoint orientation differences show that the field does not completely relax to a fully potential or linear force-free state after the flare. Magnetic and free magnetic energies increase significantly ~ 6.5-2.5 hours before the flare by ~ 10^31 erg. After the flare, the non-linear force-free magnetic energy and free magnetic energies decrease but do not return to pre-flare 'quiet' values. The post-flare non-linear force-free field configuration is closer (but not equal) to that of the linear force-free field configuration than a potential one. However, the small degree of similarity suggests that partial Taylor relaxation has occurred over a time scale of ~ 3-4 hours.Comment: Accepted for Publication in Astronomy & Astrophysics. 11 pages, 11 figure

Resilience in middle-aged partners of patients diagnosed with incurable cancer : a thematic analysis

Background : Providing care for patients with advanced cancer is often the responsibility of the partner. Being confronted with an incurable cancer diagnosis can be highly disruptive for the patient's partner and can be considered a potentially traumatic event. However, most caregivers seem to adapt well during the process of providing care. This finding is in line with the concept of resilience in literature: a dynamic process of adapting well, resulting from the interplay between intrinsic and extrinsic resources and risks. Resilience is age-related, with the elderly population being higher in resilience as compared to the younger generation. However, resilience has been understudied in middle-aged caregivers. Aim : To explore what intrinsic and extrinsic resources facilitate or hamper resilience in the middle-aged partner of a patient with incurable cancer. Methods : Nine middle-aged partners of patients who died at home of cancer were selected and interviewed in depth within the first year following the death of their partner. A thematic analysis utilizing an inductive approach was conducted. Findings : Resilience was challenged by the partner's diagnosis of incurable cancer. All participants made use of a set of interacting, caregiver-specific and context-related resources, facilitating a resilient process and leading to positive feelings and even personal growth. The partners demonstrated individual competences: adaptive flexibility, positivism, a sense of self-initiative and adaptive dependency. Furthermore, they relied on their context: cancer-related professionals and relatives. Context and situation interact continuously. The resulting dynamics were based on the context-availability, meaningful relationships and the patient's role. Conclusion : A resilient trajectory results from an interplay between individual and contextual resources. To build resilience in middle-aged partners of patients with incurable cancer, health care professionals should address all available resources. Moreover, they should be aware of being part of the caregiver's context, a complex adaptive system that can be either resilience-supporting or -threatening

Lifetimes of atoms trapped in an optical lattice in proximity of a surface

We study the lifetime of an atom trapped in an optical vertical lattice in proximity of a massive surface using a complex scaling approach. We analyze how the presence of the surface modifies the known lifetimes of Wannier-Stark states associated to Landau-Zener tunnelling. We also investigate how the existence of a hypothetical short-distance deviation from Newton's gravitational law could affect these lifetimes. Our study is relevant in order to discuss the feasibility of any atomic- interferometry experiment performed near a surface. Finally, the difficulties encountered in applying the complex-scaling approach to the atom-surface Casimir-Polder interaction are addressed.Comment: 10 pages, 8 figure

Automated Coronal Hole Identification via Multi-Thermal Intensity Segmentation

Coronal holes (CH) are regions of open magnetic fields that appear as dark areas in the solar corona due to their low density and temperature compared to the surrounding quiet corona. To date, accurate identification and segmentation of CHs has been a difficult task due to their comparable intensity to local quiet Sun regions. Current segmentation methods typically rely on the use of single EUV passband and magnetogram images to extract CH information. Here, the Coronal Hole Identification via Multi-thermal Emission Recognition Algorithm (CHIMERA) is described, which analyses multi-thermal images from the Atmospheric Image Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) to segment coronal hole boundaries by their intensity ratio across three passbands (171 \AA, 193 \AA, and 211 \AA). The algorithm allows accurate extraction of CH boundaries and many of their properties, such as area, position, latitudinal and longitudinal width, and magnetic polarity of segmented CHs. From these properties, a clear linear relationship was identified between the duration of geomagnetic storms and coronal hole areas. CHIMERA can therefore form the basis of more accurate forecasting of the start and duration of geomagnetic storms

Towards a national web in a federated country : a Belgian case study

Although the .be domain was introduced in June 1988, the Belgian web is currently not systematically archived. As of August 2016, 1.550.147 domains are registered by DNS Belgium. Without a Belgian web archive, the content of these websites will not be preserved for future generations and a significant portion of Belgian history will be lost forever. In this paper we present the initial findings of a research project exploring the policy, legal, technical and scientific issues around archiving the Belgian web. The aim of this project is to a) identify current best practices in web-archiving b) pilot a Belgian web archive and c) identify research use cases for the scientific study of the Belgian web. This case study is seen as a first step towards implementing a long-term web archiving strategy for Belgium