Connectivity measures for internet topologies.

The topology of the Internet has initially been modelled as an undirected graph, where vertices correspond to so-called Autonomous Systems (ASs),and edges correspond to physical links between pairs of ASs. However, in order to capture the impact of routing policies, it has recently become apparent that one needs to classify the edges according to the existing economic relationships (customer-provider, peer-to-peer or siblings) between the ASs. This leads to a directed graph model in which traffic can be sent only along so-called valley-free paths. Four different algorithms have been proposed in the literature for inferring AS relationships using publicly available data from routing tables. We investigate the differences in the graph models produced by these algorithms, focussing on connectivity measures. To this aim, we compute the maximum number of vertex-disjoint valley-free paths between ASs as well as the size of a minimum cut separating a pair of ASs. Although these problems are solvable in polynomial time for ordinary graphs, they are NP-hard in our setting. We formulate the two problems as integer programs, and we propose a number of exact algorithms for solving them. For the problem of finding the maximum number of vertex-disjoint paths, we discuss two algorithms; the first one is a branch-and-price algorithm based on the IP formulation, and the second algorithm is a non LP based branch-and-bound algorithm. For the problem of finding minimum cuts we use a branch-and-cut algo rithm, based on the IP formulation of this problem. Using these algorithms, we obtain exact solutions for both problems in reasonable time. It turns out that there is a large gap in terms of the connectivity measures between the undirected and directed models. This finding supports our conclusion that economic relationships need to be taken into account when building a topology of the Internet.Research; Internet;

A new anatomical variation of the musculocutaneous and the median nerve anastomosis

Variations of the brachial plexus and its terminal branches are not uncommon.Therein, the anatomical variations of the musculocutaneous and the median nerve are classified into 5 types, while the communicating branches between the musculocutaneous and the median nerve are classified into 3 types, depending on their position related to the coracobrachial muscle. The case reviewed in this paper presents a variation similar to that of the second variety, but is significantly different due to the appearance of the proximal musculocutaneous nerve and its communicating branching, the site rising from the communicating branch (through the coracobrachial), and important clinical implications of this new variation. Despite the communicating branch being located in the upper third of the upper arm, it should not be considered as being a double lateral root of the median nerve

Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators

We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that the long term dynamics of this model is finite dimensional. Following this, we prove that the global attractor of this model takes one of two forms. When coupling strength is below a critical value, the global attractor is a single equilibrium point corresponding to an incoherent state. Conversely, when coupling strength is beyond this critical value, the global attractor is a two-dimensional disk composed of radial trajectories connecting a saddle equilibrium (the incoherent state) to an invariant closed curve of locally stable equilibria (partially synchronized state). Our analysis hinges, on the one hand, upon sharp existence and uniqueness results and their consequence for the existence of a global attractor, and, on the other hand, on the study of the dynamics in the vicinity of the incoherent and synchronized equilibria. We prove in particular non-linear stability of each synchronized equilibrium, and normal hyperbolicity of the set of such equilibria. We explore mathematically and numerically several properties of the global attractor, in particular we discuss the limit of this attractor as noise intensity decreases to zero.Comment: revised version, 28 pages, 4 figure

ドイツの医療保障の動向と介護保険

第4回　最終回　ヨーロッパ諸国の医療保障の現

Ferromagnetic resonance force spectroscopy of individual sub-micron size samples

We review how a magnetic resonance force microscope (MRFM) can be applied to perform ferromagnetic resonance (FMR) spectroscopy of \emph{individual} sub-micron size samples. We restrict our attention to a thorough study of the spin-wave eigen-modes excited in permalloy (Py) disks patterned out of the same 43.3 nm thin film. The disks have a diameter of either 1.0 or $0.5 \mu$m and are quasi-saturated by a perpendicularly applied magnetic field. It is shown that \emph{quantitative} spectroscopic information can be extracted from the MRFM measurements. In particular, the data are extensively compared with complementary approximate models of the dynamical susceptibility: i) a 2D analytical model, which assumes an homogeneous magnetization dynamics along the thickness and ii) a full 3D micromagnetic simulation, which assumes an homogeneous magnetization dynamics below a characteristic length scale $c$ and which approximates the cylindrical sample volume by a discretized representation with regular cubic mesh of lateral size $c=3.9$ nm. In our analysis, the distortions due to a breaking of the axial symmetry are taken into account, both models incorporating the possibility of a small misalignment between the applied field and the normal of the disks

Complete mapping of the spin-wave spectrum in a vortex-state nanodisk

© 2016 American Physical Society.We report a study on the complete spin-wave spectrum inside a vortex-state nanodisk. Transformation of this spectrum is continuously monitored as the nanodisk becomes gradually magnetized by a perpendicular magnetic field and encounters a second-order phase transition to the uniformly magnetized state. This reveals the bijective relationship that exists between the eigenmodes in the vortex state and the ones in the saturated state. It is found that the gyrotropic mode can be continuously viewed as a uniform phase precession, which uniquely softens (its frequency vanishes) at the saturation field to transform above into the Kittel mode. By contrast, the other spin-wave modes remain finite as a function of the applied field, while their character is altered by level anticrossing

Complete mapping of the spin-wave spectrum in a vortex-state nanodisk

© 2016 American Physical Society.We report a study on the complete spin-wave spectrum inside a vortex-state nanodisk. Transformation of this spectrum is continuously monitored as the nanodisk becomes gradually magnetized by a perpendicular magnetic field and encounters a second-order phase transition to the uniformly magnetized state. This reveals the bijective relationship that exists between the eigenmodes in the vortex state and the ones in the saturated state. It is found that the gyrotropic mode can be continuously viewed as a uniform phase precession, which uniquely softens (its frequency vanishes) at the saturation field to transform above into the Kittel mode. By contrast, the other spin-wave modes remain finite as a function of the applied field, while their character is altered by level anticrossing

Ferromagnetic resonance force spectroscopy of individual submicron-size samples

We review how a magnetic-resonance force microscope (MRFM) can be applied to perform ferromagnetic resonance spectroscopy of individual submicron-size samples. We restrict our attention to a thorough study of the spin-wave eigenmodes excited in Permalloy (Py) disks patterned out of the same 43.3-nm-thin film. The disks have a diameter of either 1.0 or 0.5 μm and are quasisaturated by a perpendicularly applied magnetic field. It is shown that quantitative spectroscopic information can be extracted from the MRFM measurements. In particular, the data are extensively compared with complementary approximate models of the dynamical susceptibility: (i) a two-dimensional analytical model, which assumes a homogeneous magnetization dynamics along the thickness, and ii) a full three-dimensional micromagnetic simulation, which assumes a homogeneous magnetization dynamics below a characteristic length scale c and approximates the cylindrical sample volume by a discretized representation with regular cubic mesh of lateral size c=3.9 nm. In our analysis, the distortions due to a breaking of the axial symmetry are taken into account; both models incorporating the possibility of a small misalignment between the applied field and the normal of the disks. © 2008 The American Physical Society

Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

In Llanas and Lantarón, J. Sci. Comput. 46, 485–518 (2011) we proposed an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ℝ d . This procedure is based on adaptive splitting of the domain of the function guided by the value of an average integral. The above study was limited to the 1D and 2D versions of the algorithm. In this paper we address the three-dimensional problem. We prove an integral inequality (in the case d=3) which constitutes the basis of EDAS-3. We have performed detailed computational experiments demonstrating effective edge detection in 3D function models with different interface topologies. EDAS-1 and EDAS-2 appealing properties are extensible to the 3D cas

Myalgic encephalomyelitis/chronic fatigue Syndrome (ME/CFS) : Investigating care practices pointed out to disparities in diagnosis and treatment across European Union

ME/CFS is a chronic, complex, multisystem disease that often limits the health and functioning of the affected patients. Diagnosing patients with ME/CFS is a challenge, and many different case definitions exist and are used in clinical practice and research. Even after diagnosis, medical treatment is very challenging. Symptom relief and coping may affect how patients live with their disease and their quality of life. There is no consensus on which diagnostic criteria should be used and which treatment strategies can be recommended for patients. The purpose of the current project was to map the landscape of the Euromene countries in respect of national guidelines and recommendations for case definition, diagnosis and clinical approaches for ME/CFS patients. A 23 items questionnaire was sent out by email to the members of Euromene. The form contained questions on existing guidelines for case definitions, treatment/management of the disease, tests and questionnaires applied, and the prioritization of information for data sampling in research. We obtained information from 17 countries. Five countries reported having national guidelines for diagnosis, and five countries reported having guidelines for clinical approaches. For diagnostic purposes, the Fukuda criteria were most often recommended, and also the Canadian Consensus criteria, the International Consensus Criteria and the Oxford criteria were used. A mix of diagnostic criteria was applied within those countries having no guidelines. Many different questionnaires and tests were used for symptom registration and diagnostic investigation. For symptom relief, pain and anti-depressive medication were most often recommended. Cognitive Behavioral Therapy and Graded Exercise treatment were often recommended as disease management and rehabilitative/palliative strategies. The lack of consistency in recommendations across European countries urges the development of regulations, guidance and standards. The results of this study will contribute to the harmonization of diagnostic criteria and treatment for ME/CFS in Europe