Fiedler Vectors and Elongation of Graphs: A Threshold Phenomenon on a Particular Class of Trees

Let $G$ be a graph. Its laplacian matrix $L(G)$ is positive and we consider eigenvectors of its first non-null eigenvalue that are called Fiedler vector. They have been intensively used in spectral partitioning problems due to their good empirical properties. More recently Fiedler vectors have been also popularized in the computer graphics community to describe elongation of shapes. In more technical terms, authors have conjectured that extrema of Fiedler vectors can yield the diameter of a graph. In this work we present (FED) property for a graph $G$, i.e. the fact that diameter of a graph can be obtain by Fiedler vectors. We study in detail a parametric family of trees that gives indeed a counter example for the previous conjecture but reveals a threshold phenomenon for (FED) property. We end by an exhaustive enumeration of trees with at most 20 vertices for which (FED) is true and some perspectives.Comment: 19 page

The new Sunspot Number: assembling all corrections

The Sunspot Number, created by R.Wolf in 1849, provides a direct long-term record of solar activity from 1700 to the present. In spite of its central role in multiple studies of the solar dynamo and of the past Sun-Earth relations, it was never submitted to a global critical revision. However, various discrepancies with other solar indices recently motivated a full re-calibration of this series. Based on various diagnostics and corrections established in the framework of several Sunspot Number Workshops and described in Clette et al. 2014, we assembled all corrections in order to produce a new standard version of this reference time series. In this paper, we explain the three main corrections and the criteria used to choose a final optimal version of each correction factor or function, given the available information and published analyses. We then discuss the good agreement obtained with the Group sunspot Number derived from a recent reconstruction. Among the implications emerging from this re-calibrated series, we also discuss the absence of a rising secular trend in the newly-determined solar cycle amplitudes, also in relation with contradictory indications derived from cosmogenic radionuclides. As conclusion, we introduce the new version management scheme now implemented at the World Data Center - SILSO, which reflects a major conceptual transition: beyond the re-scaled numbers, this first revision of the Sunspot Number also transforms the former locked data archive into a living observational series open to future improvements

Discrete-time port-Hamiltonian systems: A definition based on symplectic integration

We introduce a new definition of discrete-time port-Hamiltonian systems (PHS), which results from structure-preserving discretization of explicit PHS in time. We discretize the underlying continuous-time Dirac structure with the collocation method and add discrete-time dynamics by the use of symplectic numerical integration schemes. The conservation of a discrete-time energy balance - expressed in terms of the discrete-time Dirac structure - extends the notion of symplecticity of geometric integration schemes to open systems. We discuss the energy approximation errors in the context of the presented definition and show that their order is consistent with the order of the numerical integration scheme. Implicit Gauss-Legendre methods and Lobatto IIIA/IIIB pairs for partitioned systems are examples for integration schemes that are covered by our definition. The statements on the numerical energy errors are illustrated by elementary numerical experiments.Comment: 12 pages. Preprint submitted to Systems & Control Letter

First Approach for the Modelling of the Electric Field Surrounding a Piezoelectric Transformer in View of Plasma Generation

This paper is about an open multi-physics modelling problem resulting from recent investigations into plasma generation by piezoelectric transformers. In this first approach, the electric field distribution surrounding the transformer is studied according to a weak coupling formulation. Electric potential distribution views obtained numerically are compared to real views of plasma generation observed experimentally

Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities

This paper is concerned with the compound Poisson risk model and two generalized models with still Poisson claim arrivals. One extension incorporates inhomogeneity in the premium input and in the claim arrival process, while the other takes into account possible dependence between the successive claim amounts. The problem under study for these risk models is the evaluation of the probabilities of (non-)ruin over any horizon of finite length. The main recent methods, exact or approximate, used to compute the ruin probabilities are reviewed and discussed in a unified way. Special attention is then paid to an analysis of the qualitative impact of dependence between claim amounts.compound Poisson model; ruin probability; finite-time horizon; recursive methods; (generalized) Appell polynomials; non-constant premium; non-stationary claim arrivals; interdependent claim amounts; impact of dependence; comonotonic risks; heavy-tailed distributions

Stationary-excess operator and convex stochastic orders

The present paper aims to point out how the stationary-excess operator and its iterates transform the s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone. Both discrete and continuous cases are investigated. Several extremal distributions under monotonicity conditions are derived. They are illustrated with some applications in insurance.Insurance risks; s-convex stochastic orders; Extremal distributions; t-monotone distributions; Stationary-excess operator; Discrete and continuous versions.

On the assimilation of Martian total ozone retrievals

The technique of data assimilation gives us an opportunity to further our understanding of important photochemical processes in the Martian atmosphere, through the creation of a reanalysis product that can be used to investigate the temporal and spatial agreement between model and observations and determine any possible causes of identified differences. In this study [1], we have assimilated, for the first time, total ozone retrievals into a Mars Global Circulation model (GCM) to study the ozone cycle