17,250 research outputs found
Fiedler Vectors and Elongation of Graphs: A Threshold Phenomenon on a Particular Class of Trees
Let be a graph. Its laplacian matrix 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 , 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 Generic Multiple-Precision Floating-Point Addition With Exact Rounding (as in the MPFR Library)
We study the multiple-precision addition of two positive floating-point
numbers in base 2, with exact rounding, as specified in the MPFR library, i.e.
where each number has its own precision. We show how the best possible
complexity (up to a constant factor that depends on the implementation) can be
obtain.Comment: Conference website at http://cca-net.de/rnc6
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
Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems
We present the mixed Galerkin discretization of distributed parameter
port-Hamiltonian systems. On the prototypical example of hyperbolic systems of
two conservation laws in arbitrary spatial dimension, we derive the main
contributions: (i) A weak formulation of the underlying geometric
(Stokes-Dirac) structure with a segmented boundary according to the causality
of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac
structure by a finite-dimensional Dirac structure is realized using a mixed
Galerkin approach and power-preserving linear maps, which define minimal
discrete power variables. (iii) With a consistent approximation of the
Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models.
By the degrees of freedom in the power-preserving maps, the resulting family of
structure-preserving schemes allows for trade-offs between centered
approximations and upwinding. We illustrate the method on the example of
Whitney finite elements on a 2D simplicial triangulation and compare the
eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the
CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0
On Finite-Time Ruin Probabilities for Classical Risk Models
This paper is concerned with the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard and Lefèvre (1997) for the probability of (non-)ruin within finite time. First, a standard method based on the ballot theorem and an argument of Seal-type provides an initial (known) formula for that probability. Then, a concept of pseudo-distributions for the cumulated claim amounts, combined with some simple implications of the ballot theorem, leads to the desired formula. Two expressions for the (non-)ruin probability over an infinite horizon are also deduced as corollaries. Finally, an illustration within the framework of Solvency II is briefly presented.ruin probability; finite and infinite horizon; compound binomial model; compound Poisson model; ballot theorem; pseudo-distributions; Solvency II; Value-at-Risk.
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
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