Littelmann paths and brownian paths

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.Comment: 30 pages, 1 figur

Toward a generic representation of random variables for machine learning

This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to represent random variables which splits apart dependency and distribution without losing any information. We also propound an associated metric leveraging this representation and its statistical estimate. Besides experiments on synthetic datasets, the benefits of our contribution is illustrated through the example of clustering financial time series, for instance prices from the credit default swaps market. Results are available on the website www.datagrapple.com and an IPython Notebook tutorial is available at www.datagrapple.com/Tech for reproducible research.Comment: submitted to Pattern Recognition Letter

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in \cite{bcre} to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We find that the critical wave vector is of the order of the saltation length. We provide an intuitive interpretation of the instability.Comment: 11 pages, latex, 2 encapsulated postscript figure

Repairing triangle meshes built from scanned point cloud

The Reverse Engineering process consists of a succession of operations that aim at creating a digital representation of a physical model. The reconstructed geometric model is often a triangle mesh built from a point cloud acquired with a scanner. Depending on both the object complexity and the scanning process, some areas of the object outer surface may never be accessible, thus inducing some deficiencies in the point cloud and, as a consequence, some holes in the resulting mesh. This is simply not acceptable in an integrated design process where the geometric models are often shared between the various applications (e.g. design, simulation, manufacturing). In this paper, we propose a complete toolbox to fill in these undesirable holes. The hole contour is first cleaned to remove badly-shaped triangles that are due to the scanner noise. A topological grid is then inserted and deformed to satisfy blending conditions with the surrounding mesh. In our approach, the shape of the inserted mesh results from the minimization of a quadratic function based on a linear mechanical model that is used to approximate the curvature variation between the inner and surrounding meshes. Additional geometric constraints can also be specified to further shape the inserted mesh. The proposed approach is illustrated with some examples coming from our prototype software

A proposal of a methodological framework with experimental guidelines to investigate clustering stability on financial time series

We present in this paper an empirical framework motivated by the practitioner point of view on stability. The goal is to both assess clustering validity and yield market insights by providing through the data perturbations we propose a multi-view of the assets' clustering behaviour. The perturbation framework is illustrated on an extensive credit default swap time series database available online at www.datagrapple.com.Comment: Accepted at ICMLA 201