Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density p(\x) = e^{-U(\x)} we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential 2U(\x) with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.Comment: submitted to NIPS 200

Epigenetic regulation of adaptive responses of forest tree species to the environment

Epigenetic variation is likely to contribute to the phenotypic plasticity and adaptative capacity of plant species, and may be especially important for long-lived organisms with complex life cycles, including forest trees. Diverse environmental stresses and hybridization/polyploidization events can create reversible heritable epigenetic marks that can be transmitted to subsequent generations as a form of molecular “memory”. Epigenetic changes might also contribute to the ability of plants to colonize or persist in variable environments. In this review, we provide an overview of recent data on epigenetic mechanisms involved in developmental processes and responses to environmental cues in plant, with a focus on forest tree species. We consider the possible role of forest tree epigenetics as a new source of adaptive traits in plant breeding, biotechnology, and ecosystem conservation under rapid climate change.This is the publisher’s final pdf. The published article is copyrighted by the authors and published by Blackwell Publishing Ltd. and can be found at: http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%292045-7758.Keywords: forest trees, phenotypic plasticity, epigenetic memory of stressful conditions, adaptive response, epigenetics, environmental stres

DYNAMIQUE DES ECOULEMENTS CIRCUMSTELLAIRES POLYPHASES

STRASBOURG-Sc. et Techniques (674822102) / SudocMEUDON-Observatoire (920482302) / SudocSudocFranceF

Human On-line Response to Target Expansion

McGuffin and Balakrishnan (M&B) have recently reported evidence that target expansion during a reaching movement reduces pointing time even if the expansion occurs as late as in the last 10% of the distance to be covered by the cursor. While M&B massed their static and expanding targets in separate blocks of trials, thus making expansion predictable for participants, we replicated their experiment with one new condition in which the target could unpredictably expand, shrink, or stay unchanged. Our results show that target expansion occurring as late as in M&B's experiment enhances pointing performance in the absence of expectation. We discuss these findings in terms of the basic human processes that underlie target-acquisition movements, and we address the implications for user interface design by introducing a revised design for the Mac OS X Dock

A new generator for mineral dust aerosol production from soil samples in the laboratory : GAMEL

International audienceA generator has been developed for producing mineral dust from small samples of desert soils. The objective is to perform a thorough characterization of this new tool and show that it is adapted to the future laboratory studies of the relationship between aerosols and their parent soils. This work describes the principles and operating protocol of the so-called GAMEL generator. A first series of detailed measurements was performed with a Niger soil. During these tests the aerosol size-distribution was monitored in real time with an optical counter and the particles collected on filters submitted to XRF analysis. This allowed characterizing the emission in terms of time evolution of the aerosol production, repeatability of the experiment, and assessing the influence of such generation parameters as the mass of soil and the frequency and duration of the shaking. For this sandy Niger soil, the optimal generation parameters were found to be 1 g of soil agitated 9 min at the frequency of 500 cycles/min, but the effect of modifications of these recommended values have also been quantified. In terms of size-distribution as well as of elemental composition, the generated aerosol is found to compare well to the one collected in natural conditions during local events. For testing the capability of the GAMEL to produce aerosols from different soils, tests were also performed with 3 other soils from arid and semi-arid areas. Results showed that the GAMEL is able to produce aerosols whose characteristics encompass the regional variability of naturally produced mineral aerosols

Diffusion Maps, Spectral Clustering and Reaction

A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems, where the notion of time evolution comes into play, important problems are the identification of slow variables and dynamically meaningful reaction coordinates that capture the long time evolution of the system. In this paper we provide a unifying view of these apparently different tasks, by considering a family of di#usion maps, defined as the embedding of complex (high dimensional) data onto a low dimensional Euclidian space, via the eigenvectors of suitably defined random walks defined on the given datasets. Assuming that the data is randomly sampled from an underlying general probability distribution p(x) = e -U(x) , we show that as the number of samples goes to infinity, the eigenvectors of each di#usion map converge to the eigenfunctions of a corresponding di#erential operator defined on the support of the probability distribution. Di#erent normalizations of the Markov chain on the graph lead to di#erent limiting di#erential operators

Frequency-domain simulation of power electronic systems based on multi-topology equivalent sources modelling method

International audienceElectroMagnetic Interference (EMI) simulation of power converters helps engineers in the design process. In this paper, we describe a frequency-domain simulation method based on the Multi-Topology Equivalent Sources (MTES) model. The aim is to reproduce the non-linear behavior of power switches for a fast evaluation of the conducted EMI. The method performance is validated on a DC-DC converter

Variability of the elemental composition of airborne mineral dust along the coast of Central Tunisia

International audienc