Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Sex Promotes Spatial and Dietary Segregation in a Migratory Shorebird during the Non-Breeding Season

Several expressions of sexual segregation have been described in animals, especially in those exhibiting conspicuous dimorphism. Outside the breeding season, segregation has been mostly attributed to size or age-mediated dominance or to trophic niche divergence. Regardless of the recognized implications for population dynamics, the ecological causes and consequences of sexual segregation are still poorly understood. We investigate the foraging habits of a shorebird showing reversed sexual dimorphism, the black-tailed godwit Limosa limosa, during the winter season, and found extensive segregation between sexes in spatial distribution, microhabitat use and dietary composition. Males and females exhibited high site-fidelity but differed in their distributions at estuary-scale. Male godwits (shorter-billed) foraged more frequently in exposed mudflats than in patches with higher water levels, and consumed more bivalves and gastropods and fewer polychaetes than females. Females tended to be more frequently involved and to win more aggressive interactions than males. However, the number of aggressions recorded was low, suggesting that sexual dominance plays a lesser role in segregation, although its importance cannot be ruled out. Dimorphism in the feeding apparatus has been used to explain sex differences in foraging ecology and behaviour of many avian species, but few studies confirmed that morphologic characteristics drive individual differences within each sex. We found a relationship between resource use and bill size when pooling data from males and females. However, this relationship did not hold for either sex separately, suggesting that differences in foraging habits of godwits are primarily a function of sex, rather than bill size. Hence, the exact mechanisms through which this segregation operates are still unknown. The recorded differences in spatial distribution and resource use might expose male and female to distinct threats, thus affecting population dynamics through differential mortality. Therefore, population models and effective conservation strategies should increasingly take sex-specific requirements into consideration

Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation

In this paper we propose Universal trace co-kriging, a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodological evaluation and comparisons with the recently published projection based approach by Bohorquez et al. (Stoch Environ Res Risk Assess 31(1):53–70, 2016. https://doi.org/10.1007/s00477-016-1266-y). Our evaluations and analyses were performed on synthetic (oil reservoir) and real field (uranium contamination) subsurface uncertainty quantification case studies. Monte Carlo analyses were conducted to draw important conclusions and to provide practical guidelines for all future practitioners

Towards high resolution ceramic series for production site studies: the case of Loron amphorae (Croatia, 1st–3rd c. A.D.)

International audienc

A Bayes Hilbert Space for Compartment Model Computing in Diffusion MRI

International audienceThe single diffusion tensor model for mapping the brain white matter microstructure has long been criticized as providing sensitive yet non-specific clinical biomarkers for neurodegenerative diseases because (i) voxels in diffusion images actually contain more than one homogeneous tissue population and (ii) diffusion in a single homogeneous tissue can be non-Gaussian. Analytic models for compartmental diffusion signals have thus naturally emerged but there is surprisingly little for processing such images (estimation, smoothing, registration, atlas-ing, statistical analysis). We propose to embed these signals into a Bayes Hilbert space that we properly define and motivate. This provides a unified framework for compartment diffusion image computing. Experiments show that (i) interpolation in Bayes space features improved robustness to noise compared to the widely used log-Euclidean space for tensors and (ii) it is possible to trace complex key pathways such as the pyramidal tract using basic deterministic tractography thanks to the combined use of Bayes interpolation and multi-compartment diffusion models

Analysis of an European union election using principal component analysis

Compositional data, Principal component analysis, Crude PCA, Logcontrast PCA, Electoral data, 02.50.Sk, 02.70.Rr, 62H25, 62P25,