Karhunen-Lo\`{e}ve expansions of mean-centered Wiener processes

For $\gamma>-{1/2}$, we provide the Karhunen-Lo\`{e}ve expansion of the weighted mean-centered Wiener process, defined by $$W _{\gamma}(t)=\frac{1}{\sqrt{1+2\gamma}}\Big\{W\big(t^{1+2\gamma}\big)- \int_0^1W\big(u^{1+2\gamma}\big)du\Big\},$$ for $t\in(0,1]$. We show that the orthogonal functions in these expansions have simple expressions in term of Bessel functions. Moreover, we obtain that the $L^2[0,1]$ norm of $W_{\gamma}$ is identical in distribution with the $L^2[0,1]$ norm of the weighted Brownian bridge $t^{\gamma}B(t)$.Comment: Published at http://dx.doi.org/10.1214/074921706000000761 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

A new test procedure of independence in copula models via chi-square-divergence

We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $\chi^2$-divergence on signed finite measures. The asymptotic properties of the proposed estimate and the test statistic are studied under the null and alternative hypotheses, with simple and standard limit distributions both when the parameter is an interior point or not.Comment: 23 pages (2 figures). Submitted to publicatio

Constraints on the core mu-gradient of the solar-like star HD 49385 via low-degree mixed modes

The existence of an l=1 avoided crossing in the spectrum of the solar-like pulsator CoRoT-target HD 49385 was established by Deheuvels & Michel (2009). It is the first confirmed detection of such a phenomenon. The authors showed in a preliminary modeling of the star that it was in a post main sequence status. Being a 1.3 Msun-star, HD 49385 has had a convective core during its main sequence phase. The mu-gradient left by the withdrawal of this core bears information about the processes of transport at the boundary of the core. We here investigate the constraints that the observed avoided crossing brings on the mu-gradient in the core of the star.Comment: 5 pages, 5 figures, accepted in Astron. Nach. This work was presented at the HELAS Conference in Lanzarote in February 201

Mapping plant diversity in cocoa-based agroforestry systems to improve overall productivity

In cocoa-based agroforestry systems (CAFS), the cocoa trees are associated with other cultivated plant species at variable densities. There, the spatial distribution of the cultivated plants can be regular, random or aggregated, and their age may vary even in the same species. Variables of (i) density, (ii) spatial distribution and (iii) age can thus influence the overall productivity of CAFS and its distribution in space. We studied the relationships between these 3 variables and CAFS productivity based on data collected in 34 experimental yield tracking plots placed in agroforestry fields of producers in the Dominican Republic. A mapping of the cultivated plants was carried out on each plot at their installation and harvests of the ripe products of each individual plant were carried out every two weeks over a period of one year. The first results of this study indicate that optimal CAFS productivity can be maintained along a decreasing density gradient of crops, associated with cocoa tree ageing. In addition, regular and random spatial distribution of all plant species may increase overall productivity. The analysis of the variability of cocoa, fruit, tuber and timber yields allows us to provide recommendations on the most suitable species and the optimal distance between plants to improve overall productivity and therefore the producer's income

Sobolev extension property for tree-shaped domains with self-contacting fractal boundary

International audienceIn this paper, we investigate the existence of extension operators fromW1,p( ) toW1,p(R2) (1 < p < 1) for a class of tree-shaped domains with a self-similar fractal boundary pre- viously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the results of Jones imply that there exist such extension operators for all p 2 [1,1]. In the case when the fractal boundary self-intersects, this result does not hold. Here, we prove however that extension operators exist for p < p? where p? depends only on the dimension of the self-intersection of the boundary. The construction of these operators mainly relies on the self-similar properties of the domains

Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and red giant stars. Under the assumption of local angular momentum conservation, the core contraction and envelope expansion occurring at the end of the main sequence would result in a much larger internal differential rotation than observed. This suggests that angular momentum redistribution must be taking place in the interior of these stars. Aims. We investigate the physical nature of the angular momentum redistribution mechanisms operating in stellar interiors by constraining the efficiency of post-main sequence rotational coupling. Methods. We model the rotational evolution of a 1.25 Msun star using the Yale Rotational stellar Evolution Code. Our models take into account the magnetic wind braking occurring at the surface of the star and the angular momentum transport in the interior, with an efficiency dependent on the degree of internal differential rotation. Results. We find that models including a dependence of the angular momentum transport efficiency on the radial rotational shear reproduce very well the observations. The best fit of the data is obtained with an angular momentum transport coefficient scaling with the ratio of the rotation rate of the radiative interior over that of the convective envelope of the star as a power law of exponent ~3. This scaling is consistent with the predictions of recent numerical simulations of the Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular momentum transport process whose efficiency varies during the stellar evolution through a dependence on the level of internal differential rotation is required to explain the observed post-main sequence rotational evolution of low-mass stars.Comment: 8 pages, 6 figures; accepted for publication in Astronomy & Astrophysic

Probing core overshooting using asteroseismology

Modeling properly the interface between convective cores and radiative interiors is one the most challenging and important open questions in modern stellar physics. The rapid development of asteroseismology, with the advent of space missions partly dedicated to this discipline, has provided new constraints to progress on this issue. We here give an overview of the information that can be obtained from pressure modes, gravity modes and mixed modes. We also review some of the most recent constraints obtained from space-based asteroseismology on the nature and the amount of mixing beyond convective cores.Comment: To appear in the proceedings of the workshop "How Much do we Trust Stellar Models?" held in Li\`ege in September 201

Period spacings in red giants I. Disentangling rotation and revealing core structure discontinuities

Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This relies on the properties of the global oscillations with a mixed character that are highly sensitive to the physical properties of the core. However, overlapping rotational splittings and mixed-mode spacings result in complex structures in the mixed-mode pattern, which severely complicates its identification and the measurement of the asymptotic period spacing. This work aims at disentangling the rotational splittings from the mixed-mode spacings, in order to open the way to a fully automated analysis of large data sets. An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. The \'echelle diagrams constructed with the appropriately stretched periods are used to exhibit the structure of the gravity modes and of the rotational splittings. We propose a new view on the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. This provides a direct understanding of all oscillation components, even in the case of rapid rotation. The measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes are then made easy. This work opens the possibility to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing. Revealing buoyancy glitches provides a detailed view on the radiative core.Comment: Accepted in A&