Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes

We give a partial "quasi-stratification" of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\mathbb {P}^m$. It covers the set $\sigma_t(X_{m,d})^{\dagger}$ of all points lying on the linear span of curvilinear subschemes of $X_{m,d}$, but two "quasi-strata" may overlap. For low border rank two different "quasi-strata" are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each $P\in \sigma_t(X_{m,d})^{\dagger}$ the minimal label of a quasi-stratum containing it.Comment: 16 page

B-Mode contamination by synchrotron emission from 3-years WMAP data

We study the contamination of the B-mode of the Cosmic Microwave Background Polarization (CMBP) by Galactic synchrotron in the lowest emission regions of the sky. The 22.8-GHz polarization map of the 3-years WMAP data release is used to identify and analyse such regions. Two areas are selected with signal-to-noise ratio S/N<2 and S/N<3, covering ~16% and ~26% fraction of the sky, respectively. The polarization power spectra of these two areas are dominated by the sky signal on large angular scales (multipoles l < 15), while the noise prevails on degree scales. Angular extrapolations show that the synchrotron emission competes with the CMBP B-mode signal for tensor-to-scalar perturbation power ratio $T/S = 10^{-3}$ -- $10^{-2}$ at 70-GHz in the 16% lowest emission sky (S/N<2 area). These values worsen by a factor ~5 in the S/N<3 region. The novelty is that our estimates regard the whole lowest emission regions and outline a contamination better than that of the whole high Galactic latitude sky found by the WMAP team (T/S>0.3). Such regions allow $T/S \sim 10^{-3}$ to be measured directly which approximately corresponds to the limit imposed by using a sky coverage of 15%. This opens interesting perspectives to investigate the inflationary model space in lowest emission regions.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letter

The synchrotron foreground and CMB temperature-polarization cross correlation power spectrum from the first year WMAP data

We analyse the temperature-polarization cross-correlation in the Galactic synchrotron template that we have recently developed, and between the template and CMB temperature maps derived from WMAP data. Since the polarized synchrotron template itself uses WMAP data, we can estimate residual synchrotron contamination in the CMB $C_\ell^{TE}$ angular spectrum. While $C_2^{TE}$ appears to be contamined by synchrotron, no evidence for contamination is found in the multipole range which is most relevant for the fit of the cosmological optical depth.Comment: Accepted for pubblication on MNRAS Lette

Kelvin probe characterization of buried graphitic microchannels in single-crystal diamond

In this work, we present an investigation by Kelvin Probe Microscopy (KPM) of buried graphitic microchannels fabricated in single-crystal diamond by direct MeV ion microbeam writing. Metal deposition of variable-thickness masks was adopted to implant channels with emerging endpoints and high temperature annealing was performed in order to induce the graphitization of the highly-damaged buried region. When an electrical current was flowing through the biased buried channel, the structure was clearly evidenced by KPM maps of the electrical potential of the surface region overlying the channel at increasing distances from the grounded electrode. The KPM profiling shows regions of opposite contrast located at different distances from the endpoints of the channel. This effect is attributed to the different electrical conduction properties of the surface and of the buried graphitic layer. The model adopted to interpret these KPM maps and profiles proved to be suitable for the electronic characterization of buried conductive channels, providing a non-invasive method to measure the local resistivity with a micrometer resolution. The results demonstrate the potential of the technique as a powerful diagnostic tool to monitor the functionality of all-carbon graphite/diamond devices to be fabricated by MeV ion beam lithography.Comment: 21 pages, 5 figure

Forest-grassland transitions : How livestock and fire shape grassy biomes

Plant associations are determined by complex interactions with their environment depending on resource availability, landscape features, and periodic disturbances that shape the structure and functions of these communities. Forests, savannas and grasslands extend across the global land surface, contribute to planetary processes and provide ecosystems services sustaining local production. However, the factors that explain the distribution of trees and determine these biomes are still not well understood. In this thesis, long-standing questions about the origins and distribution of these ecosystems are discussed in light of new evidence suggesting that a feedback of fire and grasses may maintain forests, savannas and grasslands as alternative tree cover states. I also address how anthropogenic land use, including the introduction of livestock, may be affecting these dynamics, particularly in the neotropics, with consequences in terms of potential transitions in tree cover regimes. I analyze the distribution of trees in the grasslands of subtropical South America, looking at what may determine current tree cover and change dynamics (Chapters 2 & 3). The results suggest that, in non-cultivated areas, the expansion of trees into grasslands is likely limited by fire, livestock and precipitation, and that livestock likely reduces fire frequency (Chapter 2). The analyses also suggest that in the Uruguayan Campos of southeastern South America, where fire frequency is low and livestock densities are high, a release in livestock density may cause a moderate expansion of forests into grasslands (Chapter 3). To understand the consequences of a potential transition to higher tree cover by increasing precipitation, I looked at the effects of tree cover in subtropical rangelands (Chapter 5). The results indicated that isolated trees can improve the forage quality and abundance of these rangelands, with potential benefits in terms of biodiversity and ecosystem services. Lastly, I analyzed correlational patterns relating livestock density to vegetation structure across the global tropics and subtropics (Chapter 4), in an attempt to generalize the findings of Chapter 2. The results indicate that extensive livestock systems reduce fire frequency and impact vegetation structure, maintaining savannas and grasslands with low tree cover, low fire frequency and a higher presence of shrubs and dwarf trees.</p

Microelectrode arrays of diamond-insulated graphitic channels for real time detection of exocytotic events from cultured chromaffin cells and slices of adrenal glands

A microstructured graphitic 4x4 multielectrode array was embedded in a single crystal diamond substrate (4x4 {uG-SCD MEA) for real-time monitoring of exocytotic events from cultured chromaffin cells and adrenal slices. The current approach relies on the development of a parallel ion beam lithographic technique, which assures the time effective fabrication of extended arrays with reproducible electrode dimensions. The reported device is suitable for performing amperometric and voltammetric recordings with high sensitivity and temporal resolution, by simultaneously acquiring data from 16 rectangularly shaped microelectrodes (20x3.5 um^2) separated by 200 um gaps. Taking advantage of the array geometry we addressed the following specific issues: i) detect both the spontaneous and KCl-evoked secretion simultaneously from several chromaffin cells directly cultured on the device surface, ii) resolve the waveform of different subsets of exocytotic events, iii) monitoring quantal secretory events from thin slices of the adrenal gland. The frequency of spontaneous release was low (0.12 Hz and 0.3 Hz respectively for adrenal slices and cultured cells) and increased up to 0.9 Hz after stimulation with 30 mM KCl in cultured cells. The spike amplitude as well as rise and decay time were comparable with those measured by carbon fiber microelectrodes and allowed to identify three different subsets of secretory events associated to "full fusion" events, "kiss and-run" and "kiss-and-stay" exocytosis, confirming that the device has adequate sensitivity and time resolution for real-time recordings. The device offers the significant advantage of shortening the time to collect data by allowing simultaneous recordings from cell populations either in primary cell cultures or in intact tissues

STOCHASTIC PERTURBATION OF A CUBIC ANHARMONIC OSCILLATOR

We perturb with an additive noise the Hamiltonian system associated to a cubic anharmonic oscillator. This gives rise to a system of stochastic differential equations with quadratic drift and degenerate diffusion matrix. Firstly, we show that such systems possess explosive solutions for certain initial conditions. Then, we carry a small noise expansion's analysis of the stochastic system which is assumed to start from initial conditions that guarantee the existence of a periodic solution for the unperturbed equation. We then investigate the probabilistic properties of the sequence of coefficients which turn out to be the unique strong solutions of stochastic perturbations of the well-known Lamé's equation. We also obtain explicit expressions of these in terms of Jacobi elliptic functions. Furthermore, we prove, in the case of Brownian noise, a lower bound for the probability that the truncated expansion stays close to the solution of the deterministic problem. Lastly, when the noise is bounded, we provide conditions for the almost sure convergence of the global expansion