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

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

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

Polarized Diffuse Emission at 2.3 GHz in a High Galactic Latitude Area

Polarized diffuse emission observations at 2.3 GHz in a high Galactic latitude area are presented. The 2\degr X 2\degr field, centred in (\alpha=5^h,\delta=-49\degr), is located in the region observed by the BOOMERanG experiment. Our observations has been carried out with the Parkes Radio telescope and represent the highest frequency detection done to date in low emission areas. Because of a weaker Faraday rotation action, the high frequency allows an estimate of the Galactic synchrotron contamination of the Cosmic Microwave Background Polarization (CMBP) that is more reliable than that done at 1.4 GHz. We find that the angular power spectra of the E- and B-modes have slopes of \beta_E = -1.46 +/- 0.14 and \beta_B = -1.87 +/- 0.22, indicating a flattening with respect to 1.4 GHz. Extrapolated up to 32 GHz, the E-mode spectrum is about 3 orders of magnitude lower than that of the CMBP, allowing a clean detection even at this frequency. The best improvement concerns the B-mode, for which our single-dish observations provide the first estimate of the contamination on angular scales close to the CMBP peak (about 2 degrees). We find that the CMBP B-mode should be stronger than synchrotron contamination at 90 GHz for models with T/S > 0.01. This low level could move down to 60-70 GHz the optimal window for CMBP measures.Comment: 5 pages, 6 figures, accepted for publication in MNRAS Letter

The use of aerial- and close-range photogrammetry for the mapping of the Lavini di Marco tracksite (Hettangian, Southern Alps, NE Italy)

(EXCERPT FROM ABSTRACT) Close-range photogrammetry was executed following the procedure proposed by Mallison & Wings (2014). More than seventy 3D models were obtained and interpreted by means of color-coded and contour line images, which allow to improve the ichno- logical knowledge of the tracksite. The 3D models of the best-preserved tracks were used for the osteological reconstruction of the trackmakers’ autopodia, supposing the arthral position of the phalangeal pads. Three indirect methods were used to correlate tracks and their trackmakers: (i) synapomorphy-based approach; (ii) phenetic correlation; (iii) coincidence correlation (see Carrano & Wilson, 2001) The final map was produced with different level of knowledge due to the distribution of tracks and current state of site preservation. Furthermore, it represents a complete documentation that will be used for future work of enhancement, preservation and valorization of the tracksite. The ichnotaxonomical review of the quadrupedal trackways led us to emend the diagnosis of Lavinipes cheminii Avanzini et al. (2003) and to assign several other sparse tracks and trackways to L. chemini. The skeletal reconstruction of fore and hind limbs points towards Gongxianosaurus sp. as the most suitable trackmaker of L. cheminii. The herein supposed Laurasian affinity of the Lavini di Marco dinosaur assemblage clashes with the previous hypotheses that always link the Southern Alps sector with the Gondwana mainland