Measure valued solutions of sub-linear diffusion equations with a drift term

In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing $C^1$ function $\beta$ with $\lim_{r\to +\infty} \beta(r)<+\infty$. By using tools of optimal transport, we will show that this kind of problems is well posed in the class of nonnegative Borel measures with finite mass $m$ and finite quadratic momentum and it is the gradient flow of a suitable entropy functional with respect to the so called $L^2$-Wasserstein distance. Due to the degeneracy of diffusion for large densities, concentration of masses can occur, whose support is transported by the drift. We shall show that the large-time behavior of solutions depends on a critical mass ${m}_{\rm c}$, which can be explicitely characterized in terms of $\beta$ and of the drift term. If the initial mass is less then ${m}_{\rm c}$, the entropy has a unique minimizer which is absolutely continuous with respect to the Lebesgue measure. Conversely, when the total mass $m$ of the solutions is greater than the critical one, the steady state has a singular part in which the exceeding mass ${m} - {m}_{\rm c}$ is accumulated.Comment: 30 page

Toward third order ghost imaging with thermal light

Recently it has been suggested that an enhancement in the visibility of ghost images obtained with thermal light can be achieved exploiting higher order correlations [3]. This paper reports on the status of an higher order ghost imaging experiment carried on at INRIM labs exploiting a pseudo-thermal source and a CCD camera.Comment: To be published in Proceedings of Recent advances in Foundations of Quantum Mechanics and Quantum Informatio

Kernel estimates for nonautonomous Kolmogorov equations with potential term

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term

Generation of large scale digital evaluation models via synthetic aperture radar interferometry

We investigate the possibility to generate a large-scale Digital Elevation Model by applying the Synthetic Aperture Radar interferometry technique and using tandem data acquired by the ERS-1/ERS-2 sensors. The presented study is mainly focused on the phase unwrapping step that represents the most critical point of the overall processing chain. In particular, we concentrate on the unwrapping problems related to the use of a large ERS tandem data set that, in order to be unwrapped, must be partitioned. The paper discusses the inclusion of external information (even rough) of the scene topography, the application of a region growing unwrapping technique and the insertion of possible constraints on the phase to be retrieved in order to minimize the global unwrapping errors. Our goal is the generation of a digital elevation model relative to an area of 300 km by 100km located in the southern part of Italy. Comparisons between the achieved result and a precise digital terrain model, relative to a smaller area, are also included

Joint multi-baseline SAR interferometry

We propose a technique to provide interferometry by combining multiple images of the same area. This technique differs from the multi-baseline approach in literature as (a) it exploits all the images simultaneously, (b) it performs a spectral shift preprocessing to remove most of the decorrelation, and (c) it exploits distributed targets. The technique is mainly intended for DEM generation at centimetric accuracy, as well as for differential interferometry. The problem is framed in the contest of single-input multiple-output (SIMO) channel estimation via the cross-relations (CR) technique and the resulting algorithm provides significant improvements with respect to conventional approaches based either on independent analysis of single interferograms or multi-baselines phase analysis of single pixels of current literature, for those targets that are correlated in all the images, like for long-term coherent areas, or for acquisitions taken with a short revisit time (as those gathered with future satellite constellations)

Full characterization of Gaussian bipartite entangled states by a single homodyne detector

We present the full experimental reconstruction of Gaussian entangled states generated by a type--II optical parametric oscillator (OPO) below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of OPO signals and represent a tool for quantum technology based on continuous variable entanglement.Comment: 4 pages, 3 figures, slightly longer version of published PR

The combination of DInSAR and facility damage data for the updating of slow-moving landslide inventory maps at medium scale

Abstract. Testing innovative procedures and techniques to update landslide inventory maps is a timely topic widely discussed in the scientific literature. In this regard remote sensing techniques – such as the Synthetic Aperture Radar Differential Interferometry (DInSAR) – can provide a valuable contribution to studies concerning slow-moving landslides in different geological contexts all over the world. In this paper, DInSAR data are firstly analysed via an innovative approach aimed at enhancing both the exploitation and the interpretation of remote sensing information; then, they are complemented with the results of an accurate analysis of survey-recorded damage to facilities due to slow-moving landslides. In particular, after being separately analysed to provide independent landslide movement indicators, the two datasets are combined in a DInSAR-Damage matrix which can be used to update the state of activity of slow-moving landslides. Moreover, together with the information provided by geomorphological maps, the two datasets are proven to be useful in detecting unmapped phenomena. The potentialities of the adopted procedure are tested in an area of southern Italy where slow-moving landslides are widespread and accurately mapped by using geomorphological criteria

The FDA “black box” warning on antidepressant suicide risk in young adults: More harm than benefits?

The decision made in the year 2004 by the U.S. Food and Drug Administration (FDA) to require a boxed warning on antidepressants regarding the risk of suicidality in young adults still represents a matter of controversy. The FDA warning was grounded on industry-sponsored trials carried one decade ago or earlier. However, within the past decade, an increasing number of reports have questioned the actual validity of the FDA warning, especially considering a decline in the prescription of the antidepressant drugs associated with an increase in the rate of suicidal events among people with severe depression. The present report provides an overview of the FDA black box warning, also documenting two Major Depressive Disorder patients whose refusal to undergo a pharmacological antidepressant treatment possibly led to an increased risk for suicidal behaviors. The concerns raised by the FDA black box warning need to be considered in real-world clinical practice, stating the associated clinical and public health implications

Systematic analysis of SNR in bipartite Ghost Imaging with classical and quantum light

We present a complete and exhaustive theory of signal-to-noise-ratio in bipartite ghost imaging with classical (thermal) and quantum (twin beams) light. The theory is compared with experiment for both twin beams and thermal light in a certain regime of interest