Radar sounding using the Cassini altimeter waveform modeling and Monte Carlo approach for data inversion observations of Titan's seas

Recently, the Cassini RADAR has been used as a sounder to probe the depth and constrain the composition of hydrocarbon seas on Saturn's largest moon, Titan. Altimetry waveforms from observations over the seas are generally composed of two main reflections: the first from the surface of the liquid and the second from the seafloor. The time interval between these two peaks is a measure of sea depth, and the attenuation from the propagation through the liquid is a measure of the dielectric properties, which is a sensitive property of liquid composition. Radar measurements are affected by uncertainties that can include saturation effects, possible receiver distortion, and processing artifacts, in addition to thermal noise and speckle. To rigorously treat these problems, we simulate the Ku-band altimetry echo received from Titan's seas using a two-layer model, where the surface is represented by a specular reflection and the seafloor is modeled using a facet-based synthetic surface. The simulation accounts for the thermal noise, speckle, analog-to-digital conversion, and block adaptive quantization and allows for possible receiver saturation. We use a Monte Carlo method to compare simulated and observed waveforms and retrieve the probability distributions of depth, surface/subsurface intensity ratio, and subsurface roughness for the individual double-peaked waveform of Ligeia Mare acquired by the Cassini spacecraft in May 2013. This new analysis provides an update to the Ku-band attenuation and results in a new estimate for its loss tangent and composition. We also demonstrate the ability to retrieve bathymetric information from saturated altimetry echoes acquired over Ontario Lacus in December 2008

Liquid filled canyons on Titan

In May 2013 the Cassini RADAR altimeter observed channels in Vid Flumina, a drainage network connected to Titan’s second largest hydrocarbon sea, Ligeia Mare. Analysis of these altimeter echoes shows that the channels are located in deep (up to ~570 m), steep-sided, canyons and have strong specular surface reflections that indicate they are currently liquid filled. Elevations of the liquid in these channels are at the same level as Ligeia Mare to within a vertical precision of about 0.7 m, consistent with the interpretation of drowned river valleys. Specular reflections are also observed in lower order tributaries elevated above the level of Ligeia Mare, consistent with drainage feeding into the main channel system

BAFF Index and CXCL13 levels in the cerebrospinal fluid associate respectively with intrathecal IgG synthesis and cortical atrophy in multiple sclerosis at clinical onset

Abstract Background B lymphocytes are thought to play a relevant role in multiple sclerosis (MS) pathology. The in vivo analysis of intrathecally produced B cell-related cytokines may help to clarify the mechanisms of B cell recruitment and immunoglobulin production within the central nervous system (CNS) in MS. Methods Paired cerebrospinal fluid (CSF) and serum specimens from 40 clinically isolated syndrome suggestive of MS or early-onset relapsing-remitting MS patients (CIS/eRRMS) and 17 healthy controls (HC) were analyzed for the intrathecal synthesis of IgG (quantitative formulae and IgG oligoclonal bands, IgGOB), CXCL13, BAFF, and IL-21. 3D-FLAIR, 3D-DIR, and 3D-T1 MRI sequences were applied to evaluate white matter (WM) and gray matter (GM) lesions and global cortical thickness (gCTh). Results Compared to HC, CIS/eRRMS having IgGOB (IgGOB+, 26 patients) had higher intrathecal IgG indexes ( p \u2009<\u20090.01), lower values of BAFF Index (11.9\u2009\ub1\u20096.1 vs 17.5\u2009\ub1\u20095.2, p \u2009<\u20090.01), and higher CSF CXCL13 levels (27.7\u2009\ub1\u200933.5 vs 0.9\u2009\ub1\u20091.5, p \u2009<\u20090.005). In these patients, BAFF Index but not CSF CXCL13 levels inversely correlated with the intrathecal IgG synthesis ( r \u2009>\u20090.5 and p \u2009<\u20090.05 for all correlations). CSF leukocyte counts were significantly higher in IgGOB+ compared to IgGOB\u2212 ( p \u2009<\u20090.05) and HC ( p \u2009<\u20090.01), and correlated to CSF CXCL13 concentrations ( r 0.77, p \u2009<\u20090.001). The gCTh was significantly lower in patients with higher CSF CXCL13 levels (2.41\u2009\ub1\u20090.1 vs 2.49\u2009\ub1\u20090.1\ua0mm, p \u2009<\u20090.05), while no difference in MRI parameters of WM and GM pathology was observed between IgGOB+ and IgGOB\u2212. Conclusions The intrathecal IgG synthesis inversely correlated with BAFF Index and showed no correlation with CSF CXCL13. These findings seem to indicate that intrathecally synthesized IgG are produced by long-term PCs that have entered the CNS from the peripheral blood, rather than produced by PCs developed in the meningeal follicle-like structures (FLS). In this study, CXCL13 identifies a subgroup of MS patients characterized by ..

Interpolation with the polynomial kernels

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their lack of strict positive definiteness. In particular they do not enjoy the usual property of unisolvency for arbitrary point sets, which is one of the key properties used to build kernel-based interpolation methods. This paper is devoted to establish some initial results for the study of these kernels, and their related interpolation algorithms, in the context of approximation theory. We will first prove necessary and sufficient conditions on point sets which guarantee the existence and uniqueness of an interpolant. We will then study the Reproducing Kernel Hilbert Spaces (or native spaces) of these kernels and their norms, and provide inclusion relations between spaces corresponding to different kernel parameters. With these spaces at hand, it will be further possible to derive generic error estimates which apply to sufficiently smooth functions, thus escaping the native space. Finally, we will show how to employ an efficient stable algorithm to these kernels to obtain accurate interpolants, and we will test them in some numerical experiment. After this analysis several computational and theoretical aspects remain open, and we will outline possible further research directions in a concluding section. This work builds some bridges between kernel and polynomial interpolation, two topics to which the authors, to different extents, have been introduced under the supervision or through the work of Stefano De Marchi. For this reason, they wish to dedicate this work to him in the occasion of his 60th birthday

Special Issue dedicated to Stefano De Marchi on the occasion of his 60th birthday

As colleagues and friends we dedicate this issue to Stefano De Marchi on the occasion of his 60th birthday, publishing works of some of his collaborators. Stefano has made many important contributions to approximation theory and beyond and is one of the “founding fathers” of this journal. Here we briefly reminisce and recount some of our experiences with Stefano in the spirit of the occasion

Early red nucleus atrophy in relapse-onset multiple sclerosis

No study has investigated red nucleus (RN) atrophy in multiple sclerosis (MS) despite cerebellum and its connections are elective sites of MS-related pathology. In this study, we explore RN atrophy in early MS phases and its association with cerebellar damage (focal lesions and atrophy) and physical disability. Thirty-seven relapse-onset MS (RMS) patients having mean age of 35.6 ± 8.5 (18–56) years and mean disease duration of 1.1 ± 1.5 (0–5) years, and 36 age- and sex-matched healthy controls (HC) were studied. Cerebellar and RN lesions and volumes were analyzed on 3 T-MRI images. RMS did not differ from HC in cerebellar lobe volumes but significantly differed in both right (107.84 ± 13.95 mm3 vs. 99.37 ± 11.53 mm3, p =.019) and left (109.71 ± 14.94 mm3 vs. 100.47 ± 15.78 mm3, p =.020) RN volumes. Cerebellar white matter lesion volume (WMLV) inversely correlated with both right and left RN volumes (r = −.333, p =.004 and r = −.298, p =.010, respectively), while no correlation was detected between RN volumes and mean cortical thickness, cerebellar gray matter lesion volume, and supratentorial WMLV (right RN: r = −.147, p =.216; left RN: r = −.153, p =.196). Right, but not left, RN volume inversely correlated with midbrain WMLV (r = −.310, p =.008), while no correlation was observed between whole brainstem WMLV and either RN volumes (right RN: r = −.164, p =.164; left RN: r = −.64, p =.588). Finally, left RN volume correlated with vermis VIIb (r =.297, p =.011) and right interposed nucleus (r =.249, p =.034) volumes. We observed RN atrophy in early RMS, likely resulting from anterograde axonal degeneration starting in cerebellar and midbrain WML. RN atrophy seems a promising marker of neurodegeneration and/or cerebellar damage in RMS

The SSDC Role in the LICIACube Mission: Data Management and the MATISSE Tool

Light Italian Cubesat for Imaging of Asteroids (LICIACube) is an Italian mission managed by the Italian Space Agency (ASI) and part of the NASA Double Asteroid Redirection Test (DART) planetary defense mission. Its main goals are to document the effects of the DART impact on Dimorphos, the secondary member of the (65803) Didymos binary asteroid system, characterizing the shape of the target body and performing dedicated scientific investigations on it. Within this framework, the mission Science Operations Center will be managed by the Space Science Data Center (ASI-SSDC), which will have the responsibility of processing, archiving, and disseminating the data acquired by the two LICIACube onboard cameras. In order to better accomplish this task, SSDC also plans to use and modify its scientific webtool Multi-purpose Advanced Tool for Instruments for the solar system Exploration (MATISSE), making it the primary tool for the LICIACube data analysis, thanks to its advanced capabilities for searching and visualizing data, particularly useful for the irregular shapes common to several small bodies

Momentum transfer from the DART mission kinetic impact on asteroid Dimorphos

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on 26 September 2022 as a planetary defence test1. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defence, intended to validate kinetic impact as a means of asteroid deflection. Here we report a determination of the momentum transferred to an asteroid by kinetic impact. On the basis of the change in the binary orbit period2, we find an instantaneous reduction in Dimorphos’s along-track orbital velocity component of 2.70 ± 0.10 mm s−1, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact3,4. For a Dimorphos bulk density range of 1,500 to 3,300 kg m−3, we find that the expected value of the momentum enhancement factor, β, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg m−3, β=3.61−0.25+0.19(1σ). These β values indicate that substantially more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos