Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

Clostridium difficile: a healthcare associated infection of unknown significance in adults in sub-Saharan Africa

Background: Clostridium difficile infection (CDI) causes a high burden of disease in high-resource healthcare systems, with significant morbidity, mortality and financial implications. CDI is a healthcare-associated infection for which the primary risk factor is antibiotic usage and it is the leading cause of bacterial diarrhoea in HIV infected patients in USA. Little is known about the disease burden of CDI in sub-Saharan Africa, where HIV and healthcare associated infection have a higher prevalence and antibiotic usage is less restricted. Aim: To review published literature on CDI in sub-Saharan Africa, highlighting areas for future research. Methods: English language publications since 1995 were identified from online databases (PubMed, Medline, Google Scholar, SCOPUS) and personal collections of articles, using combinations of keywords to include C. difficile, Africa and HIV. Results: Ten relevant studies were identified. There is considerable variation in methodology to assess for carriage of toxigenic C. difficile and its associations. Eight studies report carriage of toxigenic C. difficile. Three (of four) studies found an association with antibiotic usage. One (of four) studies showed an association with HIV infection. One study showed no association with degree of immunosuppression in HIV. Two (of three) studies showed an association between carriage of toxigenic C. difficile and diarrhoeal illness. Conclusion: Whilst the carriage of toxigenic C. difficile is well described in sub-Saharan Africa, the impact of CDI in the Region remains poorly l understood and warrants high quality research

Dust Lifting Through Surface Albedo Changes at Jezero Crater, Mars

We identify temporal variations in surface albedo at Jezero crater using first-of-their-kind high-cadence in-situ measurements of reflected shortwave radiation during the first 350 sols of the Mars 2020 mission. Simultaneous Mars Environmental Dynamics Analyzer (MEDA) measurements of pressure, radiative fluxes, winds, and sky brightness indicate that these albedo changes are caused by dust devils under typical conditions and by a dust storm at Ls ∼ 155°. The 17% decrease in albedo caused by the dust storm is one order of magnitude larger than the most apparent changes caused during quiescent periods by dust devils. Spectral reflectance measurements from Mastcam-Z images before and after the storm indicate that the decrease in albedo is mainly caused by dust removal. The occurrence of albedo changes is affected by the intensity and proximity of the convective vortex, and the availability and mobility of small particles at the surface. The probability of observing an albedo change increases with the magnitude of the pressure drop (ΔP): changes were detected in 3.5%, 43%, and 100% of the dust devils with ΔP 2.5 Pa and ΔP > 4.5 Pa, respectively. Albedo changes were associated with peak wind speeds above 15 m·s−1. We discuss dust removal estimates, the observed surface temperature changes coincident with albedo changes, and implications for solar-powered missions. These results show synergies between multiple instruments (MEDA, Mastcam-Z, Navcam, and the Supercam microphone) that improve our understanding of aeolian processes on Mars.This research has been funded by the Comunidad de Madrid Project S2018/NMT-4291 (TEC2SPACE-CM), by the Spanish State Research Agency (AEI) Project MDM-2017-0737 Unidad de Excelencia “María de Maeztu”- Centro de Astrobiología (CSIC/INTA), by the Spanish Ministry of Science and Innovation (MCIN)/State Agency of Research (10.13039/501100011033) project RTI2018-098728-B-C31, and by the project PID2021-126719OB-C41, funded by MCIN/AEI/10.13039/501100011033/FEDER, UE. RH, ASL and AM were supported by Grant PID2019-109467GB-I00 funded by MCIN/AEI/10.13039/501100011033/. Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). We want to thank J. Bell for processing Mastcam-Z projections showing the entire TIRS FOV and to S. Navarro and the entire team for generating the processed wind sensor data

Nocturnal Turbulence at Jezero Crater as Determined From MEDA Measurements and Modeling

Mars 2020 Mars Environmental Dynamics Analyzer (MEDA) instrument data acquired during half of a Martian year (Ls 13°–180°), and modeling efforts with the Mars Regional Atmospheric Modeling System (MRAMS) and the Mars Climate Database (MCD) enable the study of the seasonal evolution and variability of nocturnal atmospheric turbulence at Jezero crater. Nighttime conditions in Mars's Planetary Boundary Layer are highly stable because of strong radiative cooling that efficiently inhibits convection. However, MEDA nighttime observations of simultaneous rapid fluctuations in horizontal wind speed and air temperatures suggest the development of nighttime turbulence in Jezero crater. Mesoscale modeling with MRAMS also shows a similar pattern and enables us to investigate the origins of this turbulence and the mechanisms at play. As opposed to Gale crater, less evidence of turbulence from breaking mountain wave activity was found in Jezero during the period studied with MRAMS. On the contrary, the model suggests that nighttime turbulence at Jezero crater is explained by increasingly strong wind shear produced by the development of an atmospheric bore-like disturbance at the nocturnal inversion interface. These atmospheric bores are produced by downslope winds from the west rim undercutting a strong low-level jet aloft from ∼19:00 to 01:00 LTST and from ∼01:00 LTST to dawn when undercutting weak winds aloft. The enhanced wind shear leads to a reduction in the Richardson number and an onset of mechanical turbulence. Once the critical Richardson Number is reached (Ri ∼ <0.25), shear instabilities can mix warmer air aloft down to the surface.This research was funded by Grant RTI2018-098728-B-C31 and PN2021-PID2021-126719OB-C41 by the Spanish Ministry of Science and Innovation/State Agency of Research MCIN/AEI/10.13039/501100011033. AM, ASL, TR, and RH were supported by Grant PID2019-109467GB-I00 funded by MCIN/AEI/10.13039/501100011033/and by Grupos Gobierno Vasco IT1366-19. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). The JPL co-authors acknowledge funding from NASA's Space Technology Mission Directorate and the Science Mission Directorate. CEN was supported by funding from the Mars 2020 mission, part of the NASA Mars Exploration Program

Seismic constraints from a Mars impact experiment using InSight and Perseverance

NASA’s InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission has operated a sophisticated suite of seismology and geophysics instruments on the surface of Mars since its arrival in 2018. On 18 February 2021, we attempted to detect the seismic and acoustic waves produced by the entry, descent and landing of the Perseverance rover using the sensors onboard the InSight lander. Similar observations have been made on Earth using data from both crewed1,2 and uncrewed3,4 spacecraft, and on the Moon during the Apollo era5, but never before on Mars or another planet. This was the only seismic event to occur on Mars since InSight began operations that had an a priori known and independently constrained timing and location. It therefore had the potential to be used as a calibration for other marsquakes recorded by InSight. Here we report that no signal from Perseverance’s entry, descent and landing is identifiable in the InSight data. Nonetheless, measurements made during the landing window enable us to place constraints on the distance–amplitude relationships used to predict the amplitude of seismic waves produced by planetary impacts and place in situ constraints on Martian impact seismic efficiency (the fraction of the impactor kinetic energy converted into seismic energy)

The sound of a Martian dust devil

Dust devils (convective vortices loaded with dust) are common at the surface of Mars, particularly at Jezero crater, the landing site of the Perseverance rover. They are indicators of atmospheric turbulence and are an important lifting mechanism for the Martian dust cycle. Improving our understanding of dust lifting and atmospheric transport is key for accurate simulation of the dust cycle and for the prediction of dust storms, in addition to being important for future space exploration as grain impacts are implicated in the degradation of hardware on the surface of Mars. Here we describe the sound of a Martian dust devil as recorded by the SuperCam instrument on the Perseverance rover. The dust devil encounter was also simultaneously imaged by the Perseverance rover's Navigation Camera and observed by several sensors in the Mars Environmental Dynamics Analyzer instrument. Combining these unique multi-sensorial data with modelling, we show that the dust devil was around 25m large, at least 118m tall, and passed directly over the rover travelling at approximately 5ms-1. Acoustic signals of grain impacts recorded during the vortex encounter provide quantitative information about the number density of particles in the vortex. The sound of a Martian dust devil was inaccessible until SuperCam microphone recordings. This chance dust devil encounter demonstrates the potential of acoustic data for resolving the rapid wind structure of the Martian atmosphere and for directly quantifying wind-blown grain fluxes on Mars.We are most grateful for the support of the Mars 2020 project team, including hardware and operation teams. This project was supported in the US by the NASA Mars Exploration Program, and in France by CNES. It is based on observations with SuperCam embarked on Perseverance (Mars2020). The research carried out at the Jet Propulsion Laboratory, California Institute of Technology, is under a contract with the National Aeronautics and Space Administration (80NM0018D0004). The JPL co-author (M.T.) acknowledges funding from NASA’s Space Technology Mission Directorate and the Science Mission Directorate. A. V-R is supported by the Spanish State Research Agency (AEI) Project No. MDM-2017-0737 Unidad de Excelencia “María de Maeztu”- Centro de Astrobiología (INTA-CSIC), and by the Comunidad de Madrid Project S2018/NMT-4291 (TEC2SPACE-CM). R.H. and A.S-L. were supported by Grant PID2019-109467GB-I00 funded by MCIN/AEI/10.13039/501100011033/ and by Grupos Gobierno Vasco IT1742-22. A.M. was supported by Grant PRE2020-092562 funded by MCIN/AEI/10.13039/501100011033 and by “ESF Investing in your future”. R.L. acknowledges InSight PSP Grant 80NSSC18K1626 as well as the Mars 2020 project. B.C. is supported by the Director’s Postdoctoral Fellowship from the Los Alamos National Laboratory, grant 20210960PRD3. JA.RM., M.M, J.T and J.G-E were supported by MCIN/AEI’s Grant RTI2018-098728-B-C31