We consider morphological and linear scale spaces on the space R 3 S 2 of 3D positions and orientations naturally embedded in the group SE(3) of 3D rigid body movements. The general motivation for these (convection-)diffusions and erosions is to obtain crossing-preserving fiber enhancement on probability densities defined on the space of positions and orientations. The strength of these enhancements is that they are expressed in a moving frame of reference attached to fiber fragments, allowing us to diffuse along the fibers and to erode orthogonal to them.The linear scale spaces are described by forward Kolmogorov equations of Brownian motions on R 3 S 2 and can be solved by convolution with the corresponding Green's functions. The morphological scale spaces are Bellman equations of cost processes on R 3 S 2 and we show that their viscosity solutions are given by a morphological convolution with the corresponding morphological Green's function. For theoretical underpinning of our scale spaces on R 3 S 2 we introduce Lagrangians and Hamiltonians on R 3 S 2 indexed by a parameter η ∈ [1, ∞). The Hamiltonian induces a Hamilton-Jacobi-Bellman system that coincides with our morphological scale spaces on R 3 S 2 .By means of the logarithm on SE(3) we provide tangible estimates for both the linear-and the morphological Green's functions. We also discuss numerical finite difference upwind schemes for morphological scale spaces (erosions) of Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI), which allow extensions to data-adaptive erosions of DW-MRI.We apply our theory to the enhancement of (crossing) fibres in DW-MRI for imaging water diffusion processes in brain white matter.

Background Current evidence on vertical transmission of severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) and neonatal outcome among exposed newborns is emerging and posing a challenge for preventive interventions. Perinatal transmission to the neonates especially during breastfeeding and rooming in is also relatively unknown. Methods This prospective observational study was conducted in Kalinga Institute of Medical Science (KIMS), Odisha state from 1 st May to 20 th October 2020. A total of 165 neonates born to SARS-CoV-2 infected mothers were enrolled. Real time polymerase chain reaction (RT PCR) testing was done in first 32 neonates in initial 24 hours of life. Results The clinical characteristics of 162 mothers & 165 neonates were analyzed. Mode of delivery was by caesarian section in most (n=103, 60%) cases. Three (3/32, 9.4%) inborn and 6 outborn neonates were SARS-CoV-2 positive. Thirty-eight (23%) babies needed neonatal intensive care. Clinical characteristics of neonates were meconium-stained amniotic fluid (MSAF, [23.63%]), prematurity (16.9%), respiratory distress (10.5%), moderate to severe hypoxic ischemic encephalopathy (3.6%), sepsis (7%) and hyperbilirubinemia (8.7%). Out of 138 stable babies kept on mother side and initiated breast feeding, none of them developed any signs and symptoms attributable to SARS-CoV-2. Five (3%) neonates died in COVID hospital of which one baby was SARS-CoV-2 positive. Conclusion There was an increased rate of incidences of hypoxic ischemic encephalopathy, meconium stained liquor and cesarean section delivery in COVID hospital. We found a possible vertical transmission in 9.4% cases. None of the neonates developed sign and symptoms of SARS-CoV-2 infection during rooming in and breast feeding.

We consider the problem P curve of minimizing L 0 ξ 2 + κ 2 (s) ds for a curve x in R 3 with fixed boundary points and directions. Here, the total length L ≥ 0 is free, s denotes the arclength parameter, κ denotes the absolute curvature of x, and ξ > 0 is constant. We lift problem P curve on R 3 to a sub-Riemannian problem P mec on SE(3)/({0} × SO (2)). Here, for admissible boundary conditions, the spatial projections of sub-Riemannian geodesics do not exhibit cusps and they solve problem P curve . We apply the Pontryagin Maximum Principle (PMP) and prove Liouville integrability of the Hamiltonian system. We derive explicit analytic formulas for such sub-Riemannian geodesics, relying on the co-adjoint orbit structure, an underlying Cartan connection, and the matrix representation of SE(3) arising in the Cartan-matrix. These formulas allow us to extract geometrical properties of the sub-Riemannian geodesics with cuspless projection, such as planarity conditions, explicit bounds on their torsion, and their symmetries. Furthermore, they allow us to parameterize all admissible boundary conditions reachable by geodesics with cuspless spatial projection. Such projections lay in the upper half space. We prove this for most cases, and the rest is checked numerically. Finally, we employ the formulas to numerically solve the boundary value problem, and visualize the set of admissible boundary conditions.

The COVID-19 pandemic has affected 215 countries and territories around the world with 60,187,347 coronavirus cases and 17,125,719 currently infected patients confirmed as of the 25th of November 2020. Currently, many countries are working on developing new vaccines and therapeutic drugs for this novel virus strain, and a few of them are in different phases of clinical trials. The advancement in high-throughput sequence technologies, along with the application of bioinformatics, offers invaluable knowledge on genomic characterization and molecular pathogenesis of coronaviruses. Recent multi-disciplinary studies using bioinformatics methods like sequence-similarity, phylogenomic, and computational structural biology have provided an in-depth understanding of the molecular and biochemical basis of infection, atomic-level recognition of the viral-host receptor interaction, functional annotation of important viral proteins, and evolutionary divergence across different strains. Additionally, various modern immunoinformatic approaches are also being used to target the most promiscuous antigenic epitopes from the SARS-CoV-2 proteome for accelerating the vaccine development process. In this review, we summarize various important computational tools and databases available for systematic sequence-structural study on coronaviruses. The features of these public resources have been comprehensively discussed, which may help experimental biologists with predictive insights useful for ongoing research efforts to find therapeutics against the infectious COVID-19 disease.

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