Data depth and floating body

Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the depth stands as a generalization of a measure of symmetry for convex sets, well studied in geometry. Under a mild assumption, the upper level sets of the halfspace depth coincide with the convex floating bodies used in the definition of the affine surface area for convex bodies in Euclidean spaces. These connections enable us to partially resolve some persistent open problems regarding theoretical properties of the depth

Information Security Synthesis in Online Universities

Information assurance is at the core of every initiative that an organization executes. For online universities, a common and complex initiative is maintaining user lifecycle and providing seamless access using one identity in a large virtual infrastructure. To achieve information assurance the management of user privileges affected by events in the user's identity lifecycle needs to be the determining factor for access control. While the implementation of identity and access management systems makes this initiative feasible, it is the construction and maintenance of the infrastructure that makes it complex and challenging. The objective of this paper1 is to describe the complexities, propose a practical approach to building a foundation for consistent user experience and realizing security synthesis in online universities.Comment: 20 page

Magnetoresistance in two-component systems

Two-component systems with equal concentrations of electrons and holes exhibit non-saturating, linear magnetoresistance in classically strong magnetic fields. The effect is predicted to occur in finite-size samples at charge neutrality in both disorder- and interaction-dominated regimes. The phenomenon originates in the excess quasiparticle density developing near the edges of the sample due to the compensated Hall effect. The size of the boundary region is of the order of the electron-hole recombination length that is inversely proportional to the magnetic field. In narrow samples and at strong enough magnetic fields, the boundary region dominates over the bulk leading to linear magnetoresistance. Our results are relevant for semimetals and narrow-band semiconductors including most of the topological insulators.Comment: 11 pages, 3 figure

Initial Stages of Sodium Deposition onto Au(111) from [MPPip][TFSI]: An In‐Situ STM Study for Sodium‐Ion Battery Electrolytes

Sodium-ion batteries are promising candidates for post-lithium-ion batteries. While sodium has a less negative standard electrode potential compared to lithium, it is still a strong reducing agent. Ionic liquids are suitable solvents for sodium metal batteries, since metallic sodium is very reactive, particularly with water and molecules containing acidic hydrogen atoms. In this study, the initial stages of electrodeposition of sodium on Au(111) from N-methyl-N-propylpiperidinium [MPPip] bis(trifluoromethanesulfonyl)imide [TFSI] were studied using voltammetry and in-situ scanning tunnelling microscopy. Four subsequent underpotential deposition stages were observed: (i) nucleation at the Au(111) reconstruction elbows, followed by (ii) growth of small monoatomically high islands that form (iii) a smooth layer via coalescence, and (iv) further island growth on top of the existing layers. The electrocrystallisation mode changed from smooth layer formation to 3D growth, resulting in cauliflower-like structures. The deposition process was accompanied by simultaneous alloy formation

Digital Orthopaedics: A Glimpse Into the Future in the Midst of a Pandemic.

BackgroundThe response to COVID-19 catalyzed the adoption and integration of digital health tools into the health care delivery model for musculoskeletal patients. The change, suspension, or relaxation of Medicare and federal guidelines enabled the rapid implementation of these technologies. The expansion of payment models for virtual care facilitated its rapid adoption. The authors aim to provide several examples of digital health solutions utilized to manage orthopedic patients during the pandemic and discuss what features of these technologies are likely to continue to provide value to patients and clinicians following its resolution.ConclusionThe widespread adoption of new technologies enabling providers to care for patients remotely has the potential to permanently change the expectations of all stakeholders about the way care is provided in orthopedics. The new era of Digital Orthopaedics will see a gradual and nondisruptive integration of technologies that support the patient's journey through the successful management of their musculoskeletal disease