The maximum dimension of a subspace of nilpotent matrices of index 2

A matrix M is nilpotent of index 2 if M² = 0. Let V be a space of nilpotent n x n matrices of index 2 over a field k where card k > n and suppose that r is the maximum rank of any matrix in V. The object of this paper is to give an elementary proof of the fact that dim V ≤ r(n − r). We show that the inequality is sharp and construct all such subspaces of maximum dimension. We use the result to find the maximum dimension of spaces of anti-commuting matrices and zero subalgebras of special Jordan Algebras

An inverse-breathing encapsulation system for cell delivery

Cell encapsulation represents a promising therapeutic strategy for many hormone-deficient diseases such as type 1 diabetes (T1D). However, adequate oxygenation of the encapsulated cells remains a challenge, especially in the poorly oxygenated subcutaneous site. Here, we present an encapsulation system that generates oxygen (O2) for the cells from their own waste product, carbon dioxide (CO2), in a self-regulated (i.e., "inverse breathing") way. We leveraged a gas-solid (CO2-lithium peroxide) reaction that was completely separated from the aqueous cellular environment by a gas permeable membrane. O2 measurements and imaging validated CO2-responsive O2 release, which improved cell survival in hypoxic conditions. Simulation-guided optimization yielded a device that restored normoglycemia of immunocompetent diabetic mice for over 3 months. Furthermore, functional islets were observed in scaled-up device implants in minipigs retrieved after 2 months. This inverse breathing device provides a potential system to support long-term cell function in the clinically attractive subcutaneous site. © 2021 The Authors.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Hydrological processes interconnecting the two largest watersheds of South America from multi-decadal to inter-annual time scales: A critical review

The hydrological aspects of the Amazon and the La Plata basins are interconnected through southward moisture transport performed by the Low-Level Jet east of the Andes and the South Atlantic Convergence Zone. Remote effects of sea surface temperature variability in the Pacific and the Atlantic are of varied periodicities, from multi-decadal to inter-annual time scales. Major oscillations thus far detected are Atlantic Multi-decadal Oscillation, Pacific Multi-decadal Oscillation, North Atlantic Oscillation, Atlantic Dipole, Antarctic Oscillation, and the El Niño Southern Oscillation. In the multi-decadal, inter-decadal and decadal time scales, the effects of climate variability over the hydrological processes that interconnect the Amazon and La Plata watersheds are felt predominantly in the South American Monsoon season, while on the inter-annual scale the effects vary along the year. The hydrological memory in Amazonian soils is also responsible for the inter-annual variability of hydrology of the Amazon Basin. Due to the effects of soil water on evapotranspiration, the hydrological memory can affect the supply of moisture to the La Plata Basin, influencing the inter-annual variability of this basin. The implications of the observed oscillations to the hydrological and climatological variability in the two basins are discussed and synthesized in this article. Hypotheses for future research are formulated. © 2019 Royal Meteorological Societ