Beurling's Theorem for Valuation Hilbert Modules and Several Complex Variables

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert spaces of analytic functions in several complex variables, including $H^2$ of the polydisk the ball, and bounded symmetric domains, and weighted $A^2$ spaces on complex analytic manifolds.Comment: 30 pages. v2: Changed some terminology and added material on $R_1$ inner functions. This version (v3): Added additional matrial on $R_1$ inner functions and their relation to $A^p_\alpha$ inner functions. arXiv admin note: text overlap with arXiv:2108.12272, arXiv:2109.0069

A Proof of the Invariant Subspace Conjecture for Separable Hilbert Spaces

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.Comment: 16 pages. Depends on our paper arXiv:2202.02674, and includes a review of needed results from that paper. This version ncludes Per Enflo referenc

Georges Nzongola-Ntalaja and Margaret C. Lee (eds) The State and Democracy in Africa (Harare: A APS Books, 1997) pp. x, 232. ISBN 0-7974-1745-1 (paper)

Book review of The State and Democracy in Africa

Transforming Graph Representations for Statistical Relational Learning

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type, (iii) estimating their weight or importance, and (iv) systematically constructing their relevant features. We motivate our taxonomy through detailed examples and use it to survey and compare competing approaches for each of these tasks. We also discuss general conditions for transforming links, nodes, and features. Finally, we highlight challenges that remain to be addressed

Mitochondria and neuroprotection in stroke: Cationic arginine-rich peptides (CARPs) as a novel class of mitochondria-targeted neuroprotective therapeutics

Stroke is the second leading cause of death globally and represents a major cause of devastating long-term disability. Despite sustained efforts to develop clinically effective neuroprotective therapies, presently there is no clinically available neuroprotective agent for stroke. As a central mediator of neurodamaging events in stroke, mitochondria are recognised as a critical neuroprotective target, and as such, provide a focus for developing mitochondrial-targeted therapeutics. In recent years, cationic arginine-rich peptides (CARPs) have been identified as a novel class of neuroprotective agent with several demonstrated mechanisms of action, including their ability to target mitochondria and exert positive effects on the organelle. This review provides an overview on neuronal mitochondrial dysfunction in ischaemic stroke pathophysiology and highlights the potential beneficial effects of CARPs on mitochondria in the ischaemic brain following stroke

Poly-arginine peptide R18D reduces neuroinflammation and functional deficits following traumatic brain injury in the Long-Evans rat

We have previously demonstrated that the poly-arginine peptide R18 can improve histological and functional outcomes following traumatic brain injury (TBI) in the Sprague–Dawley rat. Since D-enantiomer peptides are often exploited in pharmacology for their increased stability and potency, the present study compared the effects of R18 and its D-enantiomer, R18D, following TBI in the Long-Evans rat. Following a closed-head impact delivered via a weight-drop apparatus, peptide was administered at a dose of 1000 nmol/kg at 30 min after TBI. Treatment with R18D, but not R18 resulted in significant reductions in sensorimotor (p = 0.026) and vestibulomotor (p = 0.049) deficits as measured by the adhesive tape removal and rotarod tests. Furthermore, treatment with R18 and R18D resulted in a significant reduction in brain protein levels of the astrocytic marker, glial fibrillary acidic protein (p = 0.019 and 0.048, respectively). These results further highlight the beneficial effects of poly-arginine peptides in TBI, however additional studies are required to confirm these positive effects

Proteomic analysis of cortical neuronal cultures treated with poly-arginine peptide-18 (R18) and exposed to glutamic acid excitotoxicity

Poly-arginine peptide-18 (R18) has recently emerged as a highly effective neuroprotective agent in experimental stroke models, and is particularly efficacious in protecting cortical neurons against glutamic acid excitotoxicity. While we have previously demonstrated that R18 can reduce excitotoxicity-induced neuronal calcium influx, other molecular events associated with R18 neuroprotection are yet to investigated. Therefore, in this study we were particularly interested in protein expression changes in R18 treated neurons subjected to excitotoxicity. Proteomic analysis was used to compare protein expression patterns in primary cortical neuronal cultures subjected to: (i) R18-treatment alone (R18); (ii) glutamic acid excitotoxic injury (Glut); (iii) R18-treatment and glutamic acid injury (R18 + Glut); (iv) no treatment (Cont). Whole cell lysates were harvested 24 h post-injury and subjected to quantitative proteomic analysis (iTRAQ), coupled with liquid chromatography-tandem mass spectrometry (LC-MS/ MS) and subsequent bioinformatic analysis of differentially expressed proteins (DEPs). Relative to control cultures, R18, Glut, and R18 + Glut treatment resulted in the detection of 5, 95 and 14 DEPs respectively. Compared to Glut alone, R18 + Glut revealed 98 DEPs, including 73 proteins whose expression was also altered by treatment with Glut and/or R18 alone, as well as 25 other uniquely regulated proteins. R18 treatment reversed the up- or down-regulation of all 73 Glut-associated DEPs, which included proteins involved in mitochondrial integrity, ATP generation, mRNA processing and protein translation. Analysis of protein-protein interactions of the 73 DEPs showed they were primarily associated with mitochondrial respiration, proteasome activity and protein synthesis, transmembrane trafficking, axonal growth and neuronal differentiation, and carbohydrate metabolism. Identified protein pathways associated with proteostasis and energy metabolism, and with pathways involved in neurodegeneration. Collectively, the findings indicate that R18 neuroprotection following excitotoxicity is associated with preservation of neuronal protein profiles, and differential protein expression that assists in maintaining mitochondrial function and energy production, protein homeostasis, and membrane trafficking

Array concepts for solid-state and vacuum microelectronics millimeter-wave generation

The authors have proposed that the increasing demand for contact watt-level coherent sources in the millimeter- and submillimeter-wave region can be satisfied by fabricating two-dimensional grids loaded with oscillators and multipliers for quasi-optical coherent spatial combining of the outputs of large numbers of low-power devices. This was first demonstrated through the successful fabrication of monolithic arrays with 2000 Schottky diodes. Watt-level power outputs were obtained in doubling to 66 GHz. In addition, a simple transmission-line model was verified with a quasi-optical reflectometer that measured the array impedance. This multiplier array work is being extended to novel tripler configurations using blocking barrier devices. The technique has also been extended to oscillator configurations where the grid structure is loaded with negative-resistance devices. This was first demonstrated using Gunn devices. More recently, a 25-element MESFET grid oscillating at 10 GHz exhibited power combining and self-locking. Currently, this approach is being extended to a 100-element monolithic array of Gunn diodes. This same approach should be applicable to planar vacuum electron devices such as the submillimeter-wave BWO (backward wave oscillator) and vacuum FET

An appraisal of the thermal decomposition mechanisms of ILs as potential lubricants

Ionic liquid (IL) lubricants are rapidly seeing increased use as either base lubricants or additives for a wide range of functionalities. This study considers the thermal stability of the ILs with the emphasis being their use as potential lubricants. The effect of IL chemistry, including anion chain length, cation chain length, anion type, and cation type, on their thermal stability is studied. The decomposition mechanism as a function of time and temperature is considered. Five ILs are studied by utilising both thermogravimetric analysis (TGA) for the dynamic thermal decomposition and Fourier transform IR spectroscopy (FTIR) for the static thermal decomposition. For static thermal decomposition, both time and temperature are varied. The results show that the variation of IL chemistry directly influences their thermal stability. The increase of either cation or anion chain length decreases their thermal stability. Both anion and cation type have a significant influence on the thermal stability

Imaging Polarimeter Arrays for Near-Millimeter Waves

An integrated-circuit antenna array has been developed that images both polarization and intensity. The array consists of a row of antennas that lean alternately left and right, creating two interlaced sub-arrays that respond to different polarizations. The arrays and the bismuth bolometer detectors are made by a photoresist shadowing technique that requires only one photolithographic mask. The array has measured polarization at a wavelength of 800 µm with an absolute accuracy of 0.8° and a relative precision of 7 arc min. and has demonstrated nearly diffraction-Iimited resolutiort of a 20° step in polarization