The topological dimension of type I C*-algebras

While there is only one natural dimension concept for separable, metric spaces, the theory of dimension in noncommutative topology ramifies into different important concepts. To accommodate this, we introduce the abstract notion of a noncommutative dimension theory by proposing a natural set of axioms. These axioms are inspired by properties of commutative dimension theory, and they are for instance satisfied by the real and stable rank, the decomposition rank and the nuclear dimension. We add another theory to this list by showing that the topological dimension, as introduced by Brown and Pedersen, is a noncommutative dimension theory of type I C*-algebras. We also give estimates of the real and stable rank of a type I C*-algebra in terms of its topological dimension.Comment: 20 pages; minor correction

A Pre-Landing Assessment of Regolith Properties at the InSight Landing Site

This article discusses relevant physical properties of the regolith at the Mars InSight landing site as understood prior to landing of the spacecraft. InSight will land in the northern lowland plains of Mars, close to the equator, where the regolith is estimated to be ≥3--5 m thick. These investigations of physical properties have relied on data collected from Mars orbital measurements, previously collected lander and rover data, results of studies of data and samples from Apollo lunar missions, laboratory measurements on regolith simulants, and theoretical studies. The investigations include changes in properties with depth and temperature. Mechanical properties investigated include density, grain-size distribution, cohesion, and angle of internal friction. Thermophysical properties include thermal inertia, surface emissivity and albedo, thermal conductivity and diffusivity, and specific heat. Regolith elastic properties not only include parameters that control seismic wave velocities in the immediate vicinity of the Insight lander but also coupling of the lander and other potential noise sources to the InSight broadband seismometer. The related properties include Poisson’s ratio, P- and S-wave velocities, Young’s modulus, and seismic attenuation. Finally, mass diffusivity was investigated to estimate gas movements in the regolith driven by atmospheric pressure changes. Physical properties presented here are all to some degree speculative. However, they form a basis for interpretation of the early data to be returned from the InSight mission.Additional co-authors: Nick Teanby and Sharon Keda

Semicompactness and dimension of increments

AbstractWe construct two examples the first of which is a Lindelöf, separable and strongly zero- dimensional space the increment of which in any compactification is collectionwise normal, countably paracompact and infinite dimensional. The second example is a Lindelöf, separable, non-semicompact space that has a compactification with discrete increment

The triterpene echinocystic acid and its 3-O-glucoside derivative are revealed as potent and selective glucocorticoid receptor agonists

Glucocorticoids are steroid hormones widely used to control many inflammatory conditions. These effects are primarily attributed to glucocorticoid receptor transrepressional activities but with concomitant receptor transactivation associated with considerable side effects. Accordingly, there is an immediate need for selective glucocorticoid receptor agonists able to dissociate transactivation from transrepression. Triterpenoids have structural similarities with glucocorticoids and exhibit anti-inflammatory and apoptotic activities via mechanisms that are not well-defined. In this study, we examined whether echinocystic acid and its 3-O-glucoside derivative act, at least in part, through the regulation of glucocorticoid receptor and whether they can constitute selective receptor activators. We showed that echinocystic acid and its glucoside induced glucocorticoid receptor nuclear translocation by 75% and 55%. They suppressed the nuclear factor-kappa beta transcriptional activity by 20% and 70%, respectively, whereas they have no glucocorticoid receptor transactivation capability and stimulatory effect on the expression of the phosphoenolopyruvate carboxykinase target gene in HeLa cells. Interestingly, their suppressive effect is diminished in glucocorticoid receptor low level COS-7 cells, verifying the receptor involvement in this process. Induced fit docking calculations predicted favorable binding in the ligand binding domain and structural characteristics which can be considered consistent with the experimental observations. Further, glucocorticoids exert apoptotic activities; we have demonstrated here that the echinocystic acids in combination with the synthetic glucocorticoid, dexamethasone, induce apoptosis. Taken together, our results indicate that echinocystic acids are potent glucocorticoid receptor regulators with selective transrepressional activities (dissociated from transactivation), highlighting the potential of echinocystic acid derivatives as more promising treatments for inflammatory conditions. © 2016 Elsevier Lt

Predictors and clinical significance of progression or regression of asymptomatic carotid stenosis

OBJECTIVE: To determine baseline clinical and ultrasonographic plaque factors predictive of progression or regression of asymptomatic carotid stenosis and the predictive value of changes in stenosis severity on risk of first ipsilateral cerebral or retinal ischemic events (including stroke). METHODS: A total of 1121 patients with asymptomatic carotid stenosis of 50% to 99% in relation to the bulb diameter (European Carotid Surgery Trial [ECST] method) underwent six monthly clinical assessments and carotid duplexes for up to 8 years (mean follow-up, 4 years). Progression or regression was considered present if there was a change of at least one grade higher or lower, respectively, persisting for at least two consecutive examinations. RESULTS: Regression occurred in 43 (3.8%), no change in 856 (76.4%), and progression in 222 (19.8%) patients. Younger age, high grades of stenosis, absence of discrete white areas in the plaque, and taking lipid lowering therapy were independent baseline predictors of increased incidence of regression. High serum creatinine, male gender, not taking lipid lowering therapy, low grades of stenosis, and increased plaque area were independent baseline predictors of progression. One hundred and thirty first ipsilateral cerebral or retinal ischemic events, including 59 strokes, occurred. Forty (67.8%) of the strokes occurred in patients whose stenosis was unchanged, 19 (32.2%) in those with progression, and zero in those with regression. For the entire cohort, the 8-year cumulative ipsilateral cerebral ischemic stroke rate was zero in patients with regression, 9% if the stenosis was unchanged, and 16% if there was progression (average annual stroke rates of 0%, 1.1%, and 2.0%, respectively; log-rank, P = .05; relative risk in patients with progression, 1.92; 95% confidence interval, 1.14-3.25). For patients with baseline stenosis 70% to 99% in relation to the distal internal carotid (North American Symptomatic Carotid Endarterectomy Trial [NASCET] method), in the absence of progression (n = 349), the 8-year cumulative ipsilateral cerebral ischemic stroke rate was 12%. In the presence of progression (n = 77), it was 21% (average annual stroke rates of 1.5% and 2.6%, respectively; log-rank, P = .34). Only nine (30%) of the 30 strokes occurred in the progression group. CONCLUSIONS: Progressive asymptomatic carotid stenosis identified a subgroup with about twice the risk of ipsilateral stroke compared with those without progression. However, the clinical value of screening for progression simply for selecting patients for carotid procedures is limited because of the low frequency of progression and its relatively low associated stroke rate. The cost effectiveness of screening for change in stenosis severity to better direct current optimal medical treatment needs testing