Probabilistic frames: An overview

Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of probabilistic frames, and we characterize one of their subclasses in terms of minimizers of some appropriate potential function. In addition, we survey a range of areas where probabilistic frames, albeit, under different names, appear. These areas include directional statistics, the geometry of convex bodies, and the theory of t-designs

On the unification of gravity and electromagnetism

Available from British Library Document Supply Centre-DSC:DXN010743 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Extremal Problems . . . OF CONVEX BODIES

Let K be a convex body in R n and let Wi(K), i = 1,..., n − 1 be its quermassintegrals. We study minimization problems of the form min{Wi(T K) | T ∈ SLn} and show that bodies which appear as solutions of such problems satisfy isotropic conditions or even admit an isotropic characterization for appropriate measures. This shows that several well known positions of convex bodies which play an important role in the local theory may be described in terms of classical convexity as isotropic ones. We provide new applications of this point of view for the minimal mean width position

Dynamic carotid plaque imaging using ultrasonography

Objective: Dynamic image analysis of carotid plaques has demonstrated that during systole and early diastole, all plaque components will move in the same direction (concordant motion) in some plaques. However, in others, different parts of the plaque will move in different directions (discordant motion). The aim of our study was (1) to determine the prevalence of discordant motion in symptomatic and asymptomatic plaques, (2) to develop a measurement of the severity of discordant motion, and (3) to determine the correlation between the severity of discordant motion and symptom prevalence. Methods: A total of 200 patients with 204 plaques resulting in 50% to 99% stenosis (112 asymptomatic and 92 symptomatic plaques) had video recordings available of the plaque motion during 10 cardiac cycles. Video tracking was performed using Farneback's method, which relies on frame comparisons. In our study, these were performed at 0.1-second intervals. The maximum angular spread (MAS) of the motion vectors at 10-pixel intervals in the plaque area was measured in degrees. Plaques were classified as concordant (MAS, <70°), moderately discordant (MAS, 70°-120°), and discordant (MAS, >120°). Results: Motion was discordant in 89.1% of the symptomatic plaques but only in 17.9% of asymptomatic plaques (P < .001). The prevalence of symptoms increased with increasing MAS. For a MAS >120°, the hazard ratio for the presence of symptoms was 47.7 (95% confidence interval, 18.1-125.6) compared with the rest of the plaques after adjustment for the degree of stenosis and mean pixel motion. The area under the receiver operating characteristic curve for the prediction of the presence of symptoms using the MAS was 0.876 (95% confidence interval, 0.823-0.929). The use of the median MAS (120°) as a cutoff point classified 86% of the plaques correctly (sensitivity, 81.4%; specificity, 91.2%; positive predictive value, 90.2%; and negative predictive value, 83.0%). Conclusions: The use of the MAS value to identify asymptomatic plaques at increased risk of developing symptoms and, in particular, stroke should be tested in prospective studies. © 2020 Society for Vascular Surger

Rheumatoid Arthritis: Atherosclerosis Imaging and Cardiovascular Risk Assessment Using Machine and Deep Learning–Based Tissue Characterization

Purpose of the Review: Rheumatoid arthritis (RA) is a chronic, autoimmune disease which may result in a higher risk of cardiovascular (CV) events and stroke. Tissue characterization and risk stratification of patients with rheumatoid arthritis are a challenging problem. Risk stratification of RA patients using traditional risk factor–based calculators either underestimates or overestimates the CV risk. Advancements in medical imaging have facilitated early and accurate CV risk stratification compared to conventional cardiovascular risk calculators. Recent Finding: In recent years, a link between carotid atherosclerosis and rheumatoid arthritis has been widely discussed by multiple studies. Imaging the carotid artery using 2-D ultrasound is a noninvasive, economic, and efficient imaging approach that provides an atherosclerotic plaque tissue–specific image. Such images can help to morphologically characterize the plaque type and accurately measure vital phenotypes such as media wall thickness and wall variability. Intelligence-based paradigms such as machine learning– and deep learning–based techniques not only automate the risk characterization process but also provide an accurate CV risk stratification for better management of RA patients. Summary: This review provides a brief understanding of the pathogenesis of RA and its association with carotid atherosclerosis imaged using the B-mode ultrasound technique. Lacunas in traditional risk scores and the role of machine learning–based tissue characterization algorithms are discussed and could facilitate cardiovascular risk assessment in RA patients. The key takeaway points from this review are the following: (i) inflammation is a common link between RA and atherosclerotic plaque buildup, (ii) carotid ultrasound is a better choice to characterize the atherosclerotic plaque tissues in RA patients, and (iii) intelligence-based paradigms are useful for accurate tissue characterization and risk stratification of RA patients. © 2019, Springer Science+Business Media, LLC, part of Springer Nature

Biomechanical Modeling to Improve Coronary Artery Bifurcation Stenting Expert Review Document on Techniques and Clinical Implementation

Cardiovascular Aspects of Radiolog