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The binary asteroids are of current interest in the modern dynamics as there have been up to 50 discoveries of binaries. Estimates are that about 20% of near-Earth asteroids may be binary asteroids. Nevertheless the known asteroids pairs are rather rare objects in the Solar System. There are a number of papers studying the various aspects of asteroid pair dynamics. In this paper we study some stationary motions in the system of binary asteroid. Using the model for the first time suggested in [1], we approximate the bigger asteroid by the dumbbell-shaped rigid body. Moreover we assume that the smaller asteroid has mass close to zero. It was shown in [1] that the motion equations for the considered system have the stationary solutions corresponding to the smaller asteroid's equilibria relative to the axis of the regular precession and the dumbbell rod These equilibria similar to the libration points in the Restricted Circular Problem of Three Bodies (RCP3B). There are two types of such equilibria. The equal distances from the dumbbell endpoints characterize the equilibria of the first type, therefore we shall name them 'the libration points similar to Lagrangian' or 'the triangular libration points' (TLPs) by analogy to a classical problem. At difference with RCP3B there are two or one TLPs or they do not exist. Equilibria of the second type in something are similar to the Eulerian libration points. They belong to the plane containing the bigger asteroid's angular momentum and the dumbbell rod. Moreover, these equilibria belong to the strip bounded by straight lines crossing the dumbbell endpoints and being perpendicular to angular momentum. Therefore we shall name them 'the coplanar libration points'(CLP). The CLPs coordinates are computed by following procedure. Two algebraic equations are deduced. One of these equations determines the curve containing all CLPs. We say that this curve is 'the Geometrical locus of CLPs' (GL). The second equation allows to locate CLPs in GL. Studying evolution of CLPs in GL it can be proved that the number of CLPs varies from 3 up to 7, but if the dumbbell consist of equal spheres then only the odd number of CLPs is possible. However, if the dumbbell is asymmetric then the number of CLPs can be equal 4 or 6 for some rare situations. [ABSTRACT FROM AUTHOR]

Background and Purpose: Previous studies have shown the presence of ulceration in atherosclerotic plaque either by categorizing the plaque as complex (irregular morphology with ulcers) or smooth or by quantifying the number of ulcers observed in a specific region of interest. The aim of this study was to quantify carotid total ulcer volume by 3-dimensional ultrasound to investigate the relationship of total ulcer volume to vascular events (strokes, transient ischemic attack, myocardial infarction, revascularization, or death because of cardiovascular reasons)., Methods: In total, 349 at-risk subjects provided written informed consent to carotid 3-dimensional ultrasound and were analyzed for ulcerations. Ulcer volume was defined as a distinct discontinuity in an atherosclerotic plaque, with a volume≥1.00 mm3 as measured using manual segmentation. The sum of the volumes of all ulcers seen in both carotids was the total ulcer volume. Participants were monitored for ≤5 years for outcomes, including cardiovascular events and death., Results: Kaplan-Meier survival analysis showed that subjects with total ulcer volume≥5 mm3 experienced a significantly higher risk of developing stroke, transient ischemic attack, or death (P=0.009) and of developing stroke/transient ischemic attack/death/myocardial infarction/revascularization (P=0.017). Lower ulcer volumes did not predict events nor did ulcer depth., Conclusions: Volume of carotid ulceration on 3-dimensional ultrasound predicts cardiovascular events. In addition to improving risk stratification, ulceration is a potential therapeutic target.

Temporal lobe epilepsy (TLE), a subset of the seizure disorder family, represents a complex neuropsychiatric illness, where the neurological presentation may be complemented by varying severity of affective, behavioral, psychotic, or personality abnormalities, which, in turn, may not only lead to misdiagnosis, but also affect the management. This paper outlines a spectrum of mental health presentations, including psychosis, mood, anxiety, panic, and dissociative states, associated with epilepsy that make the correct diagnosis a challenge.

Carotid plaque surface irregularity and ulcerations play an important role in the risk of ischemic stroke. Ulcerated or fissured plaque, characterized by irregular surface morphology, exposes thrombogenic materials to the bloodstream, possibly leading to life- or brain-threatening thrombosis and embolization. Therefore, the quantification of plaque surface irregularity is important to identify high-risk plaques that would likely lead to vascular events. Although a number of studies have characterized plaque surface irregularity using subjective classification schemes with two or more categories, only a few have quantified surface irregularity using an objective and continuous quantity, such as Gaussian or mean curvature. In this work, our goal was to use both Gaussian and mean curvatures for identifying ulcers from 3D carotid ultrasound (US) images of human subjects. Before performing experiments using patient data, we verified the numerical accuracy of the surface curvature computation method using discrete spheres and tori with different sampling intervals. We also showed that three ulcers of the vascular phantom with 2 mm, 3 mm and 4 mm diameters were associated with high Gaussian and mean curvatures, and thus, were easily detected. Finally, we demonstrated the application of the proposed method for detecting ulcers on luminal surfaces, which were segmented from the 3D US images acquired for two human subjects.