Schmidt games and Markov partitions

Let T be a C^2-expanding self-map of a compact, connected, smooth, Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff dimension. Our correction allows us to strengthen the theorem. Combining the correction with Schmidt games, we generalize the theorem in dimension one: given a point x in M, the set of points whose forward orbit closures miss x is a winning set.Comment: 32 page

Configurations of the circle of Willis: a computed tomography angiography based study on a Polish population

The aim of the study was to investigate the distribution of the circle of Willis variants in Polish population by means of computed tomography angiography (CTA). The results were then analysed and compared with another study that used similar methods but that was carried out on an ethnically distinct population. Patients presenting with intracranial pathology were excluded from the initial study population. In total, 250 CTA belonging to 129 female and 121 male patients were reviewed. A modified classification system of the circle was proposed, which took into consideration the anterior and the posterior aspects of the circle individually. The typical variant of Willis’s circle occurred in 16.80% of cases. The anterior and the posterior portions of the circle were normal in 47.20% and 26.80% of the patients respectively. As forthe anterior part, lack of the anterior communicating artery was the most frequent abnormality (22.80%). Bilateral absence of posterior communicating arteries was the most common anomaly in the posterior part of the circle (29.20%). This type of anomaly was also the most common, when taking into consideration the entire circle (12.00%). There were statistically significant differences between the age groupsand genders when considering the occurrence of an incomplete circle. Overall, a substantial proportion of patients manifested clinically important variants that were incapable of providing collateral circulation. Comparison with other imaging-based and cadaveric studies revealed noticeable differences, that may have resulted from the variable technical features of other studies or other factors such as the ethnical origins of the studied populations

Variations and morphometric analysis of the proximal segment of the superior cerebellar artery

Introduction The superior cerebral artery is a clinically significant vessel, but little is known about its radiological anatomy. The aim of this study was to describe the anatomical variations of the proximal segment of the superior cerebellar artery using Computed Tomography Angiography. Materials and methods The study group consisted of 200 subjects (54.5% female, mean age±SD 56.2±17.2 years) that had undergone head Computed Tomography Angiography. Subjects with any intracranial pathologies were excluded. Images in Maximum Intensity Projections were used to study the anatomical anomalies of the superior cerebellar artery. Results In 200 subject 388 superior cerebellar arteries were found. Twelve (3.09%) SCAs were duplicated in 11 patients and all originated from the basilar artery. In 8 (4.00%) patients the superior cerebellar artery was absent. The origin of the SCA was most often bilateral, mainly from the basilar artery (76.29%). The superior cerebellar artery diameter, measured at the site of the origin, was statistically significantly different depending on the place of the origin: wider when originating from the basilar artery as a single vessel (1.48±0.42mm vs. 1.34±0.52mm; p=0.03) and narrower when originating as duplicated one (1.38±0.48mm vs. 1.46±0.44mm; p=0.55). Conclusion Superior cerebellar artery usually originates bilaterally from the basilar artery as a single trunk. Its diameter is significantly wider in that type in comparison to other anatomical variations

Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha

A note on a generalized cohomology equation

We give a necessary and sufficient condition for the solvability of a generalized cohomology equation, for an ergodic endomorphism of a probability measure space, in the space of measurable complex functions. This generalizes a result obtained in [7]

A remark on the ergodic theorem

The article contains no abstrac