236 research outputs found
Ergodicity of polygonal slap maps
Polygonal slap maps are piecewise affine expanding maps of the interval
obtained by projecting the sides of a polygon along their normals onto the
perimeter of the polygon. These maps arise in the study of polygonal billiards
with non-specular reflections laws. We study the absolutely continuous
invariant probabilities of the slap maps for several polygons, including
regular polygons and triangles. We also present a general method for
constructing polygons with slap maps having more than one ergodic absolutely
continuous invariant probability.Comment: 17 pages, 6 figure
Hyperbolic polygonal billiards with finitely many ergodic SRB measures
We study polygonal billiards with reflection laws contracting the reflected
angle towards the normal. It is shown that if a polygon does not have parallel
sides facing each other, then the corresponding billiard map has finitely many
ergodic SRB measures whose basins cover a set of full Lebesgue measure.Comment: 26 pages, 2 figure
Characterizing videos, audience and advertising in Youtube channels for kids
Online video services, messaging systems, games and social media services are
tremendously popular among young people and children in many countries. Most of
the digital services offered on the internet are advertising funded, which
makes advertising ubiquitous in children's everyday life. To understand the
impact of advertising-based digital services on children, we study the
collective behavior of users of YouTube for kids channels and present the
demographics of a large number of users. We collected data from 12,848 videos
from 17 channels in US and UK and 24 channels in Brazil. The channels in
English have been viewed more than 37 billion times. We also collected more
than 14 million comments made by users. Based on a combination of text-analysis
and face recognition tools, we show the presence of racial and gender biases in
our large sample of users. We also identify children actively using YouTube,
although the minimum age for using the service is 13 years in most countries.
We provide comparisons of user behavior among the three countries, which
represent large user populations in the global North and the global South
Portal Cavernoma Cholangiopathy Secondary to Polycythemia Vera: Case Report and Echoendoscopic Findings
info:eu-repo/semantics/publishedVersio
Ergodic properties of polygonal billiards with strongly contracting reflection laws
We consider convex polygonal billiards with a reflection law that contracts the reflection angle towards the normal. Polygonal billiards with orthogonal reflections are called slap maps. For polygons without parallel sides facing each other, the slap map has a finite number of ergodic absolutely continuous invariant probability measures. We show that any billiard with a strongly contracting reflection law has the same number of ergodic SRB measures with the same mixing periods as the ergodic absolutely continuous invariant probabilities of its corresponding slap map. The case of billiards in regular polygons and triangles is studied in detail
Demystifying endoscopic retrograde cholangiopancreatography (ERCP) during pregnancy
Background: For many years, ERCP was avoided in pregnancy given the concerns regarding the adverse
effects that, with special focus on radiation, could occur in the developing fetus. However, the
postponement or rejection of ERCP in pregnant women, may lead to a higher risk for mother and fetus,
especially when the indication is unequivocal, namely cholangitis, biliary pancreatitis and symptomatic
choledocholithiasis.
Summary and key messages: This review aims to summarize the scarce literature on the subject in order to
plan ERCP in pregnancy with the highest safety. The use of techniques that reduce radiation and increase
the protection of pregnant women allow radiation levels far below the safety limits.
We also discuss the various alternatives of ERCP without radiation. EUS can eliminate the need for ERCP
with doubtful choledocholithiasis and plan the best approach in those with previous evidence. The possibility of performing “ERCP” with a linear echoendoscope uniquely under ultrasound control has been described. Conversely, the two-step strategy (initial sphincterotomy with stent placement without fluoroscopy and after delivery, ERCP with lithiasis extraction) proved to be safe obviating fluoroscopy. In conclusion, ERCP can be performed in pregnancy safely and effectively with minimal radiation or even no-radiation at all.info:eu-repo/semantics/publishedVersio
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