On digit frequencies in beta-expansions

We study the sets DF(β) of digit frequencies of β-expansions of numbers in [0,1]. We show that DF(β) is a compact convex set with countably many extreme points which varies continuously with β; that there is a full measure collection of non-trivial closed intervals on each of which DF(β) mode locks to a constant polytope with rational vertices; and that the generic digit frequency set has infinitely many extreme points, accumulating on a single non-rational extreme point whose components are rationally independent

Symbol ratio minimax sequences in the lexicographic order

Consider the space of sequences of letters ordered lexicographically. We study the set of all maximal sequences for which the asymptotic proportions of the letters are prescribed, where a sequence is said to be maximal if it is at least as great as all of its tails. The infimum of is called the -infimax sequence, or the -minimax sequence if the infimum is a minimum. We give an algorithm which yields all infimax sequences, and show that the infimax is not a minimax if and only if it is the -infimax for every in a simplex of dimension 1 or greater. These results have applications to the theory of rotation sets of beta-shifts and torus homeomorphisms

Modular termination verification for non-blocking concurrency

© Springer-Verlag Berlin Heidelberg 2016.We present Total-TaDA, a program logic for verifying the total correctness of concurrent programs: that such programs both terminate and produce the correct result. With Total-TaDA, we can specify constraints on a thread’s concurrent environment that are necessary to guarantee termination. This allows us to verify total correctness for nonblocking algorithms, e.g. a counter and a stack. Our specifications can express lock- and wait-freedom. More generally, they can express that one operation cannot impede the progress of another, a new non-blocking property we call non-impedance. Moreover, our approach is modular. We can verify the operations of a module independently, and build up modules on top of each other

Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator

Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) fifteen years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast with most nonlinear systems, where chaos has been actively tracked and found. This situation is probably linked to the high sensitivity of the TROPO to perturbations, which adversely affects stationary operation at high power. We report the experimental observation in this system of a burst of irregular behavior of duration 80 microseconds. Although the system is highly nonstationary over this time interval, a topological analysis allows us to extract a clearcut signature of deterministic chaos from a time series segment of only 9 base cycles (3 microseconds). This result suggests that nonstationarity is not necessarily an obstacle to the characterization of chaos

“It’s Just Addictive People That Make Addictive Videos”: Children’s Understanding of and Attitudes towards Influencer Marketing of Food and Beverages by YouTube Video Bloggers

Exposure to influencer marketing of foods and beverages high in fat, sugar, and/or salt (HFSS) increases children’s immediate intake. This study qualitatively explored children’s understanding of, and attitudes towards, this marketing, to elucidate potential mechanisms through which exposure affects behavior. In six focus groups (n = 4) children (10–11 years) were shown a YouTube video featuring influencer marketing of an HFSS product. Inductive thematic analysis identified six themes from children’s discussions of this marketing: (1) YouTubers fill a gap in children’s lives, (2) the accessibility of YouTubers increases children’s understanding of their actions, (3) influencer marketing impacts all—the influencer, the brand, and the viewer, (4) attitudes towards influencer marketing are most affected by a YouTuber’s familiarity, (5) YouTuber influencer marketing is effective because they are not ‘strangers’, (6) children feel able to resist influencer marketing of HFSS products. Children had an understanding of the persuasive intent of this marketing, and although most were sceptical, familiar YouTubers elicited particularly sympathetic attitudes. Children felt affected by influencer marketing of HFSS products, but believed they were able to resist it. Beyond theoretical insight, this study adds to the growing body of evidence to suggest children’s exposure to HFSS influencer marketing should be reduced

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Periodic orbits of period 3 in the disc

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.Comment: 7 page