On the Validity of the 0-1 Test for Chaos

In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics

Selfsimilarity and growth in Birkhoff sums for the golden rotation

We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with periodic continued fraction approximations p(n)/q(n), where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of S(q(n),a) with the existence of an experimentally established limit function f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity on the interval [0,1]. The function f satisfies a functional equation f(ax) + (1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n going to infinity can be expressed in terms of the function f.Comment: 14 pages, 8 figure

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Y

Approximation of integral operators using product-convolution expansions

International audienceWe consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on functions is a computationally intensive problem necessary for many practical problems. We analyze a technique called product-convolution expansion: the operator is locally approximated by a convolution, allowing to design fast numerical algorithms based on the fast Fourier transform. We design various types of expansions, provide their explicit rates of approximation and their complexity depending on the time varying impulse response smoothness. This analysis suggests novel wavelet based implementations of the method with numerous assets such as optimal approximation rates, low complexity and storage requirements as well as adaptivity to the kernels regularity. The proposed methods are an alternative to more standard procedures such as panel clustering, cross approximations, wavelet expansions or hierarchical matrices

The theory and method of comparative area studies

Though many now downplay the tension between area studies and disciplinary political science, there has been little substantive guidance on how to accomplish complementarity between their respective approaches. This article seeks to develop the idea of comparative area studies (CAS) as a rubric that maintains the importance of regional knowledge while contributing to general theory building using inductive intra-regional, cross-regional, inter-regional comparison. Treating regions as theoretically-grounded analytical categories, rather than inert or innate geographical entities, can help inform both quantitative and qualitative attempts to build general theory.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

A prospective longitudinal study of Pasireotide in Nelson's syndrome

PURPOSE: Nelson's syndrome is a challenging condition that can develop following bilateral adrenalectomy for Cushing's disease, with high circulating ACTH levels, pigmentation and an invasive pituitary tumor. There is no established medical therapy. The aim of the study was to assess the effects of pasireotide on plasma ACTH and tumor volume in Nelson's syndrome. METHODS: Open labeled multicenter longitudinal trial in three steps: (1) a placebo-controlled acute response test; (2) 1 month pasireotide 300-600 μg s.c. twice-daily; (3) 6 months pasireotide long-acting-release (LAR) 40-60 mg monthly. RESULTS: Seven patients had s.c. treatment and 5 proceeded to LAR treatment. There was a significant reduction in morning plasma ACTH during treatment (mean ± SD; 1823 ± 1286 ng/l vs. 888.0 ± 812.8 ng/l during the s.c. phase vs. 829.0 ± 1171 ng/l during the LAR phase, p < 0.0001). Analysis of ACTH levels using a random intercept linear mixed-random effects longitudinal model showed that ACTH (before the morning dose of glucocorticoids) declined significantly by 26.1 ng/l per week during the 28-week of treatment (95% CI - 45.2 to - 7.1, p < 0.01). An acute response to a test dose predicted outcome in 4/5 patients. Overall, there was no significant change in tumor volumes (1.4 ± 0.9 vs. 1.3 ± 1.0, p = 0.86). Four patients withdrew during the study. Hyperglycemia occurred in 6 patients. CONCLUSIONS: Pasireotide lowers plasma ACTH levels in patients with Nelson's syndrome. A longer period of treatment may be needed to assess the effects of pasireotide on tumor volume. TRIAL REGISTRATION: Clinical Trials.gov ID, NCT01617733