A Phase Transition for Circle Maps and Cherry Flows

We study $C^{2}$ weakly order preserving circle maps with a flat interval. The main result of the paper is about a sharp transition from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval. We prove that the non-wandering set has zero Hausdorff dimension in the case of degenerate geometry and it has Hausdorff dimension strictly greater than zero in the case of bounded geometry. Our results about circle maps allow to establish a sharp phase transition in the dynamics of Cherry flows

Reconciling Contemporary Approaches to School Attendance and School Absenteeism: Toward Promotion and Nimble Response, Global Policy Review and Implementation, and Future Adaptability (Part 1)

School attendance is an important foundational competency for children and adolescents, and school absenteeism has been linked to myriad short- and long-term negative consequences, even into adulthood. Many efforts have been made to conceptualize and address this population across various categories and dimensions of functioning and across multiple disciplines, resulting in both a rich literature base and a splintered view regarding this population. This article (Part 1 of 2) reviews and critiques key categorical and dimensional approaches to conceptualizing school attendance and school absenteeism, with an eye toward reconciling these approaches (Part 2 of 2) to develop a roadmap for preventative and intervention strategies, early warning systems and nimble response, global policy review, dissemination and implementation, and adaptations to future changes in education and technology. This article sets the stage for a discussion of a multidimensional, multi-tiered system of supports pyramid model as a heuristic framework for conceptualizing the manifold aspects of school attendance and school absenteeism

WroNG -- Wroclaw Neutrino Generator of events for single pion production

We constructed a new Monte Carlo generator of events for neutrino CC single pion production on free nucleon targets. The code uses dynamical models of the DIS with the PDFs modified according to the recent JLab data and of the Delta excitation. A comparison with experimental data was done in three channels for the total cross sections and for the distributions of events in invariant hadronic mass.Comment: 6 pages, 13 figures, Presented by J.T. Sobczyk at the 3rd International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region, 17-21 March, Gran Sasso(Italy),to appear in the Proceeding

Singular measures in circle dynamics

Critical circle homeomorphisms have an invariant measure totally singular with respect to the Lebesgue measure. We prove that singularities of the invariant measure are of Holder type. The Hausdorff dimension of the invariant measure is less than 1 but greater than 0

Complex bounds for multimodal maps: bounded combinatorics

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps.Comment: 20 pages, 3 figure