Invariant Peano curves of expanding Thurston maps

We consider Thurston maps, i.e., branched covering maps $f\colon S^2\to S^2$ that are postcritically finite. In addition, we assume that $f$ is expanding in a suitable sense. It is shown that each sufficiently high iterate $F=f^n$ of $f$ is semi-conjugate to $z^d\colon S^1\to S^1$, where $d$ is equal to the degree of $F$. More precisely, for such an $F$ we construct a Peano curve $\gamma\colon S^1\to S^2$ (onto), such that $F\circ \gamma(z) = \gamma(z^d)$ (for all $z\in S^1$).Comment: 63 pages, 12 figure

Tamari Lattices and the symmetric Thompson monoid

We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page

Environmental and social determinants of acute rheumatic fever:a longitudinal cohort study

Acute rheumatic fever (ARF), an auto-immune response to a group A Streptococcus infection and precursor to rheumatic heart disease (RHD), remains endemic in many socio-economically disadvantaged settings. A Global Resolution on ARF and RHD was recently adopted at the 71st World Health Assembly where governments committed to improving efforts to prevent and control ARF and RHD. To inform these efforts, the objectives of this study were to examine associations between childhood ARF in the UK between 1958 and 1969 and a range of environmental and social factors. Of 17 416 children from the nationally representative birth cohort of the National Child Development Study, ARF was reported in 23 children during early childhood (between birth and the 7-year follow-up) and in 29 additional children during middle childhood (between the 7- and 11-year follow-ups). Risk factors associated with ARF in both early and middle childhood were: a large family size; attendance at a private nursery or class; a history of nephritis, kidney or urinary tract infections; and a history of throat or ear infections. Risk factors for ARF in early childhood alone were families with fathers in a professional or semi-professional occupation and families who moved out of their local neighbourhood. Risk factors in late childhood alone included overcrowding and free school meals. These data suggest that prevention strategies in ARF endemic settings may be enhanced by targeting, for example, new members entering a community and children in environments of close contact, such as a nursery or shared bedrooms

The nature of weather and climate impacts in the energy sector

The power sector’s meteorological information needs are diverse and cover many different distinct applications and users. Recognising this diversity, it is important to understand the general nature of how weather and climate influence the energy sector and the implications they have for quantitative impact modelling. Using conceptual examples and illustrations from recent research, this chapter argues that the traditional ‘transfer function’ approach that is common to many industrial applications of weather and climate science—whereby weather can be directly mapped to an energy impact—is inadequate for many important power system applications (such as price forecasting and system operations and planning). The chapter concludes by arguing that a deeper understanding of how meteorological impacts in the energy sector are modelled is required

On normalish subgroups of the R. Thompson groups

Funding: UK EPSRC grant EP/R032866/1Results in C∗ algebras, of Matte Bon and Le Boudec, and of Haagerup and Olesen, apply to the R. Thompson groups F ≤ T ≤ V. These results together show that F is non-amenable if and only if T has a simple reduced C∗-algebra. In further investigations into the structure of C∗-algebras, Breuillard, Kalantar, Kennedy, and Ozawa introduce the notion of a normalish subgroup of a group G. They show that if a group G admits no non-trivial finite normal subgroups and no normalish amenable subgroups then it has a simple reduced C∗-algebra. Our chief result concerns the R. Thompson groups F < T < V; we show that there is an elementary amenable group E < F (where here, E ≅ ...)≀Z)≀Z)≀Z) with E normalish in V. The proof given uses a natural partial action of the group V on a regular language determined by a synchronizing automaton in order to verify a certain stability condition: once again highlighting the existence of interesting intersections of the theory of V with various forms of formal language theory.Postprin

Standardization of epidemiological surveillance of acute rheumatic fever

Acute rheumatic fever (ARF) is a multiorgan inflammatory disorder that results from the body’s autoimmune response to pharyngitis or a skin infection caused by Streptococcus pyogenes (Strep A). Acute rheumatic fever mainly affects those in low- and middle-income nations, as well as in indigenous populations in wealthy nations, where initial Strep A infections may go undetected. A single episode of ARF puts a person at increased risk of developing long-term cardiac damage known as rheumatic heart disease. We present case definitions for both definite and possible ARF, including initial and recurrent episodes, according to the 2015 Jones Criteria, and we discuss current tests available to aid in the diagnosis. We outline the considerations specific to ARF surveillance methodology, including discussion on where and how to conduct active or passive surveillance (eg, early childhood centers/schools, households, primary healthcare, administrative database review), participant eligibility, and the surveillance population. Additional considerations for ARF surveillance, including implications for secondary prophylaxis and follow-up, ARF registers, community engagement, and the impact of surveillance, are addressed. Finally, the core elements of case report forms for ARF, monitoring and audit requirements, quality control and assurance, and the ethics of conducting surveillance are discussed

A gene signature for post-infectious chronic fatigue syndrome

Background: At present, there are no clinically reliable disease markers for chronic fatigue syndrome. DNA chip microarray technology provides a method for examining the differential expression of mRNA from a large number of genes. Our hypothesis was that a gene expression signature, generated by microarray assays, could help identify genes which are dysregulated in patients with post-infectious CFS and so help identify biomarkers for the condition. Methods: Human genome-wide Affymetrix GeneChip arrays (39,000 transcripts derived from 33,000 gene sequences) were used to compare the levels of gene expression in the peripheral blood mononuclear cells of male patients with post-infectious chronic fatigue (n = 8) and male healthy control subjects (n = 7). Results: Patients and healthy subjects differed significantly in the level of expression of 366 genes. Analysis of the differentially expressed genes indicated functional implications in immune modulation, oxidative stress and apoptosis. Prototype biomarkers were identified on the basis of differential levels of gene expression and possible biological significance Conclusion: Differential expression of key genes identified in this study offer an insight into the possible mechanism of chronic fatigue following infection. The representative biomarkers identified in this research appear promising as potential biomarkers for diagnosis and treatment

Standardization of epidemiological surveillance of rheumatic heart disease

Rheumatic heart disease (RHD) is a long-term sequela of acute rheumatic fever (ARF), which classically begins after an untreated or undertreated infection caused by Streptococcus pyogenes (Strep A). RHD develops after the heart valves are permanently damaged due to ARF. RHD remains a leading cause of morbidity and mortality in young adults in resource-limited and low- and middle-income countries. This article presents case definitions for latent, suspected, and clinical RHD for persons with and without a history of ARF, and details case classifications, including differentiating between definite or borderline according to the 2012 World Heart Federation echocardiographic diagnostic criteria. This article also covers considerations specific to RHD surveillance methodology, including discussions on echocardiographic screening, where and how to conduct active or passive surveillance (eg, early childhood centers/schools, households, primary healthcare), participant eligibility, and the surveillance population. Additional considerations for RHD surveillance, including implications for secondary prophylaxis and follow-up, RHD registers, community engagement, and the negative impact of surveillance, are addressed. Finally, the core elements of case report forms for RHD, monitoring and audit requirements, quality control and assurance, and the ethics of conducting surveillance are discussed

Climate Dynamics: A Network-Based Approach for the Analysis of Global Precipitation

Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool to investigate the statistical interdependence of many interacting elements, is used here to analyze the spatial dynamics of annual precipitation over seventy years (1941-2010). The precipitation network is built associating a node to a geographical region, which has a temporal distribution of precipitation, and identifying possible links among nodes through the correlation function. The precipitation network reveals significant spatial variability with barely connected regions, as Eastern China and Japan, and highly connected regions, such as the African Sahel, Eastern Australia and, to a lesser extent, Northern Europe. Sahel and Eastern Australia are remarkably dry regions, where low amounts of rainfall are uniformly distributed on continental scales and small-scale extreme events are rare. As a consequence, the precipitation gradient is low, making these regions well connected on a large spatial scale. On the contrary, the Asiatic South-East is often reached by extreme events such as monsoons, tropical cyclones and heat waves, which can all contribute to reduce the correlation to the short-range scale only. Some patterns emerging between mid-latitude and tropical regions suggest a possible impact of the propagation of planetary waves on precipitation at a global scale. Other links can be qualitatively associated to the atmospheric and oceanic circulation. To analyze the sensitivity of the network to the physical closeness of the nodes, short-term connections are broken. The African Sahel, Eastern Australia and Northern Europe regions again appear as the supernodes of the network, confirming furthermore their long-range connection structure. Almost all North-American and Asian nodes vanish, revealing that extreme events can enhance high precipitation gradients, leading to a systematic absence of long-range patterns