The arithmetic-geometric scaling spectrum for continued fractions

To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric scaling. We will completely determine its multifractal spectrum by means of a number theoretical free energy function and show that the Hausdorff dimension of sets consisting of irrationals with the same scaling exponent coincides with the Legendre transform of this free energy function. Furthermore, we identify the asymptotic of the local behaviour of the spectrum at the right boundary point and discuss a connection to the set of irrationals with continued fraction digits exceeding a given number which tends to infinity.Comment: 22 pages, 1 figur

The epidemiology of pertussis in Germany: past and present

<p>Abstract</p> <p>Background</p> <p>Current and past pertussis epidemiology in the two parts of Germany is compared in the context of different histories of vaccination recommendations and coverage to better understand patterns of disease transmission.</p> <p>Methods</p> <p>Available regional pertussis surveillance and vaccination coverage data, supplemented by a literature search for published surveys as well as official national hospital and mortality statistics, were analyzed in the context of respective vaccination recommendations from 1964 onwards.</p> <p>Results</p> <p>Routine childhood pertussis vaccination was recommended in the German Democratic Republic (GDR) from 1964 and in former West German states (FWG) from 1969, but withdrawn from 1974–1991 in FWG. Pertussis incidence declined to <1 case/100.000 inhabitants in GDR prior to reunification in 1991, while in FWG, where pertussis was not notifiable after 1961, incidence was estimated at 160–180 cases/100.000 inhabitants in the 1970s-1980s. Despite recommendations for universal childhood immunization in 1991, vaccination coverage decreased in former East German States (FEG) and increased only slowly in FWG. After introduction of acellular pertussis vaccines in 1995, vaccination coverage increased markedly among younger children, but remains low in adolescents, especially in FWG, despite introduction of a booster vaccination for 9–17 year olds in 2000. Reported pertussis incidence increased in FEG to 39.3 cases/100.000 inhabitants in 2007, with the proportion of adults increasing from 20% in 1995 to 68% in 2007. From 2004–2007, incidence was highest among 5–14 year-old children, with a high proportion fully vaccinated according to official recommendations, which did not include a preschool booster until 2006. Hospital discharge statistics revealed a ~2-fold higher pertussis morbidity among infants in FWG than FEG.</p> <p>Conclusion</p> <p>The shift in pertussis morbidity to older age groups observed in FEG is similar to reports from other countries with longstanding vaccination programs and suggests that additional booster vaccination may be necessary beyond adolescence. The high proportion of fully vaccinated cases in older children in FEG suggests waning immunity 5–10 years after primary immunisation in infancy. The higher incidence of pertussis hospitalisations in infants suggests a stronger force of infection in FWG than FEG. Nationwide pertussis reporting is required for better evaluation of transmission patterns and vaccination policy in both parts of Germany.</p

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Acoustic risk balancing by marine mammals : anthropogenic noise can influence the foraging decisions by seals

Funding: Natural Environment Research Council (Grant Number(s): NE/J004251/1, NE/R015007/1)1. Avoidance of anthropogenic sounds has been measured in many species. The results, which are typically based on observations in limited exposure contexts, are frequently used to inform policy and the regulation of industrial activities. However, the occurrence and magnitude of avoidance may be a consequence of complex risk-balancing decisions made by animals. The importance of the factors in decision-making, such as perceived risks associated with the sounds or prey quantity and quality during sound exposure, is unknown. 2. Here we address this knowledge gap by measuring the relative influence of perceived –risk of a sound (silence, pile driving, and a tidal turbine) and prey patch quality on decision-making and foraging success in grey seals Halichoerus grypus. 3. Seals were given access to two underwater ‘prey patches’ in an experimental pool where fish were delivered at controlled rates to simulate a low-density (LD) and a high-density (HD) prey patch. Acoustic playbacks were made using an underwater speaker above one of the prey patches (randomised during the study), and three decision and foraging metrics (foraging duration, foraging effort allocation between the prey patches, and foraging success) were measured. 4. Foraging success was highest during silent controls and was similar regardless of speaker location (LD/HD). Under the tidal turbine and pile-driving treatments, foraging success was similar to the controls when the speaker was located at the HD prey patch but was significantly reduced (~16%–28% lower) when the speaker was located at the LD prey patch. Foraging decisions by the seals were consistent with a risk/profit balancing approach. Avoidance rates depend on the quality of the prey patch as well as the perceived risk. 5. Policy implications. The results suggest that foraging context is important when interpreting avoidance behaviour and should be considered when predicting the effects of anthropogenic activities. For example, sound exposure in different prey patch qualities may result in markedly different avoidance behaviour, potentially leading to contrasting predictions of impact in Environmental Assessments. We recommend future studies explicitly consider foraging context, and other contextual factors such as behavioural state (e.g. foraging or travelling) and habitat quality.Publisher PDFPeer reviewe

MicroRNA interactome analysis predicts post-transcriptional regulation of ADRB2 and PPP3R1 in the hypercholesterolemic myocardium

Little is known about the molecular mechanism including microRNAs (miRNA) in hypercholesterolemia-induced cardiac dysfunction. We aimed to explore novel hypercholesterolemia-induced pathway alterations in the heart by an unbiased approach based on miRNA omics, target prediction and validation. With miRNA microarray we identified forty-seven upregulated and ten downregulated miRNAs in hypercholesterolemic rat hearts compared to the normocholesterolemic group. Eleven mRNAs with at least 4 interacting upregulated miRNAs were selected by a network theoretical approach, out of which 3 mRNAs (beta-2 adrenergic receptor [Adrb2], calcineurin B type 1 [Ppp3r1] and calcium/calmodulin-dependent serine protein kinase [Cask]) were validated with qRT-PCR and Western blot. In hypercholesterolemic hearts, the expression of Adrb2 mRNA was significantly decreased. ADRB2 and PPP3R1 protein were significantly downregulated in hypercholesterolemic hearts. The direct interaction of Adrb2 with upregulated miRNAs was demonstrated by luciferase reporter assay. Gene ontology analysis revealed that the majority of the predicted mRNA changes may contribute to the hypercholesterolemia-induced cardiac dysfunction. In summary, the present unbiased target prediction approach based on global cardiac miRNA expression profiling revealed for the first time in the literature that both the mRNA and protein product of Adrb2 and PPP3R1 protein are decreased in the hypercholesterolemic heart

Badly approximable points on manifolds

Addressing a problem of Davenport we show that any finite intersection of the sets of weighted badly approximable points on any analytic nondegenerate manifold in has full dimension. This also extends Schmidt's conjecture on badly approximable points to arbitrary dimensions

What is a Multi-Modeling Language?

In large software projects often multiple modeling languages are used in order to cover the different domains and views of the application and the language skills of the developers appropriately. Such "multi-modeling" raises many methodological and semantical questions, ranging from semantic consistency of the models written in different sublanguages to the correctness of model transformations between the sublanguages. We provide a first formal basis for answering such questions by proposing semantically well-founded notions of a multimodeling language and of semantic correctness for model transformations. In our approach, a multi-modeling language consists of a set of sublanguages and correct model transformations between some of the sublanguages. The abstract syntax of the sublanguages is given by MOF meta-models. The semantics of a multi-modeling language is given by associating an institution, i.e., an appropriate logic, to each of its sublanguages. The correctness of model transformations is defined by semantic connections between the institutions