The Yellowstone Permutation

Define a sequence of positive integers by the rule that a(n) = n for 1 <= n = 4, a(n) is the smallest number not already in the sequence which has a common factor with a(n-2) and is relatively prime to a(n-1). We show that this is a permutation of the positive integers. The remarkable graph of this sequence consists of runs of alternating even and odd numbers, interrupted by small downward spikes followed by large upward spikes, suggesting the eruption of geysers in Yellowstone National Park. On a larger scale the points appear to lie on infinitely many distinct curves. There are several unanswered questions concerning the locations of these spikes and the equations for these curves.Comment: 10 pages, 6 figures. Mar 7 2015: mostly stylistic change

Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

THE IMPACT OF TELECOMMUNICATION AND TRANSPORT ON SPATIAL BEHAVIOUR

Telecommunication has not only for the sender but as well for the addressee both mobile and immobile elements. Regarding telecommunication in the interpersonal context with the related traffic behaviour, it becomes clear that telecommunication has so far an unknown influence on our spatial behaviour. Based on these considerations a concept is being developed to demonstrate the influence, the use and the increasing penetration of communication and information media on spatial behaviour of humans. The question, which effects are to be considered from this for the future and in which way it affects planning of interventions in the traffic sector, follows directly. On the basis of empirical results from Germany, Sweden and Korea it is shown that additional communication and information possibilities have no decreasing affect on the physical mobility of humans. Based on this result the advantages of novel communication and information services are being systematised to analyse the impacts on spatial behaviour in detail. For this it is possible to fall back on data-sets ranging from the mega-city Seoul over cities and rural regions in Germany to remote areas in Sweden. So it is to be expected that certain time-consuming, standardise and according to their nature suitable activities/ trips (e. g. telebanking) might be substituted in the every day live. At the same time, however, it is to be expected that far distant destinations can be more easily investigated by better information and communication possibilities, in order to lead afterwards to additional physical mobility - thus an induction of physical transport appears this way. The increases are to be expected fewer in everyday life transport, since the financial and temporal budget restrictions are effective here due to capacity limitations of the traffic system. Rather increases in the weekend and holiday traffic are to be expected, where either by the generated interest via simplified information access or by the decrease of initial trave) thresholds (reduction of uncertainties concerning the selected destination by telecommunications) additional journeys can be performed. Within the leisure area and the global business and service area activities and appropriate journeys are thus generated, which would not have been possible without existence of the electronic media. Finally, it is stated, which (feedback-) effects result on the structure of demand, if more spontaneous acts caused by information and communication technologies provoke critical and on a long-term basis not calculable effects

The Role of Insulin-Like Growth Factor System in Soft Tissue Sarcomas: From Physiopathology to Targeted Therapeutic Approaches

Purpose/Results. Although surgical, chemo- and radiotherapeutic treatment regimens in patients with soft tissue sarcomas have constantly been refined over the past two decades, the survival rate for these patients is rather low

Debitage Attributes, Obsidian Source Analysis, and Prehistoric Mobility in Southeastern Idaho

The purpose of this study is to complement existing knowledge on prehistoric mobility in eastern and southern Idaho. I add specific detail regarding the use of Skull Canyon and its well-known Birch Creek rockshelters during hunter-gatherers’ logistical foraging rounds. In addition, my research is a case study in combining debitage attribute analysis and intensive toolstone sourcing to read prehistoric mobility. Prior research has looked to obsidian toolstone sourcing to understand prehistoric eastern and southern Idaho mobility. However, no prior research has involved sourcing an entire, stratified assemblage of prehistoric debitage. I collected flake attribute data from all 2,846 pieces of Bobcat Shelter debitage including both obsidian and microcrystalline silicate artifacts. I collected x-ray fluorescence, obsidian sourcing data on all 1,830 pieces of Bobcat Shelter obsidian debitage. Analysis involved combining strata based on similarity in strata mean toolstone source distance. This was necessary due to strata sample sizing constraints. Mann Whitney U tests were used to find significant differences between groups based on every one of ten disparate debitage attributes. These attributes are expected to change in predictable ways with increasing mean toolstone source distance. Group median attribute values were used to verify predicted differences between groups. Debitage characteristics appear dependent on distance from toolstone source. As expected, this is especially true for exclusively obsidian samples as 100% of significant Mann Whitney U results are associated with predicted trends in group median attribute values. Obsidian material deposited before the Late Archaic/ Late Prehistoric transition originates from farther geological sources than after, pointing to an important difference in mobility levels. This research also uncovers a large increase in the proportion of specific toolstone sources during the end of the Late Archaic (2,950 –1,650 BP), detail missed during less intense sampling of Bobcat Shelter sourced obsidian

Dynamics of group II introns in plant mitogenomes and rickettsial DNA invasions in the mitogenome of <em>Haplopteris ensiformis</em>

The complexity of mitochondrial genomes (mtDNA) in vascular plants is well-known, with factors such as repetitive sequences, variable structural organization, gene synteny decline, high intron content, and RNA editing contributing to their intricate nature. However, investigations into the mtDNA of ferns belonging to the taxonomically diverse group of polypodiales have been hindered by a combination of these factors. In this study, we discovered that the fern species Haplopteris ensiformis possesses a complex mtDNA with circular chromosomes, trans-splicing of group I introns, and extensive RNA editing. Notably, it also contains DNA from chloroplasts and rickettsial bacteria, through horizontal gene transfer. The assembly of H. ensiformis mtDNA allowed for the study of mitochondrial group II introns in ferns and other land plant lineages. The search for the evolutionary origin of the enigmatic distribution of land plant mitochondrial group II intron revealed evolutionary recent and ancient intron dynamics. Additionally, rare intron configurations, like introns-within-introns (twintrons) and yet undescribed zombie-twintrons, in the vascular plant family of Lycopodiaceae and the bryophyte lineage of hornworts, have been discovered adding yet another layer of complexity of land plant mtDNAs. Through systematic investigation of group II introns and associated proteins, the maturases, we also identified evidence of ancient mobility and coevolution of plant mitochondrial group II introns with nuclear-encoded proteins responsible for organellar splicing. Here, these findings provide insights into the evolutionary interdependency between cytonuclear interactions and mitochondrial intron splicing but raise questions about the mechanistic origin of plant mitogenome intron dynamics

A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

Surgical trial in traumatic intracerebral haemorrhage (STITCH) : A randomised controlled trial of early surgery compared with Initial conservative treatment

Funding This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme.Peer reviewedPublisher PD

Mechanisms controlling anaemia in Trypanosoma congolense infected mice.

Trypanosoma congolense are extracellular protozoan parasites of the blood stream of artiodactyls and are one of the main constraints on cattle production in Africa. In cattle, anaemia is the key feature of disease and persists after parasitaemia has declined to low or undetectable levels, but treatment to clear the parasites usually resolves the anaemia. The progress of anaemia after Trypanosoma congolense infection was followed in three mouse strains. Anaemia developed rapidly in all three strains until the peak of the first wave of parasitaemia. This was followed by a second phase, characterized by slower progress to severe anaemia in C57BL/6, by slow recovery in surviving A/J and a rapid recovery in BALB/c. There was no association between parasitaemia and severity of anaemia. Furthermore, functional T lymphocytes are not required for the induction of anaemia, since suppression of T cell activity with Cyclosporin A had neither an effect on the course of infection nor on anaemia. Expression of genes involved in erythropoiesis and iron metabolism was followed in spleen, liver and kidney tissues in the three strains of mice using microarrays. There was no evidence for a response to erythropoietin, consistent with anaemia of chronic disease, which is erythropoietin insensitive. However, the expression of transcription factors and genes involved in erythropoiesis and haemolysis did correlate with the expression of the inflammatory cytokines Il6 and Ifng. The innate immune response appears to be the major contributor to the inflammation associated with anaemia since suppression of T cells with CsA had no observable effect. Several transcription factors regulating haematopoiesis, Tal1, Gata1, Zfpm1 and Klf1 were expressed at consistently lower levels in C57BL/6 mice suggesting that these mice have a lower haematopoietic capacity and therefore less ability to recover from haemolysis induced anaemia after infection