A note on the 1-prevalence of continuous images with full Hausdorff dimension

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that `prevalent' can be replaced by `1-prevalent', i.e. it is possible to \emph{witness} this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called \emph{probes} and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated `infinite dimensional' witnessing measure has to be used.Comment: 8 page

The Hausdorff dimension of graphs of prevalent continuous functions

We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function

On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

Micrococcal Nuclease Does Not Substantially Bias Nucleosome Mapping

We have mapped sequence-directed nucleosome positioning on genomic DNA molecules using high-throughput sequencing. Chromatins, prepared by reconstitution with either chicken or frog histones, were separately digested to mononucleosomes using either micrococcal nuclease (MNase) or caspase-activated DNase (CAD). Both enzymes preferentially cleave internucleosomal (linker) DNA, although they do so by markedly different mechanisms. MNase has hitherto been very widely used to map nucleosomes, although concerns have been raised over its potential to introduce bias. Having identified the locations and quantified the strength of both the chicken or frog histone octamer binding sites on each DNA, the results obtained with the two enzymes were compared using a variety of criteria. Both enzymes displayed sequence specificity in their preferred cleavage sites, although the nature of this selectivity was distinct for the two enzymes. In addition, nucleosomes produced by CAD nuclease are 8–10 bp longer than those produced with MNase, with the CAD cleavage sites tending to be 4–5 bp further out from the nucleosomal dyad than the corresponding MNase cleavage sites. Despite these notable differences in cleavage behaviour, the two nucleases identified essentially equivalent patterns of nucleosome positioning sites on each of the DNAs tested, an observation that was independent of the histone type. These results indicate that biases in nucleosome positioning data collected using MNase are, under our conditions, not significant

Continued monitoring of LMXBs with the Faulkes Telescopes

The Faulkes Telescope Project is an educational and research arm of the Las Cumbres Observatory Global Telescope Network (LCOGTN). It has two 2-metre robotic telescopes, located at Haleakala on Maui (FT North) and Siding Spring in Australia (FT South). It is planned for these telescopes to be complemented by a research network of eighteen 1-metre telescopes, along with an educational network of twenty-eight 0.4-metre telescopes, providing 24 hour coverage of both northern and southern hemispheres. We have been conducting a monitoring project of 13 low-mass X-ray binaries (LMXBs) using FT North since early 2006. The introduction of FT South has allowed us to extend this to monitor a total of 30 LMXBs (see target list, Section 4). New instrumentation will allow us to expand this project to include both infrared wavelengths (z and y band) and spectroscopy. Brighter targets (~ 16 - 18 mag.) are imaged weekly in V, R and i’ bands (SNR ~ 50), while fainter ones (> 18 mag.) are observed only in i’ band (SNR ~ 20). We alter this cadence in response to our own analysis or Astronomers Telegrams (ATels)

First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths

One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multi-pulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length, (1.3-4.7 um) in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350 cm^2/s), and absorption cross-sections (2.1-3.6 X 10^-17 cm^2/atom) among the highest previously reported.and diffusion lengths for SWCNTs.Comment: 6 pages, 3 figure

Eltrombopag for the treatment of chronic idiopathic (immune) thrombocytopenic purpura : A Single Technology Appraisal

Evidence Review Group (ERG) final report for the National Institute for Health and Clinical ExcellencePublisher PD

Effective suppression of Dengue virus using a novel group-I intron that induces apoptotic cell death upon infection through conditional expression of the Bax C-terminal domain

Introduction: Approximately 100 million confirmed infections and 20,000 deaths are caused by Dengue virus (DENV) outbreaks annually. Global warming and rapid dispersal have resulted in DENV epidemics in formally non-endemic regions. Currently no consistently effective preventive measures for DENV exist, prompting development of transgenic and paratransgenic vector control approaches. Production of transgenic mosquitoes refractory for virus infection and/or transmission is contingent upon defining antiviral genes that have low probability for allowing escape mutations, and are equally effective against multiple serotypes. Previously we demonstrated the effectiveness of an anti-viral group I intron targeting U143 of the DENV genome in mediating trans-splicing and expression of a marker gene with the capsid coding domain. In this report we examine the effectiveness of coupling expression of ΔN Bax to trans-splicing U143 intron activity as a means of suppressing DENV infection of mosquito cells. Results: Targeting the conserved DENV circularization sequence (CS) by U143 intron trans-splicing activity appends a 3’ exon RNA encoding ΔN Bax to the capsid coding region of the genomic RNA, resulting in a chimeric protein that induces premature cell death upon infection. TCID50-IFA analyses demonstrate an enhancement of DENV suppression for all DENV serotypes tested over the identical group I intron coupled with the non-apoptotic inducing firefly luciferase as the 3’ exon. These cumulative results confirm the increased effectiveness of this αDENV-U143-ΔN Bax group I intron as a sequence specific antiviral that should be useful for suppression of DENV in transgenic mosquitoes. Annexin V staining, caspase 3 assays, and DNA ladder observations confirm DCA-ΔN Bax fusion protein expression induces apoptotic cell death. Conclusion: This report confirms the relative effectiveness of an anti-DENV group I intron coupled to an apoptosis-inducing ΔN Bax 3’ exon that trans-splices conserved sequences of the 5’ CS region of all DENV serotypes and induces apoptotic cell death upon infection. Our results confirm coupling the targeted ribozyme capabilities of the group I intron with the generation of an apoptosis-inducing transcript increases the effectiveness of infection suppression, improving the prospects of this unique approach as a means of inducing transgenic refractoriness in mosquitoes for all serotypes of this important disease