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

The Effects of a High Fat Meal on Blood Flow Regulation during Arm Exercise

A diet high in saturated fats results in endothelial dysfunction and can lead to atherosclerosis, a precursor to cardiovascular disease. Exercise training is a potent stimulus though to mitigate the negative effects of a high saturated fat diet; however, it is unclear how high-saturated fat meal (HSFM) consumption impacts blood flow regulation during a single exercise session. PURPOSE: This study sought to examine the impact of a single HSFM on peripheral vascular function during an acute upper limb exercise bout. METHODS: Ten young healthy individuals completed two sessions of progressive handgrip exercise. Subjects either consumed a HSFM (0.84 g of fat/kg of body weight) 4 hours prior or remained fasted before the exercise bout. Progressive rhythmic handgrip exercise (6kg, 12kg, 18kg) was performed for 3 minutes per stage at rate of 1 Hz. The brachial artery (BA) diameter and blood velocity was obtained using Doppler Ultrasound (GE Logiq e) and BA blood flow was calculated with these values. RESULTS: BA blood flow and flow mediated dilation (normalized for shear rate) during the handgrip exercise significant increased from baseline in all workloads, but no differences were revealed in response to the HSFM consumption. CONCLUSION: Progressive handgrip exercise augmented BA blood flow and flow mediated dilation in both testing days; however, there was no significant differences following the HSFM consumption. This suggests that upper limb blood flow regulation during exercise is unaltered by a high fat meal in young healthy individuals.https://scholarscompass.vcu.edu/gradposters/1060/thumbnail.jp

Natural Variation in TBP-ASSOCIATED FACTOR 4b Controls Meiotic Crossover and Germline Transcription in Arabidopsis.

Meiotic crossover frequency varies within genomes, which influences genetic diversity and adaptation. In turn, genetic variation within populations can act to modify crossover frequency in cis and trans. To identify genetic variation that controls meiotic crossover frequency, we screened Arabidopsis accessions using fluorescent recombination reporters. We mapped a genetic modifier of crossover frequency in Col × Bur populations of Arabidopsis to a premature stop codon within TBP-ASSOCIATED FACTOR 4b (TAF4b), which encodes a subunit of the RNA polymerase II general transcription factor TFIID. The Arabidopsis taf4b mutation is a rare variant found in the British Isles, originating in South-West Ireland. Using genetics, genomics, and immunocytology, we demonstrate a genome-wide decrease in taf4b crossovers, with strongest reduction in the sub-telomeric regions. Using RNA sequencing (RNA-seq) from purified meiocytes, we show that TAF4b expression is meiocyte enriched, whereas its paralog TAF4 is broadly expressed. Consistent with the role of TFIID in promoting gene expression, RNA-seq of wild-type and taf4b meiocytes identified widespread transcriptional changes, including in genes that regulate the meiotic cell cycle and recombination. Therefore, TAF4b duplication is associated with acquisition of meiocyte-specific expression and promotion of germline transcription, which act directly or indirectly to elevate crossovers. This identifies a novel mode of meiotic recombination control via a general transcription factor.This work was supported by a BBSRC DTP studentship (EJL), European Research Area Network for Coodinating Action in Plant Sciences/BBSRC “DeCOP” (BB/M004937/1) (CAL), a BBSRC David Phillips Fellowship (BB/L025043/1) (HG, XF), the European Research Council (CoG ‘SynthHotspot’) (AJT, CAL, IRH) and (StG ‘SexMeth’) (XF) and a Sainsbury Charitable Foundation Studentship (ARB)

Spatially superposed pulse amplitude modulation using a chip-scale CMOS-integrated GaN LED array

We present a highly compact system capable of generating discrete optical wireless data signals from logic inputs, suitable for pulse amplitude modulation (PAM) transmission, in visible light communication (VLC)

Poissonian communications : free space optical data transfer at the few-photon level

Communicating information at the few photon level typically requires some complexity in the transmitter or receiver in order to operate in the presence of noise. This in turn incurs expense in the necessary spatial volume and power consumption of the system. In this work we present a self-synchronised free-space optical communications system based on simple, compact and low power consumption semiconductor devices. A temporal encoding method, implemented using a gallium nitride micro-LED source and a silicon single photon avalanche photo-detector (SPAD) demonstrates data transmission at rates up to 100 kb/s for 8.25 pW received power, corresponding to 27 photons per bit. Furthermore, the signals can be decoded in the presence of both constant and modulated background noise at levels significantly exceeding the signal power. The systems low power consumption and modest electronics requirements are demonstrated employing it as a communications channel between two nano-satellite simulator systems