Algorithmic Interpretations of Fractal Dimension

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several well-studied notions of fractal dimension for sets and measures in Euclidean space. We consider a definition of fractal dimension for finite metric spaces which agrees with standard notions used to empirically estimate the fractal dimension of various sets. We define the fractal dimension of some metric space to be the infimum delta>0, such that for any eps>0, for any ball B of radius r >= 2eps, and for any eps-net N, we have |B cap N|=O((r/eps)^delta). Using this definition we obtain faster algorithms for a plethora of classical problems on sets of low fractal dimension in Euclidean space. Our results apply to exact and fixed-parameter algorithms, approximation schemes, and spanner constructions. Interestingly, the dependence of the performance of these algorithms on the fractal dimension nearly matches the currently best-known dependence on the standard Euclidean dimension. Thus, when the fractal dimension is strictly smaller than the ambient dimension, our results yield improved solutions in all of these settings. We remark that our definition of fractal definition is equivalent up to constant factors to the well-studied notion of doubling dimension. However, in the problems that we consider, the dimension appears in the exponent of the running time, and doubling dimension is not precise enough for capturing the best possible such exponent for subsets of Euclidean space. Thus our work is orthogonal to previous results on spaces of low doubling dimension; while algorithms on spaces of low doubling dimension seek to extend results from the case of low dimensional Euclidean spaces to more general metric spaces, our goal is to obtain faster algorithms for special pointsets in Euclidean space

Identification of sex hormone-binding globulin in the human hypothalamus

Gonadal steroids are known to influence hypothalamic functions through both genomic and non-genomic pathways. Sex hormone-binding globulin ( SHBG) may act by a non-genomic mechanism independent of classical steroid receptors. Here we describe the immunocytochemical mapping of SHBG-containing neurons and nerve fibers in the human hypothalamus and infundibulum. Mass spectrometry and Western blot analysis were also used to characterize the biochemical characteristics of SHBG in the hypothalamus and cerebrospinal fluid (CSF) of humans. SHBG-immunoreactive neurons were observed in the supraoptic nucleus, the suprachiasmatic nucleus, the bed nucleus of the stria terminalis, paraventricular nucleus, arcuate nucleus, the perifornical region and the medial preoptic area in human brains. There were SHBG-immunoreactive axons in the median eminence and the infundibulum. A partial colocalization with oxytocin could be observed in the posterior pituitary lobe in consecutive semithin sections. We also found strong immunoreactivity for SHBG in epithelial cells of the choroid plexus and in a portion of the ependymal cells lining the third ventricle. Mass spectrometry showed that affinity-purified SHBG from the hypothalamus and choroid plexus is structurally similar to the SHBG identified in the CSF. The multiple localizations of SHBG suggest neurohypophyseal and neuroendocrine functions. The biochemical data suggest that CSF SHBG is of brain rather than blood origin. Copyright (c) 2005 S. Karger AG, Base

Establishing the optimum threshold value for haemoglobin in faecal immunochemical tests (FITs) for use in the primary care symptomatic population: South West Cancer Alliance FIT programme evaluation

This is the final version.Colorectal cancer is the fourth most common cancer in the UK, and the second leading cause of cancer-related deaths. Diagnosing colorectal cancer is difficult, as the symptoms are the same as many non-cancerous conditions. The NICE guideline NG12 (2015) recommends that patients consulting their GP with ‘alarm’ symptoms of colorectal cancer are urgently referred for colonoscopy. However, not all patients with colorectal cancer have these alarm symptoms. Many have vague low-risk symptoms that do not warrant a colonoscopy under NG12. In 2017, a new NICE guidance DG30 suggested that faecal immunochemical tests (FITs) are used for patients with these vague symptoms that could suggest colorectal cancer, but do not represent a great enough risk for an urgent referral. FITs measure the amount of haemoglobin (Hb) in a stool sample. A high level of Hb in a stool sample may suggest bleeding in the bowel caused by cancer. However, we don’t know how high Hb in the stool should be before the patient is offered a colonoscopy, when the patient has these vague symptoms. In this study, our primary aims are 1) to determine the optimum cut off point for Hb in FITs in a symptomatic primary care population, and 2) to estimate the diagnostic performance of FITs at detecting cancer in a symptomatic primary care population. In the South West, FITs have been in use since June 2018. We will collect data on all FITs performed in the region during the 18-month study period. This will include the amount of Hb present in the patients’ samples, whether or not they were referred for colonoscopy, patient demographic data, the type of FIT used, and whether or not the patient was diagnosed with colorectal cancer within one year of their FIT. We will also collect data on the number and type of referrals and diagnoses in the region during the study period, and the number of FITs ordered from primary care during that time. We estimate that around 30,000 FITs will be performed during the data collection period. This study will be complemented by a narrative review providing an overview of FIT use across the globe in primary care symptomatic patients, and a health economics study to evaluate the cost implications of FITs

The coregulator Alien

Alien has characteristics of a corepressor for selected members of the nuclear hormone receptor (NHR) superfamily and also for transcription factors involved in cell cycle regulation and DNA repair. Alien mediates gene silencing and represses the transactivation of specific NHRs and other transcription factors to modulate hormone response and cell proliferation. Alien is a highly conserved protein and is expressed in a wide variety of tissues. Knockout of the gene encoding Alien in mice is embryonic lethal at a very early stage, indicating an important evolutionary role in multicellular organisms. From a mechanistic perspective, the corepressor function of Alien is in part mediated by histone deacetylase (HDAC) activity. In addition, Alien seems to modulate nucleosome assembly activity. This suggests that Alien is acting on chromatin not only through recruitment of histone-modifying activities, but also through enhancing nucleosome assembly

Stable hydrogenated graphene edge types: Normal and reconstructed Klein edges

Hydrogenated graphene edges are assumed to be either armchair, zigzag or a combination of the two. We show that the zigzag is not the most stable fully hydrogenated structure along the direction. Instead hydrogenated Klein and reconstructed Klein based edges are found to be energetically more favourable, with stabilities approaching that of armchair edges. These new structures "unify" graphene edge topology, the most stable flat hydrogenated graphene edges always consisting of pairwise bonded C2H4 edge groups, irrespective the edge orientation. When edge rippling is included, CH3 edge groups are most stable. These new fundamental hydrogen terminated edges have important implications for graphene edge imaging and spectroscopy, as well as mechanisms for graphene growth, nanotube cutting, and nanoribbon formation and behaviour.Fundação para a Ciência e a Tecnologia (FCT

Engineering molecular chains in carbon nanotubes

A range of mono- and bis-functionalised fullerenes have been synthesised and inserted into single-walled carbon nanotubes. The effect of the size and shape of the functional groups of the fullerenes on the resultant 1D arrays formed within the nanotubes was investigated by high resolution transmission electron microscopy and X-ray diffraction. The addition of non-planar, sterically bulky chains to the fullerene cage results in highly ordered 1D structures in which the fullerenes are evenly spaced along the internal nanotube cavity. Theoretical calculations reveal that the functional groups interact with neighbouring fullerene cages to space the fullerenes evenly within the confines of the nanotube. The addition of two functional groups to opposite sides of the fullerene cages results in a further increase in the separation of the fullerene cages within the nanotubes at the cost of lower nanotube filling rates.This work was financially supported by FWF project I83-N20 (ESF IMPrESS), the Royal Society, the European Research Council (ERC), "Fundacao para a Ciencia ea Tecnologia" through the program Ciencia 2008, the project SeARCH (Services and Advanced Research Computing with HTC/HPC clusters) and Nottingham Nanoscience and Nanotechnology Centre (NNNC)

Self-assembled RGD dehydropeptide hydrogels for drug delivery applications

Peptide-based self-assembled hydrogels have triggered remarkable research interest in recent years owing to their biocompatibility and biomimetic properties and responsiveness, which warrant many technological and biomedical applications. Dehydrodipeptides N-capped with naproxen emerged from our research as effective hydrogelators endowed with resistance to proteolysis. Dehydrodipeptide-based hydrogels are promising nanocarriers for drug delivery applications. In this work, we demonstrate that dehydrodipetide Npx-L-Ala-Z-ΔPhe-OH can be deployed as a minimalist hydrogelator module for synthesizing a gelating construct Npx-L-Ala-Z-ΔPhe-G-R-G-D-G-OH bearing a GRGDG adhesion motif. The self-assembly of the peptide construct and the drug delivery properties of the hydrogel were studied in this work. The peptide construct showed no toxicity towards a fibroblast cell line expressing the αvβ3 integrin. Docking studies suggest that the hydrogelator block does not interfere with the recognition of the RGD motif by the integrin receptor. The self-assembly seems to be directed by intermolecular naphthalene π–π stacking interactions, with the peptide backbone assuming a random coil conformation both in solution and in the gel phase. TEM and STEM imaging revealed that the hydrogel is made of entangled bundles of long thin fibres (width circa 23 nm). The hydrogel exhibits viscoelastic properties, thermo-reversibility and recovery after mechanical fluidization. FRET studies showed that curcumin incorporated into the hydrogel interacts non-covalently with the hydrogel fibrils. Delivery of curcumin from the hydrogel into Nile red loaded model membranes (SUVs) was demonstrated by FRET. Naproxen N-capped dehydrodipeptides are efficacious minimalist hydrogelator modules for obtaining hydrogels functionalized with peptide ligands for cell receptors. These hydrogels are potential nanocarriers for drug delivery

Comparative analysis of Calanus finmarchicus demography at locations around the Northeast Atlantic

Standardized time-series sampling was carried out throughout 1997 at seven locations around the Northeast Atlantic to investigate regional variations in the seasonal demography of Calanus finmarchicus. Sites ranged from an inshore location in the North Sea, where C. finmarchicus formed only a small component of the zooplankton (2000 mgC m-2 during spring and summer). The internal consistency of the demographic time-series from each site was investigated by three partial models of life-cycle processes. In general, the demography of late copepodites could be accounted for by a relatively simple forecast model of stage development and diapause. However, there was a large discrepancy between nowcast estimates of egg production based on female abundance, temperature, and chlorophyll, and hindcast simulations of the egg production required to account for the observed abundance of early copepodite stages. The results point to a gap in our understanding of seasonal variations in rates of egg production and/or survival of nauplii. Overall, the population sampled at Weathership M appeared to be reasonably self-contained, but all other sites were reliant on invasion of overwintered stock in spring. At least two generations were observed at all but one site, but the extent to which these were generated by discrete bursts of egg production varied between sites and seemed to be partly dependent on the proximity to an overwintering location