Generalised Cantor sets and the dimension of products

In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the cardinality of local covers at all length-scales and at all points, and we show that a large class of homogeneous Moran sets have this property. We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lower box-counting dimensions provided that the set ‘attains’ these dimensions (analogous to ‘s-sets’ when considering the Hausdorff dimension), and the set is equi-homogeneous. Using this fact we show that for any α ∈ (0, 1) and any β, γ ∈ (0, 1) such that β + γ ≥ 1 we can construct two generalised Cantor sets C and D such that dimBC = αβ, dimBD = α γ, and dimAC = dimAD = dimA (C × D) = dimB (C × D) = α

Towards standard setting for patient-reported outcomes in the NHS homeopathic hospitals

We report findings from a pilot data collection study within a programme of quality assurance, improvement and development across all five homeopathic hospitals in the UK National Health Service (NHS).<p></p> <b>Aims</b> (1) To pilot the collection of clinical data in the homeopathic hospital outpatient setting, recording patient-reported outcome since first appointment; (2) to sample the range of medical complaints that secondary-care doctors treat using homeopathy, and thus identify the nature and complexity of complaints most frequently treated nationally; (3) to present a cross section of outcome scores by appointment number, including that for the most frequently treated medical complaints; (4) to explore approaches to standard setting for homeopathic practice outcome in patients treated at the homeopathic hospitals.<p></p> <b>Methods</b> A total of 51 medical practitioners took part in data collection over a 4-week period. Consecutive patient appointments were recorded under the headings: (1) date of first appointment in the current series; (2) appointment number; (3) age of patient; (4) sex of patient; (5) main medical complaint being treated; (6) whether other main medical complaint(s); (7) patient-reported change in health, using Outcome Related to Impact on Daily Living (ORIDL) and its derivative, the ORIDL Profile Score (ORIDL-PS; range, –4 to +4, where a score ≤−2 or ≥+2 indicates an effect on the quality of a patient's daily life); (8) receipt of other complementary medicine for their main medical complaint.<p></p> <b>Results</b> The distribution of patient age was bimodal: main peak, 49 years; secondary peak, 6 years. Male:female ratio was 1:3.5. Data were recorded on a total of 1797 individual patients: 195 first appointments, 1602 follow-ups (FUs). Size of clinical service and proportion of patients who attended more than six visits varied between hospitals. A total of 235 different medical complaints were reported. The 30 most commonly treated complaints were (in decreasing order of frequency): eczema; chronic fatigue syndrome (CFS); menopausal disorder; osteoarthritis; depression; breast cancer; rheumatoid arthritis; asthma; anxiety; irritable bowel syndrome; multiple sclerosis; psoriasis; allergy (unspecified); fibromyalgia; migraine; premenstrual syndrome; chronic rhinitis; headache; vitiligo; seasonal allergic rhinitis; chronic intractable pain; insomnia; ulcerative colitis; acne; psoriatic arthropathy; urticaria; ovarian cancer; attention-deficit hyperactivity disorder (ADHD); epilepsy; sinusitis. The proportion of patients with important co-morbidity was higher in those seen after visit 6 (56.9%) compared with those seen up to and including that point (40.7%; P < 0.001). The proportion of FU patients reporting ORIDL-PS ≥ +2 (improvement affecting daily living) increased overall with appointment number: 34.5% of patients at visit 2 and 59.3% of patients at visit 6, for example. Amongst the four most frequently treated complaints, the proportion of patients that reported ORIDL-PS ≥ +2 at visit numbers greater than 6 varied between 59.3% (CFS) and 73.3% (menopausal disorder).<p></p> <b>Conclusions</b> We have successfully piloted a process of national clinical data collection using patient-reported outcome in homeopathic hospital outpatients, identifying a wide range and complexity of medical complaints treated in that setting. After a series of homeopathy appointments, a high proportion of patients, often representing “effectiveness gaps” for conventional medical treatment, reported improvement in health affecting their daily living. These pilot findings are informing our developing programme of standard setting for homeopathic care in the hospital outpatient context

Patterns of space use in sympatric marine colonial predators reveals scales of spatial partitioning

E.L.J. and D.J.F.R. were funded under Scottish Government grant MMSS001/01. D.J.F.R. was funded by the UK Department of Energy and Climate Change (DECC) as part of their Offshore Energy Strategic Environmental Assessment programme. S.S. was part-funded by the EU MYFISH project.Species distribution maps can provide important information to focus conservation efforts and enable spatial management of human activities. Two sympatric marine predators, grey seals Halichoerus grypus and harbour seals Phoca vitulina have overlapping ranges on land and at sea but contrasting population dynamics around Britain: whilst grey seals have generally increased, harbour seals have shown significant regional declines. We analysed two decades of at-sea movement data and terrestrial count data from these species to produce high resolution, broad-scale maps of distribution and associated uncertainty to inform conservation and management. Our results showed that grey seals use offshore areas connected to their haul-out sites by prominent corridors and harbour seals primarily stay within 50km of the coastline. Both species show fine-scale offshore spatial segregation off the east coast of Britain and broad-scale partitioning off western Scotland. These results illustrate that for broad-scale marine spatial planning, the conservation needs of harbour seals (primarily inshore, the exception being selected offshore usage areas) are different from those of grey seals (up to 100km offshore and corridors connecting these areas to haul-out sites). More generally, our results illustrate the importance of detailed knowledge of marine predator distributions to inform marine spatial planning; for instance, spatial prioritisation is not necessarily the most effective spatial planning strategy even when conserving species with similar taxonomy.Peer reviewe

The end of the world, or just 'goodbye to all that'? Contextualising the red deer heap from Links of Noltland, Westray, within late 3rd-millennium cal BC Orkney

As part of a major international research project, The Times of Their Lives, a programme of radiocarbon dating and Bayesian modelling was undertaken to refine the chronology of activities in one small but important part of the extensive Late Neolithic and Bronze Age settlement on Links of Noltland on the island of Westray, Orkney. The selected area (Trench D) is well known for having produced, next to a wall, the remains of a heap of at least 15 red deer carcasses, on top of which had been placed a large cod, a gannet’s wing along with part of a greater black-backed gull, and a pair of large antlers. This remarkable deposit had been preceded by, and was followed by, periods of cultivation and the deposition of domestic refuse. Refined date estimates have been produced, based on 18 radiocarbon determinations obtained from 16 samples from Trench D (including nine newly obtained dates, three from individual deer in the heap). These clarify when, during this long sequence of activities, the deer were heaped up: probably in the 22nd century cal bc, around the same time as Beaker pottery was deposited elsewhere on the Links. This allows comparison between the dated activities in this part of the site with activity elsewhere on the Links and also with other episodes of deer deposition in 3rd-millennium cal bc Orkney. It encourages exploration of the possible reasons for what appears to be a remarkable act of structured deposition. The significance of an earlier, much larger scale deposit featuring cattle remains at Ness of Brodgar is discussed in exploring the nature of Orcadian society and practices during the second half of the 3rd millennium cal bc

The KMOS Cluster Survey (KCS). I. The Fundamental Plane and the Formation Ages of Cluster Galaxies at Redshift 1.4 < Z < 1.6

We present the analysis of the fundamental plane (FP) for a sample of 19 massive red-sequence galaxies (${M}_{\star }\gt 4\times {10}^{10}$ ${M}_{\odot }$) in three known overdensities at $1.39\lt z\lt 1.61$ from the K-band Multi-object Spectrograph (KMOS) Cluster Survey, a guaranteed-time program with spectroscopy from the KMOS at the VLT and imaging from the Hubble Space Telescope. As expected, we find that the FP zero-point in B band evolves with redshift, from the value 0.443 of Coma to −0.10 ± 0.09, −0.19 ± 0.05, and −0.29 ± 0.12 for our clusters at z = 1.39, z = 1.46, and z = 1.61, respectively. For the most massive galaxies ($\mathrm{log}{M}_{\star }/{M}_{\odot }\gt 11$) in our sample, we translate the FP zero-point evolution into a mass-to-light-ratio M/L evolution, finding ${\rm{\Delta }}\mathrm{log}M/{L}_{B}=(-0.46\pm 0.10)z$, ${\rm{\Delta }}\mathrm{log}M/{L}_{B}=(-0.52\pm 0.07)z$, to ${\rm{\Delta }}\mathrm{log}M/{L}_{B}=(-0.55\pm 0.10)z$, respectively. We assess the potential contribution of the galaxy structural and stellar velocity dispersion evolution to the evolution of the FP zero-point and find it to be ~6%–35% of the FP zero-point evolution. The rate of M/L evolution is consistent with galaxies evolving passively. Using single stellar population models, we find an average age of ${2.33}_{-0.51}^{+0.86}$ Gyr for the $\mathrm{log}{M}_{\star }/{M}_{\odot }\gt 11$ galaxies in our massive and virialized cluster at z = 1.39, ${1.59}_{-0.62}^{+1.40}$ Gyr in a massive but not virialized cluster at z = 1.46, and ${1.20}_{-0.47}^{+1.03}$ Gyr in a protocluster at z = 1.61. After accounting for the difference in the age of the universe between redshifts, the ages of the galaxies in the three overdensities are consistent within the errors, with possibly a weak suggestion that galaxies in the most evolved structure are older

Molecular mechanism of ligand recognition by membrane transport protein, Mhp1

The hydantoin transporter Mhp1 is a sodium-coupled secondary active transport protein of the nucleobase-cation-symport family and a member of the widespread 5-helix inverted repeat superfamily of transporters. The structure of Mhp1 was previously solved in three different conformations providing insight into the molecular basis of the alternating access mechanism. Here, we elucidate detailed events of substrate binding, through a combination of crystallography, molecular dynamics, site-directed mutagenesis, biochemical/biophysical assays, and the design and synthesis of novel ligands. We show precisely where 5-substituted hydantoin substrates bind in an extended configuration at the interface of the bundle and hash domains. They are recognised through hydrogen bonds to the hydantoin moiety and the complementarity of the 5-substituent for a hydrophobic pocket in the protein. Furthermore, we describe a novel structure of an intermediate state of the protein with the external thin gate locked open by an inhibitor, 5-(2-naphthylmethyl)-L-hydantoin, which becomes a substrate when leucine 363 is changed to an alanine. We deduce the molecular events that underlie acquisition and transport of a ligand by Mhp1

Journey decision making: the influence on drivers of dynamic information presented on variable message signs

In many highways environments electronic media such as variable message signs are increasingly being used to provide drivers with up-to-date dynamic information in order to influence driving decision making during journeys. These decisions may be associated with strategic choices, such as route selection, or tactical decisions, such as driving at a certain speed, or altering driving style. This paper presents a study that used two methods - a scenario approach and a medium-fidelity driving simulator. Data from both methods are presented here and include decision making and driving performance data. These data provide an insight into the role of information and other contextual influences in decision making in the driving context specifically, but also has useful implications for the way in which information should be designed in other decision making contexts, such as travel using public transport, or supporting real-time complex control operations. The use of multiple data collection approaches also enabled data comparisons to be made, thus improving overall confidence in conclusions. The paper highlights the role of familiarity with information wording and context, level of detail, interpreted meaning, previous experience and contextual cues on trust in information and consequently behaviour in response to the information presented

The antibacterial activity of a photoactivatable diarylacetylene against Gram-positive bacteria

The emergence of antibiotic resistance is a growing threat to human health, and therefore, alternatives to existing compounds are urgently needed. In this context, a novel fluorescent photoactivatable diarylacetylene has been identified and characterised for its antibacterial activity, which preferentially eliminates Gram-positive over Gram-negative bacteria. Experiments confirmed that the Gram-negative lipopolysaccharide-rich outer surface is responsible for tolerance, as strains with reduced outer membrane integrity showed increased susceptibility. Additionally, bacteria deficient in oxidative damage repair pathways also displayed enhanced sensitivity, confirming that reactive oxygen species production is the mechanism of antibacterial activity. This new diarylacetylene shows promise as an antibacterial agent against Gram-positive bacteria that can be activated in situ, potentially for the treatment of skin infections