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Minors for alternating dimaps
We develop a theory of minors for alternating dimaps --- orientably embedded
digraphs where, at each vertex, the incident edges (taken in the order given by
the embedding) are directed alternately into, and out of, the vertex. We show
that they are related by the triality relation of Tutte. They do not commute in
general, though do in many circumstances, and we characterise the situations
where they do. The relationship with triality is reminiscent of similar
relationships for binary functions, due to the author, so we characterise those
alternating dimaps which correspond to binary functions. We give a
characterisation of alternating dimaps of at most a given genus, using a finite
set of excluded minors. We also use the minor operations to define simple Tutte
invariants for alternating dimaps and characterise them. We establish a
connection with the Tutte polynomial, and pose the problem of characterising
universal Tutte-like invariants for alternating dimaps based on these minor
operations.Comment: 51 pages, 7 figure
Survey, characterisation and condition assessment of Palustriella dominated springs 'H7220 Petrifying springs with tufa formation (Cratoneurion)' in Gloucestershire, England
Twenty-two Gloucestershire sites were surveyed between 18th and 29th January 2017.
Gloucestershire, due to its geology, often steep topography, very high levels of saturated calcium carbonate associated with springs of the Stroud Valley area in particular and large areas of woodland, has a large potential for the H7220 petrifying spring habitat.
Fifteen sites (68%) are identified as having the European Annex 1 habitat H7220, Petrifying springs with tufa formation (Cratoneuron) while 7 sites had tufa formation without H7220.
The total estimated area for H7220 habitat surveyed within Gloucestershire is 2 ha ranging in size from just 0.0001 ha (Sedbury Cliff) to 0.76 ha (Alder Carr) with the greatest length being some 600 m (Dowdeswell).
The H7720 feature has been assessed as being in favourable condition for all of the 15 sites where it has been shown to occur although shading (planted conifers) and water quality (Nitrogen) have been highlighted as having potential for negative impact.
No plants of conservation concern were recorded as directly associated with H7220 vegetation although the following were recorded more generally from sites: the aquatic moss Fissidens rivularis (Slade Brook), 6 Red data Book England (Near Threatened) flowering plants; 8 flowering plants generally considered to be ancient woodland indicators.
Spring and seepages (particularly when calcareous and/or wooded) are of great importance for invertebrates (crane flies, soldier flies and some specialized snails and water beetles). These habitats are widespread in the UK (and include the H7720 habitat) but their associated invertebrate fauna is poorly known.
Observations suggest that Palustriella commutata starts growth on firm substrates, mainly stones or living roots, as opposed to deadwood or rotting organic matter and is associated with slower flows and often more gently sloping sites.
Restoration of H7720 is considered for two sites and restoration techniques discussed
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Initial experience in self-monitoring of intraocular pressure.
Background/aims: Diurnal variation in intraocular pressure (IOP) is a routine assessment in glaucoma management. Providing patients the opportunity to perform self-tonometry might empower them and free hospital resource. We previously demonstrated that 74% of patients can use the Icare® HOME tonometer. This study further explores Icare® HOME patient self-monitoring.
Methods: Patients were trained by standard protocol to use the Icare® HOME rebound tonometer. Patient self-tonometry was compared to Goldmann applanation tonometry (GAT) over one clinical day. Following this, each patient was instructed to undertake further data collection that evening and over the subsequent two days.
Results: Eighteen patients (35 eyes) participated. Good agreement was demonstrated between GAT and Icare® HOME for IOPs up to 15 mm Hg. Above this IOP the Icare® tended to over-read, largely explained by 2 patients with corneal thickness >600 um. The mean peak IOP during ‘clinic hours’ phasing was 16.7 mm Hg and 18.5 mm Hg (p = 0.24) over three days. An average range of 5.0, 7.0 and 9.8 mm Hg was shown during single day clinic, single day home and three day home phasing respectively (p =<0.001). The range of IOP was lower in eyes with prior trabeculectomy (6.1 mm Hg vs 12.2 mm Hg). All patients undertook one reading in the early morning at home with an average of 4.8 readings during, and 3.1 readings after office hours.
Conclusions: This small study shows that self-tonometry is feasible. The findings from home phasing demonstrated higher peak and trough IOPs, providing additional clinical information. Home phasing is a viable alternative. The cost-effectiveness of this approach has yet to be addressed
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