Integral points on elliptic curves and explicit valuations of division polynomials

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral multiple [n]P such that n > C. The proof is a modification of a proof of Ingram giving an unconditional but not uniform bound. The new ingredient is a collection of explicit formulae for the sequence of valuations of the division polynomials. For P of non-singular reduction, such sequences are already well described in most cases, but for P of singular reduction, we are led to define a new class of sequences called elliptic troublemaker sequences, which measure the failure of the Neron local height to be quadratic. As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a uniform upper bound on h(P)/h(E) for integer points having two large integral multiples.Comment: 41 pages; minor corrections and improvements to expositio

An Opportunistic Assessment of the Impact of Squirrelpox Disease Outbreaks upon a Red Squirrel Population Sympatric with Grey Squirrels in Wales

SIMPLE SUMMARY: In Europe, squirrelpox virus is carried by non-native grey squirrels and spread into native red squirrel populations. The virus causes a large proportion of infected red squirrels to die and contributes to local declines and the replacement by grey squirrels. There are relatively few published studies quantifying the impact of disease amongst red squirrels. We present findings from a short-term study in north Wales, United Kingdom. ABSTRACT: Native red squirrels (Sciurus vulgaris) persisted in the coastal mainland woodlands of northern Gwynedd whilst sympatric with an invasive grey squirrel (Sciurus carolinensis) population suppressed by culling. Squirrelpox disease in the red squirrel population was recorded in 2017 and 2020/21. An autumn 2020 outbreak was associated with only 17.4% of animals caught and marked in the preceding June known to be present in March 2021. Despite an opportunistic data collection lacking the rigour of empirical experimental design, we observed low local survival rates similar to previously published accounts reported during major squirrelpox outbreaks. The use of a conservation dog to detect red squirrel carcasses resulted in positive detection and confirmation of a temporal and spatial expansion of one disease outbreak. The study is the first in Wales to use conservation dogs and the findings reinforce the vital strategic importance of geographical isolation reducing sympatry of red with grey squirrels in European regions where the introduced congener is a source of the squirrelpox infection

Images of dissipation layers to quantify mixing within a turbulent jet

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77254/1/AIAA-13435-811.pd

Squirrelpox virus: assessing prevalence, transmission and environmental degradation

Red squirrels (Sciurus vulgaris) declined in Great Britain and Ireland during the last century, due to habitat loss and the introduction of grey squirrels (Sciurus carolinensis), which competitively exclude the red squirrel and act as a reservoir for squirrelpox virus (SQPV). The disease is generally fatal to red squirrels and their ecological replacement by grey squirrels is up to 25 times faster where the virus is present. We aimed to determine: (1) the seropositivity and prevalence of SQPV DNA in the invasive and native species at a regional scale; (2) possible SQPV transmission routes; and, (3) virus degradation rates under differing environmental conditions. Grey (n = 208) and red (n = 40) squirrel blood and tissues were sampled. Enzyme-linked immunosorbent assay (ELISA) and quantitative real-time polymerase chain reaction (qPCR) techniques established seropositivity and viral DNA presence, respectively. Overall 8% of squirrels sampled (both species combined) had evidence of SQPV DNA in their tissues and 22% were in possession of antibodies. SQPV prevalence in sampled red squirrels was 2.5%. Viral loads were typically low in grey squirrels by comparison to red squirrels. There was a trend for a greater number of positive samples in spring and summer than in winter. Possible transmission routes were identified through the presence of viral DNA in faeces (red squirrels only), urine and ectoparasites (both species). Virus degradation analyses suggested that, after 30 days of exposure to six combinations of environments, there were more intact virus particles in scabs kept in warm (25°C) and dry conditions than in cooler (5 and 15°C) or wet conditions. We conclude that SQPV is present at low prevalence in invasive grey squirrel populations with a lower prevalence in native red squirrels. Virus transmission could occur through urine especially during warm dry summer conditions but, more notably, via ectoparasites, which are shared by both species

The northern sector of the last British ice sheet : maximum extent and demise

Strongly divided opinion has led to competing, apparently contradictory, views on the timing, extent, flow configuration and decay mechanism of the last British Ice Sheet. We review the existing literature and reconcile some of these differences using remarkable new sea-bed imagery. This bathymetric data provides unprecedented empirical evidence of confluence and subsequent separation of the last British and Fennoscandian Ice Sheets. Critically, it also allows a viable pattern of ice-sheet disintegration to be proposed for the first time. Covering the continental shelf around the northern United Kingdom, extensive echosounder data reveals striking geomorphic evidence – in the form of tunnel valleys and moraines – relating to the former British and Fennoscandian Ice Sheets. The pattern of tunnel valleys in the northern North Sea Basin and the presence of large moraines on the West Shetland Shelf, coupled with stratigraphic evidence from the Witch Ground Basin, all suggest that at its maximum extent a grounded ice sheet flowed from SE to NW across the northern North Sea Basin, terminating at the continental-shelf edge. The zone of confluence between the British and much larger Fennoscandian Ice Sheets was probably across the northern Orkney Islands, with fast-flowing ice in the Fair Isle Channel focusing sediment delivery to the Rona and Foula Wedges. This period of maximum confluent glaciation (c. 30–25 ka BP) was followed by a remarkable period of large-scale ice-sheet re-organisation. We present evidence suggesting that as sea level rose, a large marine embayment opened in the northern North Sea Basin, as far south as the Witch Ground Basin, forcing the two ice sheets to decouple rapidly along a north–south axis east of Shetland. As a result, both ice sheets rapidly adjusted to new quasi-stable margin positions forming a second distinct set of moraines (c. 24–18 ka BP). The lobate overprinted morphology of these moraines on the mid-shelf west of Orkney and Shetland indicates that the re-organisation of the British Ice Sheet was extremely dynamic — probably dominated by a series of internally forced readvances. Critically, much of the ice in the low-lying North Sea Basin may have disintegrated catastrophically as decoupling progressed in response to rising sea levels. Final-stage deglaciation was marked by near-shore ice streaming and increasing topographic control on ice-flow direction. Punctuated retreat of the British Ice Sheet continued until c. 16 ka BP when, following the North Atlantic iceberg-discharge event (Heinrich-1), ice was situated at the present-day coastline in NW Scotlan

Adenovirus: an emerging factor in red squirrel Sciurus vulgaris conservation

1. Adenovirus is an emerging threat to red squirrel Sciurus vulgaris conservation, but confirming clinically significant adenovirus infections in red squirrels is challenging. Rapid intestinal autolysis after death in wild animals frequently obscures pathology characteristic of the disease in animals found dead. 2. We review the available literature to determine current understanding of both subclinical and clinically significant adenovirus infections in free-living wild and captive red squirrel populations. 3. Benefits of scientific testing for adenovirus incorporating both transmission electron microscopy (TEM) and polymerase chain reaction (PCR) technologies are compared and contrasted. We favour viral particle detection using TEM in animals exhibiting enteropathy at post-mortem and the use of PCR to detect subclinical cases where no enteric abnormalities are observed. 4. Adenoviral infections associated with re-introduction studies are evaluated by examination of sporadic cases in wild populations and of data from captive collections used to service such studies. 5. The paucity of data available on adenovirus infection in grey squirrel Sciurus carolinensis populations is documented, and we highlight that although subclinical virus presence is recorded in several locations in Great Britain and in Italy, no clinically significant disease cases have been detected in the species thus far. 6. Current speculation about potential interspecific infection between sciurids and other woodland rodents such as wood mice Apodemus sylvaticus is examined. Where subclinical adenovirus presence has been detected in sympatric populations using the same point food sources, husbandry methods may be used to diminish the potential for cross-infection. 7. Our findings highlight the importance of controlling disease in red squirrel populations by using clearly defined scientific methods. In addition, we propose hypothetical conservation benefits of restricting contact rates between red squirrels and sympatric grey squirrels and of limiting competition from other woodland rodent species

Proglacial groundwater storage dynamics under climate change and glacier retreat

Proglacial aquifers are an important water store in glacierised mountain catchments that supplement meltwater‐fed river flows and support freshwater ecosystems. Climate change and glacier retreat will perturb water storage in these aquifers, yet the climate‐glacier‐groundwater response cascade has rarely been studied and remains poorly understood. This study implements an integrated modelling approach that combines distributed glacio‐hydrological and groundwater models with climate change projections to evaluate the evolution of groundwater storage dynamics and surface‐groundwater exchanges in a temperate, glacierised catchment in Iceland. Focused infiltration along the meltwater‐fed Virkisá River channel is found to be an important source of groundwater recharge and is projected to provide 14%–20% of total groundwater recharge by the 2080s. The simulations highlight a mechanism by which glacier retreat could inhibit river recharge in the future due to the loss of diurnal melt cycling in the runoff hydrograph. However, the evolution of proglacial groundwater level dynamics show considerable resilience to changes in river recharge and, instead, are driven by changes in the magnitude and seasonal timing of diffuse recharge from year‐round rainfall. The majority of scenarios simulate an overall reduction in groundwater levels with a maximum 30‐day average groundwater level reduction of 1 m. The simulations replicate observational studies of baseflow to the river, where up to 15% of the 30‐day average river flow comes from groundwater outside of the melt season. This is forecast to reduce to 3%–8% by the 2080s due to increased contributions from rainfall and meltwater runoff. During the melt season, groundwater will continue to contribute 1%–3% of river flow despite significant reductions in meltwater runoff inputs. Therefore it is concluded that, in the proglacial region, groundwater will continue to provide only limited buffering of river flows as the glacier retreats

Causes of mortality and pathological lesions observed post-mortem in red squirrels (Sciurus vulgaris) in Great Britain

Background: The red squirrel population in Great Britain has declined dramatically in recent decades, principally due to squirrelpox. Concern exists that red squirrels may become extinct nationally and, as there has been limited research in to diseases other than squirrelpox, this study aimed to identify additional causes of mortality. Results: Post-mortem examinations on 163 red squirrels found dead on Isle of Wight (IoW) England, in Scotland and at other locations in Great Britain showed that 41.7% (n = 68) were killed by road traffic and 9.2% (n = 15) by predators, principally domestic cats and dogs. The overall male/female ratio was 1.08/1. Fleas were recorded on 34.9% of IoW squirrels and on 43.8% of Scottish squirrels but sucking lice and ixodid ticks were only seen on Scottish squirrels. Bacterial infections were significant, particularly in association with respiratory disease (n = 16); two squirrels died of Bordetella bronchiseptica bronchopneumonia. Cases of fatal exudative dermatitis (n = 5) associated with a lukM-positive clone of Staphylococcus aureus occurred only on the IoW. Toxoplasmosis (n = 12) was also confined to IoW where it was responsible for almost one tenth (9.5%) of all deaths. Hepatozoonosis was common, especially in IoW squirrels, but was not considered a primary cause of mortality. Hepatic capillariasis affected four IoW squirrels and one from Scotland. Fungal infections included oral candidiasis, adiaspiromycosis and pulmonary phaeohyphomycosis. Neoplastic conditions diagnosed were: pulmonary carcinoma, gastric spindle cell tumour, renal papillary adenoma and trichoepithelioma. Epidermal hyperplasia of unknown aetiology was seen in squirrels showing crusty lesions of the ear pinnae on IoW (n = 3) and Brownsea Island (n = 1), associated in two cases with cutaneous wart-like growths. Miscellaneous diagnoses included chylothorax, electrocution, intussusception, suspected cholecalciferol rodenticide poisoning and foetal death and mummification. No cases of squirrelpox were diagnosed. Conclusions: Red squirrels in Britain suffer premature or unnatural mortality due to a number of conditions in addition to squirrelpox, many of which result, directly or indirectly, from human activities: road traffic trauma, pet predation, toxoplasmosis, trap injuries, rodenticide poisoning and electrocution accounted for 61% of all recorded mortality in this study. Red squirrels are also affected by several diseases of unknown aetiology which merit further research