On the syntactic characterization of some model theoretic relations

In this thesis we consider binary relations over the class of L - structures , for some fixed language L . Such a binary relation R, induces a binary relation R* between the class of theories in L; in the following natural way. If T1 and T2 are theories in L then T1R*T2 if &exist;A,B A T1 , Bf T2 and ARB. We characterize syntactically those pairs of theories related by R* by introducing the concept of a notion of goodness for R. This consists of a set of ordered pairs of sentences in L, Delta, with the property that for theories T1 and T2 * T1R*T2 if for no empty1, empty2> epsilon Delta do we have T1 empty and T2empty. Provided is defined in a syntactically simple way, we find , by negating both sides of * and restricting the theories to sentences that the property * closely resembles an Interpolation Theorem for R. Actually, a notion of goodness is more complicated than this and our results are more general. In the established approaches to find Interpolation Theorems, the weak point has been in the understanding of "syntactically simple". We show, by considering certain relations which can be "described" by a theory in a particular language extending L, that a notion of goodness can often be found immediately from such a theory. Indeed we find a model theoretic condition on R for which this is possible. It turns out to be a "union of chains" condition. Using this approach we obtain many Interpolation Theorems by analysing the structure of the theories used to "describe" R. In particular the methods are used to prove a version of Feferman's Interpolation Theorem in a many-sorted language. We give a characterization of those theories with the Amalgamation Property and the Strong Amalgamation Property. We conclude with a solution of an open problem of G. Gratzer.<p

Risk factors for detection of bovine viral diarrhoea virus in low-risk herds during the latter stages of Ireland’s eradication programme

Background: A national programme to eradicate bovine viral diarrhoea (BVD) has been in place in Ireland since 2013. To inform decision making in the end stages of eradication, and support the development of posteradication surveillance strategies, an understanding of risks of infection in a low prevalence system is required. Methods: A case-control study design was implemented. The study population comprised bovine herds that had calves born and tested negative for BVD virus (BVDV) every year from 2013 to 2019 (n = 46,219 herds). We defined cases as herds which had one or more test positive calves for the first time in 2019 (n = 204). Controls (n = 816) were randomly sampled from the herds which remained test negative in 2019. The effects of herd size, management system, inward movements, including those of potential trojan dams (pregnant animals brought into the herd that could potentially be carrying infected calves in utero), and proximity to herds testing positive in the preceding year, were investigated. Network analysis approaches were used to generate variables measuring connections with test positive herds through inward cattle movements. A generalised linear mixed model, including a county-level random effect, was used to explore these risk factors. Results: Our final model retained ln (herd size) (Odds Ratio (95% CI): 1.72 (1.40, 2.12)), distance from test positive herds (0.54 (0.44, 0.66) for each extra land-parcel boundary crossed to reach the closest herd which tested positive the preceding year), and ln (potential trojan dams + 1) (1.29 (1.05, 1.60)). The same variables were retained in the model where herds with confirmed transient infections only (n = 25) were excluded. Conclusions: Our findings suggest that care with biosecurity at farm boundaries and visitors and equipment entering the farm, and avoidance or careful risk assessment of purchasing potentially pregnant animals, may help prevent introduction of BVDV to low-risk herds. At policy level, consideration of herd size, proximity to test positive herds and purchasing patterns of potentially pregnant cattle may help target surveillance measures towards the end of the eradication programme.Department of Agriculture, Food and the Marin

Spatiotemporal patterns of abundance and ecological requirements of a labrid's juveniles reveal conditions for establishment success and range shift capacity

Distribution shifts of demersal fishes are important adaptive responses to warming oceans for species' persistence. Shifts are facilitated by factors such as adult movement and dispersal of pelagic larvae to normally cooler regions, where increasing ocean temperatures are now enhancing larval and juvenile survival. However, successful recruitment (i.e. larval settlement) at these new regions can be constrained by resource availability, specialisation (food, habitat) and ecological interactions (competition, predation). Evaluating the capacity or likelihood of a species to successfully shift or expand its range, provides information relevant to biodiversity conservation and fisheries management, and is particularly important for species with restricted ranges. Choerodon rubescens (Günther, 1862) is an exploited labrid endemic to ~ 1400 km of the west Australian coastline, encompassing 13° of latitude and a 6°C temperature gradient. This region recently experienced a rapid warming event of ~ 3°C, which lasted 3 months and mirrored ocean temperatures expected in the next 50 years. Following this event, high levels of recruitment of C. rubescens occurred towards its southern, cooler distribution limit. Juvenile abundances were surveyed in this study to evaluate: (1) the effect of elevated temperatures on recruitment success across shallow water habitats spanning the species' distribution, (2) temporal variation in recruitment success in the typically cooler, southern part of its range and (3) ecological characteristics important to recruit survival, including habitat preferences, diet and behaviour. Juvenile C. rubescens were significantly more abundant at the margin between reef and sand and towards the cooler southern range end. Reef margin habitat provides access to shelter from predators within the reef and to sand-associated invertebrate prey in adjacent soft sediments, where most feeding activity occurred. Juveniles were abundant (0.3 to 4 fish/40 m 2 ) in reef margin habitats of the southern cooler region for three consecutive years, with individuals represented by multiple cohorts, indicating suitable environmental conditions for ongoing recruitment and survival. Juveniles at this habitat were able to compete effectively with other co-occurring labrids for invertebrate prey. As oceans warm, the number of recruits arriving and surviving beyond the existing cooler range limit will be dependent on factors such as successful spawning, larval delivery and survival, and availability of reef margin habitat with associated prey; these factors will determine the successful range shift or expansion of C. rubescens. We present an example of how range-wide spatiotemporal ecological studies of juvenile fish can identify range shift capacity and inform management adaptive to climate change