Models of Type Theory Based on Moore Paths

This paper introduces a new family of models of intensional Martin-L\"of type theory. We use constructive ordered algebra in toposes. Identity types in the models are given by a notion of Moore path. By considering a particular gros topos, we show that there is such a model that is non-truncated, i.e. contains non-trivial structure at all dimensions. In other words, in this model a type in a nested sequence of identity types can contain more than one element, no matter how great the degree of nesting. Although inspired by existing non-truncated models of type theory based on simplicial and cubical sets, the notion of model presented here is notable for avoiding any form of Kan filling condition in the semantics of types.Comment: This is a revised and expanded version of a paper with the same name that appeared in the proceedings of the 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017

A Harmonised Approach to Curating Research-Ready Datasets for Asthma, Chronic Obstructive Pulmonary Disease (COPD) and Interstitial Lung Disease (ILD) in England, Wales and Scotland Using Clinical Practice Research Datalink (CPRD), Secure Anonymised Information Linkage (SAIL) Databank and DataLoch

Background: Electronic healthcare records (EHRs) are an important resource for health research that can be used to improve patient outcomes in chronic respiratory diseases. However, consistent approaches in the analysis of these datasets are needed for coherent messaging, and when undertaking comparative studies across different populations.Methods and results: We developed a harmonised curation approach to generate comparable patient cohorts for asthma, chronic obstructive pulmonary disease (COPD) and interstitial lung disease (ILD) using datasets from within Clinical Practice Research Datalink (CPRD; for England), Secure Anonymised Information Linkage (SAIL; for Wales) and DataLoch (for Scotland) by defining commonly derived variables consistently between the datasets. By working in parallel on the curation methodology used for CPRD, SAIL and DataLoch for asthma, COPD and ILD, we were able to highlight key differences in coding and recording between the databases and identify solutions to enable valid comparisons.Conclusion: Codelists and metadata generated have been made available to help re-create the asthma, COPD and ILD cohorts in CPRD, SAIL and DataLoch for different time periods, and provide a starting point for the curation of respiratory datasets in other EHR databases, expediting further comparable respiratory research

Vesivirus 2117 capsids more closely resemble sapovirus and lagovirus particles than other known vesivirus structures

Vesivirus 2117 is an adventitious agent that in 2009, was identified as a contaminant of CHO cells propagated in bioreactors at a pharmaceutical manufacturing plant belonging to Genzyme. The consequent interruption in supply of Fabrazyme and Cerezyme (drugs used to treat Fabry and Gaucher disease respectively), caused significant economic losses. Vesivirus 2117 is a member of the Caliciviridae; a family of small icosahedral viruses encoding a positive sense RNA genome. We have used cryo-electron microscopy and three dimensional image reconstruction to calculate a structure of vesivirus 2117 virus like particles as well as feline calicivirus and a chimeric sapovirus. We present a structural comparison of several members of the Caliciviridae, showing that the distal P domain of vesivirus 2117 is morphologically distinct from that seen in other known vesivirus structures. Furthermore, at intermediate resolutions we found a high level of structural similarity between vesivirus 2117 and Caliciviridae from other genera, such as sapovirus and rabbit haemorrhagic disease virus. Phylogenetic analysis confirms vesivirus 2117 as a vesivirus closely related to canine vesiviruses. We postulate that morphological differences in virion structure seen between vesivirus clades may reflect differences in receptor usage

Hysteretic thermal spin-crossover in heteroleptic Fe(II) complexes using alkyl chain substituted 2,2’-dipyridylamine ligands

The alkyl chain carrying ligands N,N-di(pyridin-2-yl)butanamide (LC4) and N,N-di(pyridin-2-yl)decanamide (LC10) were combined with NCS− co-ligands to form the neutral heteroleptic Fe(II) complexes trans-[FeII(LC4)2(NCS)2] (1C4) and trans-[FeII(LC10)2(NCS)2] (1C10). Variable temperature crystallographic studies revealed that 1C4 is in the orthorhombic space group Pna21 between 85–200 K whereas 1C10 is in the monoclinic space group P21/c between 85–140 K. The average Fe–N bond lengths suggest that at 85 K 1C4 contains LS Fe(II) centres; however, the ca. 0.18 Å increase in the average Fe–N bond lengths between 85 and 120 K suggests a spin-transition to the HS state occurs within this temperature interval. 1C10 contains LS Fe(II) centres between 85 and 105 K. Upon warming from 105 to 140 K the average Fe–N bond lengths increase by ca. 0.19 Å, which suggests a spin-transition to the HS state. Solid-state magnetic susceptibility measurements showed that 1C4 undergoes semi-abrupt spin-crossover with T1/2 = 127.5 K and a thermal hysteresis of ca. 13 K whereas, 1C10 undergoes an abrupt spin-crossover with T1/2 = 119.0 K, and is also accompanied by thermal hysteresis of ca. 4 K. The crystallographic and magnetic data show that the length of the complex's alkyl chain substituents can have a large impact on the structure of the crystal lattice as well as a subtle effect on the T1/2 value for thermal spin-crossover

Foreign investment in Scotland

A significant feature of the UK economy throughout the post-war period has been the growth in direct foreign investment in manufacturing industries. For the host nation the main benefits are employment creation, income generation and import reduction or export expansion. Scotland has been particularly successful in attracting the lion's inward investment for example in the period 1945- 1965 a total of 108,500 jobs were created by foreign firms setting up manufacturing units in the despite its size, obtained 46,221 (42.6%), whereas the second most SE England, gained only 16,926 (15.6%). The reasons for this success have been attributed primarily to a combination of the availability of labour in Scotland, the financial inducements offered by central government as part of regional policy and, the undoubted attraction of the environment, notably of course golf courses, for foreign businessmen. This brief paper explores the nature of Scotland's direct foreign investment and the reasons for its success

Review of the quarter's economic trends [April 1980]

This brief paper surveys recent world and UK economic data and reveals that there are some signs to suggest that the world economy will withstand the 1979 oil price shock better than it did in 1973/74. The main difference is that the 1979 price rise was not super-imposed on as severe an inflation as that which occurred on the previous occasion. The present rate of increase in the world prices should not reach the levels of the last cycle when the twelve month increase in manufacturing prices peaked at 23%. Advance warning by US economists that 1979 was going to be a year of difficulty did not go unnoticed by businessmen in that country who took steps in 1978 to avoid a repetition of the inventory boom and bust cycle which had proved so costly in the recession of 1973/74. Also, consumer expectations are adjusting towards a continuing rise in the price of oil. In the UK real GDP is expected to fall by 2½% from mid-year 1980. Thereafter, it is assumed to grow at an average annual rate of 1% for the next four years

The tax and price index

A feature of this year's Budget was the shift in emphasis from direct taxation to indirect taxation. The annual yield of income tax has been reduced by £4½ billion while that of direct taxes was increased by a similar amount. It must be acknowledged that the new tax and price index has a number of deficiencies. It is only applicable to a proportion of the population, namely those who pay tax and whose gross income is less than £10,000 per annum. It takes no account of the social wage, nor of changes in benefits, such as the recent restructuring of child allowance. It smoothes out tax payments over a full year even though, for administrative reasons, these may fluctuate widely from month to month. This brief paper explores some of these deficiencies in more detail and assess their impact on taxation

Bisimulation as path type for guarded recursive types

In type theory, coinductive types are used to represent processes, and are thus crucial for the formal verification of non-terminating reactive programs in proof assistants based on type theory, such as Coq and Agda. Currently, programming and reasoning about coinductive types is difficult for two reasons: The need for recursive definitions to be productive, and the lack of coincidence of the built-in identity types and the important notion of bisimilarity. Guarded recursion in the sense of Nakano has recently been suggested as a possible approach to dealing with the problem of productivity, allowing this to be encoded in types. Indeed, coinductive types can be encoded using a combination of guarded recursion and universal quantification over clocks. This paper studies the notion of bisimilarity for guarded recursive types in Ticked Cubical Type Theory, an extension of Cubical Type Theory with guarded recursion. We prove that, for any functor, an abstract, category theoretic notion of bisimilarity for the final guarded coalgebra is equivalent (in the sense of homotopy type theory) to path equality (the primitive notion of equality in cubical type theory). As a worked example we study a guarded notion of labelled transition systems, and show that, as a special case of the general theorem, path equality coincides with an adaptation of the usual notion of bisimulation for processes. In particular, this implies that guarded recursion can be used to give simple equational reasoning proofs of bisimilarity. This work should be seen as a step towards obtaining bisimilarity as path equality for coinductive types using the encodings mentioned above