The generalised type-theoretic interpretation of constructive set theory

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation

Quantum teleportation on a photonic chip

Quantum teleportation is a fundamental concept in quantum physics which now finds important applications at the heart of quantum technology including quantum relays, quantum repeaters and linear optics quantum computing (LOQC). Photonic implementations have largely focussed on achieving long distance teleportation due to its suitability for decoherence-free communication. Teleportation also plays a vital role in the scalability of photonic quantum computing, for which large linear optical networks will likely require an integrated architecture. Here we report the first demonstration of quantum teleportation in which all key parts - entanglement preparation, Bell-state analysis and quantum state tomography - are performed on a reconfigurable integrated photonic chip. We also show that a novel element-wise characterisation method is critical to mitigate component errors, a key technique which will become increasingly important as integrated circuits reach higher complexities necessary for quantum enhanced operation.Comment: Originally submitted version - refer to online journal for accepted manuscript; Nature Photonics (2014

Industrial strategy and the UK regions: Sectorally narrow and spatially blind

The UK government's new Industrial Strategy could have a significant impact on the country's regions and localities. However, this has received little attention to date. The analysis presented here examines the existing location of the sectors targeted by the first phase of the Industrial Strategy Challenge Fund and the location of the R&D laboratories likely to be first in line for funding. In focusing on an extremely narrow range of sectors, the Fund is likely to have limited impact on the UK's persistent regional inequalities. The activities eligible for support account for relatively little of manufacturing or the rest of the economy and the basis of this targeting and its potential distributional consequences are spatially blind. As such, it runs the risk of widening regional divides in prosperity

Common NOTCH3 Variants and Cerebral Small-Vessel Disease.

BACKGROUND AND PURPOSE: The most common monogenic cause of cerebral small-vessel disease is cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy, caused by NOTCH3 gene mutations. It has been hypothesized that more common variants in NOTCH3 may also contribute to the risk of sporadic small-vessel disease. Previously, 4 common variants (rs10404382, rs1043994, rs10423702, and rs1043997) were found to be associated with the presence of white matter hyperintensity in hypertensive community-dwelling elderly. METHODS: We investigated the association of common single nucleotide polymorphisms (SNPs) in NOTCH3 in 1350 patients with MRI-confirmed lacunar stroke and 7397 controls, by meta-analysis of genome-wide association study data sets. In addition, we investigated the association of common SNPs in NOTCH3 with MRI white matter hyperintensity volumes in 3670 white patients with ischemic stroke. In each analysis, we considered all SNPs within the NOTCH3 gene, and within 50-kb upstream and downstream of the coding region. A total of 381 SNPs from the 1000 genome population with a mean allele frequency>0.01 were included in the analysis. A significance level of P<0.0015 was used, adjusted for the effective number of independent SNPs in the region using the Galwey method. RESULTS: We found no association of any common variants in NOTCH3 (including rs10404382, rs1043994, rs10423702, and rs1043997) with lacunar stroke or white matter hyperintensity volume. We repeated our analysis stratified for hypertension but again found no association. CONCLUSIONS: Our study does not support a role for common NOTCH3 variation in the risk of sporadic small-vessel disease.Collection of the UK Young Lacunar Stroke DNA Study (DNA lacunar) was primarily supported by the Wellcome Trust (WT072952) with additional support from the Stroke Association (TSA 2010/01). Genotyping of the DNA lacunar samples, and Dr Traylor, was supported by a Stroke Association Grant (TSA 2013/01). Funding for the genotyping at Massachusetts General Hospital was provided by the Massachusetts General Hospital- Deane Institute for the Integrative Study of Atrial Fibrillation and Stroke and the National Institute of Neurological Disorders and Stroke (U01 NS069208). Dr Rutten-Jacobs was supported by a project grant from the Stroke Association/British Heart Foundation grant (TSA BHF 2010/01). Dr Adib-Samii was supported by a Medical Research Council (United Kingdom) training fellowship. Drs Markus and Bevan were supported by the National Institute for Health Research Cambridge University Hospitals Comprehensive Biomedical Research Centre. Dr Markus was supported by a National Institute for Health Research Senior Investigator award. Dr Thijs was supported by a Clinical Investigator Grant from the scientific research fund, Fonds Wetenschappelijk Onderzoek Flanders. Dr Rost was supported by a National Institute of Neurological Disorders and Stroke grant (R01 NS082285-01).This is the final published version. It first appeared at http://stroke.ahajournals.org/content/46/6/1482.long