The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Testing the use of marine protected areas to restore and manage tropical multispecies invertebrate fisheries at the Arnavon Islands, Solomon Islands : termination report

This report aimed to determine if the number and size of commercially important invertebrates (e.g. trochus, sea cucumbers and giant clams) increases as the result of the declaration of the Arnavon Islands Marine Conservation Area (MCA) relative to fished areas

Experimental test of higher-order Laguerre–Gauss modes in the 10 m Glasgow prototype interferometer

Brownian noise of dielectric mirror coatings is expected to be one of the limiting noise sources, at the peak sensitivity, of next generation ground based interferometric gravitational wave (GW) detectors. The use of higher-order Laguerre–Gauss (LG) beams has been suggested to reduce the effect of coating thermal noise in future generations of gravitational wave detectors. In this paper we describe the first test of interferometry with higher-order LG beams in an environment similar to a full-scale gravitational wave detector. We compare the interferometric performance of higher-order LG modes and the fundamental mode beams, injected into a 10 m long suspended cavity that features a finesse of 612, a value chosen to be typical of future gravitational wave detectors. We found that the expected mode degeneracy of the injected LG3, 3 beam was resolved into a multiple peak structure, and that the cavity length control signal featured several nearby zero crossings. The break up of the mode degeneracy is due to an astigmatism (defined as |Rcy − Rcx|) of 5.25 ± 0.5 cm on one of our cavity mirrors with a radius of curvature (Rc) of 15 m. This observation agrees well with numerical simulations developed with the FINESSE software. We also report on how these higher-order mode beams respond to the misalignment and mode mismatch present in our 10 m cavity. In general we found the LG3, 3 beam to be considerably more susceptible to astigmatism and mode mismatch than a conventional fundamental mode beam. Therefore the potential application of higher-order Laguerre–Gauss beams in future gravitational wave detectors will impose much more stringent requirements on both mode matching and mirror astigmatism

Experimental demonstration of coupled optical springs

Optical rigidity will play an important role in improving the sensitivity of future generations of gravitational wave (GW) interferometers, which employ high laser power in order to reach and exceed the standard quantum limit. Several experiments have demonstrated the combined effect of two optical springs on a single system for very low-weight mirror masses or membranes. In this paper we investigate the complex interactions between multiple optical springs and the surrounding apparatus in a system of comparable dynamics to a large-scale GW detector. Using three 100 g mirrors to form a coupled cavity system capable of sustaining two or more optical springs, we demonstrate a number of different regimes of opto-mechanical rigidity and measurement techniques. Our measurements reveal couplings between each optical spring and the control loops that can affect both the achievable increase in sensitivity and the stability of the system. Hence this work establishes a better understanding of the realisation of these techniques and paves the way to their application in future GW observatories, such as upgrades to Advanced LIGO

Efficacy and safety of Cannabidiol and Tetrahydrocannabivarin on glycemic and lipid parameters in patients with Type 2 diabetes: a randomized, double-blind, placebo-controlled, parallel group pilot study

OBJECTIVE Cannabidiol (CBD) and Δ9-tetrahydrocannabivarin (THCV) are nonpsychoactive phytocannabinoids affecting lipid and glucose metabolism in animal models. This study set out to examine the effects of these compounds in patients with type 2 diabetes. RESEARCH DESIGN AND METHODS In this randomized, double-blind, placebo-controlled study, 62 subjects with noninsulin-treated type 2 diabetes were randomized to five treatment arms: CBD (100 mg twice daily), THCV (5 mg twice daily), 1:1 ratio of CBD and THCV (5 mg/5 mg, twice daily), 20:1 ratio of CBD and THCV (100 mg/5 mg, twice daily), or matched placebo for 13 weeks. The primary end point was a change in HDL-cholesterol concentrations from baseline. Secondary/tertiary end points included changes in glycemic control, lipid profile, insulin sensitivity, body weight, liver triglyceride content, adipose tissue distribution, appetite, markers of inflammation, markers of vascular function, gut hormones, circulating endocannabinoids, and adipokine concentrations. Safety and tolerability end points were also evaluated. RESULTS Compared with placebo, THCV significantly decreased fasting plasma glucose (estimated treatment difference [ETD] = −1.2 mmol/L; P < 0.05) and improved pancreatic β-cell function (HOMA2 β-cell function [ETD = −44.51 points; P < 0.01]), adiponectin (ETD = −5.9 × 106 pg/mL; P < 0.01), and apolipoprotein A (ETD = −6.02 μmol/L; P < 0.05), although plasma HDL was unaffected. Compared with baseline (but not placebo), CBD decreased resistin (−898 pg/ml; P < 0.05) and increased glucose-dependent insulinotropic peptide (21.9 pg/ml; P < 0.05). None of the combination treatments had a significant impact on end points. CBD and THCV were well tolerated. CONCLUSIONS THCV could represent a new therapeutic agent in glycemic control in subjects with type 2 diabetes

Candidates for a possible third-generation gravitational wave detector: comparison of ring-Sagnac and sloshing-Sagnac speedmeter interferometers

Speedmeters are known to be quantum non-demolition devices and, by potentially providing sensitivity beyond the standard quantum limit, become interesting for third generation gravitational wave detectors. Here we introduce a new configuration, the sloshing-Sagnac interferometer, and compare it to the more established ring-Sagnac interferometer. The sloshing-Sagnac interferometer is designed to provide improved quantum noise limited sensitivity and lower coating thermal noise than standard position meter interferometers employed in current gravitational wave detectors. We compare the quantum noise limited sensitivity of the ring-Sagnac and the sloshing-Sagnac interferometers, in the frequency range, from 5 Hz to 100 Hz, where they provide the greatest potential benefit. We evaluate the improvement in terms of the unweighted noise reduction below the standard quantum limit, and by finding the range up to which binary black hole inspirals may be observed. The sloshing-Sagnac was found to give approximately similar or better sensitivity than the ring-Sagnac in all cases. We also show that by eliminating the requirement for maximally-reflecting cavity end mirrors with correspondingly-thick multi-layer coatings, coating noise can be reduced by a factor of approximately 2.2 compared to conventional interferometers

Environmental and economic information for aggregates provision

This report describes a one-year research project entitled ‘Environmental and economic information systems for aggregates provision’. This project is an extension to previous research on Strategic Environmental Assessment (SEA) and future aggregates extraction, which was carried out by the British Geological Survey (BGS) and reported in early 2004 (Steadman, et al., 2004). Both phases of the research were co-funded by the BGS and the Mineral Industry Sustainable Technology Programme (MIST). Environmental, economic and social information are essential for sustainable planning for the provision of aggregates. There is a need to bring together disparate information relating to aggregate extraction. Datasets include the location of resources and their potential end-uses, as well as those on the environment and transport. Bringing this digital information together into one location or system will assist in supporting a more balanced and informed approach to the decision making process. A number of regulatory mechanisms are currently driving the gathering and compilation of relevant environmental, economic and social information. Current drivers for information relevant to aggregate provision include environmental appraisal of the provision of aggregates, SEA and Sustainability Appraisal (SA). The objective of this research was to provide an interactive ‘tool’ or information system for the minerals industry, land-use planners and other stakeholders to use when considering options for future aggregate provision. The study area for the research was the East Midlands Region of England. The project had three main deliverables: 1. To provide an online Geographic Information System (GIS) to access the ‘environmental sensitivity’ map which was developed for the East Midlands Region during the first phase of research; 2. to compile aggregate end-use suitability maps for the East Midland Region; and 3. to hold a stakeholder consultation exercise and dissemination seminars. Each of these was met within the agreed timeframe. The environmental sensitivity map information and associated attributes have been made available on the internet via the BGS ‘Minerals information online’ web GIS for the East Midlands Region (www.mineralsuk.com/web_gis). Accommodating these data in a web GIS environment has entailed some compromises on data resolution and system functionality. A methodology has been developed to integrate a range of aggregate technical property data. This can be used to summarise the distribution of aggregate resources suitable for particular end-uses. These summary technical data are useful in communicating issues of variable aggregate quality and economic value to non-technical stakeholders in the mineral planning process. Availability of appropriate technical property data for different aggregate resources across a wide geographical area is critical in developing these maps. Feedback from an extensive consultation and dissemination exercise has generally been very positive. Two critiques by independent consultants of the environmental sensitivity map were also undertaken. These were deemed an important aspect of the consultation process. Stakeholders raised several issues. There were some concerns about updating and maintenance of asset data and about the lack of social information. In addition, some fundamental issues of approach (particularly asset weighting) raised in the previous phase of this research resurfaced during this consultation. Environmental sensitivity mapping will be carried out for the whole of England by the BGS in the near future. The data will be made available online as each region becomes available. It is anticipated that the mineral GISs for all regions of England (except London) will be completed by December 2005. New datasets may be added to the environmental sensitivity layer as they become available. The research into end-use suitability maps will be carried on by the BGS under its Minerals Programme, with the support of co-funding where possible. The project team continue to welcome feedback and criticism of this research

Detailed study of BBN implications of neutrino oscillation generated neutrino asymmetries in some four neutrino models

We re-examine the evolution of neutrino asymmetries in several four neutrino models. The first case involves the direct creation of $L_{\nu_e}$ by $\nu_e \leftrightarrow \nu_s$ oscillations. In the second case, we consider the mass hierarchy $m_{\nu_\tau} \gg m_{\nu_\mu}, m_{\nu_e}, m_{\nu_s}$ where $\nu_\tau \leftrightarrow \nu_s$ oscillations generate a large $L_{\nu_\tau}$ and some of this asymmetry is converted into $L_{\nu_e}$ by $\nu_{\tau} \leftrightarrow \nu_{e}$ oscillations. We estimate the implications for BBN for a range of cosmologically interesting $\delta m^2$ values. The present paper improves on previous published work by taking into account the finite repopulation rate and the time dependence of the distortions to the neutrino momentum distributions. The treatment of chemical decoupling is also improved.Comment: Expanded discussion on the sign of the neutrino asymmetr

PT-Symmetry Quantum Electrodynamics--PTQED

The construction of $\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are discussed.Comment: 11 pages, 1 figure, contributed to Proceedings of 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physic