A simple construction of complex equiangular lines

A set of vectors of equal norm in $\mathbb{C}^d$ represents equiangular lines if the magnitudes of the inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is conjectured that sets of this maximum size exist in $\mathbb{C}^d$ for every $d \geq 2$. We describe a new construction for maximum-sized sets of equiangular lines, exposing a previously unrecognized connection with Hadamard matrices. The construction produces a maximum-sized set of equiangular lines in dimensions 2, 3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing a link to previously known results; correction to Theorem 1 and updates to reference

Absolute abundance estimates from shallow water baited underwater camera surveys; a stochastic modelling approach tested against field data

This research was supported by a University of Glasgow Faculty Scholarship to KMD, a Collaborative Gearing Scheme grant from the Natural Environmental Research Council and the British Antarctic Survey (CGS-77) and an ASSEMBLE infrastructure access grant to DMB.Baited underwater cameras are becoming a popular tool to monitor fish and invertebrate populations within protected and inshore environments where trawl surveys are unsuitable. Modelling the arrival times of deep-sea grenadiers using an inverse square relationship has enabled abundance estimates, comparable to those from bottom trawl surveys, to be gathered from deep-sea baited camera surveys. Baited underwater camera systems in the shallow water environments are however, currently limited to relative comparisons of assemblages based on simple metrics such as MaxN (maximum number of fish seen at any one time). This study describes a stochastic simulation approach used to model the behaviour of fish and invertebrates around a BUC system to enable absolute abundance estimates to be generated from arrival patterns. Species-specific models were developed for the tropical reef fishes the black tip grouper (Epinephelus fasciatus) and moray eel (Gymnothorax spp.) and the Antarctic scavengers; the asteroid (Odontaster validus) and the nemertean worm (Parbolasia corrugatus). A sensitivity analysis explored the impact of input parameters on the arrival patterns (MaxN, time to the arrival of the first individual and the time to reach MaxN) for each species generated by the model. Sensitivity analysis showed a particularly strong link between MaxN and abundance indicating that this model could be used to generate absolute abundances from existing or future MaxN data. It in effect allows the slope of the MaxN vs. abundance relationship to be estimated. Arrival patterns generated by each model were used to estimate population abundance for the focal species and these estimates were compared to data from underwater visual census transects. Using a Bland-Altman analysis, baited underwater camera data processed using this model were shown to generate absolute abundance estimates that were comparable to underwater visual census data.PostprintPeer reviewe

The niche construction perspective: A critical appraisal

Niche construction refers to the activities of organisms that bring about changes in their environments, many of which are evolutionarily and ecologically consequential. Advocates of niche construction theory (NCT) believe that standard evolutionary theory fails to recognize the full importance of niche construction, and consequently propose a novel view of evolution, in which niche construction and its legacy over time (ecological inheritance) are described as evolutionary processes, equivalent in importance to natural selection. Here, we subject NCT to critical evaluation, in the form of a collaboration between one prominent advocate of NCT, and a team of skeptics. We discuss whether niche construction is an evolutionary process, whether NCT obscures or clarifies how natural selection leads to organismal adaptation, and whether niche construction and natural selection are of equivalent explanatory importance. We also consider whether the literature that promotes NCT overstates the significance of niche construction, whether it is internally coherent, and whether it accurately portrays standard evolutionary theory. Our disagreements reflect a wider dispute within evolutionary theory over whether the neo-Darwinian synthesis is in need of reformulation, as well as different usages of some key terms (e.g. evolutionary process)

LiDAR mapping of tidal marshes for ecogeomorphological modelling in the TIDE project

The European research project TIDE (Tidal Inlets Dynamics and Environment) is developing and validating coupled models describing the morphological, biological and ecological evolution of tidal environments. The interactions between the physical and biological processes occurring in these regions requires that the system be studied as a whole rather than as separate parts. Extensive use of remote sensing including LiDAR is being made to provide validation data for the modelling. This paper describes the different uses of LiDAR within the project and their relevance to the TIDE science objectives. LiDAR data have been acquired from three different environments, the Venice Lagoon in Italy, Morecambe Bay in England, and the Eden estuary in Scotland. LiDAR accuracy at each site has been evaluated using ground reference data acquired with differential GPS. A semi-automatic technique has been developed to extract tidal channel networks from LiDAR data either used alone or fused with aerial photography. While the resulting networks may require some correction, the procedure does allow network extraction over large areas using objective criteria and reduces fieldwork requirements. The networks extracted may subsequently be used in geomorphological analyses, for example to describe the drainage patterns induced by networks and to examine the rate of change of networks. Estimation of the heights of the low and sparse vegetation on marshes is being investigated by analysis of the statistical distribution of the measured LiDAR heights. Species having different mean heights may be separated using the first-order moments of the height distribution

Root oxygen deprivation and the reduction of leaf stomatal aperture and gas exchange

The most ubiquitous plant abiotic stress in the global environment is generally thought to be water deficit. The opposite of water-deficit stress. flooding, initially involves relief of the abiotic factor of water deficit and only becomes stressful after flooding persists long enough to directly or indirectly interfere with a variety of plant functions via several mechanisms. The relief of stress with short term flooding (typically a day or less) is the principle upon which irrigation hinges. By contrast, the negative impacts of prolonged flooding on ecosystems, and particularly agricultural production systems, are substantial [I] and may be as significant as drought, depending on one's accounting strategy. Much of this impact is the result of the combination of soil and plant chemical, physical, and biological changes that cause stomata to close after prolonged flooding. This contributes significantly to a drastic reduction in photosynthesis and damages many other plant functions by disrupting transpiration and the complex system of hormonal control of plant systems and processes

Measurement of the Neutron Lifetime by Counting Trapped Protons

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Radiofrequency Ablation Resulting in Left Lobe Hypertrophy and Improved Resectability

Surgical resection for colorectal liver metastases may only be considered when an adequate functional residual volume can be preserved. Selective portal venous embolisation may be used to increase this volume, whilst chemotherapy and radiofrequency ablation (RFA) can be used to treat inoperable lesions. A 73-year-old man with liver metastasis proceeded to surgery, with the intention to perform a right hemi-hepatectomy. Unexpectedly at laparotomy, despite adequate pre-operative imaging, both the right and middle hepatic veins were involved. At that time extended right hemi-hepatectomy was contraindicated by insufficient residual volume and RFA was performed. Follow-up imaging revealed atrophy of the lesion. Significantly, there was also left lateral lobe hypertrophy sufficient to permit resection, which was performed without complication. Thrombosis of intra-hepatic portal veins is a recognised complication of RFA but here it appears to have been beneficial. The case highlights the need for regular review of unresectable hepatic disease by a liver surgeon and could suggest new modalities of portal embolisation

Measurement of the Neutron Lifetime by Counting Trapped Protons

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Tracking Black Holes in Numerical Relativity

This work addresses and solves the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon, as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal's solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative physics for the asymmetric collision; including: 1. Bounds on the topology of the throat connecting the holes following merger, 2. Time of merger, and 3. Continuous accounting for the surface of section areas of the black hole sources.Comment: 14 pages, 16 figure

Law, politics and the governance of English and Scottish joint-stock companies 1600-1850

This article examines the impact of law on corporate governance by means of a case study of joint-stock enterprise in England and Scotland before 1850. Based on a dataset of over 450 company constitutions together with qualitative information on governance practice, it finds little evidence to support the hypothesis that common-law regimes such as England were more supportive of economic growth than civil-law jurisdictions such as Scotland: indeed, levels of shareholder protection were slightly stronger in the civil-law zone. Other factors, such as local political institutions, played a bigger role in shaping organisational forms and business practice