Computing Linear Matrix Representations of Helton-Vinnikov Curves

Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances.Comment: 19 pages, 3 figures, minor revisions; Mathematical Methods in Systems, Optimization and Control, Birkhauser, Base

Garden varieties: how attractive are recommended garden plants to butterflies?

One way the public can engage in insect conservation is through wildlife gardening, including the growing of insect-friendly flowers as sources of nectar. However, plant varieties differ in the types of insects they attract. To determine which garden plants attracted which butterflies, we counted butterflies nectaring on 11 varieties of summer-flowering garden plants in a rural garden in East Sussex, UK. These plants were all from a list of 100 varieties considered attractive to British butterflies, and included the five varieties specifically listed by the UK charity Butterfly Conservation as best for summer nectar. A total of 2659 flower visits from 14 butterfly and one moth species were observed. We performed a principal components analysis which showed contrasting patterns between the species attracted to Origanum vulgare and Buddleia davidii. The “butterfly bush” Buddleia attracted many nymphalines, such as the peacock, Inachis io, but very few satyrines such as the gatekeeper, Pyronia tithonus, which mostly visited Origanum. Eupatorium cannibinum had the highest Simpson’s Diversity score of 0.75, while Buddleia and Origanum were lower, scoring 0.66 and 0.50 respectively. No one plant was good at attracting all observed butterfly species, as each attracted only a subset of the butterfly community. We conclude that to create a butterfly-friendly garden, a variety of plant species are required as nectar sources for butterflies. Furthermore, garden plant recommendations can probably benefit from being more precise as to the species of butterfly they attract

Sentinel node detection in N0 cancer of the pharynx and larynx

Neck lymph node status is the most important factor for prognosis in head and neck squamous cell carcinoma. Sentinel node detection reliably predicts the lymph node status in melanoma and breast cancer patients. This study evaluates the predictive value of sentinel node detection in 50 patients suffering from pharyngeal and laryngeal carcinomas with a N0 neck as assessed by ultrasound imaging. Following 99m-Technetium nanocolloid injection in the perimeter of the tumour intraoperative sentinel node detection was performed during lymph node dissection. Postoperatively the histological results of the sentinel nodes were compared with the excised neck dissection specimen. Identification of sentinel nodes was successful in all 50 patients with a sensitivity of 89%. In eight cases the sentinel node showed nodal disease (pN1). In 41 patients the sentinel node was tumour negative reflecting the correct neck lymph node status (pN0). We observed one false-negative result. In this case the sentinel node was free of tumour, whereas a neighbouring lymph node contained a lymph node metastasis (pN1). Although we have shown, that skipping of nodal basins can occur, this technique still reliably identifies the sentinel nodes of patients with squamous cell carcinoma of the pharynx and larynx. Future studies must show, if sentinel node detection is suitable to limit the extent of lymph node dissection in clinically N0 necks of patients suffering from pharyngeal and laryngeal squamous cell carcinoma

Efimov physics beyond three particles

Efimov physics originally refers to a system of three particles. Here we review recent theoretical progress seeking for manifestations of Efimov physics in systems composed of more than three particles. Clusters of more than three bosons are tied to each Efimov trimer, but no independent Efimov physics exists there beyond three bosons. The case of a few heavy fermions interacting with a lighter atom is also considered, where the mass ratio of the constituent particles plays a significant role. Following Efimov's study of the (2+1) system, the (3+1) system was shown to have its own critical mass ratio to become Efimovian. We show that the (4+1) system becomes Efimovian at a mass ratio which is smaller than its sub-systems thresholds, giving a pure five-body Efimov effect. The (5+1) and (6+1) systems are also discussed, and we show the absence of 6- and 7-body Efimov physics there

An Explicit Strategy Prevails When the Cerebellum Fails to Compute Movement Errors

In sensorimotor adaptation, explicit cognitive strategies are thought to be unnecessary because the motor system implicitly corrects performance throughout training. This seemingly automatic process involves computing an error between the planned movement and actual feedback of the movement. When explicitly provided with an effective strategy to overcome an experimentally induced visual perturbation, people are immediately successful and regain good task performance. However, as training continues, their accuracy gets worse over time. This counterintuitive result has been attributed to the independence of implicit motor processes and explicit cognitive strategies. The cerebellum has been hypothesized to be critical for the computation of the motor error signals that are necessary for implicit adaptation. We explored this hypothesis by testing patients with cerebellar degeneration on a motor learning task that puts the explicit and implicit systems in conflict. Given this, we predicted that the patients would be better than controls in maintaining an effective strategy assuming strategic and adaptive processes are functionally and neurally independent. Consistent with this prediction, the patients were easily able to implement an explicit cognitive strategy and showed minimal interference from undesirable motor adaptation throughout training. These results further reveal the critical role of the cerebellum in an implicit adaptive process based on movement errors and suggest an asymmetrical interaction of implicit and explicit processes

Causarum Investigatio and the Two Bell's Theorems of John Bell

"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bell's theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on one's basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbach's Principle of common cause. By breaking down the latter into even more basic Postulates, it is possible to obtain a version of Bell's theorem in which each camp could reject one assumption, happy that the remaining assumptions reflect its weltanschauung. Formulating Bell's theorem in terms of causation is fruitful not just for attempting to reconcile the two camps, but also for better describing the ontology of different quantum interpretations and for more deeply understanding the implications of Bell's marvellous work.Comment: 24 pages. Prepared for proceedings of the "Quantum [Un]speakables II" conference (Vienna, 2014), to be published by Springe

Chromatic Illumination Discrimination Ability Reveals that Human Colour Constancy Is Optimised for Blue Daylight Illuminations

The phenomenon of colour constancy in human visual perception keeps surface colours constant, despite changes in their reflected light due to changing illumination. Although colour constancy has evolved under a constrained subset of illuminations, it is unknown whether its underlying mechanisms, thought to involve multiple components from retina to cortex, are optimised for particular environmental variations. Here we demonstrate a new method for investigating colour constancy using illumination matching in real scenes which, unlike previous methods using surface matching and simulated scenes, allows testing of multiple, real illuminations. We use real scenes consisting of solid familiar or unfamiliar objects against uniform or variegated backgrounds and compare discrimination performance for typical illuminations from the daylight chromaticity locus (approximately blue-yellow) and atypical spectra from an orthogonal locus (approximately red-green, at correlated colour temperature 6700 K), all produced in real time by a 10-channel LED illuminator. We find that discrimination of illumination changes is poorer along the daylight locus than the atypical locus, and is poorest particularly for bluer illumination changes, demonstrating conversely that surface colour constancy is best for blue daylight illuminations. Illumination discrimination is also enhanced, and therefore colour constancy diminished, for uniform backgrounds, irrespective of the object type. These results are not explained by statistical properties of the scene signal changes at the retinal level. We conclude that high-level mechanisms of colour constancy are biased for the blue daylight illuminations and variegated backgrounds to which the human visual system has typically been exposed

A pragmatic harm reduction approach to manage a large outbreak of wound botulism in people who inject drugs, Scotland 2015

Abstract Background People who inject drugs (PWID) are at an increased risk of wound botulism, a potentially fatal acute paralytic illness. During the first 6 months of 2015, a large outbreak of wound botulism was confirmed among PWID in Scotland, which resulted in the largest outbreak in Europe to date. Methods A multidisciplinary Incident Management Team (IMT) was convened to conduct an outbreak investigation, which consisted of enhanced surveillance of cases in order to characterise risk factors and identify potential sources of infection. Results Between the 24th of December 2014 and the 30th of May 2015, a total of 40 cases were reported across six regions in Scotland. The majority of the cases were male, over 30 and residents in Glasgow. All epidemiological evidence suggested a contaminated batch of heroin or cutting agent as the source of the outbreak. There are significant challenges associated with managing an outbreak among PWID, given their vulnerability and complex addiction needs. Thus, a pragmatic harm reduction approach was adopted which focused on reducing the risk of infection for those who continued to inject and limited consequences for those who got infected. Conclusions The management of this outbreak highlighted the importance and need for pragmatic harm reduction interventions which support the addiction needs of PWID during an outbreak of spore-forming bacteria. Given the scale of this outbreak, the experimental learning gained during this and similar outbreaks involving spore-forming bacteria in the UK was collated into national guidance to improve the management and investigation of future outbreaks among PWID

How many sentinel nodes should be harvested in oral squamous cell carcinoma?

The number of harvested lymph nodes when performing sentinel lymph node (SLN) biopsy remains controversial. The aim of this study was to examine the maximum number of nodes to be harvested for histopathological analysis. We also wanted to determine if the level of radioactivity within a SLN or its size were indicators for the likelihood of nodal metastases. The SLNs from 34 neck dissection specimens from patients with T1/T2 N0 oral and oropharyngeal carcinomas were included. Altogether 76 SLNs were measured for radioactivity and lymph node dimensions and volume. Tumour was identified in 16 of 76 nodes (positive nodes), and the remaining 60 nodes were free from tumour (negative nodes). In 9 of 16 cases, metastases were in the hottest node. Two patients had more than one positive SLN: the first and fourth hottest in one and the second and fourth hottest nodes in another contained tumour. However, all patients would have been staged accurately if only the hottest three sentinel nodes had been retrieved. Lymph nodes that contained tumour had a greater maximum diameter than non-metastatic SLNs. To stage the neck accurately, only the three hottest lymph nodes required sampling