On the dimension of a certain measure in the plane

We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane. Our work generalizes work of Lewis and coauthors when the measure is $p$ harmonic and also for $p=2$, the well known theorem of Makarov regarding the Hausdorff dimension of harmonic measure relative to a point in a simply connected domain.Comment: 26 page

Complementary approaches to understanding the plant circadian clock

Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock

Complementary approaches to understanding the plant circadian clock

This is the final version of the article. Available from the Open Publishing Association via the DOI in this record.Proceedings - Third Workshop 'From Biology To Concurrency and back', Paphos, Cyprus, 27 March 2010Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock.The authors thank Gerben van Ooijen for TopCount data and Jane Hillston and Andrew Millar for their helpful comments. The Centre for Systems Biology at Edinburgh is a Centre for Integrative Systems Biology (CISB) funded by BBSRC and EPSRC, ref. BB/D019621/1. CT is supported by The International Human Frontier Science Program Organization

Lagrange structure and quantization

A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the Lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in $d+1$ dimensions, being localized on the boundary, are proved to be equivalent to the original theory in $d$ dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.Comment: Minor corrections, format changed, 40 page

On the logarithm of the minimizing integrand for certain variational problems in two dimensions

Abstract Let be a smooth convex homogeneous function of degree , 1 < < ∞, on ℂ ∖ {0}. We show that if is a minimizer for the functional whose integrand is (∇ ), in a certain subclass of the Sobolev space 1, (Ω), and ∇ ∕ = 0 at ∈ Ω, then in a neighborhood of , log (∇ ) is a sub, super, or solution (depending on whether > 2, < 2, or = 2 ) to where We then indicate the importance of this fact in previous work of the authors when ( ) = | | and indicate possible future generalizations of this work in which this fact will play a fundamental role. 2000 Mathematics Subject Classification. Primary 35J25, 35J70

Benign paroxysmal positional vertigo after radiologic scanning: a case series

<p>Abstract</p> <p>Introduction</p> <p>Benign paroxysmal positional vertigo (BPPV) is the most common type of vertigo. It is frequently seen in elderly patients, and the course of the attack may easily mimic cerebrovascular disease. A BPPV attack after a radiologic examination has not been reported previously. We report the cases of two patients who had BPPV attacks after radiologic imaging.</p> <p>Case presentation</p> <p>The first patient with headache and tremor was admitted to the radiology department for cranial computed tomography (CT) imaging. During scanning, she was asked to lie in the supine position with no other head movements for approximately 10 minutes. After the cranial CT imaging, she stood up rapidly, and suddenly experienced a vertigo attack and nausea. The second patient was admitted to the radiology department for evaluation of his renal arteries. During the renal magnetic resonance angiography, he was in the supine position for 20 minutes and asked not to move. After the examination, he stood up rapidly with the help of the technician and suddenly experienced a vertigo attack with nausea and vomiting. The results of standard laboratory analyses and their neurologic examinations were within normal limits and Dix-Hallpike tests showed rotatory nystagmus in both cases. An Epley maneuver was performed to the patients. The results of a control Dix-Hallpike tests after 1 Epley maneuver were negative in both patients.</p> <p>Conclusion</p> <p>Radiologists and clinicians must keep in mind that after radiologic imaging in which the patient is still for some time in the supine position and then helped to stand up rapidly, a BPPV attack may occur.</p

Randomised controlled single-blind study of conventional versus depot mydriatic drug delivery prior to cataract surgery

BACKGROUND: A prerequisite for safe cataract surgery is an adequately dilated pupil. The authors conducted a trial to assess the efficacy (in terms of pupil diameter) of a depot method of pre-operative pupil dilatation, as compared with repeated instillations of drops (which is time-consuming for the nursing staff and uncomfortable for the patient). METHODS: A prospective randomised masked trial was conducted comprising 130 patients with no significant ocular history undergoing elective clear corneal phacoemulsification. 65 patients had mydriatic drops (Tropicamide 1%, Phenylephrine 2.5%, Diclofenac sodium 0.1%) instilled prior to surgery, 65 had a wick soaked in the same drop mixture placed in the inferior fornix. Horizontal pupil diameters were recorded on a millimetre scale immediately prior to surgery. RESULTS: There was no significant difference in pupil size between the two groups (p = 0.255, Student's t-test). CONCLUSION: There was no significant difference between the mydriasis obtained with the depot system compared with conventional drop application. Use of a depot mydriatic delivery system appears to be a safe and efficient method of drug delivery. TRIAL REGISTRATION: International Standard Randomised Controlled Trial Number Register ISRCTN7804776

First generation immigrant judgements of offence seriousness: evidence from the crime survey for England and Wales

This exploratory paper delves into differences and similarities in the rated seriousness of offences suffered by victims of different national origin. The issue is important because a mismatch between police and victim assessments of seriousness is likely to fuel discord. It was found that first generation immigrants did not differ in their rating of the seriousness of offences against the person from either the indigenous population or according to region of birth. However those of Asian origin rated vehicle and property crime they had suffered as more serious than did other groups about crimes they suffered. The anticipated higher seriousness rating of offences reported to the police r was observed for all groups. People of Asian origin reported to the police a smaller proportion of offences they rated trivial than did people in other groups. Analysis of seriousness judgements in victimization surveys represents a much-underused resource for understanding the nexus between public perceptions and criminal justice responses