The geometry of manifolds and the perception of space

This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This notion of manifold and the geometric ideas which could be formulated and utilized in such a setting (measuring a distance between points, curvature and other geometric concepts) was an essential ingredient in Einstein's gravitational theory of space-time from 1916 and has played important roles in numerous other theories of nature ever since.Comment: arXiv admin note: substantial text overlap with arXiv:1301.064

Downregulation of genes with a function in axon outgrowth and synapse formation in motor neurones of the VEGF(delta/delta) mouse model of amyotrophic lateral sclerosis

Background: Vascular endothelial growth factor (VEGF) is an endothelial cell mitogen that stimulates vasculogenesis. It has also been shown to act as a neurotrophic factor in vitro and in vivo. Deletion of the hypoxia response element of the promoter region of the gene encoding VEGF in mice causes a reduction in neural VEGF expression, and results in adult-onset motor neurone degeneration that resembles amyotrophic lateral sclerosis (ALS). Investigating the molecular pathways to neurodegeneration in the VEGF(delta/delta) mouse model of ALS may improve understanding of the mechanisms of motor neurone death in the human disease. Results: Microarray analysis was used to determine the transcriptional profile of laser captured spinal motor neurones of transgenic and wild-type littermates at 3 time points of disease. 324 genes were significantly differentially expressed in motor neurones of presymptomatic VEGF(delta/delta) mice, 382 at disease onset, and 689 at late stage disease. Massive transcriptional downregulation occurred with disease progression, associated with downregulation of genes involved in RNA processing at late stage disease. VEGF(delta/delta) mice showed reduction in expression, from symptom onset, of the cholesterol synthesis pathway, and genes involved in nervous system development, including axonogenesis, synapse formation, growth factor signalling pathways, cell adhesion and microtubule-based processes. These changes may reflect a reduced capacity of VEGF(delta/delta) mice for maintenance and remodelling of neuronal processes in the face of demands of neural plasticity. The findings are supported by the demonstration that in primary motor neurone cultures from VEGF(delta/delta) mice, axon outgrowth is significantly reduced compared to wild-type littermates. Conclusions: Downregulation of these genes involved in axon outgrowth and synapse formation in adult mice suggests a hitherto unrecognized role of VEGF in the maintenance of neuronal circuitry. Dysregulation of VEGF may lead to neurodegeneration through synaptic regression and dying-back axonopathy

User's guide for the Solar Backscattered Ultraviolet (SBUV) and the Total Ozone Mapping Spectrometer (TOMS) RUT-S and RUT-T data sets: October 31, 1978 to November 1, 1980

Raw data from the Solar Backscattered Ultrviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus 7 operation are available on computer tape. These data are contained on two separate sets of RUTs (Raw Units Tapes) for SBUV and TOMS, labelled RUT-S and RUT-T respectively. The RUT-S and RUT-T tapes contain uncalibrated radiance and irradiance data, housekeeping data, wavelength and electronic calibration data, instrument field-of-view location and solar ephemeris information. These tapes also contain colocated cloud, terrain pressure and snow/ice thickness data, each derived from an independent source. The "RUT User's Guide" describes the SBUV and TOMS experiments, the instrument calibration and performance, operating schedules, and data coverage, and provides an assessment of RUT-S and -T data quality. It also provides detailed information on the data available on the computer tapes

Aligning scan acquisition circles in optical coherence tomography images of the retinal nerve fibre layer

Optical coherence tomography (OCT) is widely used in the assessment of retinal nerve fibre layer thickness (RNFLT) in glaucoma. Images are typically acquired with a circular scan around the optic nerve head. Accurate registration of OCT scans is essential for measurement reproducibility and longitudinal examination. This study developed and evaluated a special image registration algorithm to align the location of the OCT scan circles to the vessel features in the retina using probabilistic modelling that was optimised by an expectation-maximization algorithm. Evaluation of the method on 18 patients undergoing large numbers of scans indicated improved data acquisition and better reproducibility of measured RNFLT when scanning circles were closely matched. The proposed method enables clinicians to consider the RNFLT measurement and its scan circle location on the retina in tandem, reducing RNFLT measurement variability and assisting detection of real change of RNFLT in the longitudinal assessment of glaucoma

Quantifying discordance between structure and function measurements in the clinical assessment of glaucoma

Objective: The visual field (VF) may be predicted from retinal nerve fibre layer thickness (RNFLT) using a Bayesian Radial Basis Function (BRBF). This study aimed to evaluate a new methodology to quantify and visualise discordance between structural and functional measurements in glaucomatous eyes. Methods: Five GDxVCC RNFLT scans and 5 Humphrey SITA VF tests were obtained from 50 glaucomatous eyes from 50 patients. A best available estimate of the ‘true’ VF was calculated as the point-wise median of these 5 replications. This ‘true’ VF was compared with every single RNFLT-predicted VF from BRBF and every single measured VF. Predictability of VFs from RNFLT was established from previous data. A structure-function pattern discordance map (PDM) and structure-function discordance index (SFDI; values 0 to 1) were established from the predictability limits for each structure-function measurement pair to quantify and visualise the discordance between the structure-predicted and measured VFs. Results: Mean absolute difference (MAD) between the structure-predicted and ‘true’ VFs was 3.9dB. MAD between single and ‘true’ VFs was 2.6dB. Mean of SFDI was 0.34 (SD 0.11). 39% of the structure-predicted VFs showed significant discordance (SFDI>0.3) from measured VFs. Conclusions: BRBF, on average, predicts the ‘true’ VF from RNFLT slightly less well than a measured VF from the 5 VFs compromising the ‘true’ VF. The PDM highlights locations with structure-function discordance, with the SFDI providing a summary index. These tools may help clinicians trust the mutually confirmatory structure-function measurements with good concordance, or identify unreliable ones with poor concordance

Evaluation of Visual Field and Imaging Outcomes for Glaucoma Clinical Trials (An American Ophthalomological Society Thesis)

PURPOSE: To evaluate the ability of various visual field (VF) analysis methods to discriminate treatment groups in glaucoma clinical trials and establish the value of time-domain optical coherence tomography (TD OCT) imaging as an additional outcome. METHODS: VFs and retinal nerve fibre layer thickness (RNFLT) measurements (acquired by TD OCT) from 373 glaucoma patients in the UK Glaucoma Treatment Study (UKGTS) at up to 11 scheduled visits over a 2 year interval formed the cohort to assess the sensitivity of progression analysis methods. Specificity was assessed in 78 glaucoma patients with up to 11 repeated VF and OCT RNFLT measurements over a 3 month interval. Growth curve models assessed the difference in VF and RNFLT rate of change between treatment groups. Incident progression was identified by 3 VF-based methods: Guided Progression Analysis (GPA), 'ANSWERS' and 'PoPLR', and one based on VFs and RNFLT: 'sANSWERS'. Sensitivity, specificity and discrimination between treatment groups were evaluated. RESULTS: The rate of VF change was significantly faster in the placebo, compared to active treatment, group (-0.29 vs +0.03 dB/year, P<.001); the rate of RNFLT change was not different (-1.7 vs -1.1 dB/year, P=.14). After 18 months and at 95% specificity, the sensitivity of ANSWERS and PoPLR was similar (35%); sANSWERS achieved a sensitivity of 70%. GPA, ANSWERS and PoPLR discriminated treatment groups with similar statistical significance; sANSWERS did not discriminate treatment groups. CONCLUSIONS: Although the VF progression-detection method including VF and RNFLT measurements is more sensitive, it does not improve discrimination between treatment arms

Detecting Changes in Retinal Function: Analysis with Non-Stationary Weibull Error Regression and Spatial Enhancement (ANSWERS)

Visual fields measured with standard automated perimetry are a benchmark test for determining retinal function in ocular pathologies such as glaucoma. Their monitoring over time is crucial in detecting change in disease course and, therefore, in prompting clinical intervention and defining endpoints in clinical trials of new therapies. However, conventional change detection methods do not take into account non-stationary measurement variability or spatial correlation present in these measures. An inferential statistical model, denoted ‘Analysis with Non-Stationary Weibull Error Regression and Spatial enhancement’ (ANSWERS), was proposed. In contrast to commonly used ordinary linear regression models, which assume normally distributed errors, ANSWERS incorporates non-stationary variability modelled as a mixture of Weibull distributions. Spatial correlation of measurements was also included into the model using a Bayesian framework. It was evaluated using a large dataset of visual field measurements acquired from electronic health records, and was compared with other widely used methods for detecting deterioration in retinal function. ANSWERS was able to detect deterioration significantly earlier than conventional methods, at matched false positive rates. Statistical sensitivity in detecting deterioration was also significantly better, especially in short time series. Furthermore, the spatial correlation utilised in ANSWERS was shown to improve the ability to detect deterioration, compared to equivalent models without spatial correlation, especially in short follow-up series. ANSWERS is a new efficient method for detecting changes in retinal function. It allows for better detection of change, more efficient endpoints and can potentially shorten the time in clinical trials for new therapies

A review of treatment options for behavioural manifestations of clinical anxiety as a comorbidity in dogs with idiopathic epilepsy

Psychiatric comorbidities affect a large percentage of people with epilepsy and have a detrimental impact on their quality of life. Recently, behavioural comorbidities, with similar characteristics to human psychiatric diseases, have been identified in dogs with idiopathic epilepsy. In particular, behaviours motivated by the fear–anxiety emotional system have been found to be associated with the occurrence of idiopathic epilepsy in both dogs receiving anti-epileptic drugs, and drug-naïve dogs. There has been little research into the relationship between epilepsy and behavioural signs, and even less into potential treatment protocols. The following article will review available literature from human medicine to describe the current state of knowledge about the bi-directional relationship between anxiety and epilepsy, draw parallels from reported anxiogenic and anxiolytic properties of anti-epileptic drugs and attempt to provide pharmaceutical and behavioural guidance for veterinary patients with epilepsy and comorbid anxiety

Language and theory of mind in autism spectrum disorder : the relationship between complement syntax and false belief task performance.

This study aimed to test the hypothesis that children with autism spectrum disorder (ASD) use their knowledge of complement syntax as a means of “hacking out” solutions to false belief tasks, despite lacking a representational theory of mind (ToM). Participants completed a “memory for complements” task, a measure of receptive vocabulary, and traditional location change and unexpected contents false belief tasks. Consistent with predictions, the correlation between complement syntax score and location change task performance was significantly stronger within the ASD group than within the comparison group. However, contrary to predictions, complement syntax score was not significantly correlated with unexpected contents task performance within either group. Possible explanations for this pattern of results are considered