Measuring the effective complexity of cosmological models

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly non-informative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a non-zero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the Lambda-CDM concordance cosmology.Comment: 9 pages, 4 figures, revised version accepted for publication in PRD, updated with WMAP3 result

Direct reconstruction of the quintessence potential

We describe an algorithm which directly determines the quintessence potential from observational data, without using an equation of state parametrisation. The strategy is to numerically determine observational quantities as a function of the expansion coefficients of the quintessence potential, which are then constrained using a likelihood approach. We further impose a model selection criterion, the Bayesian Information Criterion, to determine the appropriate level of the potential expansion. In addition to the potential parameters, the present-day quintessence field velocity is kept as a free parameter. Our investigation contains unusual model types, including a scalar field moving on a flat potential, or in an uphill direction, and is general enough to permit oscillating quintessence field models. We apply our method to the `gold' Type Ia supernovae sample of Riess et al. (2004), confirming the pure cosmological constant model as the best description of current supernovae luminosity-redshift data. Our method is optimal for extracting quintessence parameters from future data.Comment: 9 pages RevTeX4 with lots of incorporated figure

The optimisation of deep neural networks for segmenting multiple knee joint tissues from MRIs.

Automated semantic segmentation of multiple knee joint tissues is desirable to allow faster and more reliable analysis of large datasets and to enable further downstream processing e.g. automated diagnosis. In this work, we evaluate the use of conditional Generative Adversarial Networks (cGANs) as a robust and potentially improved method for semantic segmentation compared to other extensively used convolutional neural network, such as the U-Net. As cGANs have not yet been widely explored for semantic medical image segmentation, we analysed the effect of training with different objective functions and discriminator receptive field sizes on the segmentation performance of the cGAN. Additionally, we evaluated the possibility of using transfer learning to improve the segmentation accuracy. The networks were trained on i) the SKI10 dataset which comes from the MICCAI grand challenge "Segmentation of Knee Images 2010″, ii) the OAI ZIB dataset containing femoral and tibial bone and cartilage segmentations of the Osteoarthritis Initiative cohort and iii) a small locally acquired dataset (Advanced MRI of Osteoarthritis (AMROA) study) consisting of 3D fat-saturated spoiled gradient recalled-echo knee MRIs with manual segmentations of the femoral, tibial and patellar bone and cartilage, as well as the cruciate ligaments and selected peri-articular muscles. The Sørensen-Dice Similarity Coefficient (DSC), volumetric overlap error (VOE) and average surface distance (ASD) were calculated for segmentation performance evaluation. DSC ≥ 0.95 were achieved for all segmented bone structures, DSC ≥ 0.83 for cartilage and muscle tissues and DSC of ≈0.66 were achieved for cruciate ligament segmentations with both cGAN and U-Net on the in-house AMROA dataset. Reducing the receptive field size of the cGAN discriminator network improved the networks segmentation performance and resulted in segmentation accuracies equivalent to those of the U-Net. Pretraining not only increased segmentation accuracy of a few knee joint tissues of the fine-tuned dataset, but also increased the network's capacity to preserve segmentation capabilities for the pretrained dataset. cGAN machine learning can generate automated semantic maps of multiple tissues within the knee joint which could increase the accuracy and efficiency for evaluating joint health.European Union's Horizon 2020 Framework Programme [grant number 761214] Addenbrooke’s Charitable Trust (ACT) National Institute of Health Research (NIHR) Cambridge Biomedical Research Centre University of Cambridge Cambridge University Hospitals NHS Foundation Trust GSK VARSITY: PHD STUDENTSHIP Funder reference: 300003198

Assumption-Free Estimation of Heritability from Genome-Wide Identity-by-Descent Sharing between Full Siblings

The study of continuously varying, quantitative traits is important in evolutionary biology, agriculture, and medicine. Variation in such traits is attributable to many, possibly interacting, genes whose expression may be sensitive to the environment, which makes their dissection into underlying causative factors difficult. An important population parameter for quantitative traits is heritability, the proportion of total variance that is due to genetic factors. Response to artificial and natural selection and the degree of resemblance between relatives are all a function of this parameter. Following the classic paper by R. A. Fisher in 1918, the estimation of additive and dominance genetic variance and heritability in populations is based upon the expected proportion of genes shared between different types of relatives, and explicit, often controversial and untestable models of genetic and non-genetic causes of family resemblance. With genome-wide coverage of genetic markers it is now possible to estimate such parameters solely within families using the actual degree of identity-by-descent sharing between relatives. Using genome scans on 4,401 quasi-independent sib pairs of which 3,375 pairs had phenotypes, we estimated the heritability of height from empirical genome-wide identity-by-descent sharing, which varied from 0.374 to 0.617 (mean 0.498, standard deviation 0.036). The variance in identity-by-descent sharing per chromosome and per genome was consistent with theory. The maximum likelihood estimate of the heritability for height was 0.80 with no evidence for non-genetic causes of sib resemblance, consistent with results from independent twin and family studies but using an entirely separate source of information. Our application shows that it is feasible to estimate genetic variance solely from within-family segregation and provides an independent validation of previously untestable assumptions. Given sufficient data, our new paradigm will allow the estimation of genetic variation for disease susceptibility and quantitative traits that is free from confounding with non-genetic factors and will allow partitioning of genetic variation into additive and non-additive components

Triggering an eruptive flare by emerging flux in a solar active-region complex

A flare and fast coronal mass ejection originated between solar active regions NOAA 11514 and 11515 on July 1, 2012 in response to flux emergence in front of the leading sunspot of the trailing region 11515. Analyzing the evolution of the photospheric magnetic flux and the coronal structure, we find that the flux emergence triggered the eruption by interaction with overlying flux in a non-standard way. The new flux neither had the opposite orientation nor a location near the polarity inversion line, which are favorable for strong reconnection with the arcade flux under which it emerged. Moreover, its flux content remained significantly smaller than that of the arcade (approximately 40 %). However, a loop system rooted in the trailing active region ran in part under the arcade between the active regions, passing over the site of flux emergence. The reconnection with the emerging flux, leading to a series of jet emissions into the loop system, caused a strong but confined rise of the loop system. This lifted the arcade between the two active regions, weakening its downward tension force and thus destabilizing the considerably sheared flux under the arcade. The complex event was also associated with supporting precursor activity in an enhanced network near the active regions, acting on the large-scale overlying flux, and with two simultaneous confined flares within the active regions.Comment: Accepted for publication in Topical Issue of Solar Physics: Solar and Stellar Flares. 25 pages, 12 figure

Effectively Measuring Exercise-Related Variations in T1ρ and T2 Relaxation Times of Healthy Articular Cartilage.

BACKGROUND: Determining the compositional response of articular cartilage to dynamic joint-loading using MRI may be a more sensitive assessment of cartilage status than conventional static imaging. However, distinguishing the effects of joint-loading vs. inherent measurement variability remains difficult, as the repeatability of these quantitative methods is often not assessed or reported. PURPOSE: To assess exercise-induced changes in femoral, tibial, and patellar articular cartilage composition and compare these against measurement repeatability. STUDY TYPE: Prospective observational study. POPULATION: Phantom and 19 healthy participants. FIELD STRENGTH/SEQUENCE: 3T; 3D fat-saturated spoiled gradient recalled-echo; T1ρ - and T2 -prepared pseudosteady-state 3D fast spin echo. ASSESSMENT: The intrasessional repeatability of T1ρ and T2 relaxation mapping, with and without knee repositioning between two successive measurements, was determined in 10 knees. T1ρ and T2 relaxation mapping of nine knees was performed before and at multiple timepoints after a 5-minute repeated, joint-loading stepping activity. 3D surface models were created from patellar, femoral, and tibial articular cartilage. STATISTICAL TESTS: Repeatability was assessed using root-mean-squared-CV (RMS-CV). Using Bland-Altman analysis, thresholds defined as the smallest detectable difference (SDD) were determined from the repeatability data with knee repositioning. RESULTS: Without knee repositioning, both surface-averaged T1ρ and T2 were very repeatable on all cartilage surfaces, with RMS-CV SDD) average exercise-induced in T1ρ and T2 of femoral (-8.0% and -5.3%), lateral tibial (-6.9% and -5.9%), medial tibial (+5.8% and +2.9%), and patellar (-7.9% and +2.8%) cartilage were observed. DATA CONCLUSION: Joint-loading with a stepping activity resulted in T1ρ and T2 changes above background measurement error. EVIDENCE LEVEL: 2 TECHNICAL EFFICACY STAGE: 1 J. MAGN. RESON. IMAGING 2020;52:1753-1764.GlaxoSmithKline National Institute of Health Research (NIHR) Cambridge Biomedical Research Centr

Physics of Solar Prominences: II - Magnetic Structure and Dynamics

Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them.Comment: 75 pages, 31 pictures, review pape

Polytetrahedral Clusters

By studying the structures of clusters bound by a model potential that favours polytetrahedral order, we find a previously unknown series of `magic numbers' (i.e. sizes of special stability) whose polytetrahedral structures are characterized by disclination networks that are analogous to hydrocarbons.Comment: 4 pages, 4 figure

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request