Statistics sunspots and settlement: Influences on sum of probability curves

Large data sets of radiocarbon dates are becoming a more common feature of archaeological research. The sheer numbers of radiocarbon dates produced, however, raise issues of representation and interpretation. This paper presents a methodology which both reduces the visible impact of dating fluctuations, but also takes into consideration the influence of the underlying radiocarbon calibration curve. By doing so, it may be possible to distinguish between periods of human activity in early medieval Ireland and the statistical tails produced by radiocarbon calibration.

Model selection for prognostic time-to-event gene signature discovery with applications in early breast cancer data

Model selection between competing models is a key consideration in the discovery of prognostic multigene signatures. The use of appropriate statistical performance measures as well as verification of biological significance of the signatures is imperative to maximise the chance of external validation of the generated signatures. Current approaches in time-to-event studies often use only a single measure of performance in model selection, such as logrank test p-values, or dichotomise the follow-up times at some phase of the study to facilitate signature discovery. In this study we improve the prognostic signature discovery process through the application of the multivariate partial Cox model combined with the concordance index, hazard ratio of predictions, independence from available clinical covariates and biological enrichment as measures of signature performance. The proposed framework was applied to discover prognostic multigene signatures from early breast cancer data. The partial Cox model combined with the multiple performance measures were used in both guiding the selection of the optimal panel of prognostic genes and prediction of risk within cross validation without dichotomising the follow-up times at any stage. The signatures were successfully externally cross validated in independent breast cancer datasets, yielding a hazard ratio of 2.55 [1.44, 4.51] for the top ranking signature.

Spatial statistics to estimate peat thickness using airborne radiometric data

Soil carbon stores are a major component of the annual returns required by EU governments to the Intergovernmental Panel on Climate Change. Peat has a high proportion of soil carbon due to the relatively high carbon density of peat and organic-rich soils. For this reason it has become increasingly important to measure and model soil carbon stores and changes in peat stocks to facilitate the management of carbon changes over time. The approach investigated in this research evaluates the use of airborne geophysical (radiometric) data to estimate peat thickness using the attenuation of bedrock geology radioactivity by superficial peat cover. Remotely sensed radiometric data are validated with ground peat depth measurements combined with non-invasive geophysical surveys. Two field-based case studies exemplify and validate the results. Variography and kriging are used to predict peat thickness from point measurements of peat depth and airborne radiometric data and provide an estimate of uncertainty in the predictions. Cokriging, by assessing the degree of spatial correlation between recent remote sensed geophysical monitoring and previous peat depth models, is used to examine changes in peat stocks over time. The significance of the coregionalisation is that the spatial cross correlation between the remote and ground based data can be used to update the model of peat depth. The result is that by integrating remotely sensed data with ground geophysics, the need is reduced for extensive ground-based monitoring and invasive peat depth measurements. The overall goal is to provide robust estimates of peat thickness to improve estimates of carbon stocks. The implications from the research have a broader significance that promotes a reduction in the need for damaging onsite peat thickness measurement and an increase in the use of remote sensed data for carbon stock estimations.

Outcomes and process in reading tutoring

Background: Large-scale randomised controlled trials are relatively rare in education. The present study approximates to, but is not exactly, a randomised controlled trial. It was an attempt to scale up previous small peer tutoring projects, while investing only modestly in continuing professional development for teachers.Purpose: A two-year study of peer tutoring in reading was undertaken in one local education authority in Scotland. The relative effectiveness of cross-age versus same-age tutoring, light versus intensive intervention, and reading versus reading and mathematics tutoring were investigated.Programme description (if relevant): The intervention was Paired Reading, a freely available cross-ability tutoring method applied to books of the pupils' choice but above the tutee's independent readability level. It involves Reading Together and Reading Alone, and switching from one to the other according to need.Sample: Eighty-seven primary schools of overall average socio-economic status, ability and gender in one council in Scotland. There were few ethnic minority students. Proportions of students with special needs were low. Children were eight and 10 years old as the intervention started. Macro-evaluation n = 3520. Micro-evaluation Year 1 15 schools n = 592, Year 2 a different 15 schools n = 591, compared with a comparison group of five schools n = 240.Design and methods: Almost all the primary schools in the local authority participated and were randomly allocated to condition. A macro-evaluation tested and retested over a two-year period using Performance Indicators in Primary Schools. A micro-evaluation tested and retested within each year using norm-referenced tests of reading comprehension. Macro-evaluation was with multi-level modelling, micro-evaluation with descriptive statistics and effect sizes, analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA).Results: Macro-evaluation yielded significant pre-post gains in reading attainment for cross-age tutoring over both years. No other differences were significant. Micro-evaluation yielded pre-post changes in Year 1 (selected) and Year 2 (random) greater than controls, with no difference between same-age and cross-age tutoring. Light and intensive tutoring were equally effective. Tutoring reading and mathematics together was more effective than only tutoring reading. Lower socio-economic and lower reading ability students did better. Girls did better than boys. Regarding observed implementation quality, some factors were high and others low. Few implementation variables correlated with attainment gain.Conclusions: Paired Reading tutoring does lead to better reading attainment compared with students not participating. This is true in the long term (macro-evaluation) for cross-age tutoring, and in the short term (micro-evaluation) for both cross-age and same-age tutoring. Tutors and tutees benefited. Intensity had no effect but dual tutoring did have an effect. Low-socio-economic status, low-ability and female students did better. The results of the different forms of evaluation were indeed different. There are implications for practice and for future research. © 2012 Copyright Taylor and Francis Group, LLC.

Gene Sets Net Correlations Analysis (GSNCA): a multivariate differential coexpression test for gene sets

Motivation: To date, Gene Set Analysis (GSA) approaches primarily focus on identifying differentially expressed gene sets (pathways). Methods for identifying differentially coexpressed pathways also exist but are mostly based on aggregated pairwise correlations, or other pairwise measures of coexpression. Instead, we propose Gene Sets Net Correlations Analysis (GSNCA), a multivariate differential coexpression test that accounts for the complete correlation structure between genes.

Results: In GSNCA, weight factors are assigned to genes in proportion to the genes' cross-correlations (intergene correlations). The problem of finding the weight vectors is formulated as an eigenvector problem with a unique solution. GSNCA tests the null hypothesis that for a gene set there is no difference in the weight vectors of the genes between two conditions. In simulation studies and the analyses of experimental data, we demonstrate that GSNCA, indeed, captures changes in the structure of genes' cross-correlations rather than differences in the averaged pairwise correlations. Thus, GSNCA infers differences in coexpression networks, however, bypassing method-dependent steps of network inference. As an additional result from GSNCA, we define hub genes as genes with the largest weights and show that these genes correspond frequently to major and specific pathway regulators, as well as to genes that are most affected by the biological difference between two conditions. In summary, GSNCA is a new approach for the analysis of differentially coexpressed pathways that also evaluates the importance of the genes in the pathways, thus providing unique information that may result in the generation of novel biological hypotheses.

Dyslexia in higher education: Implications for maths anxiety, statistics anxiety and psychological well-being

This study examined levels of mathematics and statistics anxiety, as well as general mental health amongst undergraduate students with dyslexia (n = 28) and those without dyslexia (n = 71). Students with dyslexia had higher levels of mathematics anxiety relative to those without dyslexia, while statistics anxiety and general mental health were comparable for both reading ability groups. In terms of coping strategies, undergraduates with dyslexia tended to use planning-based strategies and seek instrumental support more frequently than those without dyslexia. Higher mathematics anxiety was associated with having a dyslexia diagnosis, as well as greater levels of worrying, denial, seeking instrumental support and less use of the positive reinterpretation coping strategy. By contrast, statistics anxiety was not predicted by dyslexia diagnosis, but was instead predicted by overall worrying and the use of denial and emotion focused coping strategies. The results suggest that disability practitioners should be aware that university students with dyslexia are at risk of high mathematics anxiety. Additionally, effective anxiety reduction strategies such as positive reframing and thought challenging would form a useful addition to the support package delivered to many students with dyslexia.

Integrating Multiple Point Statistics with Aerial Geophysical Data to assist Groundwater Flow Models

The process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively ‘noisy’ magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.

Detecting the work statistics through Ramsey-like interferometry

Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola et al., Phys. Rev. Lett. 110 (2013) 230602]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancillary qubit. Here, we expand that work in two important directions. We first apply the protocol to an interesting specific physical example consisting of a superconducting qubit dispersively coupled to the field of a microwave resonator, thus enlarging the class of situations for which our scheme would be key in the task highlighted above. We then account for the interaction of the system with an additional one (which might embody an environment), and generalize the protocol accordingly.

Evaluating the use of testate amoebae for palaeohydrological reconstruction in permafrost peatlands

The melting of high-latitude permafrost peatlands is a major concern due to a potential positive feedback on global climate change. We examine the ecology of testate amoebae in permafrost peatlands, based on sites in Sweden (~ 200 km north of the Arctic Circle). Multivariate statistical analysis confirms that water-table depth and moisture content are the dominant controls on the distribution of testate amoebae, corroborating the results from studies in mid-latitude peatlands. We present a new testate amoeba-based water table transfer function and thoroughly test it for the effects of spatial autocorrelation, clustered sampling design and uneven sampling gradients. We find that the transfer function has good predictive power; the best-performing model is based on tolerance-downweighted weighted averaging with inverse deshrinking (performance statistics with leave-one-out cross validation: R2 = 0.87, RMSEP = 5.25 cm). The new transfer function was applied to a short core from Stordalen mire, and reveals a major shift in peatland ecohydrology coincident with the onset of the Little Ice Age (c. AD 1400). We also applied the model to an independent contemporary dataset from Stordalen and find that it outperforms predictions based on other published transfer functions. The new transfer function will enable palaeohydrological reconstruction from permafrost peatlands in Northern Europe, thereby permitting greatly improved understanding of the long-term ecohydrological dynamics of these important carbon stores as well as their responses to recent climate change.

A multivariate analysis of beta diversity across organisms and environments

We examined variability in hierarchical beta diversity across ecosystems, geographical gradients, and organism groups using multivariate spatial mixed modeling analysis of two independent data sets. The larger data set comprised reported ratios of regional species richness (RSR) to local species richness (LSR) and the second data set consisted of RSR: LSR ratios derived from nested species-area relationships. There was a negative, albeit relatively weak, relationship between beta diversity and latitude. We found only relatively subtle differences in beta diversity among the realms, yet beta diversity was lower in marine systems than in terrestrial or freshwater realms. Beta diversity varied significantly among organisms' major characteristics such as body mass, trophic position, and dispersal type in the larger data set. Organisms that disperse via seeds had highest beta diversity, and passively dispersed organisms showed the lowest beta diversity. Furthermore, autotrophs had lower beta diversity than organisms higher up the food web; omnivores and carnivores had consistently higher beta diversity. This is evidence that beta diversity is simultaneously controlled by extrinsic factors related to geography and environment, and by intrinsic factors related to organism characteristics.