The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page

Establishment of one-step SYBR green-based real time-PCR assay for rapid detection and quantification of chikungunya virus infection

Chikungunya virus (CHIKV) is a mosquito-borne alphavirus and one of the prevalent re-emerging arbovirus in tropical and subtropical regions of Asia, Africa, and Central and South America. It produces a spectrum of illness ranging from inapparent infection to moderate febrile illness as well as severe arthralgia or arthritis affecting multiple joints. In this study, a quantitative, one-step real-time SYBR Green-based RT-PCR system for the non-structural protein 2 (nsP2) of CHIKV that can quantify a wide range of viral RNA concentrations was developed. Comparisons between the conventional semi-quantitative RT-PCR assay, immunofluorescence detection method and the one-step SYBR Green-based RT-PCR assay in the detection of CHIKV infection revealed much rapid and increase sensitivity of the latter method. Furthermore, this newly developed assay was validated by in vitro experiments in which ribavirin, a well-known RNA virus inhibitor, showed a dose-dependent inhibition of virus replication on cells that was assessed by viral infectivity and viral RNA production. Our results demonstrate the potential of this newly developed one-step SYBR Green I-based RT-PCR assay may be a useful tool in rapid detection of CHIKV and monitoring the extent of viral replication possibly in patients' samples

Prioritising surveillance for alien organisms transported as stowaways on ships travelling to South Africa

The global shipping network facilitates the transportation and introduction of marine and terrestrial organisms to regions where they are not native, and some of these organisms become invasive. South Africa was used as a case study to evaluate the potential for shipping to contribute to the introduction and establishment of marine and terrestrial alien species (i.e. establishment debt) and to assess how this varies across shipping routes and seasons. As a proxy for the number of species introduced (i.e. 'colonisation pressure') shipping movement data were used to determine, for each season, the number of ships that visited South African ports from foreign ports and the number of days travelled between ports. Seasonal marine and terrestrial environmental similarity between South African and foreign ports was then used to estimate the likelihood that introduced species would establish. These data were used to determine the seasonal relative contribution of shipping routes to South Africa's marine and terrestrial establishment debt. Additionally, distribution data were used to identify marine and terrestrial species that are known to be invasive elsewhere and which might be introduced to each South African port through shipping routes that have a high relative contribution to establishment debt. Shipping routes from Asian ports, especially Singapore, have a particularly high relative contribution to South Africa's establishment debt, while among South African ports, Durban has the highest risk of being invaded. There was seasonal variation in the shipping routes that have a high relative contribution to the establishment debt of the South African ports. The presented method provides a simple way to prioritise surveillance effort and our results indicate that, for South Africa, port-specific prevention strategies should be developed, a large portion of the available resources should be allocated to Durban, and seasonal variations and their consequences for prevention strategies should be explored further. (Résumé d'auteur

Rate-invariant analysis of covariance trajectories

Statistical analysis of dynamic systems, such as videos and dynamic functional connectivity, is often translated into a problem of analyzing trajectories of relevant features, particularly covariance matrices. As an example, in video-based action recognition, a natural mathematical representation of activity videos is as parameterized trajectories on the set of symmetric, positive-definite matrices (SPDMs). The variable execution-rates of actions, implying arbitrary parameterizations of trajectories, complicates their analysis and classification. To handle this challenge, we represent covariance trajectories using transported square-root vector fields (TSRVFs), constructed by parallel translating scaled-velocity vectors of trajectories to their starting points. The space of such representations forms a vector bundle on the SPDM manifold. Using a natural Riemannian metric on this vector bundle, we approximate geodesic paths and geodesic distances between trajectories in the quotient space of this vector bundle. This metric is invariant to the action of the reparameterization group, and leads to a rate-invariant analysis of trajectories. In the process, we remove the parameterization variability and temporally register trajectories during analysis. We demonstrate this framework in multiple contexts, using both generative statistical models and discriminative data analysis. The latter is illustrated using several applications involving video-based action recognition and dynamic functional connectivity analysis

Bayesian linear size-and-shape regression with applications to face data

Regression models for size-and-shape analysis are developed, where the model is specified in the Euclidean space of the landmark coordinates. Statistical models in this space (which is known as the top space or ambient space) are often easier for practitioners to understand than alternative models in the quotient space of size-and-shapes. We consider a Bayesian linear size-and-shape regression model in which the response variable is given by labelled configuration matrix, and the covariates represent quantities such as gender and age. It is important to parameterize the model so that it is identifiable, and we use the LQ decomposition in the intercept term in the model for this purpose. Gamma priors for the inverse variance of the error term, matrix Fisher priors for the random rotation matrix, and flat priors for the regression coefficients are used. Markov chain Monte Carlo algorithms are used for sampling from the posterior distribution, in particular by using combinations of Metropolis-Hastings updates and a Gibbs sampler.The proposed Bayesian methodology is illustrated with an application to forensic facial data in three dimensions, where we investigate the main changes in growth by describing relative movements of landmarks for each gender over time

Assessing seismic origin of geological features by fitting equidistant parallel lines

Abstract Some planes in sedimentary rocks contain features that appear to lie near equally spaced parallel lines. Determining whether or not they do so can provide information on possible mechanisms for their formation. The problem is recast here in terms of circular statistics, enabling closeness of candidate sets of lines to the points to be measured by a mean resultant length. This leads to a test of goodness of fit and to estimates of the direction of the lines and of the spacing between them. Two contrasting data sets are analysed.</jats:p