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

Stochastic loss and gain of symmetric divisions in the C. elegans epidermis perturbs robustness of stem cell number

Biological systems are subject to inherent stochasticity. Nevertheless, development is remarkably robust, ensuring the consistency of key phenotypic traits such as correct cell numbers in a certain tissue. It is currently unclear which genes modulate phenotypic variability, what their relationship is to core components of developmental gene networks, and what is the developmental basis of variable phenotypes. Here, we start addressing these questions using the robust number of Caenorhabditis elegans epidermal stem cells, known as seam cells, as a readout. We employ genetics, cell lineage tracing, and single molecule imaging to show that mutations in lin-22, a Hes-related basic helix-loop-helix (bHLH) transcription factor, increase seam cell number variability. We show that the increase in phenotypic variability is due to stochastic conversion of normally symmetric cell divisions to asymmetric and vice versa during development, which affect the terminal seam cell number in opposing directions. We demonstrate that LIN-22 acts within the epidermal gene network to antagonise the Wnt signalling pathway. However, lin-22 mutants exhibit cell-to-cell variability in Wnt pathway activation, which correlates with and may drive phenotypic variability. Our study demonstrates the feasibility to study phenotypic trait variance in tractable model organisms using unbiased mutagenesis screens

Efficacy of Myrtus communis L. to Inactivate the Hydatid Cyst Protoscoleces

PURPOSE: The present study aims to investigate the scolicidal effects of Myrtus communis L. essential oil against protoscoleces of hydatid cysts and also its toxicity in mice model. MATERIALS AND METHODS: Protoscoleces were aseptically aspirated from sheep livers having hydatid cysts. Various concentrations of the essential oil (12.5-100 μl/ml) were used for 5-30 min. Viability of protoscoleces was confirmed using eosin exclusion test (0.1% eosin staining). Moreover, 48 male NMRI mice were used to determine the acute and sub-acute toxicity of M. communis essential oil. One-way ANOVA with Tukey's post-hoc test was used to assess differences between experimental groups. RESULTS: Findings of the present study demonstrated that the M. communis essential oil at the concentration of 100 μl/ml after 5 min of exposure killed 100% protoscoleces. Similarly, the mean mortality rate of protoscoleces after 10 min of exposure to concentration of 50 μl/ml was 100%. However, lower concentrations (12.5 and 25 μl/ml) of M. communis essential oil provoked a delayed protoscolicidal effects. The LD50 values of intraperitoneal injection of the M. communis essential oil was 2.23 mL/kg body wt. No significant difference (p > .05) was observed in the clinical chemistry and hematological parameters following oral administrations of M. communis essential oil at the doses 0.05, 0.1, 0.2, and 0.4 mL/kg for 14 days. CONCLUSION: The results showed potent scolicidal activity of M. communis with no significant toxicity, which might be used as a natural scolicidal agent in hydatid cyst surgery. KEYWORDS: cystic echinococcosis; hydatid cyst; myrtle; scolicidal effects; toxicit