Self-organization of developing embryo using scale-invariant approach

<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p

The provocative lumbar facet joint

Low back pain is the most common pain symptom experienced by American adults and is the second most common reason for primary care physician visits. There are many structures in the lumbar spine that can serve as pain generators and often the etiology of low back pain is multifactorial. However, the facet joint has been increasingly recognized as an important cause of low back pain. Facet joint pain can be diagnosed with local anesthetic blocks of the medial branches or of the facet joints themselves. Subsequent radiofrequency lesioning of the medial branches can provide more long-term pain relief. Despite some of the pitfalls associated with facet joint blocks, they have been shown to be valid, safe, and reliable as a diagnostic tool. Medial branch denervation has shown some promise for the sustained control of lumbar facet joint-mediated pain, but at this time, there is insufficient evidence that it is a wholly efficacious treatment option. Developing a universal algorithm for evaluating facet joint-mediated pain and standard procedural techniques may facilitate the performance of larger outcome studies. This review article provides an overview of the anatomy, pathophysiology, diagnosis, and treatment of facet joint-mediated pain

Body shape variation and colour change during growth in a protogynous fish

Protogynous sequential hermaphroditism is very common in marine fish. Despite a large number of studies on various aspects of sequential hermaphroditism in fish, the relationship between body shape and colour during growth in dichromatic species has not been assessed. Using geometric morphometrics, the present study explores the relationship between growth, body shape and colouration in Coris julis (L. 1758), a small protogynous labrid species with distinct colour phases. Results show that body shape change during growth is independent of change in colour phase, a result which can be explained by the biology of the species and by the social control of sex change. Also, during growth the body grows deeper and the head has a steeper profile. It is hypothesized that a deeper body and a steeper profile might have a function in agonistic interactions between terminal phase males and that the marked chromatic difference between colour phases allows the lack of strict interdependence of body shape and colour during growth

Construction of Line Densities for Parallel Coordinate Plots

The graphical representation of high dimensional data may be accomplished by using the parallel coordinate plotting system. In such a representation points in Euclidian n-space are mapped into line segments in Euclidian 2-space by a projective transformation. This representation preserves much of the geometric structure found in hyperspace but not easily representable by other methods. In large data set applications, the graphical displays may be heavily overplotted like ordinary scatterplots yielding uninterpretable displays. In this paper, we suggest replacing the raw data display with a density plot. In order to define densities for lines sensibly, we introduce the notion of line densities and develop their basic construction. We illustrate with theoretical parallel coordinate density plots for the normal and the uniform cases. Finally we illustrate sample density plots with 4-dimensional spheres

High Dimensional Clustering Using Parallel Coordinates and the Grand Tour

In this paper, we present some graphical techniques for cluster analysis of high-dimensional data. Parallel coordinate plots and parallel coordinate density plots are graphical techniques which map multivariate data into a two-dimensional display. The method has some elegant duality properties with ordinary Cartesian plots so that higher-dimensional mathematical structures can be analyzed. Our high interaction software allows for rapid editing of data to remove outliers and isolate clusters by brushing. Our brushing techniques allow not only for hue adjustment, but also for saturation adjustment. Saturation adjustment allows for the handling of comparatively massive data sets by using the ff-channel of the Silicon Graphics workstation to compensate for heavy overplotting. The grand tour is a generalized rotation of coordinate axes in a high-dimensional space. Coupled with the full-dimensional plots allowed by the parallel coordinate display, these techniques allow the da..