Applying inversion to construct rational spiral curves

A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including those, assuming inflection.Comment: 18 pages, 11 figure

Differential Gene Expression in Liver, Gill, and Olfactory Rosettes of Coho Salmon (Oncorhynchus kisutch) After Acclimation to Salinity.

Most Pacific salmonids undergo smoltification and transition from freshwater to saltwater, making various adjustments in metabolism, catabolism, osmotic, and ion regulation. The molecular mechanisms underlying this transition are largely unknown. In the present study, we acclimated coho salmon (Oncorhynchus kisutch) to four different salinities and assessed gene expression through microarray analysis of gills, liver, and olfactory rosettes. Gills are involved in osmotic regulation, liver plays a role in energetics, and olfactory rosettes are involved in behavior. Between all salinity treatments, liver had the highest number of differentially expressed genes at 1616, gills had 1074, and olfactory rosettes had 924, using a 1.5-fold cutoff and a false discovery rate of 0.5. Higher responsiveness of liver to metabolic changes after salinity acclimation to provide energy for other osmoregulatory tissues such as the gills may explain the differences in number of differentially expressed genes. Differentially expressed genes were tissue- and salinity-dependent. There were no known genes differentially expressed that were common to all salinity treatments and all tissues. Gene ontology term analysis revealed biological processes, molecular functions, and cellular components that were significantly affected by salinity, a majority of which were tissue-dependent. For liver, oxygen binding and transport terms were highlighted. For gills, muscle, and cytoskeleton-related terms predominated and for olfactory rosettes, immune response-related genes were accentuated. Interaction networks were examined in combination with GO terms and determined similarities between tissues for potential osmosensors, signal transduction cascades, and transcription factors

Geometric characteristics of conics in Bézier form

In this paper, we address the calculation of geometric characteristics of conic sections (axes, asymptotes, centres, eccentricity, foci) given in Bézier form in terms of their control polygons and weights, making use of real and complex projective and affine geometry and avoiding the use of coordinates

L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects

We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22°) and compare precisely the results with laboratory experiments. Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called μ(I) rheology that induces a Drucker-Prager yield stress and a variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel, is added to the model. We demonstrate that this term is crucial to accurately reproduce granular collapses on slopes ≳10°, whereas it remains of little effect on the horizontal slope. Quantitative comparison between the experimental and numerical changes with time of the thickness profiles and front velocity makes it possible to strongly constrain the rheology. In particular, we show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order. However, only a fine tuning of the constant viscosity (η=1 Pa s) makes it possible to predict the slow propagation phase observed experimentally at large slopes. Finally, we observed that small-scale instabilities develop when refining the mesh (also called ill-posed behavior, characterized in the work of Barker et al. [“Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow,” J. Fluid Mech. 779, 794–818 (2015)] and in the present work) associated with the mechanical model. The velocity field becomes stratified and the bands of high velocity gradient appear. These model instabilities are not avoided by using variable viscosity models such as the μ(I) rheology. However we show that the velocity range, the static-flowing transition, and the thickness profiles are almost not affected by them

Risk of Brain Tumors in Children and Susceptibility to Organophosphorus Insecticides: The Potential Role of Paraoxonase (PON1)

Prior research suggests that childhood brain tumors (CBTs) may be associated with exposure to pesticides. Organophosphorus insecticides (OPs) target the developing nervous system, and until recently, the most common residential insecticides were chlorpyrifos and diazinon, two OPs metabolized in the body through the cytochrome P450/paraoxonase 1 (PON1) pathway. To investigate whether two common PON1 polymorphisms, C-108T and Q192R, are associated with CBT occurrence, we conducted a population-based study of 66 cases and 236 controls using DNA from neonatal screening archive specimens in Washington State, linked to interview data. The risk of CBT was nonsignificantly increased in relation to the inefficient PON1 promoter allele [per PON1(-108T) allele, relative to PON1(-108CC): odds ratio (OR) = 1.4; 95% confidence interval (CI), 1.0–2.2; p-value for trend = 0.07]. Notably, this association was strongest and statistically significant among children whose mothers reported chemical treatment of the home for pests during pregnancy or childhood (per PON1(-108T) allele: among exposed, OR = 2.6; 95% CI, 1.2–5.5; among unexposed, OR = 0.9; 95% CI, 0.5–1.6) and for primitive neuroectodermal tumors (per PON1(-108T) allele: OR = 2.4; 95% CI, 1.1–5.4). The Q192R polymorphism, which alters the structure of PON1 and influences enzyme activity in a substrate-dependent manner, was not associated with CBT risk, nor was the PON1(C-108T/Q192R) haplotype. These results are consistent with an inverse association between PON1 levels and CBT occurrence, perhaps because of PON1’s ability to detoxify OPs common in children’s environments. Larger studies that measure plasma PON1 levels and incorporate more accurate estimates of pesticide exposure will be required to confirm these observations

Quasi-Bezier curves integrating localised information

Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe