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

Seasonal changes in patterns of gene expression in avian song control brain regions.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Photoperiod and hormonal cues drive dramatic seasonal changes in structure and function of the avian song control system. Little is known, however, about the patterns of gene expression associated with seasonal changes. Here we address this issue by altering the hormonal and photoperiodic conditions in seasonally-breeding Gambel's white-crowned sparrows and extracting RNA from the telencephalic song control nuclei HVC and RA across multiple time points that capture different stages of growth and regression. We chose HVC and RA because while both nuclei change in volume across seasons, the cellular mechanisms underlying these changes differ. We thus hypothesized that different genes would be expressed between HVC and RA. We tested this by using the extracted RNA to perform a cDNA microarray hybridization developed by the SoNG initiative. We then validated these results using qRT-PCR. We found that 363 genes varied by more than 1.5 fold (>log(2) 0.585) in expression in HVC and/or RA. Supporting our hypothesis, only 59 of these 363 genes were found to vary in both nuclei, while 132 gene expression changes were HVC specific and 172 were RA specific. We then assigned many of these genes to functional categories relevant to the different mechanisms underlying seasonal change in HVC and RA, including neurogenesis, apoptosis, cell growth, dendrite arborization and axonal growth, angiogenesis, endocrinology, growth factors, and electrophysiology. This revealed categorical differences in the kinds of genes regulated in HVC and RA. These results show that different molecular programs underlie seasonal changes in HVC and RA, and that gene expression is time specific across different reproductive conditions. Our results provide insights into the complex molecular pathways that underlie adult neural plasticity

Comparing faceted and smoothed tool surface descriptions in sheet metal forming simulation

This study deals with different tool surface description methods used in the finite element analysis of sheet metal forming processes. The description of arbitrarily-shaped tool surfaces using the traditional linear finite elements is compared with two distinct smooth surface description approaches: (i) Bézier patches obtained from the ComputerAided Design model and (ii) smoothing the finite element mesh using Nagata patches. The contact search algorithm is presented for each approach, exploiting its special features in order to ensure an accurate and efficient contact detection. The influence of the tool modelling accuracy on the numerical results is analysed using two sheet forming examples, the unconstrained cylindrical bending and the reverse deep drawing of a cylindrical cup. Smoothing the contact surfaces with Nagata patches allows creating more accurate tool models, both in terms of shape and normal vectors, when compared with the conventional linear finite element mesh. The computational efficiency is evaluated in this study through the total number of increments and the required CPU time. The mesh refinement in the faceted description approach is not effective in terms of computational efficiency due to large discontinuities in the normal vector field across facets, even when adopting fine meshes.The authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) via the projects PTDC/EME-TME/118420/2010 and PEst-C/EME/ UI0285/2013 and by FEDER funds through the program COMPETE – Programa Operacional Factores de Competitividade, under the project CENTRO-07-0224-FEDER-002001 (MT4MOBI). The first author is also grateful to the FCT for the PhD grant SFRH/BD/69140/2010.info:eu-repo/semantics/publishedVersio

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

Stroke Based Painterly Rendering

International audienceMany traditional art forms are produced by an artist sequentially placing a set of marks, such as brush strokes, on a canvas. Stroke based Rendering (SBR) is inspired by this process, and underpins many early and contemporary Artistic Stylization algorithms. This Chapter outlines the origins of SBR, and describes key algorithms for placement of brush strokes to create painterly renderings from source images. The chapter explores both local greedy, and global optimization based approaches to stroke placement. The issue of creative control in SBR is also briefly discussed