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This article introduces a new method to efficiently compute the distance (i.e., Lp norm of the difference) between two functions supported by two different meshes of the same 3D domain. The functions that we consider are typically finite element solutions discretized in different function spaces supported by meshes that are potentially completely unrelated. Our method computes an approximation of the distance by resampling both fields over a set of parallel 2D regular grids. By leveraging the parallel horse power of computer graphics hardware (graphics processing unit (GPU)), our method can efficiently compute distances between meshes with multimillion elements in seconds. We demonstrate our method applied to different problems (distance between known functions, Poisson solutions, and linear elasticity solutions) using different function spaces (Lagrange polynomials from order one to seven) and different meshes (tetrahedral and hexahedral, with linear or quadratic geometry). [ABSTRACT FROM AUTHOR]

The definition of the soma is fuzzy, as there is no clear line demarcating the soma of the labeled neurons and the origin of the dendrites and axon. Thus, the morphometric analysis of the neuronal soma is highly subjective. In this paper, we provide a mathematical definition and an automatic segmentation method to delimit the neuronal soma. We applied this method to the characterization of pyramidal cells, which are the most abundant neurons in the cerebral cortex. Since there are no benchmarks with which to compare the proposed procedure, we validated the goodness of this automatic segmentation method against manual segmentation by experts in neuroanatomy to set up a framework for comparison. We concluded that there were no significant differences between automatically and manually segmented somata, i.e., the proposed procedure segments the neurons more or less as an expert does. It also provides univocal, justifiable and objective cutoffs. Thus, this study is a means of characterizing pyramidal neurons in order to objectively compare the morphometry of the somata of these neurons in different cortical areas and species.

The definition of the soma is fuzzy, as there is no clear line demarcating the soma of the labeled neurons and the origin of the dendrites and axon. Thus, the morphometric analysis of the neuronal soma is highly subjective. In this paper, we provide a mathematical definition and an automatic segmentation method to delimit the neuronal soma. We applied this method to the characterization of pyramidal cells, which are the most abundant neurons in the cerebral cortex. Since there are no benchmarks with which to compare the proposed procedure, we validated the goodness of this automatic segmentation method against manual segmentation by neuroanatomists to set up a framework for comparison. We concluded that there were no significant differences between automatically and manually segmented somata, i.e., the proposed procedure segments the neurons similarly to how a neuroanatomist does. It also provides univocal, justifiable and objective cutoffs. Thus, this study is a means of characterizing pyramidal neurons in order to objectively compare the morphometry of the somata of these neurons in different cortical areas and species. [ABSTRACT FROM AUTHOR]

Abstract: Comparisons were made between ichthyoplankton samples collected in the northern Gulf of Mexico using a Bedford Institute of Oceanography Net Environmental Sampling System (BIONESS) fitted with 0.202mm and 0.333mm mesh plankton nets. Tow duration, tow speed, filtration efficiency and filtration rate were monitored in real time during paired oblique (1–18m) tows. General tow characteristics and larval assemblages were compared for samples characterized by filtering efficiencies >85%. Plankton tows characterized by relatively short durations (approximately 4.5min) and low filtered volumes (approximately 70m3) were largely overlapping in fish egg densities, larval densities, and length frequency distributions. Higher taxonomic richness (number of families) and diversity (exponential of Shannon Entropy) were observed in the 0.333mm mesh net. No significant differences in larval fish densities were observed between mesh sizes for seven families of fishes; only unidentified clupeiform fishes were more common in the 0.333mm mesh net. Mean lengths for total fish larvae, total non-clupeiform fish larvae, sciaenids and unidentified larvae were significantly larger in the 0.333mm collections. However no significant differences were noted in the length frequencies for these groups. We conclude that under controlled tow conditions, ichthyoplankton samples collected in our region with these two mesh sizes are largely comparable. [Copyright &y& Elsevier]

Abstract: This paper addresses the mesh-dependence of non-linear mechanical finite element analysis. To this end, finite element meshes that are assembled by various element types and their solutions are compared. Voxel, tetrahedron, hexahedron and mixed (hex-dominant) meshes are considered. Different benchmarking parameters for the elastic and plastic solutions as well as for the computational load are determined. First, bending beams with a square, a circular and a rail cross-section are calculated accounting for non-linear material behaviour (plasticity). A strong dependence on the mesh type is observed and the best results are obtained for mixed meshes and hexahedron-only meshes. In the second part of this study, finite element models that are based on the complex geometry of metallic foam are considered. Computed tomography data is used to generate geometrically complex finite element models and a convergence analysis is performed. Again, superior performance is found for mixed meshes. [Copyright &y& Elsevier]

Abstract: Polygonal meshes are used in several application areas to model different objects and structures. Depending on the application, mesh models sometimes have to be processed to, for instance, reduce their complexity (mesh simplification). Such operations introduce differences regarding the original mesh, whose evaluation is of paramount importance when choosing the processing methods to be applied for a particular purpose. Although some mesh analysis and comparison tools are described in the literature, little attention has been given to the way mesh features and mesh comparison results can be visualized. Moreover, particular functionalities have to be made available to enable systematic use and proper data analysis and exploration. PolyMeCo—a tool for polygonal mesh analysis and comparison—was designed and developed taking the above objectives into account. It enhances the way users analyze features and compare meshes by providing an integrated environment where various mesh quality measures and several visualization options are available and can be used in a coordinated way, thus leading to greater insight into the visualized data. [Copyright &y& Elsevier]