Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

A palaeobiologist's guide to 'virtual' micro-CT preparation

This paper provides a brief but comprehensive guide to creating, preparing and dissecting a 'virtual' fossil, using a worked example to demonstrate some standard data processing techniques. Computed tomography (CT) is a 3D imaging modality for producing 'virtual' models of an object on a computer. In the last decade, CT technology has greatly improved, allowing bigger and denser objects to be scanned increasingly rapidly. The technique has now reached a stage where systems can facilitate large-scale, non-destructive comparative studies of extinct fossils and their living relatives. Consequently the main limiting factor in CT-based analyses is no longer scanning, but the hurdles of data processing (see disclaimer). The latter comprises the techniques required to convert a 3D CT volume (stack of digital slices) into a virtual image of the fossil that can be prepared (separated) from the matrix and 'dissected' into its anatomical parts. This technique can be applied to specimens or part of specimens embedded in the rock matrix that until now have been otherwise impossible to visualise. This paper presents a suggested workflow explaining the steps required, using as example a fossil tooth of Sphenacanthus hybodoides (Egerton), a shark from the Late Carboniferous of England. The original NHMUK copyrighted CT slice stack can be downloaded for practice of the described techniques, which include segmentation, rendering, movie animation, stereo-anaglyphy, data storage and dissemination. Fragile, rare specimens and type materials in university and museum collections can therefore be virtually processed for a variety of purposes, including virtual loans, website illustrations, publications and digital collections. Micro-CT and other 3D imaging techniques are increasingly utilized to facilitate data sharing among scientists and on education and outreach projects. Hence there is the potential to usher in a new era of global scientific collaboration and public communication using specimens in museum collections.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

Evaluating links through spectral decomposition

Spectral decomposition has rarely been used to investigate complex networks. In this work we apply this concept in order to define two kinds of link-directed attacks while quantifying their respective effects on the topology. Several other kinds of more traditional attacks are also adopted and compared. These attacks had substantially diverse effects, depending on each specific network (models and real-world structures). It is also shown that the spectrally based attacks have special effects in affecting the transitivity of the networks.

The importance of mesofauna and decomposition environment on leaf decomposition in three forests in southeastern Brazil

We examined the effects of soil mesofauna and the litter decomposition environment (above and belowground) on leaf decomposition rates in three forest types in southeastern Brazil. To estimate decomposition experimentally, we used litterbags with a standard substrate in a full-factorial experimental design. We used model selection to compare three decomposition models and also to infer the importance of forest type, decomposition environment, mesofauna, and their interactions on the decomposition process. Rather than the frequently used simple and double-exponential models, the best model to describe our dataset was the exponential deceleration model, which assumed a single organic compartment with an exponential decrease of the decomposition rate. Decomposition was higher in the wet than in the seasonal forest, and the differences between forest types were stronger aboveground. Regarding litter decomposition environment, decomposition was predominantly higher below than aboveground, but the magnitude of this effect was higher in the seasonal than in wet forests. Mesofauna exclusion treatments had slower decomposition, except aboveground into the Semi-deciduous Forest, where the mesofauna presence did not affect decomposition. Furthermore, the effect of mesofauna was stronger in the wet forests and belowground. Overall, our results suggest that, in a regional scale, both decomposers activity and the positive effect of soil mesofauna in decomposition are constrained by abiotic factors, such as moisture conditions.

Mapping virtual networks onto substrate networks

Network virtualization is a promising technique for building the Internet of the future since it enables the low cost introduction of new features into network elements. An open issue in such virtualization is how to effect an efficient mapping of virtual network elements onto those of the existing physical network, also called the substrate network. Mapping is an NP-hard problem and existing solutions ignore various real network characteristics in order to solve the problem in a reasonable time frame. This paper introduces new algorithms to solve this problem based on 0–1 integer linear programming, algorithms based on a whole new set of network parameters not taken into account by previous proposals. Approximative algorithms proposed here allow the mapping of virtual networks on large network substrates. Simulation experiments give evidence of the efficiency of the proposed algorithms.