No abstract

Line Integral Convolution (LIC) is a powerful technique for generating striking images and animations from vector data. Introduced in 1993, the method has rapidly found many application areas, ranging from computer arts to scientific visualization. Based upon locally filtering an input texture along a curved stream line segment in a vector field, it is able to depict directional information at high spatial resolutions.We present a new method for computing LIC images. It employs simple box filter kernels only and minimizes the total number of stream lines to be computed. Thereby it reduces computational costs by an order of magnitude compared to the original algorithm. Our method utilizes fast, error-controlled numerical integrators. Decoupling the characteristic lengths in vector field grid, input texture and output image, it allows computation of filtered images at arbitrary resolution. This feature is of significance in computer animation as well as in scientific visualization, where it can be used to explore vector data by smoothly enlarging structure of details.We also present methods for improved texture animation, again employing box filter kernels only. To obtain an optimal motion effect, spatial decay of correlation between intensities of distant pixels in the output image has to be controlled. This is achieved by blending different phase-shifted box filter animations and by adaptively rescaling the contrast of the output frames.

Membrane proteins mediate processes that are fundamental for the flourishing of biological cells. Membrane-embedded transporters move ions and larger solutes across membranes, receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. We present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function and dynamics of membrane proteins.

In this paper we revisit the computation and visualization of equivalents to isocontours in uncertain scalar fields. We model uncertainty by discrete random fields and, in contrast to previous methods, also take arbitrary spatial correlations into account. Starting with joint distributions of the random variables associated to the sample locations, we compute level crossing probabilities for cells of the sample grid. This corresponds to computing the probabilities that the well-known symmetry-reduced marching cubes cases occur in random field realizations. For Gaussian random fields, only marginal density functions that correspond to the vertices of the considered cell need to be integrated. We compute the integrals for each cell in the sample grid using a Monte Carlo method. The probabilistic ansatz does not suffer from degenerate cases that usually require case distinctions and solutions of ill-conditioned problems. Applications in 2D and 3D, both to synthetic and real data from ensemble simulations in climate research, illustrate the influence of spatial correlations on the spatial distribution of uncertain isocontours.

The outcome of a pericyclic reaction is typically represented by arrows in the Lewis structure of the reactant, symbolizing the net electron transfer. Quantum simulations can be used to interpret these arrows in terms of electronic fluxes between neighboring bonds. The fluxes are decomposed into contributions from electrons in so-called pericyclic orbitals, which account for the mutation of the Lewis structure for the reactant into that for the product, in other valence and in core orbitals. Series of time-integrated fluxes of pericyclic electrons can be assigned to the arrows, for example 0.09-0.23 electrons for Cope rearrangement of semibullvalene, with hysteresis-type time evolutions for 27.3 fs. This means asynchronous electronic fluxes during synchronous rearrangement of all the nuclei. These predictions should become observable by emerging techniques of femto-to attosecond time-resolved spectroscopy.

Abstract

Sensory-evoked signal flow, at cellular and network levels, is primarily determined by the synaptic wiring of the underlying neuronal circuitry. Measurements of synaptic innervation, connection probabilities and subcellular organization of synaptic inputs are thus among the most active fields of research in contemporary neuroscience. Methods to measure these quantities range from electrophysiological recordings over reconstructions of dendrite-axon overlap at light-microscopic levels to dense circuit reconstructions of small volumes at electron-microscopic resolution. However, quantitative and complete measurements at subcellular resolution and mesoscopic scales to obtain all local and long-range synaptic in/outputs for any neuron within an entire brain region are beyond present methodological limits. Here, we present a novel concept, implemented within an interactive software environment called NeuroNet, which allows (i) integration of sparsely sampled (sub)cellular morphological data into an accurate anatomical reference frame of the brain region(s) of interest, (ii) up-scaling to generate an average dense model of the neuronal circuitry within the respective brain region(s) and (iii) statistical measurements of synaptic innervation between all neurons within the model. We illustrate our approach by generating a dense average model of the entire rat vibrissal cortex, providing the required anatomical data, and illustrate how to measure synaptic innervation statistically. Comparing our results with data from paired recordings in vitro and in vivo, as well as with reconstructions of synaptic contact sites at light- and electron-microscopic levels, we find that our in silico measurements are in line with previous results.

Uncertainty is ubiquitous in science, engineering and medicine. Drawing conclusions from uncertain data is the normal case, not an exception. While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature extraction methods have been devised that consider uncertainty. We present mathematical formulations for uncertain equivalents of isocontours based on standard probability theory and statistics and employ them in interactive visualization methods. As input data, we consider discretized uncertain scalar fields and model these as random fields. To create a continuous representation suitable for visualization we introduce interpolated probability density functions. Furthermore, we introduce numerical condition as a general means in feature-based visualization. The condition number-which potentially diverges in the isocontour problem-describes how errors in the input data are amplified in feature computation. We show how the average numerical condition of isocontours aids the selection of thresholds that correspond to robust isocontours. Additionally, we introduce the isocontour density and the level crossing probability field; these two measures for the spatial distribution of uncertain isocontours are directly based on the probabilistic model of the input data. Finally, we adapt interactive visualization methods to evaluate and display these measures and apply them to 2D and 3D data sets.