The quaternion-based spatial-coordinate and orientation-frame alignment problems.

The general problem of finding a global rotation that transforms a given set of spatial coordinates and/or orientation frames (the `test' data) into the best possible alignment with a corresponding set (the `reference' data) is reviewed. For 3D point data, this `orthogonal Procrustes problem' is often phrased in terms of minimizing a root-mean-square deviation (RMSD) corresponding to a Euclidean distance measure relating the two sets of matched coordinates. This article focuses on quaternion eigensystem methods that have been exploited to solve this problem for at least five decades in several different bodies of scientific literature, where they were discovered independently. While numerical methods for the eigenvalue solutions dominate much of this literature, it has long been realized that the quaternion-based RMSD optimization problem can also be solved using exact algebraic expressions based on the form of the quartic equation solution published by Cardano in 1545; focusing on these exact solutions exposes the structure of the entire eigensystem for the traditional 3D spatial-alignment problem. The structure of the less-studied orientation-data context is then explored, investigating how quaternion methods can be extended to solve the corresponding 3D quaternion orientation-frame alignment (QFA) problem, noting the interesting equivalence of this problem to the rotation-averaging problem, which also has been the subject of independent literature threads. The article concludes with a brief discussion of the combined 3D translation-orientation data alignment problem. Appendices are devoted to a tutorial on quaternion frames, a related quaternion technique for extracting quaternions from rotation matrices and a review of quaternion rotation-averaging methods relevant to the orientation-frame alignment problem. The supporting information covers novel extensions of quaternion methods to the 4D Euclidean spatial-coordinate alignment and 4D orientation-frame alignment problems, some miscellaneous topics, and additional details of the quartic algebraic eigenvalue problem.

Visible-Light, Iodine-Promoted Formation of N-Sulfonyl Imines and N-Alkylsulfonamides from Aldehydes and Hypervalent Iodine Reagents.

Alternative synthetic methodology for the direct installation of sulfonamide functionality is a highly desirable goal within the domain of drug discovery and development. The formation of synthetically valuable N-sulfonyl imines from a range of aldehydes, sulfonamides, and PhI(OAc)2 under practical and mild reaction conditions has been developed. According to mechanistic studies described within, the reaction proceeds through an initial step involving a radical initiator (generated either by visible-light or heat) to activate the reacting substrates. The reaction provides a synthetically useful and operationally simple, relatively mild alternative to the traditional formation of N-sulfonyl imines that utilizes stable, widely available reagents.

Interactions and Localization of Escherichia coli Error-Prone DNA Polymerase IV after DNA Damage.

UNLABELLED: Escherichia coli's DNA polymerase IV (Pol IV/DinB), a member of the Y family of error-prone polymerases, is induced during the SOS response to DNA damage and is responsible for translesion bypass and adaptive (stress-induced) mutation. In this study, the localization of Pol IV after DNA damage was followed using fluorescent fusions. After exposure of E. coli to DNA-damaging agents, fluorescently tagged Pol IV localized to the nucleoid as foci. Stepwise photobleaching indicated ∼60% of the foci consisted of three Pol IV molecules, while ∼40% consisted of six Pol IV molecules. Fluorescently tagged Rep, a replication accessory DNA helicase, was recruited to the Pol IV foci after DNA damage, suggesting that the in vitro interaction between Rep and Pol IV reported previously also occurs in vivo. Fluorescently tagged RecA also formed foci after DNA damage, and Pol IV localized to them. To investigate if Pol IV localizes to double-strand breaks (DSBs), an I-SceI endonuclease-mediated DSB was introduced close to a fluorescently labeled LacO array on the chromosome. After DSB induction, Pol IV localized to the DSB site in ∼70% of SOS-induced cells. RecA also formed foci at the DSB sites, and Pol IV localized to the RecA foci. These results suggest that Pol IV interacts with RecA in vivo and is recruited to sites of DSBs to aid in the restoration of DNA replication. IMPORTANCE: DNA polymerase IV (Pol IV/DinB) is an error-prone DNA polymerase capable of bypassing DNA lesions and aiding in the restart of stalled replication forks. In this work, we demonstrate in vivo localization of fluorescently tagged Pol IV to the nucleoid after DNA damage and to DNA double-strand breaks. We show colocalization of Pol IV with two proteins: Rep DNA helicase, which participates in replication, and RecA, which catalyzes recombinational repair of stalled replication forks. Time course experiments suggest that Pol IV recruits Rep and that RecA recruits Pol IV. These findings provide in vivo evidence that Pol IV aids in maintaining genomic stability not only by bypassing DNA lesions but also by participating in the restoration of stalled replication forks.

Scheduling scaffolding: the extent and arrangement of assistance during training impacts test performance.

Various kinds of assistance, including prompts, worked examples, direct instruction, and modeling, are widely provided to learners across educational and training programs. Yet, the effectiveness of assistance during training on long-term learning is widely debated. The authors examined how the extent and schedule of assistance during training on a novel mouse movement task impacted unassisted test performance. Learners received different schedules of assistance during training, including constant assistance, no assistance, probabilistic assistance, alternating assistance, and faded assistance. Constant assistance led to better performance during training than no assistance. However, constant assistance during training resulted in the worst unassisted test performance. Faded assistance during training resulted in the best test performance. This suggests that fading may allow learners to create an internal model of the assistance without depending on the assistance in a manner that impedes successful transfer to unassisted circumstances.

Putting science first: distinguishing visualizations from pretty pictures.

How do we tell whether a proposed visualization is a valid pictorial representation of the truth or just an accidental but appealing image? Art and science can work brilliantly together in visualization science, but we must know when, and how, to distinguish them.

On the mutational topology of the bacterial genome.

By sequencing the genomes of 34 mutation accumulation lines of a mismatch-repair defective strain of Escherichia coli that had undergone a total of 12,750 generations, we identified 1625 spontaneous base-pair substitutions spread across the E. coli genome. These mutations are not distributed at random but, instead, fall into a wave-like spatial pattern that is repeated almost exactly in mirror image in the two separately replicated halves of the bacterial chromosome. The pattern is correlated to genomic features, with mutation densities greatest in regions predicted to have high superhelicity. Superimposed upon this pattern are regional hotspots, some of which are located where replication forks may collide or be blocked. These results suggest that, as they traverse the chromosome, the two replication forks encounter parallel structural features that change the fidelity of DNA replication.

Quaternion maps of global protein structure.

The geometric structures of proteins are vital to the understanding of biochemical interactions. However, there is much yet to be understood about the spatial arrangements of the chains of amino acids making up any given protein. In particular, while conventional analysis tools like the Ramachandran plot supply some insight into the local relative orientation of pairs of amino acid residues, they provide little information about the global relative orientations of large groups of residues. We apply quaternion maps to families of coordinate frames defined naturally by amino acid residue structures as a way to expose global spatial relationships among residues within proteins. The resulting visualizations enable comparisons of absolute orientations as well as relative orientations, and thus generalize the framework of the Ramachandran plot. There are a variety of possible quaternion frames and visual representation strategies that can be chosen, and very complex quaternion maps can result. Just as Ramachandran plots are useful for addressing particular questions and not others, quaternion tools have characteristic domains of relevance. In particular, quaternion maps show great potential for answering specific questions about global residue alignment in crystallographic data and statistical orientation properties in Nuclear Magnetic Resonance (NMR) data that are very difficult to treat by other methods.

GL4D: a GPU-based architecture for interactive 4D visualization.

This paper describes GL4D, an interactive system for visualizing 2-manifolds and 3-manifolds embedded in four Euclidean dimensions and illuminated by 4D light sources. It is a tetrahedron-based rendering pipeline that projects geometry into volume images, an exact parallel to the conventional triangle-based rendering pipeline for 3D graphics. Novel features include GPU-based algorithms for real-time 4D occlusion handling and transparency compositing; we thus enable a previously impossible level of quality and interactivity for exploring lit 4D objects. The 4D tetrahedrons are stored in GPU memory as vertex buffer objects, and the vertex shader is used to perform per-vertex 4D modelview transformations and 4D-to-3D projection. The geometry shader extension is utilized to slice the projected tetrahedrons and rasterize the slices into individual 2D layers of voxel fragments. Finally, the fragment shader performs per-voxel operations such as lighting and alpha blending with previously computed layers. We account for 4D voxel occlusion along the 4D-to-3D projection ray by supporting a multi-pass back-to-front fragment composition along the projection ray; to accomplish this, we exploit a new adaptation of the dual depth peeling technique to produce correct volume image data and to simultaneously render the resulting volume data using 3D transfer functions into the final 2D image. Previous CPU implementations of the rendering of 4D-embedded 3-manifolds could not perform either the 4D depth-buffered projection or manipulation of the volume-rendered image in real-time; in particular, the dual depth peeling algorithm is a novel GPU-based solution to the real-time 4D depth-buffering problem. GL4D is implemented as an integrated OpenGL-style API library, so that the underlying shader operations are as transparent as possible to the user.

Visualizing multiwavelength astrophysical data.

With recent advances in the measurement technology for allsky astrophysical imaging, our view of the sky is no longer limited to the tiny visible spectral range over the 2D Celestial sphere. We now can access a third dimension corresponding to a broad electromagnetic spectrum with a wide range of allsky surveys; these surveys span frequency bands including long wavelength radio, microwaves, very short X-rays, and gamma rays. These advances motivate us to study and examine multiwavelength visualization techniques to maximize our capabilities to visualize and exploit these informative image data sets. In this work, we begin with the processing of the data themselves, uniformizing the representations and units of raw data obtained from varied detector sources. Then we apply tools to map, convert, color-code, and format the multiwavelength data in forms useful for applications. We explore different visual representations for displaying the data, including such methods as textured image stacks, the horseshoe representation, and GPU-based volume visualization. A family of visual tools and analysis methods is introduced to explore the data, including interactive data mapping on the graphics processing unit (GPU), the mini-map explorer, and GPU-based interactive feature analysis.

Enhanced efficiency of direct-space structure solution from powder X-ray diffraction data in the case of conformationally flexible molecules.

A strategy is reported for assessing the feasibility of molecular conformations within direct-space structure-solution calculations of organic molecular crystal structures from powder X-ray diffraction data, focusing in particular on the genetic algorithm technique for structure solution in which fitness is defined as a function of the whole-profile figure-of-merit Rwp. The strategy employs a readily computed distance-based function to assess the feasibility of the molecular conformation in each trial structure generated in the genetic algorithm calculation, and structures considered to have low-feasibility conformations are penalized within the evolutionary process. The strategy is shown to lead to significant improvements in the success rate of structure-solution calculations in the case of flexible molecules with a significant number of conformational degrees of freedom.

A transparently scalable visualization architecture for exploring the universe.

Modern astronomical instruments produce enormous amounts of three-dimensional data describing the physical Universe. The currently available data sets range from the solar system to nearby stars and portions of the Milky Way Galaxy, including the interstellar medium and some extrasolar planets, and extend out to include galaxies billions of light years away. Because of its gigantic scale and the fact that it is dominated by empty space, modeling and rendering the Universe is very different from modeling and rendering ordinary three-dimensional virtual worlds at human scales. Our purpose is to introduce a comprehensive approach to an architecture solving this visualization problem that encompasses the entire Universe while seeking to be as scale-neutral as possible. One key element is the representation of model-rendering procedures using power scaled coordinates (PSC), along with various PSC-based techniques that we have devised to generalize and optimize the conventional graphics framework to the scale domains of astronomical visualization. Employing this architecture, we have developed an assortment of scale-independent modeling and rendering methods for a large variety of astronomical models, and have demonstrated scale-insensitive interactive visualizations of the physical Universe covering scales ranging from human scale to the Earth, to the solar system, to the Milky Way Galaxy, and to the entire observable Universe.

Scalable WIM: effective exploration in large-scale astrophysical environments.

Navigating through large-scale virtual environments such as simulations of the astrophysical Universe is difficult. The huge spatial range of astronomical models and the dominance of empty space make it hard for users to travel across cosmological scales effectively, and the problem of wayfinding further impedes the user's ability to acquire reliable spatial knowledge of astronomical contexts. We introduce a new technique called the scalable world-in-miniature (WIM) map as a unifying interface to facilitate travel and wayfinding in a virtual environment spanning gigantic spatial scales: Power-law spatial scaling enables rapid and accurate transitions among widely separated regions; logarithmically mapped miniature spaces offer a global overview mode when the full context is too large; 3D landmarks represented in the WIM are enhanced by scale, positional, and directional cues to augment spatial context awareness; a series of navigation models are incorporated into the scalable WIM to improve the performance of travel tasks posed by the unique characteristics of virtual cosmic exploration. The scalable WIM user interface supports an improved physical navigation experience and assists pragmatic cognitive understanding of a visualization context that incorporates the features of large-scale astronomy.

Binary-space-partitioned images for resolving image-based visibility.

We propose a novel 2D representation for 3D visibility sorting, the Binary-Space-Partitioned Image (BSPI), to accelerate real-time image-based rendering. BSPI is an efficient 2D realization of a 3D BSP tree, which is commonly used in computer graphics for time-critical visibility sorting. Since the overall structure of a BSP tree is encoded in a BSPI, traversing a BSPI is comparable to traversing the corresponding BSP tree. BSPI performs visibility sorting efficiently and accurately in the 2D image space by warping the reference image triangle-by-triangle instead of pixel-by-pixel. Multiple BSPIs can be combined to solve "disocclusion," when an occluded portion of the scene becomes visible at a novel viewpoint. Our method is highly automatic, including a tensor voting preprocessing step that generates candidate image partition lines for BSPIs, filters the noisy input data by rejecting outliers, and interpolates missing information. Our system has been applied to a variety of real data, including stereo, motion, and range images.