Set Of Rotations Research Articles

Fast and sensitive rigid-body fitting into cryo-EM density maps with PowerFit

Cryo-EM is a rapidly developing method to investigate the three dimensional structure of large macromolecular complexes. In spite of all the advances in the field, the resolution of most cryo-EM density maps is too low for <em>de novo</em> model building. Therefore, the data are often complemented by fitting high-resolution subunits in the density to allow for an atomic interpretation. Typically, the first step in the modeling process is placing the subunits in the density as a rigid body. An objective method for automatic placement is full-exhaustive six dimensional cross correlation search between the model and the cryo-EM data, where the three translational and three rotational degrees of freedom are systematically sampled. In this article we present PowerFit, a Python package and program for fast and sensitive rigid body fitting. We introduce a novel, more sensitive scoring function, the core-weighted local cross correlation, and show how it can be calculated using FFTs for fast translational cross correlation scans. We further improved the search algorithm by using optimized rotational sets to reduce rotational redundancy and by limiting the cryo-EM data size through resampling and trimming the density. We demonstrate the superior scoring sensitivity of our scoring function on simulated data of the 80S D. melanogaster ribosome and on experimental data for four different cases. Through these advances, a fine-grained rotational search can now be performed within minutes on a CPU and seconds on a GPU. PowerFit is free software and can be downloaded from https://github.com/haddocking/powerfit.

Nucleosome organizations in induced pluripotent stem cells reprogrammed from somatic cells belonging to three different germ layers.

BackgroundNucleosome organization determines the chromatin state, which in turn controls gene expression or silencing. Nucleosome remodeling occurs during somatic cell reprogramming, but it is still unclear to what degree the re-established nucleosome organization of induced pluripotent stem cells (iPSCs) resembles embryonic stem cells (ESCs), and whether the iPSCs inherit some residual gene expression from the parental fibroblast cells.ResultsWe generated genome-wide nucleosome maps in mouse ESCs and in iPSCs reprogrammed from somatic cells belonging to three different germ layers using a secondary reprogramming system. Pairwise comparisons showed that the nucleosome organizations in the iPSCs, regardless of the iPSCs’ tissue of origin, were nearly identical to the ESCs, but distinct from mouse embryonic fibroblasts (MEF). There is a canonical nucleosome arrangement of -1, nucleosome depletion region, +1, +2, +3, and so on nucleosomes around the transcription start sites of active genes whereas only a nucleosome occupies silent transcriptional units. Transcription factor binding sites possessed characteristic nucleosomal architecture, such that their access was governed by the rotational and translational settings of the nucleosome. Interestingly, the tissue-specific genes were highly expressed only in the parental somatic cells of the corresponding iPS cell line before reprogramming, but had a similar expression level in all the resultant iPSCs and ESCs.ConclusionsThe re-established nucleosome landscape during nuclear reprogramming provides a conserved setting for accessibility of DNA sequences in mouse pluripotent stem cells. No persistent residual expression program or nucleosome positioning of the parental somatic cells that reflected their tissue of origin was passed on to the resulting mouse iPSCs.Electronic supplementary materialThe online version of this article (doi:10.1186/s12915-014-0109-x) contains supplementary material, which is available to authorized users.

Formability in synchronous multipass spinning using simple pass set

This study is an investigation into the effect of the different parameters of the pass set on the formability in synchronous multipass spinning. Synchronous multipass spinning is a metal spinning method that can produce a noncircular cylindrical shape with a noncircular bottom and vertical walls from a metal sheet. The radial position of the roller tool is synchronized with the spindle rotation while the work piece is formed from a flat disk into the shape of the mandrel step by step along varying trajectories. The tool trajectory is calculated by linear interpolation between the mandrel shape and the blank disk shape along a pass set. Here, a pass is the tool trajectory in the normalized two-dimensional space defined by the radial and axial directions of the mandrel. The aim of this study is to examine the effect of different parameters of the pass set on the formability of two sample shapes, a circular cup and a rectangular box.The formability was experimentally examined using a rotational pass set and a translational pass set as simple tool trajectories. The rotational pass set consists of curved passes with the same start point and a constantly increasing angle inclination. The translational pass set consists of passes with the same inclination and a start point that is moved by a constant amount. The angle of growth of the rotational pass set, the incremental movement of the translational pass set, and the nominal product height are varied for comparison in the experiments.

Rotational chaos and strange attractors on the 2-torus

We construct a 2-torus homeomorphism $$h$$ homotopic to the identity with an attracting R. H. Bing’s pseudocircle $$C$$ such that the rotation set of $$h|C$$ is not a unique vector. The only known examples of such an attractor were Birkhoff’s attractors, arising for dissipative maps with a twist. Our construction relies heavily on the Barge–Martin method for constructing attractors as inverse limits of graphs.

Interaction of Movement Difficulty due to the Misalignment Effect and Response Latency

In previous reports we measured and analyzed the Misalignment Effect Function, a function describing the decrement in human performance due to rotation between operators’ display and control axes. This prior work allowed us to determine difficulty-matched sets of rotations for a generalized 3D Fitts-like movement task. We consequently are now able to study the interaction of system latency and movement difficulty in a highly generalized way in a virtual telerobotic environment using wide variety of conditions and targets. Our targets are located on a spherical shell near our participants’ starting point in a high dynamic fidelity virtual environment. Analysis of participants’ ability to make movements to these targets has revealed a purely multiplicative interaction between control latency and task difficulty. Interestingly, we show that this the observed interaction supports work on Fitts’ Law by E.R. Hoffmann and that it depends upon accounting for an internal human processing latency of ~250 ms. Our data suggest that the interaction varies nonlinearly due to task difficulty in a manner consistent with Hoffmann’s results. We propose a descriptive equation to reflect the observed interaction that can be seen as a spatiotemporal generalization of Fitts’ Law. Our results provide a basis for generalizing latency requirements for reference tasks that may be varied in difficulty in a manner analogous to the Fitts’ Index of Difficulty.

Symbol ratio minimax sequences in the lexicographic order

Consider the space of sequences of $k$letters ordered lexicographically. We study the set ${\mathcal{M}}(\boldsymbol{{\it\alpha}})$of all maximal sequences for which the asymptotic proportions $\boldsymbol{{\it\alpha}}$of the letters are prescribed, where a sequence is said to be maximal if it is at least as great as all of its tails. The infimum of${\mathcal{M}}(\boldsymbol{{\it\alpha}})$is called the$\boldsymbol{{\it\alpha}}$-infimaxsequence, or the$\boldsymbol{{\it\alpha}}$-minimaxsequence if the infimum is a minimum. We give an algorithm which yields all infimax sequences, and show that the infimax isnota minimax if and only if it is the$\boldsymbol{{\it\alpha}}$-infimax for every$\boldsymbol{{\it\alpha}}$in a simplex of dimension 1 or greater. These results have applications to the theory of rotation sets of beta-shifts and torus homeomorphisms.

A Branch-and-Price Algorithm for the Multidepot Vehicle Routing Problem with Interdepot Routes

This paper proposes a column generation algorithm for the multidepot vehicle routing problem with interdepot routes. This problem is an extension of the multidepot vehicle routing problem in which the vehicles are allowed to stop at intermediate depots along their routes to replenish. The problem can be modeled as a set covering problem in which the variables are rotations corresponding to feasible combinations of routes. We consider two pricing subproblems to generate rotations. The first one generates rotations directly by solving an elementary shortest path problem with resource constraints on a modified version of the original customer-depot network. The second one exploits the relationship between the sets of routes and rotations but results in a model with many columns. We discuss some issues related to solving this second pricing subproblem by column generation and we introduce an alternate approach to alleviate these difficulties. We show through computational experiments that the second pricing mechanism performs better than the first to compute the linear programming relaxation lower bound. We then embed it within a branch-and-bound algorithm to compute optimal integer solutions. Moreover, we assess the benefits of allowing interdepot routes in multidepot vehicle routing.

Improving Pre-Operative Flexion in Primary TKA: A Surgical Technique Emphasizing Knee Flexion with 5-Year Follow-Up

This study prospectively reviews a consecutive series of 228 primary total knee arthroplasty (TKA) procedures utilizing a technique to optimize knee flexion. The main features include: (1)the use of a “patellar friendly” femoral component and reduced thickness patellar components, (2) patient individualized adjustment of the femoral component rotation set strictly to the anterior-posterior femoral axis, (3)a rigorous flexion compartment debridement to remove non-essential posterior femoral bone with a Z-osteotome, and (4)incorporation of a rapid recovery protocol with features to promote knee flexion.Results were categorized into three groups: low pre-op flexion (90 degrees and below), regular pre-op flexion (91-125 degrees), and high pre-op flexion (126 degrees and above). Average flexion in the low flexion group improved by 20 degrees at 6 weeks, 28 degrees at 3 months, 31 degrees at 1 year, and 30 degrees at 5 years. In the regular flexion group, average flexion improved by 2 degrees at 6 weeks, 10 degrees at 3 months, 12 degrees at 1 year, and 13 degrees at 5 years. Finally, in the high flexion group, average flexion decreased by 7 degrees at 6 weeks, regained preoperative levels at 3 months, and increased by 3 degrees at 1 year and 4 degrees at 5 years.In summary, a technique that emphasizes patellofemoral kinematics can consistently improve flexion in TKA in short and long-term follow-up.Keywords: Total knee arthroplasty, range of motion, high flexion, surgical technique, implant design, AP AxisLevel of Evidence: AAOS Therapeutic Study Level III

Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

We construct a $C^\infty$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose rotation set is $\{(0,0)\}$, which in addition has the property that almost every orbit by the lifted dynamics is unbounded and accumulates in every direction of the circle at infinity.

Bounded and unbounded behavior for area-preserving rational pseudo-rotations

A rational pseudo-rotation f of the torus is a homeomorphism homotopic to the identity with a rotation set consisting of a single vector v of rational coordinates. We give a classification for rational pseudo-rotations with an invariant measure of full support, in terms of the deviations from the constant rotation x ↦ x + v in the universal covering. For the simpler case that v = ( 0 , 0 ) , it states that either every orbit by the lifted dynamics is bounded, or the displacement of orbits in the universal covering is uniformly bounded in some rational direction (implying that the dynamics is annular) or the set of fixed points of f contains a large continuum which is the complement of a disjoint union of disks (that is, a fully essential continuum). In the analytic setting, the latter case is ruled out. In order to prove this classification, we introduce tools that are of independent interest and can be applied in a more general setting: in particular, a geometric result about the quasi-convexity and existence of asymptotic directions for certain chains of disks, and a Poincaré recurrence theorem on the universal covering for irrotational measures.

Integrating Structured Learning and Scholarly Activities into Clerkship Rotations: A Win-Win for Students and Preceptors.

Objective: To merge scholarly activity into the curriculum developed for medical students electing a rotation in wound care and/or dermatology. Approach: The authors adapted the unique wound care curriculum developed for medical student rotators and residents to incorporate structured scholarly projects, opportunities for mentorship, and feedback for continued improvement. Results: Benefits have been observed to both students and to the clinic, as reflected by online survey results, increased productivity in the form of posters and manuscripts, and opportunities for professional networking. Discussion: Rotations and clerkships can be transformed from haphazard, bystander observational experiences to active participation that enhances comprehension and retention, while also providing benefits to preceptors. Innovation: Integration between research, education, and clinical activities in a structured way can provide opportunity for enhanced learning experiences and promote the concept of evidence-based practice. Conclusion: With observed benefits to students, researchers, and staff in this clinical setting, other clerkship rotation settings should consider an integrated and structured approach to learning, which includes scholarly activities. Further rigorous program evaluation is necessary to further quantify preliminary positive feedback regarding this approach.

Histone H3 Lysine 14 (H3K14) Acetylation Facilitates DNA Repair in a Positioned Nucleosome by Stabilizing the Binding of the Chromatin Remodeler RSC (Remodels Structure of Chromatin)

Histone H3 acetylation is induced by UV damage in yeast and may play an important role in regulating the repair of UV photolesions in nucleosome-loaded genomic loci. However, it remains elusive how H3 acetylation facilitates repair. We generated a strongly positioned nucleosome containing homogeneously acetylated H3 at Lys-14 (H3K14ac) and investigated possible mechanisms by which H3K14 acetylation modulates repair. We show that H3K14ac does not alter nucleosome unfolding dynamics or enhance the repair of UV-induced cyclobutane pyrimidine dimers by UV photolyase. Importantly, however, nucleosomes with H3K14ac have a higher affinity for purified chromatin remodeling complex RSC (Remodels the Structure of Chromatin) and show greater cyclobutane pyrimidine dimer repair compared with unacetylated nucleosomes. Our study indicates that, by anchoring RSC, H3K14 acetylation plays an important role in the unfolding of strongly positioned nucleosomes during repair of UV damage.

Investigation into the effect of overlap factors and process parameters on surface roughness and machined depth during micro-turning process with Nd:YAG laser

Abstract One of the emerging laser material processing technologies to process cylindrical shaped materials is the laser micro-turning process. This process is used to machine micro-turned groove or surface on the difficult-to-process materials for a specific length of turn along its axis. The present experimental study investigates the laser micro-turning operation of a cylindrical shaped aluminum oxide (Al2O3) ceramic to explore the effect of successive spot overlap and circumferential overlap on the surface roughness (Ra) criterion. Moreover, depth of machining has also been studied by varying various process parameters such as pulse frequency, workpiece rotating speed and laser beam average power. Various amounts of spot overlap have been accomplished by different combined settings of related parameters i.e. workpiece rotating speed and pulse frequency. In contrast, various circumferential overlap between successive rotational scan widths have been achieved by varying the rotational speed and also axial feed rate of the workpiece. Surface roughness (Ra) and machined depth have been measured as output response for machining at various parametric combinations. Analyses have been made through different plots of surface roughness (Ra) and machined depth to study the influence of these overlaps and different process parameters. The experimental results revealed that surface roughness decreases with the increase of both the overlap factors. It is observed from the results that with the increase in circumferential overlap, roughness of the machined surface decreases for each workpiece rotating speed setting. Further, wide spot crater is achieved at a higher value of average power. Minimum surface roughness is achieved as 5.25 µm at average power 10 W, pulse frequency 3000 Hz, workpiece rotating speed 400 rpm and Y feed rate 0.3 mm/s. The achieved machined depth is high at a low speed of rotation and pulse frequency settings. With the increase of average power of laser beam, the machined depth is found to increase linearly. The maximum micro-turning depth is achieved as 0.146 mm at parametric combination of average power of 10 W, pulse frequency of 3000 Hz, workpiece rotating speed of 400 rpm and Y feed rate of 0.3 mm/s.

Canonical Correlation Analysis on Riemannian Manifolds and Its Applications.

Canonical correlation analysis (CCA) is a widely used statistical technique to capture correlations between two sets of multi-variate random variables and has found a multitude of applications in computer vision, medical imaging and machine learning. The classical formulation assumes that the data live in a pair of vector spaces which makes its use in certain important scientific domains problematic. For instance, the set of symmetric positive definite matrices (SPD), rotations and probability distributions, all belong to certain curved Riemannian manifolds where vector-space operations are in general not applicable. Analyzing the space of such data via the classical versions of inference models is rather sub-optimal. But perhaps more importantly, since the algorithms do not respect the underlying geometry of the data space, it is hard to provide statistical guarantees (if any) on the results. Using the space of SPD matrices as a concrete example, this paper gives a principled generalization of the well known CCA to the Riemannian setting. Our CCA algorithm operates on the product Riemannian manifold representing SPD matrix-valued fields to identify meaningful statistical relationships on the product Riemannian manifold. As a proof of principle, we present results on an Alzheimer's disease (AD) study where the analysis task involves identifying correlations across diffusion tensor images (DTI) and Cauchy deformation tensor fields derived from T1-weighted magnetic resonance (MR) images.

Effect of Pass-set Shape on Formability in Synchronous Multipass Spinning

Synchronous multi pass spinning is a metal spinning method that can form asymmetric shapes with a noncircular bottom and vertical walls from a metal sheet. In this method, the tool trajectory is calculated by linear interpolation between the mandrel shape and the blank disk shape along a pass set. Here, the pass set corresponds to the tool trajectory in conventional spinning. The aim of this study is to examine the effect of a pass set on the formability of a circular cup shape and a rectangular box shape. We have experimentally examined the formability using various pass sets made by simple rule. The angle growth of the rotational pass set, the incremental movement of the translational pass set, and the nominal product height are varied for comparison in the experiments.

The Hencky strain energy ‖log U‖2 measures the geodesic distance of the deformation gradient to SO(n) in the canonical left‐invariant Riemannian metric on GL(n)

AbstractThe well‐known isotropic Hencky strain energy appears naturally as a distance measure of the deformation gradient to the set of rigid rotations in a canonical left‐invariant Riemannian metric on the general linear group GL(n). Objectivity requires the Riemannian metric to be left‐GL(n) invariant, isotropy requires the Riemannian metric to be right‐O(n) invariant. The latter two conditions are satisfied for a three‐parameter family of Riemannian metrics on the tangent space of GL(n). Surprisingly, the final result is basically independent of the chosen parameters.In deriving the result, geodesics on GL(n) have to be parametrized and a novel minimization problem, involving the matrix logarithm for non‐symmetric arguments, has to be solved. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Abstract 9813: Verifying Cardiac Mechanics From 3D-Wall Motion Tracking Processed for Rotation Determination

Background: This study assessed 3D-Wall Motion Tracking (3D-WMT) for determining rotation of a pumped heart model. Methods: Latex balloons were sutured inside the LV of 10 pig hearts and attached to a pulsatile pump. The heart phantom and a Toshiba Matrix Array PST-25SX 2.5 MHz Transducer were fixed within a water filled tank. The hearts were firmly attached to a rotating plate at the base and lightly affixed at the apex, and pumped at a stroke volume of 50ml while the base of the heart was variably rotated at 0, 3,5,7,10,12 and 15 degrees. Three images were acquired at each rotation setting and a 3D WMT program was used to assess cardiac rotation. Results: The 3D-WMT derived rotation angles were found to be most precise at physiologically normal values (3-5°), but consistently underestimated at angles greater than 5°. For the 3D-WMT calculated rotation, the mean and standard deviation at 0°,3°,5°,7°,10°,12°,15° was 1.049° ± 0.688°, 2.80° ± 0.647°, 4.178° ± 0.835°, 5.723° ± 0.851°,7.809° ± 0.815°, 9.131° ± 1.481°,11.144° ± 1.307°, respectively. The P value is less than 0.0001 A Bland Altman plot showed 96% of data were within a 95% confidence interval and a slight underestimation. Conclusions: Despite observed underestimation at higher degrees of rotation, Toshiba 3D-WMT may provide clinically important determinations of LV rotation.

Radiographic quantification of dynamic hip screw migration.

This study aimed to propose a technique to quantify dynamic hip screw (DHS®) migration on serial anteroposterior (AP) radiographs by accounting for femoral rotation and flexion. Femoral rotation and flexion were estimated using radiographic projections of the DHS® plate thickness and length, respectively. The method accuracy was evaluated using a synthetic femur fixed with a DHS® and positioned at pre-defined rotation and flexion settings. Standardised measurements of DHS® migration were trigonometrically adjusted for femoral rotation and flexion, and compared with unadjusted estimates in 34 patients. The mean difference between the estimated and true femoral rotation and flexion values was 1.3° (95% CI 0.9-1.7°) and -3.0° (95% CI - 4.2° to -1.9°), respectively. Adjusted measurements of DHS® migration were significantly larger than unadjusted measurements (p = 0.045). The presented method allows quantification of DHS® migration with adequate bias correction due to femoral rotation and flexion.

Rotational positioning of nucleosomes facilitates selective binding of p53 to response elements associated with cell cycle arrest

The tumor suppressor protein p53 exhibits high affinity to the response elements regulating cell cycle arrest genes (CCA-sites), but relatively low affinity to the sites associated with apoptosis (Apo-sites). This in vivo tendency cannot be explained solely by the p53-DNA binding constants measured in vitro. Since p53 can bind nucleosomal DNA, we sought to understand if the two groups of p53 sites differ in their accessibility when embedded in nucleosomes. To this aim, we analyzed the sequence-dependent bending anisotropy of human genomic DNA containing p53 sites. For the 20 CCA-sites, we calculated rotational positioning patterns predicting that most of the sites are exposed on the nucleosomal surface. This is consistent with experimentally observed positioning of human nucleosomes. Remarkably, the sequence-dependent DNA anisotropy of both the p53 sites and flanking DNA work in concert producing strong positioning signals. By contrast, both the predicted and observed rotational settings of the 38 Apo-sites in nucleosomes suggest that many of these sites are buried inside, thus preventing immediate p53 recognition and delaying gene induction. The distinct chromatin organization of the CCA response elements appears to be one of the key factors facilitating p53-DNA binding and subsequent activation of genes associated with cell cycle arrest.

Rational polygons as rotation sets of generic homeomorphisms of the two torus

We prove the existence of an open and dense set 𝔇⊂Homeo0(𝕋2) (where Homeo0(𝕋2) denotes the set of toral homeomorphisms homotopic to the identity) such that the rotation set of any element in 𝔇 is a rational polygon. We also extend this result to the set of axiom A diffeomorphisms in Homeo0(𝕋2). Further, we observe the existence of minimal sets whose rotation set is a non-trivial segment, for an open set in Homeo0(𝕋2).