Rotation Of Group Research Articles

From QCD Strings to WZW

According to the Axionic String Ansatz (ASA) confining flux tubes in pure gluodynamics are in the same equivalence class as a new family of integrable non-critical strings, called axionic strings. In addition to translational modes, axionic strings carry a set of worldsheet axions transforming as an antisymmetric tensor under the group of transverse rotations. We initiate a study of integrable axionic strings at general number of space-time dimensions D. We show that in the infinite tension limit worldsheet axions should be described by a peculiar “pseudofree” theory — their S-matrix is trivial, but the corresponding action cannot be brought into a free form by a local field redefinition. This requirement fixes the axionic action to take a form of the O(D − 2) Wess-Zumino-Witten (WZW) model.

An agent-based model for assessing grazing strategies and institutional arrangements in Zeku, China

The assessment of grassland grazing strategies and institutional arrangements is essential for ensuring the sustainable development of grassland grazing systems. By employing per-pixel grazing information derived from remote sensing data, this paper presents an agent-based model of grassland grazing (ABMGG) for Zeku, China that was designed as a framework for assessing the effects of different combinations of grazing strategies and institutional arrangements on grassland status. By calibrating the parameter values of the ABMGG to the system status values under a policy that has already been implemented, the ABMGG can help us to understand grassland degradation in response to management interventions for each patch of land. In the Zeku implementation, it was found that although different grazing policy scenarios could not significantly improve or decrease the overall grassland leaf area index, a rotational group grazing scenario with a land market tenure system did produce a smaller number of severely degraded grass patches than other policy scenarios (except regional continuous grazing). This provides a new perspective on the consequences of grassland management practices where past research has concentrated more on overall grassland productivity. The ABMGG can extend the ability of policy assessment tools to a high resolution level with pixel-specific real-time remote sensing data, making the assessment results more accurate and representative.

On the classification of two-qubit group orbits and the use of coarse-grained 'shape' as a superselection property

Recently a complete set of entropic conditions has been derived for the interconversion structure of states under quantum operations that respect a specified symmetry action, however the core structure of these conditions is still only partially understood. Here we develop a coarse-grained description with the aim of shedding light on both the structure and the complexity of this general problem. Specifically, we consider the degree to which one can associate a basic `shape' property to a quantum state or channel that captures coarse-grained data either for state interconversion or for the use of a state within a simulation protocol. We provide a complete solution for the two-qubit case under the rotation group, give analysis for the more general case and discuss possible extensions of the approach.

The Impact of Decreased Scapulothoracic Upward Rotation on Subacromial Proximities.

Decreased scapulothoracic upward rotation has been theorized to increase an individual's risk for rotator cuff compression by reducing the clearance for the tendons in the subacromial space (ie, subacromial proximities). However, the impact of decreased scapulothoracic upward rotation on subacromial proximities has not been tested during dynamic in vivo shoulder motion. To determine the impact of decreased scapulothoracic upward rotation on subacromial proximities. Shoulder kinematics were quantified in 40 participants, classified as having high or low scapulothoracic upward rotation, during scapular plane abduction using single-plane fluoroscopy and 2-D/3-D shape-matching. Subacromial proximities were calculated as (1) the normalized minimum distance between the coracoacromial arch and humeral rotator cuff insertion, and (2) the surface area of the humeral rotator cuff insertion in immediate proximity to the coracoacromial arch. The effect of decreased scapulothoracic upward rotation on subacromial proximities was assessed using 2-factor mixed-model analyses of variance. The prevalence of contact between the coracoacromial arch and rotator cuff was also quantified. Subacromial distances were generally smallest below 70° of humerothoracic elevation. With the arm at the side, the normalized minimum distance for participants in the low scapulothoracic upward rotation group was 34.8% smaller compared to those in the high upward rotation group (P = .049). Contact between the coracoacromial arch and rotator cuff tendon occurred in 45% of participants. Decreased scapulothoracic upward rotation shifts the range of risk for subacromial rotator cuff compression to lower angles. However, the low prevalence of contact suggests that subacromial rotator cuff compression may be less common than traditionally presumed. J Orthop Sports Phys Ther 2019;49(3):180-191. Epub 18 Jan 2019. doi:10.2519/jospt.2019.8590.

Isobar Collisions at RHIC to Test Local Parity Violation in Strong Interactions

The discovery of the Higgs boson has completed the Standard Model of fundamental interactions. The Standard Model describes the strong and electroweak interactions by generalizing the concept of local gauge invariance that underlies the Maxwell theory of electromagnetism to non-Abelian gauge groups. A non-Abelian group has the elements that do not commute, such as the group of rotations in three dimensions, where a rotation around axis x followed by a rotation around axis γ yields a different result from doing these rotations the other way around. The resulting theory is both elegant and powerful—it is believed to describe all known properties of the physical world, except gravity. In spite of their deceptively simple structure, non-Abelian gauge theories possess many surprising features that are still not understood.

Rotation versus non-rotation of intraocular lens for prevention of posterior capsular opacification.

Purpose:To study the effect of rotation of intraocular lens (IOL) on posterior capsular opacification (PCO) in eyes with phacoemulsification.Methods:This was a prospective, comparative, randomized case series. One eye of each patient was randomized to one of two groups. The 360-degree rotation of IOL was carried out after its placement in the capsular bag (rotation group). The control group had no rotation of IOL. PCO was analyzed by an independent observer on EPCO computer analysis system at 6, 12, 24, and 36 months.Results:The study included 50 patients (100 eyes) with senile cataracts scheduled for phacoemulsification and IOL implantation. The median age in 2 groups was 66 years. 25% quartile age in both the group was 62 years (P = 0.06). There were 30 males, and 20 females. The median PCO score at 6, 12 and 24 months was significantly low in the rotation group (0.15, 0.13, 0.22) compared to the control group (0.22, 0.23, 0.25). There was no significant difference in PCO score between the two groups from 24-36 months. The median PCO score at 36 months was 0.2 in both the groups. At the end of three years, 4 eyes (8%) in the rotation group, and 10 eyes (20%) in the control group needed Nd:YAG capsulotomy (P = 0.04).Conclusion:Rotation of IOL in the capsular bag decreases PCO and Nd:YAG capsulotomy rate.

A Follow-Up on Projection Theory: Theorems and Group Action

In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory. We have already established that one-parameter projection operators can be constructed from the unit circle . As discussed in the previous article these operators form a Lie group known as the Projection Group. In the first section, we will show that the concepts from my first article are consistent with existing theory [1] [2]. In the second section, it will be demonstrated that not only such operators are mutually congruent but also we can define a group action on by using the rotation group [3] [4]. It will be proved that the group acts on elements of in a non-faithful but ∞-transitive way consistent with both group operations. Finally, in the last section we define the group operation in terms of matrix operations using the operator and the Hadamard Product; this construction is consistent with the group operation defined in the first article.

Self-organization on Riemannian manifolds

We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up the model on general Riemannian manifolds and provide a framework for constructing interaction potentials which lead to equilibria that are constant on their supports. We consider such potentials for two specific cases (the two-dimensional sphere and the two-dimensional hyperbolic space) and investigate analytically and numerically the long-time behaviour and equilibrium solutions of the aggregation model on these manifolds. Equilibria obtained numerically with other interaction potentials and an application of the model to aggregation on the rotation group $ SO(3) $ are also presented.

A relaxed approach for curve matching with elastic metrics

In this paper, we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family ofH2-metrics with constant coefficients and scale-invariantH2-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.

Missing Data in Imputed Highest Grade Completed in the 2015–2018 NBER CPS Extracts

In 2015, the Current Population Survey (CPS) eliminated three questions related to educational attainment. These questions are used by the NBER to calculate the variable, Highest Grade (ihigrdc) in their Monthly Outgoing Rotation Group (MORG) extracts. Imputed Highest Grade Completed provides a convenient measure of years of education and is based on the credential oriented CPS variable that is coded from 31 to 46. Because the NBER continues to use coding that relies on these eliminated questions to calculate ihigrdc, this variable has a missing value for 27.5% of the observations in the 2015-2018 extracts. These missing values, in turn, lead to an average Imputed Highest Grade Completed of about 1.2 fewer years after 2014 than would result from using the whole CPS. We informed the NBER of this issue in January 2019; however, because this variable with missing values remains on their website for download as of this writing (July 15, 2019), we are posting this working paper to inform users of these data so that they may address the issue appropriately in their own work.

Missing Data in Imputed Highest Grade Completed in the 2015-2018 NBER CPS Extracts

In 2015, the Current Population Survey (CPS) eliminated three questions related to educational attainment. These questions are used by the NBER to calculate the variable, Highest Grade (ihigrdc) in their Monthly Outgoing Rotation Group (MORG) extracts. Imputed Highest Grade Completed provides a convenient measure of years of education and is based on the credential oriented CPS variable that is coded from 31 to 46. Because the NBER continues to use coding that relies on these eliminated questions to calculate ihigrdc, this variable has a missing value for 27.5% of the observations in the 2015A¢â‚¬â€œ2018 extracts. These missing values, in turn, lead to an average Imputed Highest Grade Completed of about 1.2 fewer years after 2014 than would result from using the whole CPS. We informed the NBER of this issue in January 2019; however, because this variable with missing values remains on their website for download as of this writing (July 15, 2019), we are posting this working paper to inform users of these data so that they may address the issue appropriately in their own work.

Influence of different motions on the cyclic fatigue resistance of Reciproc and Reciproc Blue endodontic instruments.

Aim:The aim of this study was to evaluate the cyclic fatigue resistance of Reciproc (RCP) and RPC Blue (RCPB) instruments used in continuous rotation, “RECIPROC” mode, and “WAVEONE” mode.Materials and Methods:Sixty RCP and 60 RCPB R25 files were used. For each file type, three groups (n = 20) were defined depending on the used kinematics: continuous rotation, “RECIPROC” mode, and “WAVEONE” mode. A stainless-steel artificial canal with 60° angle and 5-mm radius of curvature was milled reproducing the size and taper of the used files. The test device was electrically heated to 35°C to simulate the clinical environment. All files were reciprocated or rotated until fracture. The time to failure and the length of the fractured fragments were measured. A fractographic examination was performed by scanning the electron microscopy to confirm the cause of fracture. Collected data underwent a two-way analysis of variance (α = 0.05).Results:RCPB files exhibited better cyclic fatigue resistance than RCP. The “RECIPROC” motion yielded greater cyclic fatigue resistance than the “WAVEONE” movement; the least resistance was observed in the continuous rotation groups. No significant differences were found among groups in terms of length of the fractured fragment. The fractographic analysis confirmed that all scanned samples separated due to cyclic fatigue.Conclusions:Within the limitation of the present study, the “RECIPROC” mode increased the cyclic fatigue resistance of the tested instruments compared to “WAVEONE” mode and continuous rotation. To prevent RCP and RCPB file separation, motion kinematics other than the native “RECIPROC” movement should be discouraged in the clinical setting.

Tightly-Coupled Monocular Visual-Odometric SLAM Using Wheels and a MEMS Gyroscope

In this paper, we present a novel tightly-coupled probabilistic monocular visual-odometric Simultaneous Localization and Mapping algorithm using wheels and a MEMS gyroscope, which can provide accurate, robust and long-term localization for the ground robot moving on a plane. Firstly, we present an odometer preintegration theory that integrates the wheel encoder measurements and gyroscope measurements to a local frame. The preintegration theory properly addresses the manifold structure of the rotation group SO(3) and carefully deals with uncertainty propagation and bias correction. Then the novel odometer error term is formulated using the odometer preintegration model and it is tightly integrated into the visual optimization framework. Furthermore, we introduce a complete tracking framework to provide different strategies for motion tracking when (1) both measurements are available, (2) visual measurements are not available, and (3) wheel encoder experiences slippage, which leads the system to be accurate and robust. Finally, the proposed algorithm is evaluated by performing extensive experiments, the experimental results demonstrate the superiority of the proposed system.

Adsorptive properties of graphene oxide on vitamin B12 and their effect on the promotion of peripheral nerve regeneration

ABSTRACTObjectives: To observe whether Graphene oxide (GO) can absorb vitamin B12 (VB12) and Decellularized scaffold – acellular nerve allograft (ANA) modified GO-VB12 promote the repair of ischiadic nervus defects in a rat model. Methods: The adsorption of GO on vitamin and the optimum adsorption conditions were investigated by single factor experiment. The adsorption properties of the material were observed by scanning electron microscopy (SEM) and energy dispersive spectrometer (EDS) to determine the success of adsorption on VB12. GO-VB12-ANA was prepared by vibration mixing method and bridged to injured ischiadic nervus. The nerve action potential, wet weight ratio of gastrocnemius muscle and the expression of GAP-43 were investigated by contrast test to detect its effect on nerve regeneration. Results: The optimized adsorption conditions for GO on VB12 solution were listed as follows: adsorbent dosage was 6 mg, shaking time was 70 min, the pH value was 6, the optimum concentration of VB12 was 50 mg/L and the theoretical saturated adsorption capacity was 21.51 mg/g. The nerve action potential, wet weight ratio of gastrocnemius muscle and the expression of GAP-43 in nerve fiber of GO-VB12-ANA group were close to the normal values and significantly higher than those of ANA and rotation group. Conclusions: Based on the adsorption function of GO on VB12, GO-VB12-ANA can promote regeneration of injured ischiadic nervus, providing the experimental basis for the clinical application of nanomaterials.

Invariants of Multidimensional Time Series Based on Their Iterated-Integral Signature

We introduce a novel class of features for multidimensional time series that are invariant with respect to transformations of the ambient space. The general linear group, the group of rotations and the group of permutations of the axes are considered. The starting point for their construction is Chen’s iterated-integral signature.

ACUTE EFFECTS OF MUSCLE ENERGY TECHNIQUE AND JOINT MOBILIZATION ON SHOULDER TIGHTNESS IN YOUTH THROWING ATHLETES: A RANDOMIZED CONTROLLED TRIAL

Posterior shoulder tightness (PST), defined as limited glenohumeral (GH) horizontal adduction and internal rotation motion, is a common occurrence in overhead athletes, particularly baseball and softball players, as a result of the extreme forces on the GH joint and the high number of throwing repetitions. Despite clinical evidence suggesting the use of joint mobilizations and muscle energy techniques (MET) for treating PST, there currently are no data examining the overall effectiveness of joint mobilizations and MET to determine optimal treatment for posterior shoulder tightness. To compare the acute effectiveness of MET and joint mobilizations for reducing posterior shoulder tightness, as measured by passive GH horizontal adduction and internal rotation ROM, among high school baseball and softball players. Randomized controlled study. Forty-two asymptomatic high school baseball and softball players were randomly assigned to one of three groups (14 MET, 14 joint mobilization, 14 control). Glenohumeral passive adduction and internal rotation ROM were measured in all participants in a pre-test post-test fashion. Between testing, the joint mobilization group received one application of GH posterior joint mobilizations. The MET group received one cycle of MET applied to the GH horizontal abductors. The control group received no intervention. Posttests measures were completed immediately following intervention or a similar amount of time resting for the control group and then again 15 minutes later. One-way analyses of covariance showed that the MET group had significantly more horizontal adduction ROM post-treatment compared to the control group (p = 0.04). No significant differences existed between groups in horizontal adduction (p > 0.16) or internal rotation (p>.28) or at the 15-minute posttests (p > 0.70). The results of this study indicate the application of MET to the horizontal abductors provides acute improvements to GH horizontal adduction ROM in high school baseball and softball players, while joint mobilizations provide no improvements. 1.

Breaking and restoration of rotational symmetry in the low energy spectrum of light $ \alpha$α-conjugate nuclei on the lattice I: 8Be and 12C

The breaking of rotational symmetry on the lattice for bound eigenstates of the two lightest alpha conjugate nuclei is explored. Moreover, a macroscopic alpha-cluster model is used for investigating the general problems associated with the representation of a physical many-body problem on a cubic lattice. In view of the descent from the 3D rotation group to the cubic group symmetry, the role of the squared total angular momentum operator in the classification of the lattice eigenstates in terms of SO(3) irreps is discussed. In particular, the behaviour of the average values of the latter operator, the Hamiltonian and the inter-particle distance as a function of lattice spacing and size is studied by considering the $0^+$, $2^+$, $4^+$ and $6^+$ (artificial) bound states of $^{8}\mathrm{Be}$ and the lowest $0^+$, $2^+$ and $3^-$ multiplets of $^{12}\mathrm{C}$.

Symmetries of first-order Lovelock gravity

We apply the converse of Noether’s second theorem to the first-order n-dimensional Lovelock action, considering the frame rotation group as both or as . As a result, we get the well-known invariance under local Lorentz transformations or transformations and diffeomorphisms, for odd- and even-dimensional manifolds. We also obtain the so-called ‘local translations’ with nonvanishing constant Λ for odd-dimensional manifolds when a certain relation among the coefficients of the various terms of the first-order Lovelock Lagrangian is satisfied. When this relation is fulfilled, we report the existence of a new gauge symmetry emerging from a Noether identity. In this case the fundamental set of gauge symmetries of the Lovelock action is composed by the new symmetry, local translations with and local Lorentz transformations or transformations. The commutator algebra of this set closes with structure functions. We also get the invariance under local translations with of the highest term of the Lovelock action in odd-dimensional manifolds. Furthermore, we report a new gauge symmetry for the highest term of the first-order Lovelock action for odd-dimensional manifolds. In this last case, the fundamental set of gauge symmetries can be considered as Poincaré or Euclidean transformations together with the new symmetry. The commutator algebra of this set also closes with structure functions.

A Variational Approach to Registration with Local Exponential Coordinates

AbstractWe identify a novel parameterization for the group of finite rotations (SO3), consisting of an atlas of exponential maps defined over local tangent planes, for the purpose of computing isometric transformations in registration problems that arise in machine vision applications. Together with a simple representation for translations, the resulting system of coordinates for rigid body motions is proper, free from singularities, is unrestricted in the magnitude of motions that can be represented and poses no difficulties in computer implementations despite their multi‐chart nature. Crucially, such a parameterization helps to admit varied types of data sets, to adopt data‐dependent error functionals for registration, seamlessly bridges correspondence and pose calculations, and inspires systematic variational procedures for computing optimal solutions. As a representative problem, we consider that of registering point clouds onto implicit surfaces without introducing any discretization of the latter. We derive coordinate‐free stationarity conditions, compute consistent linearizations, provide algorithms to compute optimal solutions and examine their performance with detailed examples. The algorithm generalizes naturally to registering curves and surfaces onto implicit manifolds, is directly adaptable to handle the familiar problem of pairwise registration of point clouds and allows for incorporating scale factors during registration.

Invariant surfaces in Euclidean space with a log-linear density

A λ-translating soliton with density vector v→ is a surface in Euclidean space whose mean curvature H satisfies 2H=2λ+〈N,v→〉, where N is the Gauss map. We classify all λ-translating solitons that are invariant by a one-parameter group of translations and a one-parameter group of rotations.