Rotation Of Group Research Articles

Birds of a Feather: Estimating the Value of Statistical Life from Dual-Earner Families

Economists have long employed hedonic wage analysis to estimate income-fatality risk trade-offs, but some scholars have raised concerns about systematic measurement error and omitted variable bias in the empirical applications of this model. Recent studies have employed panel methods to remove time-invariant individual-specific characteristics that could induce bias in estimation. In an analogous manner, this paper proposes to exploit assortative matching on risk attitudes within married couples to control for worker characteristics that are unobserved to the econometrician. I develop and implement a modified hedonic wage estimator based on a within-coupled differenced wage equation for full-time working married couples with the Current Population Survey Merged Outgoing Rotation Group over 1996-2002. The key assumption builds on the findings in the assortative matching literature that individuals often marry those who have common traits across many dimensions, including those that may influence worker wages and are correlated with observed occupational fatality risks. This estimator identifies the compensating differential for occupation fatality risk by using within-couple differencing to remove unobserved determinants of risk attitudes and risk-mitigation ability, on which couples match, from the error term. I find that the value of statistical life (VSL) varies from $9 to $13 million (2016$). The within-couple differenced VSL estimates are stable and more robust to variation in specification of the hedonic wage model than conventional, cross-sectional hedonic wage models. I also find that the value of statistical life takes an inverted-U shape with respect to age.

Dynamic scapular recognition exercise improves scapular upward rotation and shoulder pain and disability in patients with adhesive capsulitis: a randomized controlled trial

ABSTRACT Background Examine the ability of a dynamic scapular recognition exercise to improve scapular upward rotation and decrease shoulder pain and disability in patients with adhesive capsulitis of the shoulder. Methods A test-retest randomized controlled study design was used. A total of sixty-six patients with unilateral adhesive capsulitis were equally divided into two groups. The study group received a dynamic scapular recognition exercise using a wireless biofeedback system, while the control group received placebo treatment in the form of active range-of-motion (ROM) exercises of the sound upper limb. A digital inclinometer was used to measure the scapular upward rotation and ROM of the shoulder joint, and the Shoulder Pain and Disability Index (SPADI) was used to measure the shoulder pain and disability. Results Study results showed that after two weeks, there were statistically significant differences between the study and control groups in scapular upward rotation and shoulder flexion and abduction (P < .05) and nonsignificant differences in shoulder external rotation and SPADI (P > .05). After two and six months, there were statistically significant differences between study and control groups in scapular upward rotation; shoulder flexion, abduction and external rotation; and SPADI scores (P < .05). Conclusion This study showed that a dynamic scapular recognition exercise significantly improves scapular upward rotation and the ROM of shoulder flexion and abduction after two weeks. At two and six months, this exercise improves scapular upward rotation; ROM of shoulder flexion, abduction, and external rotation; and SPADI scores. These improvements persisted for six months after the performance of this exercise

Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization

We propose a general theory for studying the landscape of nonconvex optimization with underlying symmetric structures for a class of machine learning problems (e.g., low-rank matrix factorization, phase retrieval, and deep linear neural networks). In particular, we characterize the locations of stationary points and the null space of Hessian matrices of the objective function via the lens of invariant groups. As a major motivating example, we apply the proposed general theory to characterize the global landscape of the nonconvex optimization in low-rank matrix factorization problem. We illustrate how the rotational symmetry group gives rise to infinitely many nonisolated strict saddle points and equivalent global minima of the objective function. By explicitly identifying all stationary points, we divide the entire parameter space into three regions: ( $ \mathcal {R}_{1}$ ) the region containing the neighborhoods of all strict saddle points where the objective has negative curvature; ( $ \mathcal {R}_{2}$ ) the region containing neighborhoods of all global minima, where the objective enjoys strong convexity along certain directions; and ( $ \mathcal {R}_{3}$ ) the complement of the above regions, where the gradient has sufficiently large magnitude. We further extend our result to the matrix sensing problem. Such global landscape implies that strong global convergence guarantees for popular iterative algorithms with arbitrary initial solutions.

Birds of a feather: Estimating the value of statistical life from dual-earner families

Economists have long employed hedonic wage analysis to estimate income-fatality risk trade-offs, but some scholars have raised concerns about systematic measurement error and omitted variable bias in the empirical applications of this model. Recent studies have employed panel methods to remove time-invariant individual-specific characteristics that could induce bias in estimation. In an analogous manner, this paper proposes to exploit assortative matching on risk attitudes within married couples to control for worker characteristics that are unobserved to the econometrician. I develop and implement a modified hedonic wage estimator based on a within-coupled differenced wage equation for full-time working married couples with the Current Population Survey Merged Outgoing Rotation Group over 1996-2002. The key assumption builds on the findings in the assortative matching literature that individuals often marry those who have common traits across many dimensions, including those that may influence worker wages and are correlated with observed occupational fatality risks. This estimator identifies the compensating differential for occupation fatality risk by using within-couple differencing to remove unobserved determinants of risk attitudes and risk-mitigation ability, on which couples match, from the error term. I find that the value of statistical life (VSL) varies from $9 to $13 million (2016$). The within-couple differenced VSL estimates are stable and more robust to variation in specification of the hedonic wage model than conventional, cross-sectional hedonic wage models. I also find that the value of statistical life takes an inverted-U shape with respect to age.

Comparison of radiographic parameters after anterior cervical discectomy and fusion with semiconstrained translational versus rotational plate systems

ObjectiveA plate is commonly applied after anterior cervical discectomy and fusion (ACDF); particularly in cases of multilevel fusion. Recent comparative studies have focused on constrained versus semiconstrained plates, however little data is available to assess differences between semiconstrained plates. Patients and MethodsA retrospective review of 60 consecutive adult patients undergoing a 1, 2 or 3 level ACDF with a lordotic allograft for treatment of symptomatic cervical spondylosis was conducted at a single center. The cohort was separated into two groups depending on the cervical plating system used. Patients in the first group had a semiconstrained translational plate and those in the second group had a semiconstrained rotational plate. Plain neutral radiographs were assessed preoperatively, immediately after surgery and at most recent follow-up. The measured radiographic parameters focused on sagittal alignment, adjacent segment pathology, fusion rate and implant failure. ResultsThere were 30 patients in each group. There were no significant differences in demographic characteristics or distribution of levels fused between groups. All patients had at least 6 months of follow-up and mean follow-up was 14.8 ± 6.2 months in the translational plate group and 13.1 ± 4.8 months in the rotational plate group (p = 0.227). Significant improvement in sagittal segmental alignment was noted in both groups following surgery. The translational plate group improved from 1.0 ± 7.5 degrees to 4.8 ± 7.6 degrees (p = 0.03) and the rotational group improved from 2.7 ± 9.1 degrees to 8.4 ± 7.8 degrees (p = 0.001). This significant sagittal correction was maintained through follow-up for those in the rotational plate group; 5.5 ± 9.1 degrees (p = 0.002). However, a partial loss of segmental lordosis was observed in the translational plate group leading to a failure to maintain significance of the lordotic correction; 1.7 ± 8.3 degrees (p = 0.280) over the follow-up period. Segmental fusion rates were not significantly different between groups. However, there was a higher rate of screw breakage within the rotational plate group (4 instances versus 0 instances in the translational plate group). ConclusionThis comparative cohort series suggests that performing an ACDF with a lordotic allograft using either semiconstrained translational or rotational plate system allows for correction and maintenance of cervical alignment, however the rotational plate appears more effective at maintaining segmental lordotic correction. Further prospective controlled study will be needed to determine if this may come at the expense of greater rates of instrumentation failure in the rotational plate group.

Is It Safe to Inject Corticosteroids Into the Glenohumeral Joint After Arthroscopic Rotator Cuff Repair?

Background: Injection of intra-articular corticosteroids is effective for improving the recovery of range of motion (ROM) and pain in various conditions of the shoulder but its use is limited after rotator cuff repair owing to concern over the possible harmful effects of steroids on the repaired tendon. Purpose: To evaluate the effect of intra-articular corticosteroid injections on the clinical outcomes and cuff integrity of patients after rotator cuff repair. Study Design: Randomized controlled trial; Level of evidence, 1. Methods: Between March 2011 and April 2014, 80 patients with a small- to medium-sized rotator cuff tear were enrolled in this study and underwent arthroscopic rotator cuff repair. Forty patients received an injection of triamcinolone (40 mg) and lidocaine (1.5 mL) into the glenohumeral joint 8 weeks after surgery (group 1), while the remaining 40 patients received normal saline injection (group 2). Outcome measures—including ROM, American Shoulder and Elbow Surgeons (ASES) score, Constant score, pain visual analog scale, and Simple Shoulder Test score—were evaluated at 3, 6, and 12 months after surgery and at the last follow-up. The integrity of the repaired tendon was evaluated by magnetic resonance imaging (MRI) and classified per Sugaya classification at 8 weeks (before injection) and 12 months after surgery. Results: The mean follow-up period was 25.7 months. At 3 months postoperatively, patients in group 1 had a significantly higher ROM with respect to forward flexion (P = .05), external rotation at the side (P = .05), and external rotation at abduction (P = .04) as compared with group 2, whereas no significant difference was noted between the groups for internal rotation behind the back (P = .65). Patients in group 1 had significantly lower visual analog scale pain scores (P = .02) and higher ASES scores (group 1, 68.90; group 2, 60.28; P = .02) at 3-month follow-up. However, there was no significant difference after 6 months with respect to ROM and ASES scores (group 1, 77.80; group 2, 75.88; P = .33). Retears (Sugaya classification IV and V) were determined by MRI at 12 months and observed in a total of 7 patients (8.8%): 3 from group 1 (7.5%) and 4 from group 2 (10%). No retears were observed on MRI in the remaining 73 patients (91.2%): 37 patients from group 1 and 36 patients from group 2. There was no statistically significant difference in rate of retears between groups (P = .69). Conclusion: Intra-articular injection of corticosteroids after rotator cuff repair does not increase the risk of retears and is thus an effective and safe treatment method for increasing ROM (forward flexion, external rotation) and improving clinical score (ASES) during the early postoperative period of patients undergoing rotator cuff repair.

Reconstruction of Stochastic 3D Signals With Symmetric Statistics From 2D Projection Images Motivated by Cryo-Electron Microscopy.

Cryo-electron microscopy provides 2D projection images of the 3D electron scattering intensity of many instances of the particle under study (e.g., a virus). Both symmetry (rotational point groups) and heterogeneity are important aspects of biological particles and both aspects can be combined by describing the electron scattering intensity of the particle as a stochastic process with a symmetric probability law and, therefore, symmetric moments. A maximum likelihood estimator implemented by an expectation-maximization algorithm is described, which estimates the unknown statistics of the electron scattering intensity stochastic process from the images of instances of the particle. The algorithm is demonstrated on the bacteriophage HK97 and the virus [Formula: see text]. The results are contrasted with the existing algorithms, which assume that each instance of the particle has the symmetry rather than the less restrictive assumption that the probability law has the symmetry.

Conservative management following closed reduction of traumatic anterior dislocation of the shoulder.

Conservative management following closed reduction of traumatic anterior dislocation of the shoulder.

A Common Framework for Complete and Incomplete Attitude Synchronization in Networks With Switching Topology

In this paper, we study attitude synchronization for elements in the unit sphere in $\mathbb {R}^{\scriptscriptstyle {\scriptscriptstyle {3}}}$ and for elements in the three-dimensional (3-D) rotation group, for a network with switching topology. The agents’ angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a region, which we identify later in the paper. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in $\mathbb {R}^{\scriptscriptstyle {3}}$ as incomplete synchronization, and of 3-D rotation matrices as complete synchronization. Our main contribution lies in showing that these two problems can be analyzed under a common framework, where all agents’ dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension.

Representing seesaw neutrino models and their motion in lepton flavour space

We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular how certain texture zero models are ruled out. We also introduce a new matrix, the bridging matrix, that brings from the light to the heavy neutrino mass flavour basis, showing how this is related to the orthogonal matrix and how different quantities are easily expressed through it. We then show how one can randomly generate orthogonal and leptonic mixing matrices uniformly covering all flavour space in an unbiased way (Haar-distributed matrices). Using the isomorphism between the group of complex rotations and the Lorentz group, we also introduce the concept of Lorentz boost in flavour space for a seesaw model and how this has an insightful physical interpretation. Finally, as a significant application, we consider N2-leptogenesis. Using current experimental values of low energy neutrino parameters, we show that the probability that at least one flavoured decay parameter of the lightest right-handed neutrino is smaller than unity is about 49% (to be compared with the tiny probability that the total decay parameter is smaller than unity, P (KI< 1) ∼ 0.1%, confirming the crucial role played by flavour effects). On the other hand when m1 ≳ 0.1 eV this probability reduces to less than 5%, showing how also N2-leptogenesis disfavours degenerate light neutrinos.

Raman scattering mediated by Majorana fermions in Kitaev nanoribbons

We study magnetic Raman, i.e. inelastic light, scattering of Kitaev’s quantum spin liquids realizable in honeycomb nanoribbons. Elementary excitations in the Kitaev spin liquids consist of itinerant Majorana (matter) fermions and localized gauge fluxes (visons). Matter fermions are characterized by the projective point (gauged rotation) group inherent in the lattice. Inelastic light scattering is mediated by a pair of matter fermions without any vison excitation. We can selectively “observe” matter fermions of the same symmetry and those of different symmetries depending on the polarization of incoming and/or outgoing lights. A pair of matter fermions with particular translational quantum numbers ±k cannot be Raman active.

Unusual sum rule for Clebsch–Gordan coefficients

We present a new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is obtained from an integral involving Gegenbauer ultraspherical polynomials. A similar procedure can be applied for other types of integrals of such polynomials, and may therefore lead to the derivation of further new relations.

Sensing Matrix Design and Sparse Recovery on the Sphere and the Rotation Group

In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing matrices, which consists of random samples of Wigner D-functions, satisfy the Restricted Isometry Property (RIP) with proper preconditioning and can be used for sparse recovery on the rotation group. The mutual coherence, however, is used to assess the performance of deterministic and regular sensing matrices. We show that many of widely used regular sampling patterns yield sensing matrices with the worst possible mutual coherence, and therefore are undesirable for sparse recovery. Using tools from angular momentum analysis in quantum mechanics, we provide a new expression for the mutual coherence, which encourages the use of regular elevation samples. We construct low coherence deterministic matrices by fixing the regular samples on the elevation and minimizing the mutual coherence over the azimuth-polarization choice. It is shown that once the elevation sampling is fixed, the mutual coherence has a lower bound that depends only on the elevation samples. This lower bound, however, can be achieved for spherical harmonics, which leads to new sensing matrices with better coherence than other representative regular sampling patterns. This is reflected as well in our numerical experiments where our proposed sampling patterns perfectly match the phase transition of random sampling patterns.

A Geometric Interpretation of the Simplicity of SO(3)

This article aims to present a geometric interpretation of the simplicity of the rotation group of three-dimensional Euclidean space. Some historical remarks on the subject and an overview of a collection of different proofs of this result are also given.

Hamiltonian and primary constraints of new general relativity

We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms. Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations. We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads. The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group. Using this, we demonstrate that there are nine different classes of theories, which are distinguished by the occurrence or non-occurrence of certain primary constraints. We visualize these different classes and show that the decomposition into irreducible parts allows us to write the Hamiltonian in a common form for all nine classes, which reproduces the specific Hamiltonians of more restricted classes in which particular primary constraints appear.

Effects of Epidural Needle Rotation on Evolution of Unilateral Epidural Block and Patients' Hemodynamics beside Recovery Profile in Patients Undergoing Arthroscopic Knee Surgeries; A Randomized Clinical Trial.

Objective:To evaluate the evolution pattern of epidural block after rotating the needle tip 45° to the operative side and evaluate its effects on patients’ hemodynamics and recovery profile in those undergoing arthroscopic knee surgery.Methods:Forty participants were randomly subdivided into control and rotation group (n=20). An 18-gauge, 3.5 inch, Tuohy needle was placed at the level of L4-5 and pushed forward into the epidural space through parasagittal approach, in control group, the needle was pushed forward to the epidural space in cephaldad 90 degrees. For the rotation group, the needle was pushed forward to the epidural space and the tip was rotated 45 degrees to the surgical side.15 mL of bupivacaine 0.5% was injected and evolution of sensory and motor blocks until 2-segment regression of the sensory level below to T10 as well as total duration of motor block and surgery were recorded. Hemodynamic parameters (HR, MAP, and SPO2), hypotension, fluid intake, vasopressors, first ambulation and spontaneous urination were recorded. Statistical analysis was performed using SPSS and P≤0.5 considered significant.Results: Sensory block up to T10 level, Complete motor block and time for 2-segment regression of sensory level were earlier in the 45°-rotation than in the control group (p<0.001). Total duration of motor block in control group was lower than rotation group (p<0.001).Hypotension, N&V, vasopressors and fluid intake showed no statistically difference between the two groups (p=0.219). First spontaneous urination and ambulation were significantly lower in rotation group (p<0.001).Conclusion:45 degrees’ needle rotation to the surgical side provides a faster block evolution and hastened recovery profile with no significant difference in hemodynamic fluctuations.Clinical trial registry: IRCT20130518013364N7

Unbounded formulation of the rotation group

The rotation group is formulated based on the abstract B(X)-module framework. Although the infinitesimal generators of rotation group include differential operators, the rotation group has been formulated utilizing the framework of bounded operator algebra. In this article, unbounded formulation of rotation group is established.

Oscillating about coplanarity in the 4 body problem

For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result for collinear instants ("syzygies") in the zero angular momentum planar 3-body problem, and extends to the $d+1$ body problem in $d$-space. The proof, for $d=3$, starts by identifying the center-of-mass zero configuration space with real $3 \times 3$ matrices, the coplanar configurations with matrices whose determinant is zero, and the mass metric with the Frobenius (standard Euclidean) norm. Let $S$ denote the signed distance from a matrix to the hypersurface of matrices with determinant zero. The proof hinges on establishing a harmonic oscillator type ODE for $S$ along solutions. Bounds on inter-body distances then yield an explicit lower bound $\omega$ for the frequency of this oscillator, guaranteeing a degeneration within every time interval of length $\pi/\omega$. The non-negativity of the curvature of oriented shape space (the quotient of configuration space by the rotation group) plays a crucial role in the proof.

Remarks on Texture Coefficients of Polycrystals with Improper Crystallite Symmetry

The orientation distribution function (ODF) in classical texture analysis is defined on the rotation group SO(3). For polycrystalline aggregates with crystallite symmetry defined by a crystallographic point group $G_{\mathrm{cr}}$ which is not a subgroup of SO(3), the improper group $G_{\mathrm{cr}}$ is routinely replaced by its proper peer (i.e., a subgroup of SO(3)) in the same Laue class. In this note we examine how the texture coefficients obtained from such a practice are related to their counterparts that pertain to the corresponding ODF defined on the orthogonal group O(3) as it should.

Short-term pharyngeal airway space changes after mandibular advancement surgery in Class II patients-a two-dimensional retrospective study.

Planning successful treatment for the correction of anatomic abnormalities of the upper airways, by surgical advancement of the mandible, depends on extensive knowledge of the pharyngeal airway space (PAS). However, there is limited scientific evidence about changes in PAS after mandibular advancement surgery. To evaluate the immediate changes in superior posterior airway space (SPAS) in Class II patients, after mandibular advancement surgery. A cephalometric evaluation of 37 patients with skeletal Class II deformity was performed at 2 distinct time intervals: Pre-operative (T0) and immediate post-operative (T1), using Dolphin Image & Management Solutions, version 11.9, according to the method of Arnett/Gunson FAB Surgery. The differences due to the surgical intervention were assessed with Student's t test, and a Principal Component Analysis was used to evaluate the relationship between mandibular advancement and SPAS variables. Anticlockwise and clockwise rotation groups were also evaluated with Mann-Whitney tests. The statistical analysis was conducted in SPSS and R assuming a 0.05 level of significance. As an effect of mandibular advancement, an anteroposterior statistically significant increase in SPAS (P<0.001) was perceived at all points measured. Our findings indicate that mandibular advancement surgery is a viable option to achieve widening of the SPAS in patients with Class II skeletal morphology.