Rotation Of Circle Research Articles

How anatomic should anatomic total shoulder arthroplasty be? Evaluation of humeral head reconstruction with the best-fit circle

IntroductionHumeral implant designs for anatomic total shoulder arthroplasty (aTSA) focus on anatomic reconstruction of the articular segment. Likewise, the pathoanatomy of advanced glenohumeral osteoarthritis (GHOA) often results in humeral head deformity. We hypothesized the anatomic reconstruction of the humeral head in aTSA risks overstuffing the glenohumeral joint. Methods97 cases (52 females) of primary GHOA in patients treated with aTSA were evaluated. Preoperative computed tomography (CT) scans were used to classify glenoid morphology according to the Walch classification. Coronal plane images in the plane of the humerus were used to determine the anatomic perfect circle as described by Youderian et al. Humeral head thinning was determined as the distance from the center of rotation (COR) of the perfect circle to the nearest point along the humeral articular surface. aTSA was modeled with a predicted anatomic humeral head and a simulated 4 mm polyethylene glenoid component. The change in the position of the native humerus was determined. Wilcoxon Rank Sum tests were used to evaluate differences in humeral head thinning and humeral lateralization between monoconcave and biconcave glenoid morphologies. Spearman’s rank correlation coefficients were used to assess the relationship between humeral head thinning with preoperative active forward elevation and external rotation. ResultsThe mean radius of the perfect circle was 25.0±2.1 mm. There was a mean thinning of 2.4±2.0 mm (Range -1.7–8.3). Mean percent thinning of the humeral head was 9.4%±7.7%. The mean humeral lateralization was 6.4±2.0 mm. Humeral head thinning was not significantly associated with active forward elevation (r=-0.15, p=0.14) or active external rotation (r= -0.12, p=0.25). There were no significant differences in the percentage of humeral head thinning (p=0.324) or humeral lateralization (p=0.350) between concentric and eccentric glenoid wear patterns ConclusionsUtilization of the perfect circle as a guide in aTSA may risk excessive lateralization of the humerus and overstuffing the glenohumeral joint. This may have implications for subscapularis repair and healing, as well as glenoid implant and rotator cuff longevity. These findings call into question whether recreation of normal glenohumeral anatomy in aTSA is appropriate for all patients. Humeral head reconstruction in aTSA should account for glenohumeral joint volume and soft tissue contracture.

Chinese English language learners’ vocabulary retention: Investigating the effectiveness of neuro/metacognitive and socio-cultural strategies

BackgroundThe acquisition of a rich vocabulary is foundational to language proficiency. In the pedagogical pursuit of effective vocabulary teaching, educators explore diverse methodologies. Researchers investigated the impact of different neurocognitive, metacognitive, and socio-cultural strategies on enhancing vocabulary learning, particularly among Chinese English Language Learners.ObjectivesThe study aims to determine the effectiveness of techniques derived from these theories compared to traditional teaching methods in enhancing vocabulary recall and recognition among English language learners.MethodologyA quasi-experimental pre-test/post-test design was employed for the experimental and control groups, comprising 90 Chinese EFL learners selected from educational institutions in 2022–2023. The experimental group (n = 45) received instruction involving visual imagery, multisensory rotation, circle rotation, and mind mapping over eight sessions, while the control group (n = 45) received traditional teaching methods.FindingsStatistical analysis, utilizing covariance and analysis of variance with SPSS software version 22, revealed significant improvements in recall and vocabulary recognition within and between the experimental and control groups.ConclusionsThe results indicate that incorporating techniques based on Neuro-Cognitive, Multimedia, Socio-Cultural, and Metacognitive theories positively influences vocabulary recall and recognition. This suggests the efficacy of these innovative methods in enhancing English language learning, highlighting their potential for broader integration into EFL instruction.

Forcing minimal patterns of triods

Rotation numbers for some maps of triods were introduced in [9]. The goal of this paper is to study patterns of triods which don't force other patterns with the same rotation number which we name triod twists. We obtain their complete characterization and show that these patterns can be conjugated to circle rotations by a piecewise monotone map. We also describe the dynamics of unimodal triod twist patterns with a given rational rotation number.

Slot-pole structure investigation for radial flux permanent magnet generator

Recently, Radial Flux Permanent Magnet Generator (RF-PMG) has been applied in various applications of generator. The configuration of the radial flux permanent magnet is the magnetic rotor arranged in a circle rotation while the inner core attached to the rotor’s center. However, various sizes and structure of RF-PMG can produce different output power levels, cogging torque and generator’s flux regulation capability. By investigating the output voltage and cogging torque value, this paper showed the suitable slot-pole combinations that can influence the output performance of the generator by using 2D-Finite Element Analysis. This investigation shows the comparison of the slot-pole that resulting the least cogging torque value and high output voltage, 0.1739Nm and 180.81V respectively. Hence, 36slots-30poles indicates as the best slot-pole combinations.

Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems

AbstractKoopman operators are infinite‐dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra and infinite‐dimensional invariant subspaces, making computing their spectral information a considerable challenge. This paper describes data‐driven algorithms with rigorous convergence guarantees for computing spectral information of Koopman operators from trajectory data. We introduce residual dynamic mode decomposition (ResDMD), which provides the first scheme for computing the spectra and pseudospectra of general Koopman operators from snapshot data without spectral pollution. Using the resolvent operator and ResDMD, we compute smoothed approximations of spectral measures associated with general measure‐preserving dynamical systems. We prove explicit convergence theorems for our algorithms (including for general systems that are not measure‐preserving), which can achieve high‐order convergence even for chaotic systems when computing the density of the continuous spectrum and the discrete spectrum. Since our algorithms have error control, ResDMD allows aposteri verification of spectral quantities, Koopman mode decompositions, and learned dictionaries. We demonstrate our algorithms on the tent map, circle rotations, Gauss iterated map, nonlinear pendulum, double pendulum, and Lorenz system. Finally, we provide kernelized variants of our algorithms for dynamical systems with a high‐dimensional state space. This allows us to compute the spectral measure associated with the dynamics of a protein molecule with a 20,046‐dimensional state space and compute nonlinear Koopman modes with error bounds for turbulent flow past aerofoils with Reynolds number >105 that has a 295,122‐dimensional state space.

Semantics of Verbs of Rotation in the Khanty language

The article is devoted to the identification of the national specifics of the representation of rotational movement in the Khanty linguoculture, the analysis of the semantics of verbs of rotation, the possibility of their lexical compatibility on the material of the Western dialects of the Khanty language (Kazym, Shuryshkar, Uralic) and one of the eastern (Surgut) by the types of situations described by them. The purpose of our study is to identify the parameters relevant to the lexical rotation zone. The article uses the method of corpus research: a sample of examples with verbs of rotation is analyzed and the boundaries of their compatibility are determined. The method of field research is used. There is a difference between movement along a trajectory close to an ideal circle (rotation in a circle) and movement along a chaotic trajectory, i.e. rotation of a set of homogeneous objects / gaseous particles (deer, snow vortex, smoke). In this case, the second type of rotation is marked. The subject performs multiple or single rotations around its axis or causates a rotational movement. The key parameter for distinguishing verbs of rotation and skating is animateness. Verbs of rotation around a landmark reflect the way of movement. Verbs of rolling and rotation do not reflect the environment of movement, but may reflect the direction of movement, which is regulated by the special compatibility of the subject and the predicate, or the word-formation capabilities of the predicate. The rolling zone reflects rotation in contact with the plane during translational motion and multidirectional rotation (about natural phenomena and about the movement of deer). The selected parameters and values are not lexicalized into separate verbs, but are combined inside lexemes. One lexeme describes situations of rotation in the same plane with and above the landmark, however, skating on the surface and rotation around the landmark is marked in dialects by separate lexemes.

Limit Laws of Maximal Birkhoff Sums for Circle Rotations via Quantum Modular Forms

Abstract In this paper, we show how quantum modular forms naturally arise in the ergodic theory of circle rotations. Working with the classical Birkhoff sum $S_{N}(\alpha )=\sum _{n=1}^{N} (\{ n \alpha \}-1/2)$, we prove that the maximum and the minimum as well as certain exponential moments of $S_{N}(r)$ as functions of $r \in \mathbb{Q}$ satisfy a direct analogue of Zagier’s continuity conjecture, originally stated for a quantum invariant of the figure-eight knot. As a corollary, we find the limit distribution of $\max _{0 \le N<M} S_{N}(\alpha )$ and $\min _{0 \le N<M} S_{N}(\alpha )$ with a random $\alpha \in [0,1]$.

An improved method of concentric circle positioning in visual measurement

Target with concentric circles has been widely used in artificial target and camera calibration of visual measurement systems. The accuracy of concentric circle target directly affects the accuracy of vision measurement system. In this study, an improved method for accurate positioning of concentric circles projection center is proposed. Compared with similar methods, the proposed method has high accuracy and does not need to know the radius of the concentric circle in advance. The influence of inner and outer circle radius and rotation angle of concentric circles on the position error of circular projection center is analyzed by single camera experiment. The experimental results show that the position error of this method is lower than that of similar methods. The concentric circles calibration board is designed as an application to calibrate the binocular vision system. It is shown that the calibration results of the camera’s intrinsic parameters are almost the same as those of PPAGC. However, compared with PPAGC, the total projection error of the left camera is reduced by 30.77% and that of the right camera by 28.29%.

Crossing edge minimization in radial outerplanar layered graphs using segment paths

Crossing minimization is a natural problem in graph drawing, which consists of drawing it in the plane with a minimum number of crossings on the edges. We present an algorithm to minimize the crossing edges in radial layered graphs. The algorithm determines the optimal location of nodes in their corresponding circle layer and consists of two phases. In the first phase, a counterclockwise rotation of concentric circles is performed; in the next phase, edges are converted into segment paths. Unlike other algorithms with circular drawings, our algorithm does not require the insertion or removal of nodes and edges; only rotation and path construction operations are utilized. Two versions of the algorithm were created; the exhaustive version tests all the possible paths, while the random version tests a few number of paths. The goal is to minimize the crossing edges to obtain a clear visualization using three criteria: rotation, crossing edge detection and segment path construction. The algorithm has been successfully implemented in 30 instances of graphs with 20, 35 and 50 layers, where crossings are minimized in 86–93%, 93–96% and 95–97%, respectively.

Mental rotation and schizotypal personality traits: A Bayesian approach.

People diagnosed with schizophrenia exhibit mental rotation differences, suggesting that clinical levels of positive symptoms, such as psychotic hallucinations, are related to disruptions in their monitoring and manipulation of mental representations. According to the psychosis continuum, findings in people with a high level of schizotypal personality traits are expected to be qualitatively similar, but research concerning this topic is scarce. A spared mental imagery manipulation in this population only could suggest that this ability might be a possible protective factor, or that the emergence of clinical-level positive symptoms could be paired with disruptions in this capacity. To explore this issue, 205 undergraduate students (122 women) completed a novel mental rotation task identifying the stimulus that was a 90, 180, or 270° rotation of a black circle with colored portions and were assessed with the Schizotypal Personality Questionnaire. Men performed better in most conditions. No relationship was detected between schizotypal personality traits and accuracy in the task. These results do not support that mental imagery manipulation disruptions may be related to schizotypal personality traits in non-clinical populations. Thus, they might instead be associated with the onset of psychosis disorders as mental representation handling is hindered. However, additional research is required including the general population, as well as those with higher levels of psychotic symptoms and psychosis disorders. Future research could also focus on working memory processes related to mental representation manipulations of different sensory modalities such as auditory mental representations and their relationship with schizotypal personality traits and clinical populations.

A highly accurate bound-preserving phase field method for incompressible two-phase flows

In this paper, we propose a phase-field-based spectral element method by solving the Navier–Stokes/Cahn–Hilliard equations for incompressible two-phase flows. With the use of the Newton–Raphson method for the Cahn–Hilliard equation and the time-stepping scheme for the Navier–Stokes equation, we construct three constant (time-independent) coefficient matrixes for the solutions of velocity, pressure, and phase variable. Moreover, we invoke the modified bulk free energy density to guarantee the boundness of the solution for the Cahn–Hilliard equation. The above strategies enhanced computation efficiency and accurate capture of the interfacial dynamics. For the canonical tests of diagonal motion of a circle and Zalesak's disk rotation, the lowest relative errors for the interface profile in contrast to the published solutions highlight the high accuracy of the proposed approach. In contrast to our previous work, the present method approximately produces only one tenth relative errors after one rotation cycle but saves 27.2% computation cost. Furthermore, we note that the mobility parameter adopted appears to produce convergent solutions for the phase field but the distribution of the chemical potential remains divergent, which thereby results in diverse coalescence processes in the two merging droplets example. Therefore, a criterion for the choice of the mobility parameter is proposed based on these observations, i.e., the mobility adopted should ensure the convergence solution for the chemical potential. Finally, the rising bubble is presented to verify the proposed method's versatility under large density (1000) and viscosity contrasts (100), and its advantage in efficiency over previous solver is manifested by 44.9% savings in computation cost.

Data Augmentation for Building Footprint Segmentation in SAR Images: An Empirical Study

Building footprints provide essential information for mapping, disaster management, and other large-scale studies. Synthetic Aperture Radar (SAR) provides consistent data availability over optical images owing to its unique properties, which consequently makes it more challenging to interpret. Previous studies have demonstrated the success of automated methods using Convolutional Neural Networks to detect buildings in Very High Resolution (VHR) SAR images. However, the scarcity of such datasets that are available to the public can limit research progress in this field. We explored the impact of several data augmentation (DA) methods on the performance of building detection on a limited dataset of SAR images. Our results show that geometric transformations are more effective than pixel transformations. The former improves the detection of objects with different scale and rotation variations. The latter creates textural changes that help differentiate edges better, but amplifies non-object patterns, leading to increased false positive predictions. We experimented with applying DA at different stages and concluded that applying similar DA methods in training and inference showed the best performance compared with DA applied only during training. Some DA can alter key features of a building’s representation in radar images. Among them are vertical flips and quarter circle rotations, which yielded the worst performance. DA methods should be used in moderation to prevent unwanted transformations outside the possible object variations. Error analysis, either through statistical methods or manual inspection, is recommended to understand the bias presented in the dataset, which is useful in selecting suitable DAs. The findings from this study can provide potential guidelines for future research in selecting DA methods for segmentation tasks in radar imagery.

Asymptotic scaling and universality for skew products with factors in SL(2,)

AbstractWe consider skew-product maps over circle rotations $x\mapsto x+\alpha \;(\mod 1)$ with factors that take values in ${\textrm {SL}}(2,{\mathbb {R}})$ . In numerical experiments, with $\alpha $ the inverse golden mean, Fibonacci iterates of maps from the almost Mathieu family exhibit asymptotic scaling behavior that is reminiscent of critical phase transitions. In a restricted setup that is characterized by a symmetry, we prove that critical behavior indeed occurs and is universal in an open neighborhood of the almost Mathieu family. This behavior is governed by a periodic orbit of a renormalization transformation. An extension of this transformation is shown to have a second periodic orbit as well, and we present some evidence that this orbit attracts supercritical almost Mathieu maps.

Type synthesis of single-loop 3T1R-parallel mechanisms with a multi-DOF drive system

This paper systematically develops the type synthesis of single-loop parallel mechanisms (PMs) with three translations (T) along three independent directions and one rotation (R) around one fixed direction (3T1R-PMs). Each limb is driven by a multi-degree of freedom (DOF) drive system, and the output link can generate large rotational angle. Based on previously presented multi-DOF drive systems (DSs), a novel systematic method is proposed to synthesize single-loop 3T1R-PMs based on Lie group theory. To improve the rotation function of the single-loop 3T1R-PM, two types of connecting styles between the output link and the ends of two limbs are introduced to construct the single-loop 3T1R-PM with a full circle rotation function. A class of single-loop 3T1R-PM with two serial limbs driven by a 2-DOF driver and a class of single-loop 3T1R-PM with a hybrid limb driven by a 3-DOF DS and a serial limb driven by a 1-DOF joint are constructed. Moreover, the simulations are implemented to display large pose operation capability of two examples of presented 3T1R-PMs.

Golden mean renormalization for the almost Mathieu operator and related skew products

Considering SL(2,R) skew-product maps over circle rotations, we prove that a renormalization transformation associated with the golden mean α* has a nontrivial periodic orbit of length 3. We also present some numerical results, including evidence that this period 3 describes scaling properties of the Hofstadter butterfly near the top of the spectrum at α* and scaling properties of the generalized eigenfunction for this energy.

The cardinality of factors of infinite binary words for irrational circle rotations

The cardinality of factors of infinite binary words for irrational circle rotations

Periodic point free homeomorphisms and irrational rotation factors

AbstractWe provide a complete characterization of periodic point free homeomorphisms of the $2$ -torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$ -torus without periodic points and exhibiting uniformly bounded rotational deviations with respect to a rational direction, we show that annularity and the geometry of its non-wandering set are the only possible obstructions for the existence of an irrational circle rotation as topological factor. Through a very precise study of the dynamics of the induced $\rho $ -centralized skew-product, we extend and generalize considerably previous results of Jäger.

Spectral disjointness of rescalings of some surface flows

We study self-similarity problem for two classes of flows: (1) special flows over circle rotations and under roof functions with symmetric logarithmic singularities (2) special flows over interval exchange transformations and under roof functions which are of two types * piecewise constant with one additional discontinuity which is not a discontinuity of the IET; * piecewise linear over exchanged intervals with non-zero slope. We show that if $\{T^f_t\}_{t\in\mathbb R}$ is as in (1) then for a full measure set of rotations, and for every two distinct natural numbers $K$ and $L$, we have that $\{T^f_{Kt}\}_{t\in\mathbb R}$ and $\{T^f_{Lt}\}_{t\in\mathbb R}$ are spectrally disjoint. Similarly, if $\{T^f_t\}_{t\in\mathbb R}$ is as in (2), then for a full measure set of IET's, a.e. position of the additional discontinuity (of $f$, in piecewise constant case) and every two distinct natural numbers $K$ and $L$, the flows $\{T^f_{Kt}\}_{t\in\mathbb R}$ and $\{T^f_{Lt}\}_{t\in\mathbb R}$ are spectrally disjoint.

Criterion for Substitutivity of Sturmian Palindromes and One-Dimensional Factor Dynamics

The paper provides a criterion for substitutivity of symmetric Sturmian words infinite on both sides and its proof, and a theorem on the substitutivity of factor dynamics of circle rotations.

Urbanization and eco-environment coupling circle theory and coupler regulation

A near-distance, nonlinear coupling relationship objectively exists between urbanization and the eco-environment. The issue of how to coordinate the relationship between them has become a global strategic and scientific issue. This study reveals the nature, relationship and intensity of coupling between urbanization and the eco-environment from a theoretical perspective. Based on the strength of coupling, relationships can be characterized as having very-low, low, medium, high, very-high or full coupling intensity, which correspond to the categories of random coupling, indirect coupling, loose coupling, cooperative coupling, close coupling, and controlled coupling. Together, these make up an urbanization and eco-environment “coupling tower.” This study also develops an urbanization and eco-environment coupling circle theory and generates 45 coupling graphs (including linear, exponential-curve, logarithmic-curve, double exponential-curve and S-curve graphs) per 10° of rotation of the coupling circle, with different graphs corresponding to different urban development stages and development models. Of the various coupling graphs, the S-curve graph is considered the optimum, as it reflects the best interactivity scenario between urbanization and the eco-environment. Using an S-curve coupling graph, and with the help of an SD model and based on the complex one-to-one, one-to-many, and many-to-many relationships between the variables, this study develops the Urbanization and Eco-environment Coupler (UEC). The UEC is composed of 11 regulating elements and 201 variables. If one variable changes, it changes the whole, affecting the structure, function and regulation of the entire coupler. The UEC includes three spatio-temporal scales: static regulation between multiple urbanization areas and eco-environment areas at the same time, dynamic regulation between the same urbanization area and eco-environment area at different times, and dynamic regulation between multiple urbanization areas and eco-environment areas at different times. Regulation gradually promotes evolution from low-level coupling to high-level coupling between urbanization and the eco-environment.