Set Of Rotations Research Articles

On the dynamics of minimal homeomorphisms of $T^2$ which are not pseudo-rotations

We prove that any minimal $2$-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a consequence of this, we show that any such homeomorphism is topologically mixing and we prove Franks-Misiurewicz conjecture under the assumption of minimality.

Effect of the Center of Rotation Setting of the X-ray Tube for the Resolution Characteristics of the Tomosynthesis Projection Image

Effect of the Center of Rotation Setting of the X-ray Tube for the Resolution Characteristics of the Tomosynthesis Projection Image

Undergraduate neurology teaching: Comparison of an inpatient versus outpatient clinical setting.

Neurology is often perceived as a difficult discipline by medical students, yet it is an essential part of medical training. While the most common disorders of the nervous system can be observed in the outpatient setting, positive neurological signs are more likely to be found in neurology wards. We aimed to compare the impact of a neurology outpatient versus inpatient rotation setting on the grades obtained by medical students as a proxy measure of the learning outcomes. We compared the results obtained by fourth year medical students in practical (OSCE) and multiple choice question (MCQ) exams in neurology, between students whose main (total of 24h contact) teaching allocation was either the outpatient or inpatient setting, controlling for students' gender, teacher, academic year and student' previous achievement (measured by their scores on practical evaluation). A total of 1127 students were included, of whom 644 (57.14%) were allocated mainly to the neurology ward and 483 (42.86%) to the outpatient clinic. Students assigned to the ward obtained significantly higher grades in the OSCE and MCQ exams than those placed in the outpatient clinic. Teaching setting was an independent predictor of both classifications after adjustment. The teaching setting had a significant impact on the learning outcomes. This may be due to a higher likelihood of observing abnormal neurological signs or to more student-centered teaching on the ward. These results highlight the importance of a balanced distribution of students by different clinical settings.

Generic rotation sets

AbstractLet$(X,T)$be a topological dynamical system. Given a continuous vector-valued function$F \in C(X, \mathbb {R}^{d})$called apotential, we define its rotation set$R(F)$as the set of integrals ofFwith respect to allT-invariant probability measures, which is a convex body of$\mathbb {R}^{d}$. In this paper we study the geometry of rotation sets. We prove that ifTis a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map$R(\cdot )$is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has$C^{1}$boundary. Furthermore, we prove that the map$R(\cdot )$is surjective, extending a result of Kucherenko and Wolf.

A General Purpose Formulation for Nonsmooth Dynamics With Finite Rotations: Application to the Woodpecker Toy

Abstract The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized.

Fractional‐order generalized Laguerre moments and moment invariants for grey‐scale image analysis

Here, a new set of fractional-order moments, named fractional-order generalized Laguerre moments (FGLM), is introduced. These proposed moments are defined on the Cartesian coordinate system and their basis functions are represented by the fractional-order generalized Laguerre polynomials. Contrary to the classical Chebyshev, Legendre and Gegenbauer moments, which provide only global feature, our proposed FGLM have the ability to extract both global and local features. Moreover, a new set of rotation, scale and translation invariants of the FGLM, is derived and introduced for image classification and invariant pattern recognition. Just as important, we have presented a systematic parameter selection method for finding the optimal fractional parameter values with respect to pattern recognition applications. Finally, several recursive methods for reducing the computation time of our proposed invariants are also provided in this study. Therefore, to demonstrate the performance of the introduced fractional-order moments and moment invariants, a number of experimental analysis are performed in terms of global and local features extraction, robustness to noise, invariance to geometric deformations, object recognition and computational speed. The presented theoretical and experimental results clearly show that the proposed fractional-order moments and their corresponding invariants could be extremely useful in the field of image analysis.

Cylinder diameter measurement with displacement and rotation error correction for non-telecentric optics

The paper presents the implementation of a method for measuring the diameter of cylinders in traffic along a transport line using machine vision systems with correction of the error of displacement and rotation of the product for the case of using non-telecentric optics. Diameters were measured for a set of displacements and rotations of the cylinder, and estimates of the achievable errors of this implementation of the layout of the measuring installation were made.

Analytical modeling for design and performance evaluations of a new low aspect ratio soft rotary pneumatic actuator

This paper presents a different type of rotary actuator in contrast to conventional rotary actuators that operate by fiber wound in the form of a helix on a cylinder-shaped elastomer. Our actuator has a fiber set placed in the rθ plane of an elastomer in the form of an annulus, this elastomer expands under pneumatic pressure input to deliver rotation and torque to a rigid shaft connected to the elastomer’s inner circumference. In addition to the description and testing of our actuator’s novel mechanism, the main contribution of this paper is the design’s verification through a theoretical analysis of the rotational motion generated by the mutual influence of the elastomer and inflexible fiber elements. We also show how the design parameters are related to the wound angle of how much the fiber set inserted in the elastomer was wound in a spiral configuration. For various wound angles, computer simulation and experiments were carried out to prove the validity of our analytical model. Further experiments were conducted to measure the performance of the actuators by conducting a torque test with rotation set to zero.

Roto-translation equivariant convolutional networks: Application to histopathology image analysis.

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean motion group SE(2) in convolutional networks to yield translation and rotation equivariance via the introduction of SE(2)-group convolution layers. This structure enables models to learn feature representations with a discretized orientation dimension that guarantees that their outputs are invariant under a discrete set of rotations. Conventional approaches for rotation invariance rely mostly on data augmentation, but this does not guarantee the robustness of the output when the input is rotated. At that, trained conventional CNNs may require test-time rotation augmentation to reach their full capability. This study is focused on histopathology image analysis applications for which it is desirable that the arbitrary global orientation information of the imaged tissues is not captured by the machine learning models. The proposed framework is evaluated on three different histopathology image analysis tasks (mitosis detection, nuclei segmentation and tumor detection). We present a comparative analysis for each problem and show that consistent increase of performances can be achieved when using the proposed framework.

A Simulation-Based Method for Planning Delivery of TTFields to Brain Tumors

Tumor Treating Fields (TTFields) are alternating electric fields that inhibit tumor growth. TTFields are delivered using two pairs of transducer arrays placed on the skin. Each pair of arrays creates a field oriented along the axis between the arrays. Arrays are placed to generate two fields that are roughly orthogonal to one another. Simulation-based studies have shown that TTFields distribution within the body is heterogeneous, and depends on the location of the arrays, the patient anatomy and the location and size of the tumor. A recent study showed a connection between increased TTFields dose at the tumor bed and extended patient survival in newly diagnosed Glioblastoma (ndGBM) patients [1]. This emphasizes the need for simulation-based algorithms for patient-specific TTFields treatment planning. Here we present a novel algorithm that utilizes numerical simulations in order to maximize TTFields dose in brain tumors. The outline for our optimization algorithm is as follows: First a patient-specific computational head model is created in a semi-automatic manner from patient MRI data. Next, machine vision algorithms are used in order to define an axial slice passing above the eyes and eyebrows. To ensure transducer arrays are placed in a practical manner, only transducer array layouts in which all arrays are placed above this slice are tested. Next, a finite set of pairs of virtual transducer arrays are placed on the head model and the electric field created by each pair simulated using a finite elements method. To ensure maximal delivery of TTFields to the tumor, the arrays are placed such that the “imaginary” line connecting their centers passes through the tumor bed. A set of layouts is created by combining pairs of arrays (all possible combinations of pairs are created), and the dose delivered by the layouts calculated. The layout that maximizes TTFields dose at the tumor bed is found, and a set of small shifts and rotations is applied to the arrays in the chosen layout order eliminate overlaps between the transducers of the different arrays. The algorithm was tested on MRI data from ten Glioblastoma patients. In all cases, the algorithm converged to yield an optimal array layout that could be placed in a practical manner. Generally, the arrays of the optimal layout were located on the scalp in close proximity to the tumor. In all cases, the optimal layouts delivered average TTFields intensities above the therapeutic threshold of 1 V/cm to the tumors. The average dose delivered by the optimal layouts to the tumors were well above 1 mW/cm3, which has been associated with prolonged patient survival. We have developed a novel simulation-based method for optimizing TTFields treatment planning for brain tumors. Incorporation of such algorithms into sophisticated treatment planning systems is expected to improve the management of TTFields patients by the treating physician, ultimately improving patient outcomes.

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.

On the rotation sets of generic homeomorphisms on the torus

AbstractWe study the rotation sets for homeomorphisms homotopic to the identity on the torus $\mathbb T^d$ , $d\ge 2$ . In the conservative setting, we prove that there exists a Baire residual subset of the set $\text {Homeo}_{0, \lambda }(\mathbb T^2)$ of conservative homeomorphisms homotopic to the identity so that the set of points with wild pointwise rotation set is a Baire residual subset in $\mathbb T^2$ , and that it carries full topological pressure and full metric mean dimension. Moreover, we prove that for every $d\ge 2$ the rotation set of $C^0$ -generic conservative homeomorphisms on $\mathbb T^d$ is convex. Related results are obtained in the case of dissipative homeomorphisms on tori. The previous results rely on the description of the topological complexity of the set of points with wild historic behavior and on the denseness of periodic measures for continuous maps with the gluing orbit property.

Feasibility study of a blind-type photovoltaic roof-shade system designed for simultaneous production of crops and electricity in a greenhouse

The use of renewable energy in modern greenhouse management is important to achieve efficient and sustainable food supplies for a world with increasing population. This study assessed the performance of a blind-type shading regulator that can automatically rotate semi-transparent photovoltaic (PV) blades installed on the greenhouse roof in response to sunlight variation. The PV blind oriented parallel to the roof partially blocked intense sunlight penetration into the greenhouse, but it transmitted sunlight during cloudy time by turning the blind bearing to be perpendicular to the roof. A stable irradiation environment is therefore producible in the greenhouse under variable sky conditions. Annual operations demonstrated that the blinds’ own generated electrical energy can sustain PV blind operation and produce surplus electrical energy. The PV blind electricity generation and sunlight availability for crops below the PV blind roof were calculated based on a mathematical model developed using theoretical sunlight parameters and the experimentally obtained PV blind system parameters. Assuming cloudless skies and threshold irradiance for blind rotation set at 500 W m−2, 13.0 and 12.3 kWh m−2 yr−1 surplus electrical energy can be generated, respectively, by north–south and east–west oriented model greenhouses. Cloudy skies reduce surplus electrical energy production by 50%, but PV blinds can supply greenhouse electrical energy demands partially or completely, depending on the degree of greenhouse electrification. Below the PV blinds, 8–10 MJ m−2 day−1 of insolation is expected to irradiate crops under actual sky conditions. This insolation is sufficient to cultivate major horticultural crops. Regulating the threshold irradiance level for PV blind turning can control the sunlight apportionment ratio for cultivation and electricity generation, thereby enabling sustainable energy–food dual production in a greenhouse.

Elaboration, study and implementation of innovation technology of recovery of rolling rollers and other bodies of rotation workability

When manufacturing bodies of rotation the main task is to provide reliable connection of their component parts. The known methods of bodies of rotation connection, based on pin, dowel, spline or flange kinds of mechanical coupling, have significant drawbacks. Specialists of PAO “Uralmashzavod” elaborated principally new designs of bandage rollers, which enables to avoid completely the shifting of component parts one relatively the other and to increase their service life. The main idea of the proposed solutions is in creation of an eccentricity at the body of rotation setting area. The falcated parts, run out of the contour in the rotation plane (from one side or from both sides) fix the component parts of the coupling reliably and avoid their shifting one relative the other, at that no fixing details are required. By reliability and manufacturability the proposed designs of compound roller exceed all the domestic and foreign analogs. Based on innovative development in PAO “Uralmashzavod”, a recovery of workability of written-off supporting rollers 1400*1300 for OJSC “VIZ-Stal” cold mill 1300 was accomplished. The running of bandage rollers under conditions of heavy-loaded mill 1300 confirmed the propriety of the design and technology solutions, providing their stable operation and stability in emergency situations. The recovery of workability of he written-off rollers by using the bandage rollers will enable to metallurgical plants to increase significantly the efficiency of the rolling production due to costs decrease for buying rollers and to increase the quality of the finished product. Thanks to its universality the elaborated variants of the design and coupling principles are reasonable for usage in industrial fans, bridge cranes, mine elevators and other equipment of different industries.

Continuous flows generate few homeomorphisms

We describe topological obstructions (involving periodic points, topological entropy and rotation sets) for a homeomorphism on a compact manifold to embed in a continuous flow. We prove that homeomorphisms in a$C^{0}$-open and dense set of homeomorphisms isotopic to the identity in compact manifolds of dimension at least two are not the time-1 map of a continuous flow. Such property is also true for volume-preserving homeomorphisms in compact manifolds of dimension at least five. In the case of conservative homeomorphisms of the torus$\mathbb {T}^{d} (d\ge 2)$isotopic to identity, we describe necessary conditions for a homeomorphism to be flowable in terms of the rotation sets.

Role and limitations of the geometric mean method regarding head rotation in salivary gland scintigraphy: a phantom study.

To investigate the possible influence of head rotation on the results of salivary gland scintigraphy, a phantom study was designed to simulate clinical salivary gland scintigraphy. The quantitative accuracy of regional activity counts was compared for two data acquisition methods involving head rotation: (i) an anterior planar projection-only (ANT) method and (ii) a geometric mean (GM) method using both the anterior and posterior planar projections. The roles and limitations of the GM and ANT methods when used at different head rotation angles were examined. Parallel planar projections of a head phantom with four salivary gland simulators, containing 3.7 MBq 99mTc-sodium pertechnetate, at various rotational settings were acquired using a dual-head gamma camera. The difference between the standard activity counts (no phantom rotation) and the activity counts affected by the phantom rotation was calculated and defined as the rotational bias that decreased the accuracy of activity quantification. For small-angle rotation (≤10°), use of the GM method decreased the bias for all salivary gland simulators. In contrast, the bias of large-angle rotation (>10°) between four salivary gland simulators became conspicuous and complex in both methods. This bias may reflect different attenuation effects caused by displacement of the structures. Our data suggest that the GM method can be used when the head rotation angle is small (≤10°); however, when the head rotation angle is >10°, the non-negligible influence of head rotation should be considered during image acquisition.

Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations

By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for general monotone recurrence relations the rotation set is closed, and each element in the rotation set is realized by a Birkhoff orbit. Moreover, if there is an orbit without rotation number, then the system has positive topological entropy, and we can construct orbits shadowing different rotation numbers.

Dosimetric characterization of an X-ray irradiator for use with cells

PurposeThis study aims to characterize an X-ray irradiator (CellRad™, Precision X-ray Inc., North Branford, CT) for use with cells using its internal parallel-plate ionization chamber by evaluating the linearity and repeatability of dose and dose rates delivered by the machine. MethodologyUsing the on-board software modules for X-ray irradiation, dose linearity and repeatability tests were performed at the following setting: 130 kVp, 5.0 mA, and 33.0 cm source-to-shelf distance. Four (4) setups with distinct combinations of 0.5-mm Al added filtration and turntable rotation settings were employed. The measurements obtained from the internal ionization chamber were analyzed using statistical tests. ResultsThe X-ray irradiator can generate temporally linear and repeatable doses from aluminum-filtered (0.5 mm) and unfiltered X-ray beams (130 kV, 5.0 mA). At a 33.0-cm source-to-shelf distance, the computed dose rates indicate that the X-ray irradiator can deliver 1.345 ± 0.046 Gy/min and 6.718 ± 0.11 Gy/min at the specified tube and shelf settings, with and without the 0.5 mm Al added filter, respectively. An acceptable level of repeatability of the dose is achieved after at least 20 s of irradiation time. The automatic dose control function of the irradiator was also found to measure accumulated doses within ±5% of the target dose for all the setups employed in this study. The results also revealed that turntable rotation has no significant effect on the dose measured by the internal dosimeter for both filtered and unfiltered beams. On the other hand, adding a 0.5-mm Al filtration significantly alters the beam by decreasing the measured dose rate to only 20% of that of the unfiltered beam. Conclusions and recommendationsThis study demonstrates that the X-ray irradiator can generate and measure precise radiation doses that vary linearly with irradiation time. The available irradiation modules in the on-board software can be used to deliver doses within ±5% of the target dose, although irradiation time should be at least 20 s to achieve acceptable dose repeatability. Further dosimetric calibration and output verification using external dosimetry system(s) should be conducted for the complete dosimetric characterization of this X-ray irradiator.

Development of a rotation phantom for phase contrast MRI sequence validation and quality control

To develop a reliable, consistent, and reproducible reference phantom for error quantification of phase-contrast MRI so it can be used for validation and quality control. An air-driven rotation phantom consisting of a steadily rotating cylinder surrounded by a static ring both filled with agarose gel was developed. Rotational speed was measured and controlled in real time using an optical counter and a closed-loop controller. Consistency of the phantom was assessed by recording variations in rotational speed. The phantom was imaged with 2D phase-contrast MRI, and the velocity at each point was compared with analytically predicted velocity. Additionally, to examine reproducibility, the phantom was run with the same rotational speed on 2 different days and imaged using the same phase-contrast MRI protocol. The rotation phantom provided consistent rotational speed with 2 revolutions per minute SD from the set value for 20 min. Comparison between predicted and measured velocities demonstrated excellent agreement (intraclass correlation coefficient of 0.99). The RMS error in velocity components were less than 1% of maximum value. The scan-rescan experiment showed that the phantom can reproduce the same velocity distributions (intraclass correlation coefficient of 0.99) using the same rotational speed and MRI settings. The developed rotation phantom provided well-defined and reproducible linear velocity distributions, which can be used for systematic and quantitative error analysis of phase-contrast MRI for a range of known velocities.

Rift segment interaction in orthogonal and rotational extension experiments: Implications for the large-scale development of rift systems

During extension of the continental lithosphere, rift basins develop. These are often initially offset, and must interact and connect in order to create a continuous rift system that may ultimately achieve break-up. When simulating extensional tectonics and rift interaction structures, analogue and numerical modellers often apply a continuous extension rate along the strike of a rift or rift system. Yet in nature significant extension velocity variations occur along rifts and plate boundaries as a natural consequence of tectonic plates moving apart about a pole of rotation, resulting in rotational extension, and associated rift propagation and structural gradients. Here we present various analogue tectonic experiments to assess rift interaction structures forming in orthogonal extension settings versus rotational extension settings. Our modelling efforts show that rotational extension and orthogonal extension produce significantly different large-scale structures. Rotational extension can cause important variations in rift maturity between rift segments, delay rift interaction zone development, and make rift segments propagate in opposite directions. Still, local features in a rotational extension system can often be regarded as evolving in an orthogonal extension setting. Furthermore, we find that various degrees of rift underlap produce three basic modes of rift linkage structures. Low underlap distance (high angle φ) experiments develop rift pass structures. With increasing underlap distance (φ = ca. 40°), transfer zone basins develop. High degrees of underlap (φ ≤ 30°) tend to result in en echelon sub-basins. Our results match with data from previous modelling efforts and natural examples. We furthermore propose a large-scale tectonic scenario for the East African Rift System based on rotational extension and associated rift propagation. These insights may also be applicable when studying other large-scale rift systems.