polar coordinates
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2022 ◽  
Author(s):  
Joanna von Berg ◽  
Michelle ten Dam ◽  
Sander W. van der Laan ◽  
Jeroen de Ridder

Pleiotropic SNPs are associated with multiple traits. Such SNPs can help pinpoint biological processes with an effect on multiple traits or point to a shared etiology between traits. We present PolarMorphism, a new method for the identification of pleiotropic SNPs from GWAS summary statistics. PolarMorphism can be readily applied to more than two traits or whole trait domains. PolarMorphism makes use of the fact that trait-specific SNP effect sizes can be seen as Cartesian coordinates and can thus be converted to polar coordinates r (distance from the origin) and theta (angle with the Cartesian x-axis). r describes the overall effect of a SNP, while theta describes the extent to which a SNP is shared. r and theta are used to determine the significance of SNP sharedness, resulting in a p-value per SNP that can be used for further analysis. We apply PolarMorphism to a large collection of publicly available GWAS summary statistics enabling the construction of a pleiotropy network that shows the extent to which traits share SNPs. This network shows how PolarMorphism can be used to gain insight into relationships between traits and trait domains. Furthermore, pathway analysis of the newly discovered pleiotropic SNPs demonstrates that analysis of more than two traits simultaneously yields more biologically relevant results than the combined results of pairwise analysis of the same traits. Finally, we show that PolarMorphism is more efficient and more powerful than previously published methods.


2022 ◽  
Author(s):  
Sami Ryan Yousif

Mental representations are the essence of cognition. Yet, to understand how the mind works, we must understand not just the content of mental representations (i.e., what information is stored), but also the format of those representations (i.e., how that information is stored). But what does it mean for representations to be formatted? How many formats are there? Is it possible that the mind represents some pieces of information in multiple formats at once? To address these questions, I discuss a ‘case study’ of representational format: the representation of spatial location. I review work (a) across species and across development, (b) across spatial scales, and (c) across levels of analysis (e.g., high-level cognitive format vs. low-level neural format). Along the way, I discuss the possibility that the same information may be organized in multiple formats simultaneously (e.g., that locations may be represented in both Cartesian and polar coordinates). Ultimately, I argue that seemingly ‘redundant’ formats may support the flexible spatial behavior observed in humans, and that we should approach the study of all mental representations with this possibility in mind.


Author(s):  
Bhimsen Shivamoggi ◽  
G Heijst ◽  
Leon Kamp

Abstract The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.


2022 ◽  
Author(s):  
Rui He ◽  
Xiangyuan Liu ◽  
Xiangfei Wei ◽  
Congbing Wu

Abstract In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU (2) symmetric description, SU (1, 1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.


2022 ◽  
Vol 22 (1&2) ◽  
pp. 17-37
Author(s):  
Xiao Chen ◽  
Zhihao Liu ◽  
Hanwu Chen ◽  
Liang Wang

Quantum image representation has a significant impact in quantum image processing. In this paper, a bit-plane representation for log-polar quantum images (BRLQI) is proposed, which utilizes $(n+4)$ or $(n+6)$ qubits to store and process a grayscale or RGB color image of $2^n$ pixels. Compared to a quantum log-polar image (QUALPI), the storage capacity of BRLQI improves 16 times. Moreover, several quantum operations based on BRLQI are proposed, including color information complement operation, bit-planes reversing operation, bit-planes translation operation and conditional exchange operations between bit-planes. Combining the above operations, we designed an image scrambling circuit suitable for the BRLQI model. Furthermore, comparison results of the scrambling circuits indicate that those operations based on BRLQI have a lower quantum cost than QUALPI. In addition, simulation experiments illustrate that the proposed scrambling algorithm is effective and efficient.


2021 ◽  
Vol 12 (1) ◽  
pp. 37
Author(s):  
Mohd Saufi Ahmad ◽  
Dahaman Ishak ◽  
Tiang Tow Leong ◽  
Mohd Rezal Mohamed

This paper proposes an analytical subdomain model for predicting magnetic field distributions in a three-phase double-stator permanent magnet synchronous machine (DS-PMSM) during open-circuit and on-load conditions. The geometric structure of DS-PMSM is quite challenging since the stator cores are located in the outer and inner parts of the motor, while the rotor magnets are placed between these two stators. Parameters that influence the motor performance in DS-PMSM include stator outer radius, stator inner radius, magnet thickness, magnet arc, slot opening, outer and inner airgap thickness and the number of winding turns. The analytical subdomain model proposed in this paper, which can accurately predict the performances of DS-PMSM with less computational time, has an excellent advantage as a rapid design tool. The model is initially generated using the separation of variables technique in four subdomains, namely, outer airgap, outer magnet, inner magnet, and inner airgap, based on Laplace’s and Poisson’s equations in polar coordinates. The field solutions in each subdomain are derived by applying the appropriate boundary and interface conditions. Furthermore, finite element analysis (FEA) is used to validate the analytical results in fractional DS-PMSM with a different number of slots between outer and inner stators and a non-overlapping winding configuration. The electromagnetic performances that have been evaluated are the slotted airgap flux density, back-emf and output torque. The results demonstrate that the proposed analytical model is able to predict the magnetic field distributions accurately in DS-PMSM.


Author(s):  
Wenjin Mao ◽  
Hongwei Li

Purpose The purpose of this study is to provide a non-iterative linear method to solve the power flow equations of alternating current (AC) power grid. Traditional iterative power flow calculation is limited in speed and reliability, and it is unsuitable for the real-time and online applications of the modern distribution power system (DPS). Thus, it would be of great significance if a fast and flexible linear power flow (LPF) solution could be introduced particularly necessary for the robust and fast control of DPS, especially when the system consists of star and delta connections ZIP load (a constant impedance, Z, load, a constant current, I, load and a constant power, P, load) and the high penetration of distributed solar and wind power generators. Design/methodology/approach Based on the features of DPS and considering the approximate balance of three-phase DPS, several approximations corresponding to the three-phase power flow equations have been discussed and analyzed. Then, based on those approximations, two three-phase LPF models have been developed under the polar coordinates. One model has been formulated with the voltage magnitudes [referred to the voltage magniudes based linear power flow method (VMLPF)], and another model has been formulated with the logarithmic transform of voltage magnitudes [referred to the logarithmic transform of voltage based linear power flow method LGLPF)]. Findings The institute of electrical and electronic engineers (IEEE) 13-bus, 37-bus, 123-bus and an improved 615-bus unbalanced DPSs are used to test the performances of the methods considering star and delta connections ZIP load and PV buses (voltage-controlled buses). The test results validate the effectiveness and accuracy of the proposed two models. Especially when considering the PV buses and delta connection ZIP load, the proposed two models perform much well. Moreover, the results show that VMLPF performs a bit better than LGLPF. Research limitations/implications Except for the transformer with Yg–Yg connection winding can be dealt with directly, the transformers with other connections are not discussed in this proposed paper and need to be further studied. Originality/value These proposed two models can deal with ZIP load with star and delta connections as well as multi slack buses and PV buses. The single-phase, two-phase and three-phase hybrid networks can be directly included too. The proposed two models are capable of offering enough accuracy level, and they are therefore suitable for online applications that require a large number of repeated power flow calculations.


2021 ◽  
pp. 63-71
Author(s):  
D. A Pozharskii ◽  
E. D Pozharskaia

Plane contact problems of the elasticity theory are investigated for a wedge when Poisson’s ratio is an arbitrary smooth function with respect to the angular coordinate while shear modulus is constant. For this case Young’s modulus is also variable with respect to the angular coordinate. A finite contact domain is given on one wedge face, it does not include the wedge apex, while the other wedge face is rigidly fixed (problem A) or stress-free (problem B). To reduce the problems to integral equations with respect to the contact pressure, we use the general Freiberger type representation for the solution of elastic equilibrium equations written in polar coordinates with variable Poisson’s ratio. Exact solutions of auxiliary problems are constructed with the help of Mellin integral transforms. The regular asymptotic method employed is effective for contact domains relatively distant from the wedge apex. It is shown that logarithmic terms appear in the asymptotic solutions for the inhomogeneous material which are missing in the well-known asymptotics for the homogeneous one. In contact problem C which is corresponding to problem A, the friction and roughness are taken into account in the contact region. The roughness of the wedge surface is simulated by a Winkler type coating. The collocation method is used for solving integral equations of the second kind. Unlike problem A, in problem C the contact pressure does not have square root singularities at end-points where it takes finite values. Calculations are made for the cases when Poisson’s ratio and Young’s modulus increase or decrease from the surface of the wedge.


2021 ◽  
Vol 3 ◽  
Author(s):  
Juan Pablo Morillo-Baro ◽  
Belén Troyano-Gallegos ◽  
José Luis Pastrana-Brincones ◽  
Juan Antonio Vázquez-Diz ◽  
Rafael E. Reigal ◽  
...  

The open nature of basketball gives it a large uncertainty that makes hard the tactical analysis of the situations that happen in the game. Specifically, screens are one of the offensive tactical elements most used in basketball and one example of a tactical situation that needs the highest preparation level to get a good performance in the competition. The aim of this study is to differentiate these player behaviors by gender using data mining and polar coordinates analysis. Therefore, one ad hoc observational tool made by 17 criteria and 97 exhaustive and mutually exclusive (E/ME) categories has been designed and validated using the data quality analysis (correlation coefficients and concordance index 0.98) and generalizability analysis (G coefficients 0.94) to perform such a study. The observational design is nomothetic, punctual, and multidimensional. A total of 176 ball screens situations have been analyzed for the men's category and 118 for women's category, corresponding to three different teams of each gender playing in the highest competition level in Spain during the 2018/2019 season using Hoisan software tool. The analysis of the relationships among behaviors has been performed using Polar Coordinates analysis as well as data mining analysis: clustering and decision tree classifier. Results show significant relationships that allow us to tactically interpret the pick and roll situations in men's and women's professional basketball players in Spain, allowing us to develop more intervention programs which will optimize training and improve players performance.


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