Mises Distribution Research Articles

Hip joint biomechanical analysis of the acetabular anatomical reconstruction and nonanatomical reconstruction in total hip arthroplasty for Crowe type Ⅲ developmental dysplasia of the hip by finite element method

To analyze the hip joint biomechanics of the acetabular anatomical reconstruction and nonanatomical reconstruction in total hip arthroplasty (THA) for Crowe type Ⅲ developmental dysplasia of the hip (DDH) by finite element method, which provided theoretical foundation and experimental basis for the anatomical acetabular reconstruction during THA in clinical practice. One patient with left end-stage hip arthritis secondary to Crowe type Ⅲ DDH was selected in this study, who underwent total hip arthroplasty in the orthopedic department of the First Affiliated Hospital of Bengbu Medical College in April 2020. This patient was female, 57 years old. The preoperative and postoperative three dimentional CT scan of the patient's pelvis were performed. Fourteen acetabular cup models with different anteversion, inclination and rotation center height were established in Mimics and 3-Matic software. The boundary and load conditions were set in Abaqus software. The Von Mises and stress distribution of the hip joint were calculated and observed. In the Crowe type Ⅲ DDH THA, if the hip rotation center was restored anatomically and the acetabular cup's inclination was set as 40°, the cup's anteversion varied from 5° to 25°, the lowest Von Mises value of acetabular cup and polyethylene liner occured in 20°anteversioin;if the hip rotation center was restored anatomically and the acetabular cup's anteversion was set as 15°, the cup's inclination varied from 35° to 55°, the lowest Von Mises value of acetabular cup and polyethylene liner occured in 35° inclination;if the acetabular cup's anteversion and inclination were set as 15°and 40°respectively, the up migration of hip rotaion center varied from 0 mm to 20 mm, the lowest Von Mises value of acetabular cup and polyethylene liner occured in 10 mm up migration. In all fourteen models, the Von Mises value of the acetabulum, acetabulum cup and polyethylene liner were lowest when the acetabular cup's anteversion and inlcination were 15°, 35° respectively, as well as the rotation center was restored anatomically. In total hip arthroplasty for Crowe type Ⅲ DDH, the anatomical restoration of hip rotation center with 15° anteversion and 35° inclination of the acetabular cup are suggested, bone graft above the acetabular cup and additional screws are recommended simultaneously to further reduce the Von Mises of hip joint.

An enhanced sparrow search swarm optimizer via multi-strategies for high-dimensional optimization problems

With the development of science and technology, high-dimensional global optimization problems have become increasingly prevalent for scientific research and engineering, such as gene recognition, vehicle routing, job scheduling, and network topology. These problems are typically characterized by enormous and complex search spaces and numerous local minima, making it challenging to find the global optimal solution with limited computing resources. This paper introduces an enhanced sparrow search swarm optimizer (ESSSO) based on a bio-mimetic method. The ESSSO employs an adaptive sinusoidal walk strategy based on the von Mises distribution, a learning strategy utilizing roulette wheel selection, a two-stage evolution strategy, and a selection mutation strategy to address these issues. The proposed sinusoidal walk strategy, grounded in the von Mises distribution, supports a balanced evolutionary search. This mechanism disperses the individuals in a swarm in various directions based on a circular normal distribution. It then leads the search and adaptively adjusts their step sizes according to the size of the search domain during each generation of evolution. The learning strategy, based on roulette wheel selection, enhances the diversity of the population and improves the global search capability of the algorithm during the initial iterations. The two-stage evolution strategy involves a sine-learning mechanism based on the von Mises distribution and an adaptive mutation mechanism. The former is designed to boost the convergence speed of ESSSO, while the latter prevents ESSSO from getting trapped in a local optimum. Additionally, the selection mutation strategy further enhances convergence speed while maintaining population diversity. These strategies promote exploration in the early stages of evolution and exploitation in the later stages, enabling a well-balanced search for optimal solutions. We conducted comprehensive experiments two standard benchmark sets (i.e., CEC2010 and CEC2013), antenna array optimization, feature selection, and four engineering design problems. The results indicate that ESSSO outperforms ten comparison algorithms, especially in scenarios with smaller population sizes. This confirms its effectiveness in high-dimensional global optimization tasks and demonstrates that it can achieve better results with less computational resource consumption.

Underlying Topography Estimation over Forest Using Maximum a Posteriori Inversion with Spaceborne Polarimetric SAR Interferometry

This paper presents a method for extracting the digital elevation model (DEM) of forested areas from polarimetric interferometric synthetic aperture radar (PolInSAR) data. The method models the ground phase as a Von Mises distribution, with a mean of the topographic phase computed from an external DEM. By combining the prior distribution of the ground phase with the complex Wishart distribution of the observation covariance matrix, we derive the maximum a posterior (MAP) inversion method based on the RVoG model and analyze its Cramer–Rao Lower Bound (CRLB). Furthermore, considering the characteristics of the objective function, this paper introduces a Four-Step Optimization (FSO) method based on gradient optimization, which solves the inefficiency problem caused by exhaustive search in solving ground phase using the MAP method. The method is validated using spaceborne L-band repeat-pass SAOCOM data from a test forest area. The test results for FSO indicate that it is approximately 5.6 times faster than traditional methods without compromising accuracy. Simultaneously, the experimental results demonstrate that the method effectively solves the problem of elevation jumps in DEM inversion when modeling the ground phase with the Gaussian distribution. ICESAT-2 data are used to evaluate the accuracy of the inverted DEM, revealing that our method improves the root mean square error (RMSE) by about 23.6% compared to the traditional methods.

Digital PLLs for phase noise channels: a concept based on the Tikhonov distribution

Digital PLLs for phase noise channels: a concept based on the Tikhonov distribution

A characteristic function based circular distribution family and its goodness of fit : The flexible wrapped Linnik family

In this article, the primary aim is to introduce a new flexible family of circular distributions, namely the wrapped Linnik family which possesses the flexibility to model the inflection points and tail behavior often better than the existing popular flexible symmetric unimodal circular models. The second objective of this article is to obtain a simple and efficient estimator of the index parameter α of symmetric Linnik distribution exploiting the fact that it is preserved in the wrapped Linnik family. This is an interesting problem for highly volatile financial data as has been studied by several authors. Our final aim is to analytically derive the asymptotic distribution of our estimator, not available for other estimator. This estimator is shown to outperform the existing estimator over the range of the parameter for all sample sizes. The proposed wrapped Linnik distribution is applied to some real-life data. A measure of goodness of fit proposed in one of the authors' previous works is used for the above family of distributions. The wrapped Linnik family was found to be preferable as it gave better fit to those data sets rather than the popular von-Mises distribution or the wrapped stable family of distributions.

Performance analysis of RIS-Assisted wireless networks in the presence of imperfect phase errors

In this article, an analysis of the average symbol error probability (ASEP) for a reconfigurable intelligent surface (RIS)-assisted wireless network with imperfect phase noise errors is proposed. In particular, we focus on a RIS-assisted wireless transmission in which imperfect phase errors are modeled by the Tikhonov distribution. The source (S) and destination (D) nodes are equipped with a single antenna, and the channels between the S-RIS and RIS-D nodes exhibit Rayleigh fading which is a good fit for the non-line-of-sight instances. For this system, we derive novel and exact analytical and asymptotic expressions for the ASEP, and the obtained ASEP expressions are then exploited to evaluate the error performance of under different network configurations. The proposed theoretical analysis is confirmed through the exact simulation results.

Assessing ice sheet models against the landform record: The Likelihood of Accordant Lineations Analysis (LALA) tool

AbstractPalaeo‐ice sheets leave behind a rich database regarding their past behaviour, recorded in the landscape in the form of glacial geomorphology. The most numerous landform created by these ice sheets are subglacial lineations, which generate snapshots of the direction of ice flow at fixed (yet typically unknown) points in time. Despite their relative density within the landform record, the information provided by subglacial lineations is currently underutilised in tests of numerical ice sheet models. To some extent, this is a consequence of ongoing debate regarding lineation formation, but predominantly, it reflects the lack of rigorous model‐data comparison techniques that would enable lineation information to be properly integrated. Here, we present the Likelihood of Accordant Lineations Analysis (LALA) tool. LALA provides a statistically rigorous measure of the log‐likelihood of a supplied ice sheet simulation through comparison of simulation output with both the location and direction of observed lineations. Given an ensemble of ice sheet simulations, LALA provides a formal, and statistically underpinned, quantitative assessment of each simulation's quality‐of‐fit to mapped lineations. This enables a comparison of each simulation's relative plausibility, including identification of the most likely ice sheet simulations amongst the ensemble. This is achieved by modelling lineation formation as a marked Poisson point process and comparison of observed to modelled flow directions using the von Mises distribution. LALA is flexible—users can adapt parameters to account for differing assumptions regarding lineation formation, and for variations in the level of precision required for differing model‐data comparison experiments. We provide guidelines and rationale for assigning parameter values, including an assessment of the variability between users when mapping lineations. Finally, we demonstrate the utility of LALA through application to an ensemble of simulations of the last British‐Irish Ice Sheet. This comparison highlights the benefits of LALA over previous tools and demonstrates some of the considerations of experimental design required when identifying the fit between ice sheet model simulations and the landform record.

تقدير واختبار أنموذج انحدار زاوي بخطأ توزيع فون موزيس للبيانات الدائرية

The study of circular variables is one of the important processes in our present time because of the phenomena that are described in this way. Therefore, the study included the use of a simple angular regression model with an error that follows a circular distribution, which is the Von Mises distribution, and estimating the parameters in the greatest possible way, and testing the quality of reconciliation of the model in general by proposing a test that depends mainly on the Fisher distribution . This was applied to two circular variables, the wind direction in the city of Nasiriyah as a dependent variable and the direction of high atmospheric pressure as an independent variable. The results showed that the model represented the data correctly by passing the estimated model to test the quality of reconciliation, and that the relationship between the direction of high atmospheric pressure and the direction of the wind in the city of Nasiriyah is a direct relationship, i. The city of Nasiriyah and the smaller the angle measure in the direction of the high atmospheric pressure, the lower it is in the city of Nasiriyah.

Numerical analysis on seismic behavior of the assembled modular steel plate shear wall with inclined slots

This paper proposes a novel multi-grids steel plate shear wall with inclined slots (called MSPSW). This MSPSW composed of the steel plates with inclined slots, precast concrete panels, the transverse and longitudinal (T&L) connecting stiffeners, and external frame components. Smaller single plates can be used in the design and installation process since the space size of individual frames inside the frame is reduced as a result of the T&L connecting stiffeners. The direction of inclined slots in the adjacent grids is opposite, which makes the lateral resistance and stiffness close to symmetry. Numerical analysis is conducted to evaluate the seismic behavior. With the correct finite element model, finite element analysis is performed on the key parameters of MSPSW, such as the cross-sectional dimension of T&L connecting stiffeners, the thickness of steel plate, the width of inclined slots and the width of plate slot strips. The Mises distribution and development regular pattern of MSPSW are also explored. The FE numerical analysis discovered that the MSPSW increased the bearing capacity and energy consumption capacity of the members due to the installation of T&L connecting stiffeners. Additionally, the thickness required for concrete panels is lowered when the components are subjected to cyclical loads. Finally, the internal force development curves in frame beams and columns are extracted, it can be found that the internal forces become smaller, which weakens the demand of frame members. The theoretical calculation formulas of the maximum internal forces of frame beams and columns are provided.

Characterization and modeling of the in-plane collagen fiber distribution in the porcine dermis.

The structural arrangement of collagen fibers in the plane of the dermis layer plays a critical role in accurately predicting the mechanical behavior of skin tissues. This paper combines a histological analysis with statistical modeling to characterize and model the in-plane collagen fiber distribution in the porcine dermis. The histology data reveals that the fiber distribution in the plane of the porcine dermis is non-symmetric. The histology data forms the basis of our model, which employs a combination of two π-periodic von-Mises distribution density functions to create a non-symmetric distribution. We demonstrate that a non-symmetric in-plane fiber distribution is a significant improvement over a symmetric distribution.

Probabilistic characterization of the dates of occurrence of annual floods using the von Mises distribution

La planeación y manejo de los recursos hidráulicos de un río y la elaboración de los planes ―de tipo no estructural― de mitigación de daños causados por sus inundaciones dependen de la relación que guarda el gasto máximo anual con su fecha de ocurrencia. Tales fechas, al acontecer durante el año, pueden ser tratadas como datos circulares, cuyos estadísticos de dirección media y dispersión, o índice de estacionalidad, definen los dos parámetros de ajuste de la distribución de von Mises (dvM), la cual permite la caracterización probabilística de las fechas de ocurrencia de las crecientes anuales; es decir, define su función de distribución de probabilidades. En este estudio se describe la dvM y su método de ajuste por máxima verosimilitud cuando los datos o fechas anuales son unimodales y abarcan todo el año. Cuando las fechas anuales se concentran en una porción del año, la dvM se ajusta con optimización numérica, vía el algoritmo de Rosenbrock. Por último, se describe cómo se representan, con una mezcla de tres dvM, las fechas de ocurrencia que son bimodales, cuyo ajuste, vía optimización numérica restringida, se realizó con el algoritmo Complex. Como un caso de aplicación, se procesaron las fechas de ocurrencia de 777 crecientes anuales registradas en 21 estaciones hidrométricas de la Región Hidrológica No. 10 (Sinaloa), México; se exponen con detalle siete aplicaciones típicas de los tres tipos de ajuste de la dvM. Las conclusiones ratifican a la dvM como modelo probabilístico de las fechas de ocurrencia de las crecientes anuales, sean unimodales o bimodales.

Wind load assessment with the JPDF of wind speed and direction based on SHM data

The calculation of basic wind speed (wind load) in return period is directly related to the wind resistance design of long-span bridge, high-rise building and etc. Nowadays, the calculation of basic wind speed in Chinese codes (GB50009-2012) mainly depends on the probability distribution function (PDF) of extreme wind speed, that is, univariate Gumbel PDF. However, this method doesn’t consider the influence of wind direction and the finite mixture (FM) of Gumbel PDF. In this paper, we use the Angular-linear (AL) model to characterize the extreme wind speed and wind direction, that is, joint PDF (JPDF). Specially, the FM Gumbel PDF is used to model the extreme wind speed and FM von Mises PDF is used to model the wind direction based on structural health monitoring (SHM) data. Then, the Genetic algorithm (GA) method is applied to solve the multi parameter solution in FM-AL model. Finally, the results of basic wind speed with return period of 100 years are compared based on the univariate Gumbel PDF (GB50009-2012 of Chinese code), FM Gumbel distribution, univariate Gumbel distribution + FM von Mises distribution and FM Gumbel distribution + FM von Mises distribution.

Estimating size of finite fracture networks in layered reservoirs

Conductive fractures in petroleum reservoirs may be totally isolated or fully interconnected. There is an intermediate state between the two extremities. Partially fractured reservoirs include finite fracture networks (FFN), which are bundles of interconnected fractures embedded in a sea of isolated fractures. Devising measures for sizes of FFNs is crucial in estimating critical engineering aspects such as productivity index, production decline rate and expected ultimate recovery of wells especially in reservoirs with low matrix porosity and permeability. Here, we present results of statistical evaluation of FFN size in relation to fracture connectivity which is in essence the number of fracture intersections per fracture. The analysis is based on a large number of stochastic 2-dimensional (2D) Poisson models of sub-vertical layer bound fractures. Fracture length in the models has log normal or truncated power distribution and fracture strike has circular normal distribution. The models may have single or multiple fracture sets and various truncation modes with different probabilities.The analysis shows that number of fracture intersections per fracture can be accurately estimated by a fracture connectivity index, which is defined as product of facture scan-line density, average fracture length and sine of strike standard deviation. The statistically significant finding of this study is that the number of fractures within a FFN is an exponential function of fracture connectivity index. All three fracture properties defining the index can be measured on borehole image logs. Hence it should be possible to estimate fracture connectivity and corresponding FFN size from borehole image data. The analysis pertains to 2D fracture connectivity which is always the lower bound of number of fracture intersections in 3-dimensions. Therefore the exponential relationships must also hold for actual 3-dimensional layer-bound fractures with variable dips.

Probabilistic characterization of the dates of occurrence of annual floods using the von Mises distribution

Probabilistic characterization of the dates of occurrence of annual floods using the von Mises distribution

Statistical channel modelling of full‐angle 3.5 GHz OAM in indoor corridor scenario

A 3.5 GHz OAM antenna with ±1 mode was designed and fabricated, and the channel measurement in frequency domain was used to measure the channel in full angle domain under indoor multipath scenarios. Then, the modified probability density function of Gaussian distribution, Laplacian distribution, and Von Mises distribution are used to establish the OAM full-angle statistical channel model. The fitting curve results well represent the statistical characteristics of OAM in indoor multipath scenario.

Bayesian Inference on the Bimodality of the Generalized von Mises Distribution

This article introduces Bayesian inference on the bimodality of the generalized von Mises (GvM) distribution for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007). The GvM distribution is a flexible model that can be axial symmetric or asymmetric, unimodal or bimodal. Two inferential approaches are analysed. The first is the test of null hypothesis of bimodality and Bayes factors are obtained. The second approach provides a two-dimensional highest posterior density (HPD) credible set for two parameters relevant to bimodality. Based on the identification of the two-dimensional parametric region associated with bimodality, the inclusion of the HPD credible set in that region allows us to infer on the bimodality of the underlying GvM distribution. A particular implementation of the Metropolis–Hastings algorithm allows for the computation of the Bayes factors and the HPD credible sets. A Monte Carlo study reveals that, whenever the samples are generated under a bimodal GvM, the Bayes factors and the HPD credible sets do clearly confirm the underlying bimodality.

Transport of Solar Energetic Particles along Stochastic Parker Spirals

Abstract It was recently shown that, owing to the turbulent nature of the solar wind, the interplanetary magnetic field lines can be well described by stochastic Parker spirals. These are realizations of Brownian diffusion on a sphere of increasing radius, superimposed on the angular drift due to the solar rotation. In this work, we present a model for the transport of solar energetic particles along stochastic Parker spirals in the inner heliosphere. The transport model is governed by a set of four stochastic differential equations for the heliographic position ( r , α = cos θ , ϕ ) of the guiding centers and the cosine of the pitch angle between the velocity vector and the Parker field. The model accounts for the role played by the combination of pitch angle scattering and magnetic focusing in the interplanetary medium. The effects of the dynamical evolution of the turbulence are included in the model by taking the field line angular diffusivity to be a function of the radial distance from the Sun. The heliolongitudinal distribution of particles propagating along stochastic Parker spirals is given by the wrapped Gaussian distribution. This angular distribution can also well be represented by the von Mises distribution that interpolates between the Gaussian distribution at small angular spread and the uniform distribution at large distances from the acceleration region of energetic particles in the aftermath of a solar eruption.

Theoretical Relationship Between Two Measures of Spike Synchrony: Correlation Index and Vector Strength.

Information processing in the nervous system critically relies on temporally precise spiking activity. In the auditory system, various degrees of phase-locking can be observed from the auditory nerve to cortical neurons. The classical metric for quantifying phase-locking is the vector strength (VS), which captures the periodicity in neuronal spiking. More recently, another metric, called the correlation index (CI), was proposed to quantify the temporally reproducible response characteristics of a neuron. The CI is defined as the peak value of a normalized shuffled autocorrelogram (SAC). Both VS and CI have been used to investigate how temporal information is processed and propagated along the auditory pathways. While previous analyses of physiological data in cats suggested covariation of these two metrics, general characterization of their connection has never been performed. In the present study, we derive a rigorous relationship between VS and CI. To model phase-locking, we assume Poissonian spike trains with a temporally changing intensity function following a von Mises distribution. We demonstrate that VS and CI are mutually related via the so-called concentration parameter that determines the degree of phase-locking. We confirm that these theoretical results are largely consistent with physiological data recorded in the auditory brainstem of various animals. In addition, we generate artificial phase-locked spike sequences, for which recording and analysis parameters can be systematically manipulated. Our analysis results suggest that mismatches between empirical data and the theoretical prediction can often be explained with deviations from the von Mises distribution, including skewed or multimodal period histograms. Furthermore, temporal relations of spike trains across trials can contribute to higher CI values than predicted mathematically based on the VS. We find that, for most applications, a SAC bin width of 50 ms seems to be a favorable choice, leading to an estimated error below 2.5% for physiologically plausible conditions. Overall, our results provide general relations between the two measures of phase-locking and will aid future analyses of different physiological datasets that are characterized with these metrics.

A universal elliptical disc (UED) model to represent natural rock fractures

Since natural fractures are often non-equidimensional, the circular disc model still has great limitations. By contrast, the elliptical disc model is more applicable to representing natural fractures, especially for slender ones. This paper developed a universal elliptical disc (UED) model by incorporating the center point, size, and azimuth of fractures as variables. Specifically, with respect to the azimuth of elliptical fractures in three-dimensional (3D) space, we proposed a paradigm to construct its probability density function (PDF) by coupling the orientation and rotation angle of long axis based on three coordinate transformations. To illustrate the construction process of the PDF of the fracture azimuth, we took the orientation following the Fisher distribution and the rotation angle following Von Mises distribution as an example. A rock slope is used to show the use of the developed UED model, and the 3D DFNs for the slope rock mass are generated by Monte Carlo simulation. In addition, the DFNs for the rock mass are also generated based on the existing circular disc model and non-universal elliptical disc model. The comparison results from the three models clearly illustrate the superiority of the UED model over the existing circular and non-universal elliptical disc models.

Outage Probability Analysis of RIS-Assisted Wireless Networks With Von Mises Phase Errors

In this letter, we investigate the performance of a communication link assisted by a reconfigurable intelligent surface (RIS) over line-of-sight (LOS) channels. The phase configuration of the RIS is imperfect and the phase error for each reflective element is modeled by a Von Mises distribution. First, we derive novel closed-form approximations for the lower tail distribution of the magnitude of the equivalent channel coefficient. Then, we use the obtained expressions to evaluate the outage probability and diversity order of the proposed system. Approximation errors of the proposed method are analyzed in detail. Simulation results validate the theoretical analysis is accurate at a high signal-to-noise ratio (SNR) regime.