Circular Data Research Articles

Symmetric Circular Model Induced by Inverse Stereographic Projection On Double Weibull Distribution with Application

In practical life usually we come across angular or periodic data which needs distributions that are invariant of zero direction and sense of rotation for analysis. Inverse stereographic projection/ Bilinear transformation defined by a one to one mapping generate a class of probability distributions on unit circle that are flexible to analyse circular data. The probability density f unction of many life testing models ranges from 0 to ∞ . Aiming to construct new circular model by applying Inverse Stereographic Projection, we consider Double Weibull distribution and derive density, distribution and characteristic functions of new circular model coined by us Stereographic Double Weibull distribution. Also an attempt is made to study the mathematical aspects in evaluating trigonometric moments of new circular model and present the population characteristics. Goodness of fit to a live data is verified.

Molecular interference in antibody–antigen interaction studied with magnetic force immunoassay

Molecular interferences are an important challenge in biotechnologies based on antibody-antigen interactions, such as sandwich immunoassays. We report how a sandwich immunoassay with magnetic particles as label can be used to probe interference by surfactants. Surfactants are often used to improve the performance of immunoassays, however the surfactants can affect the involved proteins and the mechanism of action of surfactant molecules on the antibody-antigen system is mostly unknown. As an example, we investigated molecular interference by a nonionic surfactant (Pluronic F-127) in a cardiac troponin (cTn) sandwich immunoassay with two monoclonal antibodies. The influence of the surfactant below the critical micelle concentration (0.00-0.04%) on dissociation properties was quantified in a magnetic tweezers setup, where a force is applied to the molecules via magnetic particle labels. The force-dependent dissociation curves revealed the existence of two distinct cTn-dependent bond types, namely a weak bond attributable to non-specific binding of cTn, and a strong bond attributable to the specific binding of cTn. The dissociation rate constant of the strong bonds increased with the surfactant concentration by about a factor of two. Circular dichroism spectroscopy data showed that the nonionic surfactant influences the conformation of cTn while not noticeably affecting the two monoclonal antibodies. This suggests that the surfactant-induced increase of the dissociation rate of the specific sandwich-type cTn binding may be related to a conformational change of the antigen molecule. The described methodology is an effective tool to study the influence of surfactants and other interferences on assays based on protein interactions.

Cat coexistence in central Sumatra: ecological characteristics, spatial and temporal overlap, and implications for management

AbstractAt least six species of wild cats live in Sumatra. Many are globally threatened and yet their ecology is poorly understood. We investigated ecological characteristics and spatial and temporal overlap among cats in central Sumatra using data from systematic and opportunistic camera trapping in five major forest blocks. We developed occupancy models assessing probability of site use by each cat based on (1) photo‐trap rates of other species at the same locations and (2) landscape‐level factors extracted from geographic information systems. We also used two‐species co‐occurrence models to assess spatial overlap and used kernel density estimates on circular data to assess temporal overlap between species pairs. We photographed five cat species: Sumatran tigers, Sunda clouded leopards, Asiatic golden cats, marbled cats and leopard cats. Four cats were present in all sampling blocks and one sampling block had all five cats. Spatially, cat distributions varied among forest types, within the sampling blocks and across elevation. We placed camera traps at elevations ranging from 6 to 460 m above sea level. The five cats used statistically different elevations, with golden cats found at highest elevation. Site use by tigers and leopard cats negatively covaried with distance to protected areas. Clouded leopard presence covaried positively with altitude. Leopard cat presence covaried with the photo‐trap rate of tigers, whereas the presence of tigers covaried with the photo‐trap rate of non‐cat carnivores. We found little evidence of spatial avoidance among cats at camera sites. Temporally, species more similar in size, or with similar‐sized prey, had lower overlap, suggesting temporal avoidance. We identified six mechanisms promoting coexistence of central Sumatra cats. Knowledge of interspecific interactions may improve the effectiveness of management aimed at conserving the increasingly threatened wild cat community.

Penalized contrast estimation in functional linear models with circular data

Our aim is to estimate the unknown slope function in the functional linear model when the response Y is real and the random function X is a second-order stationary and periodic process. We obtain our estimator by minimizing a standard (and very simple) mean-square contrast on linear finite dimensional spaces spanned by trigonometric bases. Our approach provides a penalization procedure which allows to automatically select the adequate dimension, in a non-asymptotic point of view. In fact, we can show that our penalized estimator reaches the optimal (minimax) rate of convergence in the sense of the prediction error. We complete the theoretical results by a simulation study and a real example that illustrates how the procedure works in practice.

On Discordance Tests for the Wrapped Cau-chy Distribution

Circular data as any other types of data are subjected to contamination with some unexpected observations which are known outliers. In this paper, four tests of discordancy for circular data based on M, C, D, and A statistics are extended to the wrapped Cauchy distribution to detect possible outliers. The cut-off points and the power of performances are investigated via extensive simulation study. Results show that tests perform better as the concentration of the samples is increased. Two real circular data sets are analysed for illustration.

Dairesel Verilerde Tekdüzelik Testleri

Yönsel veri içerisinde önemli bir yer tutan dairesel veriler ile birçok farklı alanda ilgilenilmektedir. Açısal verilere günün saatine (hastane ziyaretleri, doğum zamanları vb.) veya yılın günlerine (işsizlik veya satışta meydana gelen değişimler) bağlı zaman içinde meydana gelen periyodik olaylar örnek olarak verilebilir. Dairesel verinin basit ancak temel özelliği, ölçeğin başlangıç ve bitiş (0° ile 360°) değerlerinin çakışmasıdır. Üstelik bu tür verilerde aritmetik ortalamanın özetleyici bilgi olarak kötü bir gösterge olma ihtimali yüksektir. Çünkü 1° ile 359°?nin ortalamasının 180° olması mantıklı değildir. Bu durumda çözüm, ortalama vektör yönünün dairesel ortalama olarak kullanılmasıdır. Açısal veya dairesel verilerin istatistiksel analizi doğrusal veri analizinden farklıdır. Sınırsız ve iki kuyruklu doğrusal dağılımların aksine dairesel dağılımlar sonlu bir yapı sergilemektedir. Bundan dolayı 0° ile 360° bir dairede gerçekte aynı noktadır. Dairesel verilere ait istatistikler temelde, düzlemde birim vektör olarak ifade edilen gözlemler ile ilgilidir. Dolayısıyla örneklem uzayının daire veya küre olmasından dolayı, tek değişkenli veya çok değişkenli ölçüm değerlerinin analizinde kullanılan standart yöntemler kullanılmamalıdır. Bu tür örneklem uzaylarının dikkate alındığı durumlarda, özel olarak geliştirilmiş dairesel yöntemlerin kullanılması gerekmektedir. Dairesel verilerin söz konusu olduğu birçok durumda yapılan istatistiksel analizlerde dikkate alınan yokluk hipotezinde tek düze dağılım tüm yönlerin ortaya çıkmasının olasılıklarının eşit olduğunu ifade etmektedir. Bu çalışmada, açısal verilerde tekdüzelik testi olarak geliştirilmiş sekiz farklı yöntem tanıtılmış ve literatürden elde edilen bilgilerden yararlanarak yöntemler birbirleri ile karşılaştırılmıştır.

Recovering a Function from Circular Means or Wave Data on the Boundary of Parabolic Domains

Determining a function from its circular means with restricted centers is crucial for many modern medical imaging and remote sensing applications. Examples include photo- and thermoacoustic tomography, ultrasound imaging, and synthetic aperture radar. In this paper we derive an explicit inversion formula for the case where the centers of the circles of integration are restricted to the boundary of parabolic domains. A similar result is obtained for recovering the initial data of the wave equation from data on the boundary of a parabolic domain. These results show that the universal back-projection formulas, previously known to be exact for half-spaces, discs, and ellipsoids, are also exact for parabolic domains. We further present numerical simulations supporting our theoretical results. There, we also include two previously proposed strategies (dynamic aperture length correction and weight factor correction) accounting for the truncation of the parabola in practical applications.

Solid-State Nanopore Characterization of Single-Strand DNA-SSB Interactions

Single strand binding protein (SSB) plays a central role in genome replication by binding single-strand (ss) regions of DNA to prevent hybridization and nuclease digestion. Here, we study ssDNA-SSB interactions using solid-state nanopores. We show that a systematic increase in the molar ratio of SSB to ssDNA results in increased translocation event depth until DNA saturation is reached. These results are recapitulated in a bulk electromobility shift assay and indicate the weak cooperativity in SSB binding under high ionic strength conditions. We demonstrate that the strong selectivity of SSB for ssDNA over double-strand molecules can be used to differentiate a heterogeneous mixture and use comparisons of linearized and circular ssDNA data to suggest structural characteristics of SSB binding at high salt.

A New Information Criterion Based on Langevin Mixture Distribution for Clustering Circular Data with Application to Time Course Genomic Data

A New Information Criterion Based on Langevin Mixture Distribution for Clustering Circular Data with Application to Time Course Genomic Data

Bayesian Nonparametric Models of Circular Variables Based on Dirichlet Process Mixtures of Normal Distributions

This article introduces two new Bayesian nonparametric models for circular data based on Dirichlet process (DP) mixtures of normal distributions. The first model is a projected DP mixture of bivariate normals and the second approach is based on a wrapped DP mixture of normal distributions. We show how to carry out inference for these models based on a slice sampling scheme and introduce an approach to estimating a variant of the deviance information criterion which is appropriate in the context of latent variable models. Our models are then compared with both simulated and real data examples.

A tractable and interpretable four-parameter family of unimodal distributions on the circle

This article presents a class of four-parameter distributions for circular data that are unimodal, possess simple characteristic and density functions and a tractable distribution function, can be interpretably parameterized directly in terms of their trigonometric moments, afford a very wide range of skewness and kurtosis, envelop numerous interesting submodels including the wrapped Cauchy and cardioid distributions, allow straightforward parameter estimation by both method of moments and maximum likelihood, and are closed under convolution. This class of distributions exhibits the widest range of attractive properties yet available while retaining unimodality.

Determination of oil content in whole corn (Zea mays L.) seeds by means of near infrared reflectance spectroscopy

The objective of this study was to evaluate the ability of near infrared reflectance (NIR) spectroscopy to determine oil content in whole corn (Zea mays L.) samples sourced from a breeding program. Kernel samples were analysed in reflectance in the VIS and NIR regions (400–2500nm) at 2nm intervals using a scanning monochromator. Samples were scanned in a circular cell cup and reflectance data were stored as logarithm of the reciprocal reflectance (log1/R). Samples were not rotated when spectra collection was made. The coefficients of determination (R2) and the standard error of cross validation (SECV) obtained for the prediction of oil content in the calibration set were 0.90% and 0.17%, respectively. The residual predictive deviation (RPD=SD/SECV) value obtained was 2.3, indicating that these calibrations can be used for qualitative determination of oil content (e.g. low, medium and high) or preliminary screening in whole corn.

On the consistency of magnetic field measurements of Ap stars: lessons learned from the FORS1 archive

CONTEXT. The ESO archive of FORS1 spectropolarimetric observations may be used to create a homogeneous database of magnetic field measurements. However, no systematic comparison of FORS field measurements to those obtained with other instruments has been undertaken so far. AIMS. We exploit the FORS archive of circular spectropolarimetric data to examine in a general way how reliable and accurate field detections obtained with FORS are. METHODS. We examine the observations of Ap and Bp stars, on the grounds that almost all of the unambiguous detections of magnetic fields in the FORS1 archive are in these kinds of stars. We assess the overall quality of the FORS1 magnetic data by examining the consistency of field detections with what is known from previous measurements obtained with other instruments, and we look at patterns of internal consistency. RESULTS. FORS1 magnetic measurements are fully consistent with those made with other instruments, and the internal consistency of the data is excellent. However, it is important to recognise that each choice of grism and wavelength window constitutes a distinct instrumental measuring system, and that simultaneous field measurements in different instrumental systems may produce field strength values that differ up to 20 %, or more. Furthermore, we found that field measurements using hydrogen lines only yield results that meaningfully reflect the field strength as sampled specifically by lines of hydrogen for stars with effective temperatures above about 9000 K. CONCLUSIONS. In general the magnetic field measurements of Ap and Bp stars obtained with FORS1 are of excellent quality, accuracy and precision, and FORS1 provides an extremely useful example that offers valuable lessons for field measurements with other low- resolution Cassegrain spectropolarimeters.

Density estimation of circular data with Bernstein polynomials

Density estimation of circular data with Bernstein polynomials

Ice calving and deformation from Antarctic Ice margins using RISAT-1 circular polarization SAR data

Abstract. In the present study, quantification of spatial and temporal changes has been carried out between Indian Antarctic Research station Bharati and Amery ice shelf by monitoring the ice margins using RISAT-1 Synthetic Aperture Radar (SAR) data. Spatio-temporal change detection was carried out by comparing the feature's geographic locations from geometrically rectified SAR data from RISAT-1 (Dec. 2013), Radarsat-2 (Feb. 2013), and Antarctic Mapping Mission products of Radarsat-1 (1997 & 2000). We report large scale disintegrations at two prominent glacier tongues namely Polar Record Glacier (PRG) and Polar Times Glacier(PTG). The results are verified against in-situ ground observations made during Summer period of 33rd ISEA (Dec. 2013–Feb. 2014) and MODIS images from NSIDC archive. Polar Record Glacier Tongue (PRGT) was drastically deformed by 135.8 km2 and Polar Times Glacier Tongue (PTGT) was partly calved by ~195.6 km2 and moved away by ~23 km especially between February and December 2013.

A GROUP SEQUENTIAL TEST OF CIRCULAR DATA USING THE VON MISES DISTRIBUTION

In this study, the group sequential test is suggested for the mean direction parameter of the von Mises distribution when the concentration parameter is known and unknown. An application of the proposed test is illustrated by using a medical data of the patients, who were complained about internal rotation angles of the shoulder and treated in a rehabilitation and physical therapy center in Eskisehir, Turkey. It is shown that the results of the study demonstrate that the group sequential test can provide a great advantage not only for linear data but also for circular data in terms of sample size.

Turbulent velocity distribution with dip phenomenon in conic open channels

ABSTRACTConic open-channel flow as occurs in sub-drains, sewers, and culverts is computed by Manning's or Darcy's resistance equations for the cross-sectional average velocity only. Yet, fish passage culvert design requires the cross-sectional velocity distribution, which is proposed in this paper based on two hypotheses: (i) centreline velocity distribution follows the conventional log-law with a cubic deduction near the water surface; (ii) cross-sectional velocity distribution is described by Guo and Julien's modified log-wake-law but neglecting the squared sine function. These hypotheses result in a novel and simple velocity distribution model without any fitting parameter. Its graphical interpretation for the elliptic, parabolic, and hyperbolic channels indicates reasonable velocity contours with dip phenomenon. Further, it agrees well with circular pipe data related to the average shear velocity, velocity-dip position, centreline and cross-sectional velocity distributions. A potential application includes fish passage culvert design by specifying a low velocity zone near the wall.

Distribuição Von Mises na avaliação de dados apícolas

Circular statistics is applied to data that show a periodic behavior, which characterizes the obtaining of what is called circular data. The existence of a circadian rhythm in the metabolism of Africanized bees can influence the mortality time of workers and the emergence of queen bees, in which case we obtain circular data characterized by the time of occurrence of these events. Bees visits to flowers of a plant can also provide circular data. The aim of this research was to verify the applicability of circular statistics to apicultural data. Data from three experiments were used: 1- bees foraging for field rosemary; 2- emergence of queen bees; 3- the mortality time of workers (considering the experimental setup time at night (19:30) and during the day (7:30)). All data sets used were tested in relation to two distributions: uniform and Von Mises (or circular normal), and fitted to the latter. It was concluded that, when bees are foraging on rosemary, the circular normal model mean time equals 11 h 29 min with large dispersion. There is also a circadian rhythm that regulates the emergence time of queens and the mortality of worker bees. In the experiment on the emergence of queen bees, a confidence interval of 95 % was obtained for the circular mean equal to (4 h 12 min; 9 h 05 min). The mean mortality time in the setup carried out during the day occurs after 4 h 18 min, with longevity estimated at 8 h 37 min. The life expectancy of individuals maintained under the same conditions, except for an experimental setup time at 19 h 30 min, is estimated at 19 h 37 min. Therefore, in order to carry out laboratory experiments on adult bees, it is advisable to include the experimental setup time in the experimental methodology.

Performance Analysis of the nc-FastICA Algorithm

The noncircular complex Fast Independent Component Analysis (nc-FastICA) algorithm is one of the most popular algorithms for solving the ICA problems with circular and noncircular complex-valued data. However, the performance of nc-FastICA has not been comprehensively studied in the past. In this paper, this matter is addressed. Based on the global analysis of fixed-point iteration and cost function, we get that there exist undesirable fixed points for nc-FastICA algorithm. To get rid of the undesirable fixed points, a simple check of undesirable points is proposed based on the kurtosis of the estimated sources. Furthermore, theoretical analysis in this paper shows that the nc-FastICA algorithm can work well even when the sources fall into the area of instability. Computer simulations validate the correctness of the theoretical findings in the paper.

Modelling complex geological circular data with the projected normal distribution and mixtures of von Mises distributions

Abstract. Circular data are commonly encountered in the earth sciences and statistical descriptions and inferences about such data are necessary in structural geology. In this paper we compare two statistical distributions appropriate for complex circular data sets: the mixture of von Mises and the projected normal distribution. We show how the number of components in a mixture of von Mises distribution may be chosen, and how one may choose between the projected normal distribution and the mixture of von Mises for a particular data set. We illustrate these methods with a few structural geological data, showing how the fitted models can complement geological interpretation and permit statistical inference. One of our data sets suggests a special case of the projected normal distribution which we discuss briefly.