Two-dimensional Kolmogorov-Smirnov Test Research Articles

On the evolution of Seyfert galaxies, BL Lacertae objects and flat-spectrum radio quasars

The concept of the evolutionary sequence of jetted active galactic nuclei (AGNs) has been challenged in the last few decades since AGN subclasses are considered to be different due to their viewing angle. In this paper, we collected a sample of 1108 blazars (472 flat-spectrum radio quasars, FSRQs and 636 BL Lacertae objects, BL Lacs) and 120 Seyfert galaxies (SGs) with available redshifts and spectral properties in radio, optical, X-ray, and gamma-ray bands in order to compare the properties of SGs and the blazar subclasses and also explore their possible unification through evolution. It is found that the ratio of the relative difference of SGs and the blazar subclasses are approximately the same implying that they have an evolutionary relationship. We discovered from the results of a two-dimensional Kolmogorov-Smirnov (K.S.) test, that the probabilities (p) for the composite spectral indices: optical-X-ray radio-X-ray radio-optical and X-ray-gamma-ray to come from the same parent population is p, less than 0.05, implying that the null hypothesis cannot be rejected, thus, supports SGs-BL Lacs-FSRQs evolutionary sequence................. These results agree with the prediction that SGs have an evolutionary relationship with the blazar subclasses.

Luminol reagent control materials in bloodstain pattern analysis: A silicon sol-gel polymer alternative

Peroxidase-based reagents that react with whole blood typically undergo internal quality control tests for reactivity prior to their use at a crime scene. This study presents a synthetic polymer alternative to using whole mammalian blood as a luminol reagent control testing material. The luminol-reactive polymer was developed by integrating horseradish peroxidase into a silicon-based sol-gel matrix. Liquid formulations of the polymer were made to simulate forensically relevant luminol reactivity with dried, whole ovine blood at dilutions up to 1:1 × 106. Photoemission from chemiluminescence reactions were characterized as a function of time using a SpectraMax® M3 microplate reader luminometer over a duration of three minutes. The maximum chemiluminescence intensity, time at maxima, reaction half-life, and overall behaviour of the sol-gels and two commercially available materials are reported. The behaviour of each material was statistically compared to the whole blood standards using a two-dimensional Kolmogorov-Smirnov test, which suggests that the sol-gels have a more realistic and statistically similar reactivity to neat (p = 0.835) and diluted (1:1 × 106) blood (p = 0.998) than the commercially available materials (p < 0.05). The operational deliverable of this sol-gel technology is a reagent control test system, where the polymer is deposited onto cotton swabs that can be sprayed with luminol to test the working order of the solution. The sol-gel’s stability in the liquid form as well as when deposited on a cotton swab was monitored under three environmental conditions based on temperature and light for six weeks. This work establishes the sol-gel material as a practical luminol reagent control test for operational bloodstain pattern analysis.

A harmful-intrusion detection method based on background reconstruction and two-dimensional K-S test in an optical fiber pre-warning system

The key technology and main difficulty for optical fiber intrusion pre-warning systems (OFIPS) is the extraction of harmful-intrusion signals. After being processed by a phase-sensitive optical time-domain reflectometer (Φ-OTDR), vibration signals can be preliminarily extracted. Generally, these include noises and intrusions. Here, intrusions can be divided into harmful and harmless intrusions. With respect to the close study of signal characteristics, an effective extraction method of harmful intrusion is proposed in the paper. Firstly, in the part of the background reconstruction, all intrusion signals are first detected by a constant false alarm rate (CFAR). We then reconstruct the backgrounds by extracting two-part information of alarm points, time and amplitude. This ensures that the detection background consists of intrusion signals. Secondly, in the part of the two-dimensional Kolmogorov-Smirnov (K-S) test, in order to extract harmful ones from all extracted intrusions, we design a separation method. It is based on the signal characteristics of harmful intrusion, which are shorter time interval and higher amplitude. In the actual OFIPS, the detection method is used in some typical scenes, which includes a lot of harmless intrusions, for example construction sites and busy roads. Results show that we can effectively extract harmful intrusions.

Modeling the evolution and distribution of the frequency's second derivative and the braking index of pulsar spin**Supported by the National Natural Science Foundation of China.

We model the evolution of the spin frequency's second derivative v̈ and the braking index n of radio pulsars with simulations within the phenomenological model of their surface magnetic field evolution, which contains a long-term power-law decay modulated by short-term oscillations. For the pulsar PSR B0329+54, a model with three oscillation components can reproduce its v̈ variation. We show that the “averaged” n is different from the instantaneous n, and its oscillation magnitude decreases abruptly as the time span increases, due to the “averaging” effect. The simulated timing residuals agree with the main features of the reported data. Our model predicts that the averaged v̈ of PSR B0329+54 will start to decrease rapidly with newer data beyond those used in Hobbs et al. We further perform Monte Carlo simulations for the distribution of the reported data in |v̈| and |n| versus characteristic age τC diagrams. It is found that the magnetic field oscillation model with decay index α = 0 can reproduce the distributions quite well. Compared with magnetic field decay due to the ambipolar diffusion (α = 0.5) and the Hall cascade (α = 1.0), the model with no long term decay (α = 0) is clearly preferred for old pulsars by the p-values of the two-dimensional Kolmogorov-Smirnov test.

Operational Analysis of a Freeway Variable Speed Limit System in St. Louis, Missouri

Variable speed limit (VSL) systems have been more widely implemented in Europe compared to the United States. Studies have demonstrated positive safety impacts of such systems; however, there are very few studies that used actual deployment data to investigate the operational benefits of VSL systems. This article presents the operational impacts of a VSL deployment on Interstate 270 in the state of Missouri in the United States. Techniques such as parametric curve fitting, nonparametric methods, and other statistical tests were used to identify the changes between before and after traffic conditions. The effect of VSL on traffic performance was investigated at eight heavily congested locations. The two-dimensional Kolmogorov–Smirnov test results indicated that flow–occupancy diagram changes were statistically significant at seven out of eight locations. The slopes of flow–occupancy plots for over critical occupancies were found to be steeper after VSL. Slight changes in critical occupancy were observed after VSL implementation. However, the changes were inconsistent across locations, with some witnessing an increase and others witnessing a decrease. The maximum flow prior to breakdown (the prebreakdown flow) decreased at four locations and increased at four locations after VSL. The maximum flow after breakdown (the postbreakdown flow) decreased at three locations and increased at five locations after VSL. The average daily duration of congestion decreased at five locations and increased at three locations after VSL. Findings of this study help to develop VSL control algorithms that are more efficient in improving VSL traffic operations benefits.

Possible structure in the GRB sky distribution at redshift two

Context. Research over the past three decades has revolutionized cosmology while supporting the standard cosmological model. However, the cosmological principle of Universal homogeneity and isotropy has always been in question, since structures as large as the survey size have always been found each time the survey size has increased. Until 2013, the largest known structure in our Universe was the Sloan Great Wall, which is more than 400 Mpc long located approximately one billion light years away. Aims. Gamma-ray bursts are the most energetic explosions in the Universe. As they are associated with the stellar endpoints of massive stars and are found in and near distant galaxies, they are viable indicators of the dense part of the Universe containing normal matter. The spatial distribution of gamma-ray bursts can thus help expose the large scale structure of the Universe. Methods. As of July 2012, 283 GRB redshifts have been measured. Subdividing this sample into nine radial parts, each containing 31 GRBs, indicates that the GRB sample having 1.6 < z < 2.1 differs significantly from the others in that 14 of the 31 GRBs are concentrated in roughly 1/8 of the sky. A two-dimensional Kolmogorov-Smirnov test, a nearest-neighbour test, and a Bootstrap Point-Radius Method explore the significance of this clustering. Results. All tests used indicate that there is a statistically significant clustering of the GRB sample at 1.6 < z < 2.1. Furthermore, this angular excess cannot be entirely attributed to known selection biases, making its existence due to chance unlikely. Conclusions. This huge structure lies ten times farther away than the Sloan Great Wall, at a distance of approximately ten billion light years. The size of the structure defined by these GRBs is about 2000-3000 Mpc, or more than six times the size of the Sloan Great Wall.

Kolmogorov-Smirnov test as a tool to study the distribution of ultra-high energy cosmic ray sources

We analyse in detail the two-dimensional Kolmogorov–Smirnov test as a tool to learn about the distribution of the sources of the ultra-high energy cosmic rays. We confront, in particular, models based on active galactic nuclei observed in X-rays, galaxies observed in H i and isotropic distributions, discussing how this method can be used not only to reject isotropy but also to support or reject specific source models, extending results obtained recently in the literature.

Computationally efficient algorithms for the two-dimensional Kolmogorov–Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Ω(n2lgn), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test.

Heterogeneity in homogeneous Brabantian loess during the Late Pleniglacial

The Brabantian loess is often seen as a homogeneous sediment package, deposited under cold and dry climatic conditions (Haesaerts et al., 1981). However, in 1981 two small tundra gleysols were discovered in the Brabantian loess (Haesaerts et al., 1981). To unravel other possible changes in the sedimentary system during deposition, a more detailed look at the homogeneous Brabantian loess is carried out. The loess transporting process is reconstructed based on the combination of both grain size and grain shape parameters. These parameters are defined with automated dynamic image analysis and statistically compared with the two-dimensional Kolmogorov–Smirnov test. As suggested by Vandenberghe et al. (1998), our gleysols are generally correlated to a period of reduced grain size. Most likely, the more subtle the gleysols, the weaker the link between their formation and grain size reduction. Mazzullo et al. (1992) already stated that aeolian transport was very selective regarding grain size and sorting capacities. Our research points toward an extremely selective aeolian transport regarding the shape of the grains. Therefore, combining both particle size and particle shape can be very useful when reconstructing aeolian transport processes. This combination can also discriminate samples with a different transport and sedimentation history.

Size and Shape Analysis of Sedimentary Grains by Automated Dynamic Image Analysis

The application of Automated Dynamic Image Analysis (ADIA) for measuring the size and shape of sedimentary grains is presented. This technique determines the size and shape of a large number of particles (typically 5,000 to 50,000 or greater) in the size range between 10 to 1,500 μm. ADIA measurements are carried out using a RapidVue particle analyzer. The size and shape of particles are obtained by analyzing digital images. Each image is composed of shapes representing two-dimensional projections of particles. The analysis yields the area and perimeter of each particle cross-section, which are transformed into size-independent shape values. The analysis of such a large number of particles results in a very small statistical variation of the results, ca. 0.3% for 50,000 particles. Since operator selection of images does not enter the measurement procedure, the risk of bias caused by subjective sample selection is eliminated. The combination of ADIA with a two-dimensional Kolmogorov-Smirnov test, allows the identification of similarities and differences between sedimentary grains.

Survey of sampling-based methods for uncertainty and sensitivity analysis

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (i) definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (ii) generation of samples from uncertain analysis inputs, (iii) propagation of sampled inputs through an analysis, (iv) presentation of uncertainty analysis results, and (v) determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two-dimensional Kolmogorov–Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition.

X-ray sources overdensity around the 3C 295 galaxy cluster

Abstract We present a statistical analysis of the Chandra observation of the source field around the 3C 295 galaxy cluster ( z =0.46). The logN-logS of this field is in good agreement with that computed for the Chandra Deep Field South in this work and in previous ones. Nevertheless, the logN-logS computed separately for the four ACIS-I chips reveals that there is a significant excess of sources to the North-North East and a void to the South of the central cluster. Such an asymmetric distribution is confirmed by the two-dimensional Kolmogorov-Smirnov test, which excludes ( P ∼3%) a uniform distribution. In addition, a strong spatial correlation emerges from the study of the angular correlation function of the field: the angular correlation function is above that expected for X-ray sources on a few arcmin scales. In synthesis, the present analysis may indicate a filament of the large scale structure of the Universe toward 3C 295. This kind of study may open-up a new way to map (with high efficiency) high-density peaks of large scale structures at high redshift.

Gamma-ray bursts and magnetars as possible sources of ultrahigh energy cosmic rays: Correlation of cosmic ray event positions with IRAS galaxies

We use the two-dimensional Kolmogorov-Smirnov (KS) test to study the correlation between the 60 cosmic ray events above $4\ifmmode\times\else\texttimes\fi{}{10}^{19}\mathrm{eV}$ from the Akeno Giant Air Shower Array (AGASA) experiment and the positions of infrared luminous galaxies from the IRAS Point Source Catalog. These galaxies are expected to be hosts to gamma ray bursts (GRB's) and magnetars, both of which are associated with core collapse supernovae and have been proposed as possible acceleration sites for ultrahigh energy cosmic rays. We find consistency between the models and the AGASA events to have been drawn from the same underlying distribution of positions on the sky with KS probabilities \ensuremath{\gtrsim}50%. Application of the same test to the 11 highest AGASA events above ${10}^{20}\mathrm{eV},$ however, yields a KS probability of 0.5%, rejecting the models at 99.5% significance level. Taken at face value, these highest energy results suggest that the existing cosmic ray events above ${10}^{20}\mathrm{eV}$ do not owe their origin to long burst GRB's, rapidly rotating magnetars, or any other events associated with core collapse supernovae. The larger data set expected from the AUGER experiment will test whether this conclusion is real or is a statistical fluke that we estimate to be at the 2\ensuremath{\sigma} level.

A two-dimensional Kolmogorov-Smirnov test for crowded field source detection:ROSATsources in NGC 6397

We present a two-dimensional version of the classical one-dimensional Kolmogorov–Smirnov (KS) test, extending an earlier idea due to Peacock and an implementation proposed by Fasano and Franceschini. The two-dimensional KS test is used to optimize the goodness of fit in an iterative source-detection scheme for astronomical images. The method is applied to a ROSAT/HRI X-ray image of the post-core-collapse globular cluster NGC 6397 to determine the most probable source distribution in the cluster core. Comparisons to other widely used source-detection methods, and to a Chandra image of the same field, show that our iteration scheme is superior in measuring statistics-limited sources in severely crowded fields.

Endocardial wave front organization during ventricular fibrillation in humans

ObjectivesThis study was designed to characterize the organization of ventricular fibrillation (VF) on the endocardium of humans. BackgroundMost proposed mechanisms for the maintenance of VF postulate the propagation of a number of activation wave fronts that reenter to maintain the arrhythmia. We tested the hypothesis that, in patients undergoing internal cardioverter-defibrillator implantation, VF consists primarily of a few large wave fronts on the endocardium. MethodsElectrograms were recorded from a 36-electrode catheter in the left ventricle of 16 patients during VF. Activation times were chosen for a 2-s epoch for each fibrillation episode, and a two-dimensional Kolmogorov-Smirnov test was performed to determine if activation occurred randomly along the catheter over that time interval. The maximum cross-correlation was found for all possible pairs of electrodes on the catheter, and these values were plotted relative to the distance between the two electrodes. An exponential curve was then fit to the data, and a length constant was determined. Activation times were grouped into wave fronts along the catheter, and the lengths of the wave fronts were estimated. ResultsThe Kolmogorov-Smirnov test showed that activation was not random along the catheter in any of the patients studied. The correlation length determined was 9 ± 2 cm. The number of wave fronts recorded by the catheter was 9.2 ± 2.9 wave fronts/s. The length of the pathway of each wave front along the catheter was 6.5 ± 4.5 cm. ConclusionsVentricular fibrillation is well organized on the endocardial surface of humans, consisting primarily of a few large wave fronts on the order of 6 to 9 cm.

FROM STAR CHARTS TO STONEFLIES: DETECTING RELATIONSHIPS IN CONTINUOUS BIVARIATE DATA

Within many ecological systems, relationships between controlling factors and associated response variables are complex. In many cases, the response should vary little when the controlling factor exerts strong effects. Conversely, when the effect of the controlling factor is weak or absent, the response may vary greatly with effects of other factors. Correlation or regression analyses often may not be appropriate for testing these relationships, because variance of the response changes with values of the controlling factor. We suggest using a technique from the astronomy literature, a two-dimensional Kolmogorov-Smirnov (2DKS) test, to detect relationships in bivariate data with these patterns of variance. This technique successfully identified simulated bivariate data composed of paired independent values as having nonsignificant relationships and simulated bivariate data in which mean and variance of y was constrained at high levels of x as having significant relationships. Using these simulations and examples from aquatic and terrestrial systems, we demonstrate that the 2DKS is a robust test for detecting nonrandom patterns in bivariate distributions that commonly arise in many ecological systems.

Synthetic HR-diagrams for massive stars

Observations of luminous stars are compared to synthetic HR diagrams generated from three sets of evolutionary models with different treatment of mass loss, convective overshoot, and considering or not variations in the opacity due to heavy elements. We take into account also different values for the slope of the initial mass function, and the possibility that a fraction of the earliest spectral type stars is missing either because of photometric incompleteness or because they spend part of their Main-Sequence lifetime being not visible as still embedded in their parental cloud (shortly abbreviated as phase of invisibility). The statistical comparison between theory and observations is performed by means of a two-dimensional Kolmogorov-Smirnov test. Models computed taking into account a moderate opacity enhancement in the region of the CNO ionization, in addition to mass loss and convective overshoot, can be accepted at the 95% significance level. However, even in this case, the distribution of luminous stars in the HR diagram can be fitted only adopting an initial mass function slightly steeper than the Salpter one, and supposing that a fraction of the luminous stars are still not included in our counts either by photometric incompleteness of the data or intrinsic invisibility. On the contrary, the other models that incorporate mass loss and convective overshoot only, can be rejected at better than 95% confidence under any assumption for the IMF slope and fraction of missing stars.