scholarly journals Cosmological cross-correlations and nearest neighbour distributions

2021 ◽  
Vol 504 (2) ◽  
pp. 2911-2923
Author(s):  
Arka Banerjee ◽  
Tom Abel
Keyword(s):  
Cross Correlation ◽  
Cosmological Parameters ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Nearest Neighbour ◽  
Gaussian Density ◽  
Cosmological Data ◽  
Cross Correlations ◽  
Sparse Samples

ABSTRACT Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

AUTO- AND CROSS-CORRELATION OF PHASES OF THE WHOLE-SKY CMB AND FOREGROUND MAPS FROM THE 1-YEAR WMAP DATA

2006 ◽  
Vol 15 (08) ◽  
pp. 1283-1298 ◽  
Author(s):  
LUNG-YIH CHIANG ◽  
PAVEL D. NASELSKY
Keyword(s):  
Cross Correlation ◽  
Random Phase ◽  
Cosmological Parameters ◽  
Microwave Background ◽  
Return Mapping ◽  
Auto Correlation ◽  
Dimensional Uniformity ◽  
Cross Correlations ◽  
Wmap Data

The issue of non-Gaussianity is not only related to distinguishing the theories of the origin of primordial fluctuations, but also crucial for the determination of cosmological parameters in the framework of inflation paradigm. We present a method for testing non-Gaussianity on the whole-sky cosmic microwave background (CMB) anisotropies. This method is based on the Kuiper's statistic to probe the two-dimensional uniformity on a periodic mapping square associating phases: return mapping of phases of the derived CMB (similar to auto-correlation) and cross-correlations between phases of the derived CMB and foregrounds. Since phases reflect morphology, detection of cross-correlation of phases signifies the contamination of foreground signals in the derived CMB map. The advantage of this method is that one can cross-check the auto- and cross-correlation of phases of the derived maps and foregrounds, and mark off those multipoles in which the non-Gaussianity results from the foreground contaminations. We apply this statistic on the derived signals from the 1-year WMAP data. The auto-correlations of phases from the internal linear combination map show the significance above 95% C.L. against the random phase hypothesis on 17 spherical harmonic multipoles, among which some have pronounced cross-correlations with the foreground maps. We find that most of the non-Gaussianity found in the derived maps are from foreground contaminations. With this method we are better equipped to approach the issue of non-Gaussianity of primordial origin for the upcoming Planck mission.

scholarly journals MINKOWSKI FUNCTIONALS AND CLUSTER ANALYSIS FOR CMB MAPS

1999 ◽  
Vol 08 (03) ◽  
pp. 291-306 ◽  
Author(s):  
D. NOVIKOV ◽  
HUME A. FELDMAN ◽  
SERGEI F. SHANDARIN
Keyword(s):  
Large Data ◽  
Threshold Level ◽  
Distribution Functions ◽  
Large Data Sets ◽  
Cumulative Distribution ◽  
Temperature Threshold ◽  
Data Sets ◽  
Minkowski Functionals ◽  
And Cluster Analysis ◽  
Non Gaussian

We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, the procedure makes it possible to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique.

scholarly journals Constraining the ΛCDM and Galileon models with recent cosmological data

2017 ◽  
Vol 600 ◽  
pp. A40 ◽  
Author(s):  
J. Neveu ◽  
V. Ruhlmann-Kleider ◽  
P. Astier ◽  
M. Besançon ◽  
J. Guy ◽  
...  
Keyword(s):  
Cosmological Parameters ◽  
Acoustic Oscillation ◽  
Gravity Models ◽  
Accelerated Expansion ◽  
Data Sets ◽  
Late Time ◽  
Lunar Laser Ranging ◽  
Cosmological Constraints ◽  
Cosmological Data ◽  
Speed Of Propagation

Aims. The Galileon theory belongs to the class of modified gravity models that can explain the late-time accelerated expansion of the Universe. In previous works, cosmological constraints on the Galileon model were derived, both in the uncoupled case and with a disformal coupling of the Galileon field to matter. There, we showed that these models agree with the most recent cosmological data. In this work, we used updated cosmological data sets to derive new constraints on Galileon models, including the case of a constant conformal Galileon coupling to matter. We also explored the tracker solution of the uncoupled Galileon model. Methods. After updating our data sets, especially with the latest Planck data and baryonic acoustic oscillation (BAO) measurements, we fitted the cosmological parameters of the ΛCDM and Galileon models. The same analysis framework as in our previous papers was used to derive cosmological constraints, using precise measurements of cosmological distances and of the cosmic structure growth rate. Results. We show that all tested Galileon models are as compatible with cosmological data as the ΛCDM model. This means that present cosmological data are not accurate enough to distinguish clearly between the two theories. Among the different Galileon models, we find that a conformal coupling is not favoured, contrary to the disformal coupling which is preferred at the 2.3σ level over the uncoupled case. The tracker solution of the uncoupled Galileon model is also highly disfavoured owing to large tensions with supernovae and Planck+BAO data. However, outside of the tracker solution, the general uncoupled Galileon model, as well as the general disformally coupled Galileon model, remain the most promising Galileon scenarios to confront with future cosmological data. Finally, we also discuss constraints coming from the Lunar Laser Ranging experiment and gravitational wave speed of propagation.

scholarly journals Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 264 ◽  
Author(s):  
M. El-Morshedy ◽  
Ziyad Ali Alhussain ◽  
Doaa Atta ◽  
Ehab M. Almetwally ◽  
M. S. Eliwa
Keyword(s):  
Real Data ◽  
Bivariate Distribution ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Type Ii ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Modeling Data

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

UPPER-TRUNCATED POWER LAW DISTRIBUTIONS

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 209-222 ◽  
Author(s):  
STEPHEN M. BURROUGHS ◽  
SARAH F. TEBBENS
Keyword(s):  
Power Law ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Generalized Function ◽  
Data Sets ◽  
Scaling Exponent ◽  
Cumulative Number ◽  
Size Distributions ◽  
Data Set ◽  
Binned Data

Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhibit a "fall-off" from a power law at the largest object sizes. Previous work has often either ignored the fall-off region or described this region with a different function. We demonstrate that when a data set is abruptly truncated at large object size, fall-off from a power law is expected for the cumulative distribution. Functions to describe this fall-off are derived for both linearly and logarithmically binned data. These functions lead to a generalized function, the upper-truncated power law, that is independent of binning method. Fitting the upper-truncated power law to a cumulative number-size distribution determines the parameters of the power law, thus providing the scaling exponent of the data. Unlike previous approaches that employ alternate functions to describe the fall-off region, an upper-truncated power law describes the data set, including the fall-off, with a single function.

scholarly journals Steady-state cross-correlations for live two-colour super-resolution localization data sets

2015 ◽  
Vol 6 (1) ◽  
Author(s):  
Matthew B. Stone ◽  
Sarah L. Veatch
Keyword(s):  
Steady State ◽  
Dynamic Systems ◽  
Cross Correlation ◽  
Super Resolution ◽  
Cell Receptor ◽  
Live Cells ◽  
Data Sets ◽  
Lyn Kinase ◽  
Cross Correlations ◽  
Localization Data

Abstract Cross-correlation of super-resolution images gathered from point localizations allows for robust quantification of protein co-distributions in chemically fixed cells. Here this is extended to dynamic systems through an analysis that quantifies the steady-state cross-correlation between spectrally distinguishable probes. This methodology is used to quantify the co-distribution of several mobile membrane proteins in both vesicles and live cells, including Lyn kinase and the B-cell receptor during antigen stimulation.

scholarly journals Nearest neighbour distributions: New statistical measures for cosmological clustering

2020 ◽  
Vol 500 (4) ◽  
pp. 5479-5499 ◽  
Author(s):  
Arka Banerjee ◽  
Tom Abel
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Cosmological Parameters ◽  
Higher Order ◽  
Cumulative Distribution ◽  
Summary Statistics ◽  
Nearest Neighbour ◽  
Statistical Measures ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT The use of summary statistics beyond the two-point correlation function to analyse the non-Gaussian clustering on small scales, and thereby, increasing the sensitivity to the underlying cosmological parameters, is an active field of research in cosmology. In this paper, we explore a set of new summary statistics – the k-Nearest Neighbour Cumulative Distribution Functions (kNN-CDF). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the k-nearest data points, and is sensitive to all connected N-point correlations in the data. The kNN-CDF can be used to measure counts in cell, void probability distributions, and higher N-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets – both discrete points, and the generalization for continuous fields. We use data from a large suite of N-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of kNN-CDF improves the constraints on the cosmological parameters by more than a factor of 2 when applied to the clustering of dark matter in the range of scales between 10 and $40\, h^{-1}\, {\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of haloes in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the kNN-CDF are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data, provided the higher order correlation functions are sensitive to cosmology on the scales of interest.

scholarly journals Detrended Multiple Cross-Correlation Coefficient applied to solar radiation, air temperature and relative humidity

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andrea de Almeida Brito ◽  
Heráclio Alves de Araújo ◽  
Gilney Figueira Zebende
Keyword(s):  
Relative Humidity ◽  
Solar Radiation ◽  
Solar Energy ◽  
Correlation Coefficient ◽  
Air Temperature ◽  
Cross Correlation ◽  
Global Solar Radiation ◽  
Meteorological Variables ◽  
Hourly Data ◽  
Cross Correlations

AbstractDue to the importance of generating energy sustainably, with the Sun being a large solar power plant for the Earth, we study the cross-correlations between the main meteorological variables (global solar radiation, air temperature, and relative air humidity) from a global cross-correlation perspective to efficiently capture solar energy. This is done initially between pairs of these variables, with the Detrended Cross-Correlation Coefficient, ρDCCA, and subsequently with the recently developed Multiple Detrended Cross-Correlation Coefficient, $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2. We use the hourly data from three meteorological stations of the Brazilian Institute of Meteorology located in the state of Bahia (Brazil). Initially, with the original data, we set up a color map for each variable to show the time dynamics. After, ρDCCA was calculated, thus obtaining a positive value between the global solar radiation and air temperature, and a negative value between the global solar radiation and air relative humidity, for all time scales. Finally, for the first time, was applied $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2 to analyze cross-correlations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}={\bf{1}}$$DMCx2=1 (which varies from 0 to 1) is the ideal value for the capture of solar energy, our analysis finds some patterns (differences) involving these meteorological stations with a high intensity of annual solar radiation.

Sign in / Sign up

Export Citation Format

Share Document