Probing the statistic in the cosmic microwave background

Kolmogorov's statistic is used for the analysis of properties of perturbations in the Cosmic Microwave Background signal. We obtain the maps of the Kolmogorov stochasticity parameter for W and V band temperature data of WMAP which are differently affected by the Galactic disk radiation and then we model datasets with various statistic of perturbations. The analysis shows that the Kolmogorov's parameter can be an efficient tool for the separation of Cosmic Microwave Background from the contaminating radiations due to their different statistical properties.Comment: 6 pages, 4 figure

Effect of Degrees of Freedom on Effort and Rate of Fatigue Accumulation During the Supine Chest Press

INTRODUCTION For workplace tool design and exercise equipment design alike, the number of the degrees of freedom to be controlled in a tool or machine has been shown to affect the biological response of the user. Studies show more muscle activation when either the load, or the supporting surface is less stable (i.e. has more degrees of freedom). Despite this, there has been little research on the effect of added degrees of freedom on neuromuscular fatigue, although it may be an intervening variable of interest as fatigue has been shown to increase the incidence of labour accidents leading to injuries at the workplace due to diminished motor control, increased force variability and reduced maximal strength. The purpose of this study is twofold. Firstly, it is to analyze the effect which the demand of controlling additional degrees of freedom has on effort and rate of fatigue accumulation in a strength trained population. Secondly, it is to observe how activation of non prime mover muscles changes with fatigue with different stability requirements, and how prime mover muscle activation changes in response. METHODS In this study, the supine chest press exercise was utilized to demonstrate the effect of allowing more degrees of freedom at the hands, on effort and fatigue. A Smith machine was modified to allow uncoupled side-side and coupled back-forward degrees of freedom. Six bench press “modes” were tested, each with varying number of degrees of freedom; four Smith machine bench press modes, barbell bench press and dumbbell bench press. 19 strength trained participants were recruited. 1RM barbell bench press was tested and each participant performed 50%1RM bench press to fatigue on every bench press mode over two sessions. Mean EMG and mean power frequency from every repetition, mean hand and elbow action tremor, load path deviation, mean thoraco-humeral angle were collected. A mixed effect linear model was used to obtain initial values and rate of change with fatigue. Initial value differences were used to compare effort between modes and rate of change between modes was used to compare rate of fatigue accumulation between modes. Initial and final rate of perceived difficulty were collected and analyzed using a repeated measures ANOVA. RESULTS There was a significant main effect on all prime mover muscles’ activity for condition (p<0.01). Overall, there was greater overall initial muscle activity in modes with more unrestrained degrees of freedom. Most notably, there was a redistribution of muscle stress from elbow extensors to shoulder (horizontal) flexors during modes which had uncoupled side-side degree of freedom unrestrained. For instance, during the Smith machine mode with all degrees of freedom unlocked, there was a 17% increase in pectoralis major activity and a 5% decrease in triceps’ activity. This muscle redistribution, which corresponded with the mechanical nature of the task was correlated with perceived difficulty of control. There was a significant main effect on the number of repetitions completed to failure (p<0.01). Only modes which had uncoupled side-side degree of freedom unlocked had a significant effect on fatigue. These modes produced, on average, 5 less repetitions. Out of initial non-prime mover muscle activation, only biceps showed a general trend towards increasing with more unrestricted degrees of freedom, while shoulder musculature was unchanged in the absence of fatigue. However, with fatigue accumulation, modes which had more degrees of freedom unrestricted generally had greater rate of non-prime mover musculature activation increase, which was also correlated with prime mover muscle activation and prime mover mean power frequency decrease. Additionally, the results showed a trend towards individuals with more strength training experience being able to perform better with the more unstable dumbbell and barbell bench press as compared to less strength trained individuals. CONCLUSION Although each degree of freedom altered did not have the same effect, general findings included: as the unrestrained degrees of freedom increased, effort required increased and participants fatigued more rapidly. The findings give insights into the effects of people exerting forces against unstable loads in strength training and occupational settings

A weakly random Universe?

The cosmic microwave background (CMB) radiation is characterized by well-established scales, the 2.7 K temperature of the Planckian spectrum and the $10^{-5}$ amplitude of the temperature anisotropy. These features were instrumental in indicating the hot and equilibrium phases of the early history of the Universe and its large scale isotropy, respectively. We now reveal one more intrinsic scale in CMB properties. We introduce a method developed originally by Kolmogorov, that quantifies a degree of randomness (chaos) in a set of numbers, such as measurements of the CMB temperature in some region. Considering CMB as a composition of random and regular signals, we solve the inverse problem of recovering of their mutual fractions from the temperature sky maps. Deriving the empirical Kolmogorov's function in the Wilkinson Microwave Anisotropy Probe's maps, we obtain the fraction of the random signal to be about 20 per cent, i.e. the cosmological sky is a weakly random one. The paper is dedicated to the memory of Vladimir Arnold (1937-2010).Comment: 4 pages, 3 figs, A & A (Lett) in press; to match the published versio

The power spectrum of the cosmic microwave background Kolmogorov maps: possible clue to correlation of voids

The power spectrum is obtained for the Kolmogorov stochasticity parameter map for WMAP's cosmic microwave background (CMB) radiation temperature datasets. The interest for CMB Kolmogorov map is that it can carry direct information about voids in the matter distribution, so that the correlations in the distribution of voids have to be reflected in the power spectrum. Although limited by the angular resolution of the WMAP, this analysis shows the possibility of acquiring this crucial information via CMB maps. Even the already obtained behavior, some of which is absent in the simulated maps, can influence the development of views on the void correlations at the large-scale web formation.Comment: A & A (Lett.) (accepted), 4 pages, 3 fig

Degree of randomness: numerical experiments for astrophysical signals

Astrophysical and cosmological signals such as the cosmic microwave background radiation, as observed, typically contain contributions of different components, and their statistical properties can be used to distinguish one from the other. A method developed originally by Kolmogorov is involved for the study of astrophysical signals of randomness of various degrees. Numerical performed experiments based on the universality of Kolmogorov distribution and using a single scaling of the ratio of stochastic to regular components, reveal basic features in the behavior of generated signals also in terms of a critical value for that ratio, thus enable the application of this technique for various observational datasetsComment: 6 pages, 9 figures; Europhys.Letters; to match the published versio

Kolmogorov cosmic microwave background sky

A new map of the sky representing the degree of randomness in the cosmic microwave background (CMB) temperature has been obtained. The map based on estimation of the Kolmogorov stochasticity parameter clearly distinguishes the contribution of the Galactic disk from the CMB and reveals regions of various degrees of randomness that can reflect the properties of inhomogeneities in the Universe. For example, among the high randomness regions is the southern non-Gaussian anomaly, the Cold Spot, with a stratification expected for the voids. Existence of its counterpart, a Northern Cold Spot with almost identical randomness properties among other low-temperature regions is revealed. By its informative power, Kolmogorov's map can be complementary to the CMB temperature and polarization sky maps.Comment: A & A (in press), to match the published version, 4 pages, 5 figs, 2 Table

Plane-mirroring anomaly in the cosmic microwave background maps

The plane-mirror symmetry previously noticed in the Cosmic Microwave Background (CMB) temperature anisotropy maps of Wilkinson Microwave Anisotropy Probe is shown to possess certain anomalous properties. The degree of the randomness determined by the Kolmogorov stochasticity parameter in the both symmetry regions appears to have identical values which, however, essentially differ from the corresponding values for other sky regions. If the mirroring were of cosmological origin, this would imply either additional randomizing properties in those directions of the Universe or their different line-of-sight depth. This analysis also provides a way to test the hypothesis of a link between the nature of dark energy and inhomogeneities.Comment: A & A (Lett.) in press; 3 pages, 2 fig

Detection of X-ray galaxy clusters based on the Kolmogorov method

The detection of clusters of galaxies in large surveys plays an important part in extragalactic astronomy, and particularly in cosmology, since cluster counts can give strong constraints on cosmological parameters. X-ray imaging is in particular a reliable means to discover new clusters, and large X-ray surveys are now available. Considering XMM-Newton data for a sample of 40 Abell clusters, we show that their analysis with a Kolmogorov distribution can provide a distinctive signature for galaxy clusters. The Kolmogorov method is sensitive to the correlations in the cluster X-ray properties and can therefore be used for their identification, thus allowing to search reliably for clusters in a simple way