The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are much extended
, now including systems that are; (1) non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent perturbation; (3) non-conservative (with dissipation). These systems cover various types of N-body gravitating systems of astrophysical and cosmological interest, such as the orbital evolution of planets, minor planets, artificial satellites due to tidal, non-tidal perturbations and thermal thrust, evolving close binary stellar systems, and the dynamics of accretion disks.
The Kolmogorov-Arnold stochasticity parameter technique is applied for the first time to the study of cancer genome sequencing, to reveal mutations. Using data generated by next generation sequencing technologies, we have analyzed the exome sequences
of brain tumor patients with matched tumor and normal blood. We show that mutations contained in sequencing data can be revealed using this technique thus providing a new methodology for determining subsequences of given length containing mutations i.e. its value differs from those of subsequences without mutations. A potential application for this technique involves simplifying the procedure of finding segments with mutations, speeding up genomic research, and accelerating its implementation in clinical diagnostic. Moreover, the prediction of a mutation associated to a family of frequent mutations in numerous types of cancers based purely on the value of the Kolmogorov function, indicates that this applied marker may recognize genomic sequences that are in extremely low abundance and can be used in revealing new types of mutations.
Extensive N-body simulations are among the key means for the study of numerous astrophysical and cosmological phenomena, so various schemes are developed for possibly higher accuracy computations. We demonstrate the principal possibility for revealin
g the evolution of a perturbed Hamiltonian system with an accuracy independent on time. The method is based on the Laplace transform and the derivation and analytical solution of an evolution equation in the phase space for the resolvent and using computer algebra.
The structure of the cold spot, of a non-Gaussian anomaly in the cosmic microwave background (CMB) sky first detected by Vielva et al. is studied using the data by Planck satellite. The obtained map of the degree of stochasticity (K-map) of CMB for t
he cold spot, reveals, most clearly in 100 GHz band, a shell-type structure with a center coinciding with the minima of the temperature distribution. The shell structure is non-Gaussian at a 4sigma confidence level. Such behavior of the K-map supports the void nature of the cold spot. The applied method can be used for tracing voids that have no signatures in redshift surveys.
We apply the Kolmogorov statistic to analyse the residual data of two LAGEOS satellites on General Relativistic Lense-Thirring effect, and show that it reveals a tiny difference in the properties of the satellites, possibly related to Yarkovsky-Rubin
cam effect. The recently launched LAser RElativity Satellite (LARES) can provide constraints to the extensions of General Relativity such as the Chern-Simons (CS) gravity with metric coupled to a scalar field through the Pontryagin density, so an explicit dependence on the frame dragging measurements vs the CS parameter is given.
Arrows of time - thermodynamical, cosmological, electromagnetic, quantum mechanical, psychological - are basic properties of Nature. For a quantum system-bath closed system the de-correlated initial conditions and no-memory (Markovian) dynamics are o
utlined as necessary conditions for the appearance of the thermodynamical arrow. The emergence of the arrow for the system evolving according to non-unitary dynamics due to the presence of the bath, then, is a result of limited observability, and we conjecture the arrow in the observable Universe as determined by the dark sector acting as a bath. The voids in the large scale matter distribution induce hyperbolicity of the null geodesics, with possible observational consequences.
According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss the corre
spondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem, and in the context of the recently launched LAser RElativity Satellite (LARES). Being possibly the highest mean density orbiting body in the Solar system, this satellite provides the best realization of a test particle ever reached experimentally and provides a unique possibility for testing the predictions of General Relativity.
When the electrons stored in the ring of the European Synchrotron Radiation Facility (ESRF, Grenoble) scatter on a laser beam (Compton scattering in flight) the lower energy of the scattered electron spectra, the Compton Edge (CE), is given by the tw
o body photon-electron relativistic kinematics and depends on the velocity of light. A precision measurement of the position of this CE as a function of the daily variations of the direction of the electron beam in an absolute reference frame provides a one-way test of Relativistic Kinematics and the isotropy of the velocity of light. The results of GRAAL-ESRF measurements improve the previously existing one-way limits, thus showing the efficiency of this method and the interest of further studies in this direction.
The Kolmogorov stochasticity parameter is shown to act as a tool to detect point sources in the cosmic microwave background (CMB) radiation temperature maps. Kolmogorov CMB map constructed for the WMAPs 7-year datasets reveals tiny structures which i
n part coincide with point radio and Fermi/LAT gamma-ray sources. In the first application of this method, we identified several sources not present in the then available 0FGL Fermi catalog. Subsequently they were confirmed in the more recent and more complete 1FGL catalog, thus strengthening the evidence for the power of this methodology.
The power spectrum is obtained for the Kolmogorov stochasticity parameter map for WMAPs cosmic microwave background (CMB) radiation temperature datasets. The interest for CMB Kolmogorov map is that it can carry direct information about voids in the m
atter 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.
