Stochasticity: A Feature for the Structuring of Large and Heterogeneous Image Databases

Atto, Abdourrahmane M.; Berthoumieu, Yannick; Megret, Rémi

doi:10.3390/e15114782

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…The interval 0.3 ≤ λ n ≤ 2.4 corresponds to the variation scale of Φ as of objective measure of degree of randomness. This approach has been applied for several sequences of the theory of dynamical systems and number theory (Arnold 2008;Arnold 2009a;Arnold 2009b;Atto et al 2013) and for extensive modeling of generated systems (see and references therein). In the applications to CMB in view of its Gaussian feature, the Gaussian CDF was used for analyzing of the temperature sequences.…”

Section: K-mapsmentioning

confidence: 99%

To the center of cold spot withPlanck

Gurzadyan

Кашин

Khachatryan

et al. 2014

A&A

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The structure of the cold spot, of a non-Gaussian anomaly in the cosmic microwave background (CMB) sky detected earlier by Vielva et al. (2004, ApJ, 609, 22), is studied using the data by Planck satellite. The map obtained of the degree of stochasticity (K-map) of CMB for the 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 4σ confidence level. Such behavior of the K-map supports the void nature of the cold spot. The method applied can be used for tracing voids that have no signatures in redshift surveys.

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Section: K-mapsmentioning

confidence: 99%

To the center of cold spot withPlanck

Gurzadyan

Кашин

Khachatryan

et al. 2014

A&A

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“…This method thus provides the measure of the degree of randomness (stochasticity) for sequences of n values within the interval of λ n [0.3, 2.4] ([ 2 , 3 ], see also [ 9 ]).…”

Section: Methodsmentioning

confidence: 99%

Detecting somatic mutations in genomic sequences by means of Kolmogorov–Arnold analysis

et al. 2015

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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 analysed the exome sequences of brain tumour patients with matched tumour 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 diagnostics. Moreover, the prediction of a mutation associated with 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.

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“…The importance of this descriptor is that it is applicable even to sequences of few tens of length Arnold ( 2009a), which is not the case for most of statistical methods and is rather sensitive to the deviation from randomness. These features of the descriptor appear to be efficient at non-linear data analysis, see Atto et al ( 2013); Rossmanith ( 2013). We then applied KSP-analysis to the observational data of a strong lensed object, namely, to the SDP.81 galaxy ALMA (2015); Tamura ( 2015).…”

Section: Kolmogorov Stochasticity Parametermentioning

confidence: 99%

Machine learning and Kolmogorov analysis to reveal gravitational lenses

Mirzoyan

Khachatryan

Yegorian

et al. 2019

Monthly Notices of the Royal Astronomical Society: Letters

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We present an automated approach to detect and extract information from the astronomical datasets on the shapes of such objects as galaxies, star clusters and, especially, elongated ones such as the gravitational lenses. First, the Kolmogorov stochasticity parameter is used to retrieve the sub-regions that worth further attention. Then we turn to image processing and machine learning Principal Component Analysis algorithm to retrieve the sought objects and reveal the information on their morphologies. We show the capability of our automated method to identify distinct objects and to classify them based on the input parameters. A catalog of possible lensing objects is retrieved as an output of the software, then their inspection is performed for the candidates that survive the filters applied.

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Stochasticity: A Feature for the Structuring of Large and Heterogeneous Image Databases

Cited by 5 publications

References 31 publications

To the center of cold spot withPlanck

To the center of cold spot withPlanck

Detecting somatic mutations in genomic sequences by means of Kolmogorov–Arnold analysis

Machine learning and Kolmogorov analysis to reveal gravitational lenses

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