Multifractal methodology

Salat, Hadrien; Murcio, Roberto; Arcaute, Elsa

doi:10.1016/j.physa.2017.01.041

Cited by 137 publications

(101 citation statements)

References 56 publications

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“…In order to evaluate the performance of the algorithm objectively, the receiver operating characteristic (ROC) curve, Precision-Recall (PR) curve, comprehensive evaluation index (F-measure), and Intersection-over-Union (IOU) are used to evaluate the performance of the algorithm. The proposed method will be compared with fractaldim [40], DivisorstepTP [48], MaxMedian, EightpixelTP [49], singularityExponent [50], and areaMeasure methods [51].…”

Section: Discussionmentioning

confidence: 99%

Cirrus Detection Based on RPCA and Fractal Dictionary Learning in Infrared imagery

et al. 2020

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In earth observation systems, especially in the detection of small and weak targets, the detection and recognition of long-distance infrared targets plays a vital role in the military and civil fields. However, there are a large number of high radiation areas on the earth’s surface, in which cirrus clouds, as high radiation areas or abnormal objects, will interfere with the military early warning system. In order to improve the performance of the system and the accuracy of small target detection, the method proposed in this paper uses the suppression of the cirrus cloud as an auxiliary means of small target detection. An infrared image was modeled and decomposed into thin parts such as the cirrus cloud, noise and clutter, and low-order background parts. In order to describe the cirrus cloud more accurately, robust principal component analysis (RPCA) was used to get the sparse components of the cirrus cloud, and only the sparse components of infrared image were studied. The texture of the cirrus cloud was found to have fractal characteristics, and a random fractal based infrared image signal component dictionary was constructed. The k-cluster singular value decomposition (KSVD) dictionary was used to train the sparse representation of sparse components to detect cirrus clouds. Through the simulation test, it was found that the algorithm proposed in this paper performed better on the the receiver operating characteristic (ROC) curve and Precision-Recall (PR) curve, had higher accuracy rate under the same recall rate, and its F-measure value and Intersection-over-Union (IOU) value were greater than other algorithms, which shows that it has better detection effect.

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Section: Discussionmentioning

confidence: 99%

Cirrus Detection Based on RPCA and Fractal Dictionary Learning in Infrared imagery

et al. 2020

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“…Fractal methods such as DFA (Detrended Fluctuation Analysis) [3], [32], rescaled range plot (R/S) [30] and MFDFA (MultiFractal Detrended Fluctuation Analysis) [31], [33] have been used in the developed web application for nonlinear HRV analysis.…”

Section: Methods For Hrv Analysismentioning

confidence: 99%

Implementing a Web-based Application for Analysis and Evaluation of Heart Rate Variability Using Serverless Architecture

Gospodinov¹,

Gospodinova²

2019

Int. J. Adv. Sci. Eng. Inf. Technol.

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This article is devoted to the development of a web-based application for analysis and evaluation of Heart Rate Variability (HRV) using serverless architecture. Advancements in information algorithms and computing technologies have been playing an increasingly important role in cardiology, as continuous monitoring of patients' health can be vital to their well-being. One physiological parameter that can be easily measured and that can provide indispensable insight into the state of the human body is the HRV. HRV analysis can assess not only the physiological state of the body but also provide the capability to monitor its dynamics and predict future diseases. As the research in the sphere of cardiology is constantly growing there is a multitude of new ways to assess the physiological state of patients and provide an early indicator to pathological conditions. Therefore, there is a need to bring these advances to a growing number of end-users (health-care professionals and patients) in the shortest possible time. To address this problem, this study proposes the development of a web-based application for analysis and evaluation of HRV by applying linear and nonlinear mathematical methods. The application is created using a serverless architectural approach, which allows for fast development time, as there is no need to manage server infrastructure, and for automatic scaling to dynamically match the number of requests. The developer can instead focus on implementing the logic for the HRV analysis algorithms and deliver new improvements at a faster rate. The proposed web application can be accessed by any device that is connected to the Internet and is optimized to handle both an intermittent and a consistent volume of requests. The algorithms implemented in the web application have been validated by examining two groups of subjects (young adults and older adults) using linear and non-linear models. The obtained results from the two groups can be compared with a set of reference values (only for the linear methods) and an assessment can be made whether each studied parameter is within the normal range or outside it (its value is too high or too low). To aid the assessment for HRV, the results obtained by the linear and nonlinear analysis are presented using a set of both graphs and tables.

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“…For q = 0, the mass exponent is equal to the negative of the dimension of the support, in this case the support is a square lattice, therefore τ (q = 0) = −2. A multifractal distribution is defined as a distribution which possesses a nonlinear dependence between the mass exponent τ and the order of the moment q [74][75][76] . For non-fractal systems, their mass exponent is simply given as τ (q) = 2(q − 1) for a system with support on a square lattice.…”

Section: Multifractal Analysismentioning

confidence: 99%

Local density of the Bose-glass phase

et al. 2018

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We study the Bose-Hubbard model in the presence of on-site disorder in the canonical ensemble and conclude that the local density of the Bose glass phase behaves differently at incommensurate filling than it does at commensurate one. Scaling of the superfluid density at incommensurate filling of ρ = 1.1 and on-site interaction U = 80t predicts a superfluid-Bose glass transition at disorder strength of ∆c ≈ 30t. At this filling the local density distribution shows skew behavior with increasing disorder strength. Multifractal analysis also suggests a multifractal behavior resembling that of the Anderson localization. Percolation analysis points to a phase transition of percolating non-integer filled sites around the same value of disorder. Our findings support the scenario of percolating superfluid clusters enhancing Anderson localization near the superfluid-Bose glass transition. On the other hand, the behavior of the commensurate filled system is rather different. Close to the tip of the Mott lobe (ρ = 1, U = 22t) we find a Mott insulator-Bose glass transition at disorder strength of ∆c ≈ 16t. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition. The behaviors of the superfluid-Bose glass transition call for a thorough finite size scaling analysis of percolation and multifractality to understand the universality of the transition.

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Multifractal methodology

Cited by 137 publications

References 56 publications

Cirrus Detection Based on RPCA and Fractal Dictionary Learning in Infrared imagery

Cirrus Detection Based on RPCA and Fractal Dictionary Learning in Infrared imagery

Implementing a Web-based Application for Analysis and Evaluation of Heart Rate Variability Using Serverless Architecture

Local density of the Bose-glass phase

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