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Wang H, Zhao X, Yu D. Nonlinear features of gaze behavior during joint attention in children with autism spectrum disorder. Autism Res 2023; 16:1786-1798. [PMID: 37530201 DOI: 10.1002/aur.3000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 07/16/2023] [Indexed: 08/03/2023]
Abstract
Since children with autism spectrum disorder (ASD) might exhibit a variety of aberrant response to joint attention (RJA) behaviors, there is growing interest in identifying robust, reliable and valid eye-tracking metrics for determining differences in RJA behaviors between typically developing (TD) children and those with ASD. Previous eye-tracking studies have not been deeply investigated nonlinear features of gaze time-series during RJA. As a main motivation, this study aimed to extract three nonlinear features (i.e., complexity, long-range correlation, and local instability) of gaze time-series during RJA in children with ASD, which can be measured by fractal dimension (FD), Hurst exponent (H), and largest Lyapunov exponent (LLE), respectively. To illustrate our idea, this study adopted a publicly accessible database, including eye-tracking data collected during RJA from 19 children with ASD (7.74 ± 2.73) and 30 TD children (8.02 ± 2.89), and conducted a battery of nonparametric analysis of covariance (ANCOVA), where gender was used as covariable. Findings showed that gaze time-series during RJA in autistic children may generally have greater FD but lower H than that in TD controls. This implies that children with ASD possess more complex and unpredictable gaze behaviors during RJA than TD children. Furthermore, nonlinear metrics outperformed traditional eye-tracking metrics in obtaining higher identification performance with an accuracy of 82% and an AUC value of 0.81, distinguishing the differences between successful and failed RJA trails, and predicting the severity of ASD symptoms. Findings might bring some new insights into the understanding of the impairments in RJA behaviors for children with ASD.
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Affiliation(s)
- Hongan Wang
- Key Laboratory of Child Development and Learning Science of Ministry of Education, School of Biological Science and Medical Engineering, Southeast University, Nanjing, China
| | - Xin Zhao
- Department of Radiology, The Third Affiliated Hospital of Zhengzhou University, Zhengzhou, China
| | - Dongchuan Yu
- Key Laboratory of Child Development and Learning Science of Ministry of Education, School of Biological Science and Medical Engineering, Southeast University, Nanjing, China
- Henan Provincial Medical Key Lab of Child Developmental Behavior and Learning, The Third Affiliated Hospital of Zhengzhou University, Zhengzhou, China
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Abstract
A Non-Binary Snow Index for Multi-Component Surfaces (NBSI-MS) is proposed to map snow/ice cover. The NBSI-MS is based on the spectral characteristics of different Land Cover Types (LCTs), such as snow, water, vegetation, bare land, impervious, and shadow surfaces. This index can increase the separability between NBSI-MS values corresponding to snow from other LCTs and accurately delineate the snow/ice cover in non-binary maps. To test the robustness of the NBSI-MS, regions in Greenland and France–Italy where snow interacts with highly diversified geographical ecosystems were examined. Data recorded by Landsat 5 TM, Landsat 8 OLI, and Sentinel-2A MSI satellites were used. The NBSI-MS performance was also compared against the well-known Normalized Difference Snow Index (NDSI), NDSII-1, S3, and Snow Water Index (SWI) methods and evaluated based on Ground Reference Test Pixels (GRTPs) over non-binarized results. The results show that the NBSI-MS achieved an overall accuracy (OA) ranging from 0.99 to 1 with kappa coefficient values in the same range as the OA. The precision assessment confirmed the performance superiority of the proposed NBSI-MS method for removing water and shadow surfaces over the compared relevant indices.
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Sikora G, Höll M, Gajda J, Kantz H, Chechkin A, Wyłomańska A. Probabilistic properties of detrended fluctuation analysis for Gaussian processes. Phys Rev E 2020; 101:032114. [PMID: 32289956 DOI: 10.1103/physreve.101.032114] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2019] [Accepted: 02/11/2020] [Indexed: 11/07/2022]
Abstract
Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes. Our main attention is paid to the distribution of the squared error sum of the detrended process. We use a probabilistic approach to derive general formulas for the expected value and the variance of the squared fluctuation function of DFA for Gaussian processes. We also get analytical results for the expected value of the squared fluctuation function for particular examples of Gaussian processes, such as Gaussian white noise, fractional Gaussian noise, ordinary Brownian motion, and fractional Brownian motion. Our analytical formulas are supported by numerical simulations. The results obtained can serve as a starting point for analyzing the statistical properties of DFA-based estimators for the fluctuation function and long-memory parameter.
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Affiliation(s)
- Grzegorz Sikora
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
| | - Marc Höll
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 5290002 Israel
| | - Janusz Gajda
- Faculty of Economic Sciences, University of Warsaw, 00-241 Warsaw, Poland
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Aleksei Chechkin
- Institute of Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Akhiezer Institute for Theoretical Physics NSC "Kharkov Institute of Physics and Technology", 61108 Kharkov, Ukraine
| | - Agnieszka Wyłomańska
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
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Höll M, Kiyono K, Kantz H. Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average. Phys Rev E 2019; 99:033305. [PMID: 30999507 DOI: 10.1103/physreve.99.033305] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Indexed: 06/09/2023]
Abstract
We present a bottom-up derivation of fluctuation analysis with detrending for the detection of long-range correlations in the presence of additive trends or intrinsic nonstationarities. While the well-known detrended fluctuation analysis (DFA) and detrending moving average (DMA) were introduced ad hoc, we claim basic principles for such methods where DFA and DMA are then shown to be specific realizations. The mean-squared displacement of the summed time series contains the same information about long-range correlations as the autocorrelation function but has much better statistical properties for large time lags. However, the scaling exponent of its estimator on a single time series is affected not only by trends on the data but also by intrinsic nonstationarities. We therefore define the fluctuation function as mean-squared displacement with weighting kernel. We require that its estimator be unbiased and exhibit the correct scaling behavior for the random component of a signal, which is only achieved if the weighting kernel implies detrending. We show how DFA and DMA satisfy these requirements and we extract their kernel weights.
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Affiliation(s)
- Marc Höll
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Ken Kiyono
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
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Bakhshian S, Sahimi M. Computer simulation of the effect of deformation on the morphology and flow properties of porous media. Phys Rev E 2016; 94:042903. [PMID: 27841555 DOI: 10.1103/physreve.94.042903] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2016] [Indexed: 06/06/2023]
Abstract
We report on the results of extensive computer simulation of the effect of deformation on the morphology of a porous medium and its fluid flow properties. The porous medium is represented by packings of spherical particles. Both random and regular as well as dense and nondense packings are used. A quasistatic model based on Hertz's contact theory is used to model the mechanical deformation of the packings, while the evolution of the permeability with the deformation is computed by the lattice-Boltzmann approach. The evolution of the pore-size and pore-length distributions, the porosity, the particles' contacts, the permeability, and the distribution of the stresses that the fluid exerts in the pore space are all studied in detail. The distribution of the pores' lengths, the porosity, and the particles' connectivity change strongly with the application of an external strain to the porous media, whereas the pore-size distribution is not affected as strongly. The permeability of the porous media strongly reduces even when the applied strain is small. When the permeabilities and porosities of the random packings are normalized with respect to their predeformation values, they all collapse onto a single curve, independent of the particle-size distribution. The porosity reduces as a power law with the external strain. The fluid stresses in the pore space follow roughly a log-normal distribution, both before and after deformation.
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Affiliation(s)
- Sahar Bakhshian
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| | - Muhammad Sahimi
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
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Carbone A, Kiyono K. Detrending moving average algorithm: Frequency response and scaling performances. Phys Rev E 2016; 93:063309. [PMID: 27415389 DOI: 10.1103/physreve.93.063309] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2016] [Indexed: 06/06/2023]
Abstract
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) over either time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent, and finite scale range behavior will be discussed.
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Affiliation(s)
- Anna Carbone
- Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Ken Kiyono
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan
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Arianos S, Carbone A, Türk C. Self-similarity of higher-order moving averages. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046113. [PMID: 22181233 DOI: 10.1103/physreve.84.046113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Revised: 10/02/2011] [Indexed: 05/31/2023]
Abstract
In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).
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Affiliation(s)
- Sergio Arianos
- Physics Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
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