scholarly journals Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection

2007 ◽  
Vol 11 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Rachid Jennane ◽  
Rachid Harba ◽  
Gérald Lemineur ◽  
Stéphanie Bretteil ◽  
Anne Estrade ◽  
...  
Keyword(s):  
Trabecular Bone ◽  
Self Similarity ◽  
Similarity Parameter

PATH PROPERTIES OF THE LINEAR MULTIFRACTIONAL STABLE MOTION

Fractals ◽  
2005 ◽  
Vol 13 (02) ◽  
pp. 157-178 ◽  
Author(s):  
STILIAN STOEV ◽  
MURAD S. TAQQU
Keyword(s):  
Heavy Tails ◽  
Hölder Regularity ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Stable Motion ◽  
Multifractional Brownian Motion ◽  
Sample Paths ◽  
Hölder Exponents ◽  
Fractional Stable Motion ◽  
Holder Regularity

The linear multifractional stable motion (LMSM) processes Y = {Y(t)}t∈ℝ is an α-stable (0 < α < 2) stochastic process, which exhibits local self-similarity, has heavy tails and can have skewed distributions. The process Y is obtained from the well-known class of linear fractional stable motion (LFSM) processes by replacing their self-similarity parameter H by a function of time H(t). We show that the paths of Y(t) are bounded on bounded intervals only if 1/α ≤ H(t) < 1, t ∈ ℝ. In particular, if 0 < α ≤ 1, then Y has everywhere discontinuous paths, with probability one. On the other hand, Y has a version with continuous paths if H(t) is sufficiently regular and 1/α < H(t), t ∈ ℝ. We study the Hölder regularity of the sample paths when these are continuous and establish almost sure bounds on the pointwise and uniform pointwise Hölder exponents of the (random) function Y(t,ω), t ∈ ℝ, in terms of the function H(t) and its corresponding Hölder exponents. The Gaussian multifractional Brownian motion (MBM) processes are LMSM processes when α = 2. We obtain some new results on the Hölder regularity of their paths.

scholarly journals Multi-Feature Based Ocean Oil Spill Detection for Polarimetric SAR Data Using Random Forest and the Self-Similarity Parameter

2019 ◽  
Vol 11 (4) ◽  
pp. 451 ◽  
Author(s):  
Shengwu Tong ◽  
Xiuguo Liu ◽  
Qihao Chen ◽  
Zhengjia Zhang ◽  
Guangqi Xie
Keyword(s):  
Wind Speed ◽  
Random Forest ◽  
Oil Spill ◽  
The Self ◽  
Detection Accuracy ◽  
Self Similarity ◽  
Polarimetric Sar ◽  
Similarity Parameter ◽  
Oil Spill Detection ◽  
Sar Data

Synthetic aperture radar (SAR) is an important means to detect ocean oil spills which cause serious damage to the marine ecosystem. However, the look-alikes, which have a similar behavior to oil slicks in SAR images, will reduce the oil spill detection accuracy. Therefore, a novel oil spill detection method based on multiple features of polarimetric SAR data is proposed to improve the detection accuracy in this paper. In this method, the self-similarity parameter, which is sensitive to the randomness of the scattering target, is introduced to enhance the discrimination ability between oil slicks and look-alikes. The proposed method uses the Random Forest classification combing self-similarity parameter with seven well-known features to improve oil spill detection accuracy. Evaluations and comparisons were conducted with Radarsat-2 and UAVSAR polarimetric SAR datasets, which shows that: (1) the oil spill detection accuracy of the proposed method reaches 92.99% and 82.25% in two datasets, respectively, which is higher than three well-known methods. (2) Compared with other seven polarimetric features, self-similarity parameter has the better oil spill detection capability in the scene with lower wind speed close to 2–3 m/s, while, when the wind speed is close to 9–12 m/s, it is more suitable for oil spill detection in the downwind scene where the microwave incident direction is similar to the sea surface wind direction and performs well in the scene with incidence angle range from 29.7° to 43.5°.

scholarly journals A NEW DISTRIBUTION-BASED TEST OF SELF-SIMILARITY

Fractals ◽  
2004 ◽  
Vol 12 (03) ◽  
pp. 331-346 ◽  
Author(s):  
SERGIO BIANCHI
Keyword(s):  
Necessary Conditions ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Probability Distribution Functions ◽  
Self Similar ◽  
The One ◽  
New Distribution

In studying the scale invariance of an empirical time series a twofold problem arises: it is necessary to test the series for self-similarity and, once passed such a test, the goal becomes to estimate the parameter H0 of self-similarity. The estimation is therefore correct only if the sequence is truly self-similar but in general this is just assumed and not tested in advance. In this paper we suggest a solution for this problem. Given the process {X(t),t∈T}, we propose a new test based on the diameter δ of the space of the rescaled probability distribution functions of X(t). Two necessary conditions are deduced which contribute to discriminate self-similar processes and a closed formula is provided for the diameter of the fractional Brownian motion (fBm). Furthermore, by properly choosing the distance function, we reduce the measure of self-similarity to the Smirnov statistics when the one-dimensional distributions of X(t) are considered. This permits the application of the well-known two-sided test due to Kolmogorov and Smirnov in order to evaluate the statistical significance of the diameter δ, even in the case of strongly dependent sequences. As a consequence, our approach both tests the series for self-similarity and provides an estimate of the self-similarity parameter.

Stochastic properties of the linear multifractional stable motion

2004 ◽  
Vol 36 (04) ◽  
pp. 1085-1115 ◽  
Author(s):  
Stilian Stoev ◽  
Murad S. Taqqu
Keyword(s):  
Sufficient Conditions ◽  
Infinite Variance ◽  
Regularity Conditions ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Stable Motion ◽  
Linear Fractional Stable Motion ◽  
Motion Process ◽  
Self Similar ◽  
Fractional Stable Motion

We study a family of locally self-similar stochastic processes Y = {Y(t)} t∈ℝ with α-stable distributions, called linear multifractional stable motions. They have infinite variance and may possess skewed distributions. The linear multifractional stable motion processes include, in particular, the classical linear fractional stable motion processes, which have stationary increments and are self-similar with self-similarity parameter H. The linear multifractional stable motion process Y is obtained by replacing the self-similarity parameter H in the integral representation of the linear fractional stable motion process by a deterministic function H(t). Whereas the linear fractional stable motion is always continuous in probability, this is not in general the case for Y. We obtain necessary and sufficient conditions for the continuity in probability of the process Y. We also examine the effect of the regularity of the function H(t) on the local structure of the process. We show that under certain Hölder regularity conditions on the function H(t), the process Y is locally equivalent to a linear fractional stable motion process, in the sense of finite-dimensional distributions. We study Y by using a related α-stable random field and its partial derivatives.

scholarly journals Self-Similarity in Magnetostrictive Materials: An Experimental Point of View

2021 ◽  
Vol 7 (9) ◽  
pp. 130
Author(s):  
Carmine Stefano Clemente ◽  
Daniele Davino ◽  
Pavel Krejčí ◽  
Vincenzo Paolo Loschiavo
Keyword(s):  
Magnetic Field ◽  
Mechanical Stress ◽  
Point Of View ◽  
Experimental Point ◽  
Stress And Strain ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Different Types ◽  
Self Similar ◽  
Magnetostrictive Behavior

Magnetostrictive behavior is characterized by a complex coupling between magnetic and mechanical quantities. While this behavior can be quite easily exploited for both actuation and sensing or energy conversion purposes, the complex hysteresis interaction between magnetization and magnetic field and mechanical stress and strain is hard to model. Nevertheless, magnetic and magnetostrictive experimental curves are quite self-similar, assuming stress as self-similarity parameter. The quantification of this concept would help modeling. Here, this concept is quantified and experimentally confirmed over different types of magnetostrictive samples.

scholarly journals Remarks on Confidence Intervals for Self-Similarity Parameter of a Subfractional Brownian Motion

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Junfeng Liu ◽  
Litan Yan ◽  
Zhihang Peng ◽  
Deqing Wang
Keyword(s):  
Brownian Motion ◽  
Confidence Intervals ◽  
The Self ◽  
Concentration Inequalities ◽  
Self Similarity ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Convergence Results ◽  
Subfractional Brownian Motion ◽  
Quadratic Variations

We first present two convergence results about the second-order quadratic variations of the subfractional Brownian motion: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we combine these results and concentration inequalities to build confidence intervals for the self-similarity parameter associated with one-dimensional subfractional Brownian motion.

scholarly journals Estimation of the self-similarity parameter in long memory processes

1970 ◽  
Vol 38 ◽  
pp. 32-37 ◽  
Author(s):  
MMA Sarker
Keyword(s):  
Long Memory ◽  
The Self ◽  
Similar Process ◽  
Long Range Dependence ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Data Set ◽  
Memory Processes ◽  
Long Memory Processes ◽  
Self Similar

Long memory processes, where positive correlations between observations far apart in time and space decay very slowly to zero with increasing time lag, occur quite frequently in fields such as hydrology and economics. Stochastic processes that are invariant in distribution under judicious scaling of time and space, called self-similar process, can parsimoniously model the long-run properties of phenomena exhibiting long-range dependence. Four of the heuristic estimation approaches have been presented in this study so that the self-similarity parameter, H that gives the correlation structure in long memory processes, can be effectively estimated. Finally, the methods presented in this paper were applied to two observed time series, namely Nile River Data set and the VBR (Variable- Bit-Rate) data set. The estimated values of H for two data sets found from different methods suggest that all methods are not equally good for estimation. Keywords: Long memory process, long-range dependence, Self-similar process, Hurst Parameter, Gaussian noise. DOI: 10.3329/jme.v38i0.898 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.32-37  

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