Journal articles on the topic 'Fractal neighbour distance'

Abstract A model for the liquid-glass transition, based on a percolation blocking of local chemical order, is proposed. The case of metallic liquids and glasses, whose structure is dominated by first neighbour chemical arrangement, is first treated. The chemical ordering "reaction" of the liquid phase is studied at thermodynamical equilibrium and the increase of the chemical order parameter with decreasing temperature is calculated. Within a given composition interval, however, a geometrical percolation process is shown to block this reaction below a "percolation temperature" (corresponding to null cooling rate) where the liquid is irreversibly frozen into a glass. The liquid-glass "phase diagram" is established and kinetic arguments, involving "frustrated" finite clusters which are formed close to the percolation threshold, provide an evaluation of the experimentally measured "glass transition temperature" as a function of cooling rate. The validity of this one order parameter model is then discussed with the help of the irreversible thermodynamics theory of Prigogine.The formation of tetracoordinated glasses is explained by the formation of tetrahedral bonds, when the liquid temperature decreases, and represented by a "hole ordering" reaction. A general description of the structure of tetracoordinated glasses is thus achieved, which applies to amorphous silicon and germanium, 111 -V compounds, silica, amorphous water etc. Furthermore, an estimation of the temperature interval for the glass transformation of silica is obtained, which agrees well with experiment.The existence of frustrated clusters gives to glasses a composite structure in the "medium distance order", which could explain the "fractal nature" of glass fracture surfaces down to the nanometer scale.

The fault classification of a small sample of high dimension is challenging, especially for a nonlinear and non-Gaussian manufacturing process. In this paper, a similarity-based feature selection and sub-space neighbor vote method is proposed to solve this problem. To capture the dynamics, nonlinearity, and non-Gaussianity in the irregular time series data, high order spectral features, and fractal dimension features are extracted, selected, and stacked in a regular matrix. To address the problem of a small sample, all labeled fault data are used for similarity decisions for a specific fault type. The distances between the new data and all fault types are calculated in their feature subspaces. The new data are classified to the nearest fault type by majority probability voting of the distances. Meanwhile, the selected features, from respective measured variables, indicate the cause of the fault. The proposed method is evaluated on a publicly available benchmark of a real semiconductor etching dataset. It is demonstrated that by using the high order spectral features and fractal dimensionality features, the proposed method can achieve more than 84% fault recognition accuracy. The resulting feature subspace can be used to match any new fault data to the fingerprint feature subspace of each fault type, and hence can pinpoint the root cause of a fault in a manufacturing process.

Classification is an important task in time series mining. It is often reported in the literature that nearest neighbor classifiers perform quite well in time series classification, especially if the distance measure properly deals with invariances required by the domain. Complexity invariance was recently introduced, aiming to compensate from a bias towards classes with simple time series representatives in nearest neighbor classification. To this end, a complexity correcting factor based on the ratio of the more complex to the simpler series was proposed. The original formulation uses the length of the rectified time series to estimate its complexity. In this paper the authors investigate an alternative complexity estimate, based on fractal dimension. Results show that this alternative is very competitive with the original proposal, and has a broader application as it does neither depend on the number of points in the series nor on a previous normalization. Furthermore, these results also verify, using a different formulation, the validity of complexity invariance in time series classification.

AbstractThe fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance.

Optical coherence tomography is a high resolution, rapid, and noninvasive diagnostic tool for angle closure glaucoma. In this paper, we present a new strategy for the classification of the angle closure glaucoma using morphological shape analysis of the iridocorneal angle. The angle structure configuration is quantified by the following six features: (1) mean of the continuous measurement of the angle opening distance; (2) area of the trapezoidal profile of the iridocorneal angle centered at Schwalbe's line; (3) mean of the iris curvature from the extracted iris image; (4) complex shape descriptor, fractal dimension, to quantify the complexity, or changes of iridocorneal angle; (5) ellipticity moment shape descriptor; and (6) triangularity moment shape descriptor. Then, the fuzzyknearest neighbor (fkNN) classifier is utilized for classification of angle closure glaucoma. Two hundred and sixty-four swept source optical coherence tomography (SS-OCT) images from 148 patients were analyzed in this study. From the experimental results, the fkNN reveals the best classification accuracy (99.11±0.76%) and AUC (0.98±0.012) with the combination of fractal dimension and biometric parameters. It showed that the proposed approach has promising potential to become a computer aided diagnostic tool for angle closure glaucoma (ACG) disease.

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

The authors build on a recent development in urban geographic theory, providing evidence of an oscillatory behavior in spatiotemporal patterns of urban growth. With the aid of remotely sensed data, the spatial extent of urban areas in the Houston (USA) metropolitan region from 1974 to 2002 was analyzed by spatial metrics. Regularities in the spatial urban growth pattern were identified with temporal periods as short as thirty years by means of spatial metric values, including mean nearest-neighbor distance, mean patch area, total number of urban patches, and mean patch fractal dimension. Through changes in these values, a distinct oscillation between phases of diffusion and coalescence in urban growth was revealed. The results suggest that the hypothesized process of diffusion and coalescence may occur over shorter time periods than previously thought, and that the patterns are readily observable in real-world systems.

Abstract The properties of blown polyethylene (PE) films depend on various factors, including crystallinity, morphology, and orientation, in addition to chemical composition. It has been shown that the optical properties are strongly influenced by surface morphology. In this work, non-contact atomic force microscopy (AFM) and polarized light microscopy (PLM) were used to visualize surface and bulk morphology. Various techniques, such as surface and line roughness, surface and line fractal dimension, pair-correlation function and nearest neighbor distance distribution function, are employed to quantify the description of morphology and to compare the morphological characteristics of a number of polyethylene (PE) films of commercial interest. A comprehensive quantitative analysis of surface topography has been performed. The co-monomer of the PE resins was found to play a significant role in the formation and the orientation of spherulite-like domains. The film cross-section microstructure has been evaluated qualitatively by using both AFM and PLM. However, quantitative analysis of bulk morphology cannot be obtained due to knife effects.

Abstract. 1. The conference The third conference on "Nonlinear VAriability in Geophysics: scaling and multifractal processes" (NVAG 3) was held in Cargese, Corsica, Sept. 10-17, 1993. NVAG3 was joint American Geophysical Union Chapman and European Geophysical Society Richardson Memorial conference, the first specialist conference jointly sponsored by the two organizations. It followed NVAG1 (Montreal, Aug. 1986), NVAG2 (Paris, June 1988; Schertzer and Lovejoy, 1991), five consecutive annual sessions at EGS general assemblies and two consecutive spring AGU meeting sessions. As with the other conferences and workshops mentioned above, the aim was to develop confrontation between theories and experiments on scaling/multifractal behaviour of geophysical fields. Subjects covered included climate, clouds, earthquakes, atmospheric and ocean dynamics, tectonics, precipitation, hydrology, the solar cycle and volcanoes. Areas of focus included new methods of data analysis (especially those used for the reliable estimation of multifractal and scaling exponents), as well as their application to rapidly growing data bases from in situ networks and remote sensing. The corresponding modelling, prediction and estimation techniques were also emphasized as were the current debates about stochastic and deterministic dynamics, fractal geometry and multifractals, self-organized criticality and multifractal fields, each of which was the subject of a specific general discussion. The conference started with a one day short course of multifractals featuring four lectures on a) Fundamentals of multifractals: dimension, codimensions, codimension formalism, b) Multifractal estimation techniques: (PDMS, DTM), c) Numerical simulations, Generalized Scale Invariance analysis, d) Advanced multifractals, singular statistics, phase transitions, self-organized criticality and Lie cascades (given by D. Schertzer and S. Lovejoy, detailed course notes were sent to participants shortly after the conference). This was followed by five days with 8 oral sessions and one poster session. Overall, there were 65 papers involving 74 authors. In general, the main topics covered are reflected in this special issue: geophysical turbulence, clouds and climate, hydrology and solid earth geophysics. In addition to AGU and EGS, the conference was supported by the International Science Foundation, the Centre Nationale de Recherche Scientifique, Meteo-France, the Department of Energy (US), the Commission of European Communities (DG XII), the Comite National Francais pour le Programme Hydrologique International, the Ministere de l'Enseignement Superieur et de la Recherche (France). We thank P. Hubert, Y. Kagan, Ph. Ladoy, A. Lazarev, S.S. Moiseev, R. Pierrehumbert, F. Schmitt and Y. Tessier, for help with the organization of the conference. However special thanks goes to A. Richter and the EGS office, B. Weaver and the AGU without whom this would have been impossible. We also thank the Institut d' Etudes Scientifiques de Cargese whose beautiful site was much appreciated, as well as the Bar des Amis whose ambiance stimulated so many discussions. 2. Tribute to L.F. Richardson With NVAG3, the European geophysical community paid tribute to Lewis Fry Richardson (1881-1953) on the 40th anniversary of his death. Richardson was one of the founding fathers of the idea of scaling and fractality, and his life reflects the European geophysical community and its history in many ways. Although many of Richardson's numerous, outstanding scientific contributions to geophysics have been recognized, perhaps his main contribution concerning the importance of scaling and cascades has still not received the attention it deserves. Richardson was the first not only to suggest numerical integration of the equations of motion of the atmosphere, but also to attempt to do so by hand, during the First World War. This work, as well as a presentation of a broad vision of future developments in the field, appeared in his famous, pioneering book "Weather prediction by numerical processes" (1922). As a consequence of his atmospheric studies, the nondimensional number associated with fluid convective stability has been called the "Richardson number". In addition, his book presents a study of the limitations of numerical integration of these equations, it was in this book that - through a celebrated poem - that the suggestion that turbulent cascades were the fundamental driving mechanism of the atmosphere was first made. In these cascades, large eddies break up into smaller eddies in a manner which involves no characteristic scales, all the way from the planetary scale down to the viscous scale. This led to the Richardson law of turbulent diffusion (1926) and tot he suggestion that particles trajectories might not be describable by smooth curves, but that such trajectories might instead require highly convoluted curves such as the Peano or Weierstrass (fractal) curves for their description. As a founder of the cascade and scaling theories of atmospheric dynamics, he more or less anticipated the Kolmogorov law (1941). He also used scaling ideas to invent the "Richardson dividers method" of successively increasing the resolution of fractal curves and tested out the method on geographical boundaries (as part of his wartime studies). In the latter work he anticipated recent efforts to study scale invariance in rivers and topography. His complex life typifies some of the hardships that the European scientific community has had to face. His educational career is unusual: he received a B.A. degree in physics, mathematics, chemistry, biology and zoology at Cambridge University, and he finally obtained his Ph.D. in mathematical psychology at the age of 47 from the University of London. As a conscientious objector he was compelled to quit the United Kingdom Meteorological Office in 1920 when the latter was militarized by integration into the Air Ministry. He subsequently became the head of a physics department and the principal of a college. In 1940, he retired to do research on war, which was published posthumously in book form (Richardson, 1963). This latter work is testimony to the trauma caused by the two World Wars and which led some scientists including Richardson to use their skills in rational attempts to eradicate the source of conflict. Unfortunately, this remains an open field of research. 3. The contributions in this special issue Perhaps the area of geophysics where scaling ideas have the longest history, and where they have made the largest impact in the last few years, is turbulence. The paper by Tsinober is an example where geometric fractal ideas are used to deduce corrections to standard dimensional analysis results for turbulence. Based on local spontaneous breaking of isotropy of turbulent flows, the fractal notion is used in order to deduce diffusion laws (anomalous with respect to the Richardson law). It is argued that his law is ubiquitous from the atmospheric boundary layer to the stratosphere. The asymptotic intermittency exponent i hypothesized to be not only finite but to be determined by the angular momentum flux. Schmitt et al., Chigirinskaya et al. and Lazarev et al. apply statistical multifractal notions to atmospheric turbulence. In the former, the formal analogy between multifractals and thermodynamics is exploited, in particular to confirm theoretical predictions that sample-size dependent multifractal phase transitions occur. While this quantitatively explains the behavior of the most extreme turbulent events, it suggests that - contrary to the type of multifractals most commonly discussed in the literature which are bounded - more violent (unbounded) multifractals are indeed present in the atmospheric wind field. Chigirinskaya et al. use a tropical rather than mid-latitude set to study the extreme fluctuations form yet another angle: That of coherent structures, which, in the multifractal framework, are identified with singularities of various orders. The existence of a critical order of singularity which distinguishes violent "self-organized critical structures" was theoretically predicted ten years ago; here it is directly estimated. The second of this two part series (Lazarev et al.) investigates yet another aspect of tropical atmospheric dynamics: the strong multiscaling anisotropy. Beyond the determination of universal multifractal indices and critical singularities in the vertical, this enables a comparison to be made with Chigirinskaya et al.'s horizontal results, requiring an extension of the unified scaling model of atmospheric dynamics. Other approaches to the problem of geophysical turbulence are followed in the papers by Pavlos et al., Vassiliadis et al., Voros et al. All of them share a common assumption that a very small number of degrees of freedom (deterministic chaos) might be sufficient for characterizing/modelling the systems under consideration. Pavlos et al. consider the magnetospheric response to solar wind, showing that scaling occurs both in real space (using spectra), and also in phase space; the latter being characterized by a correlation dimension. The paper by Vassiliadis et al. follows on directly by investigating the phase space properties of power-law filtered and rectified gaussian noise; the results further quantify how low phase space correlation dimensions can occur even with very large number of degrees of freedom (stochastic) processes. Voros et al. analyze time series of geomagnetic storms and magnetosphere pulsations, also estimating their correlation dimensions and Lyapounov exponents taking special care of the stability of the estimates. They discriminate low dimensional events from others, which are for instance attributed to incoherent waves. While clouds and climate were the subject of several talks at the conference (including several contributions on multifractal clouds), Cahalan's contribution is the only one in this special issue. Addressing the fundamental problem of the relationship of horizontal cloud heterogeneity and the related radiation fields, he first summarizes some recent numerical results showing that even for comparatively thin clouds that fractal heterogeneity will significantly reduce the albedo. The model used for the distribution of cloud liquid water is the monofractal "bounded cascade" model, whose properties are also outlined. The paper by Falkovich addresses another problem concerning the general circulation: the nonlinear interaction of waves. By assuming the existence of a peak (i.e. scale break) at the inertial oscillation frequency, it is argued that due to remarkable cancellations, the interactions between long inertio-gravity waves and Rossby waves are anomalously weak, producing a "wave condensate" of large amplitude so that wave breaking with front creation can occur. Kagan et al., Eneva and Hooge et al. consider fractal and multifractal behaviour in seismic events. Eneva estimates multifractal exponents of the density of micro-earthquakes induced by mining activity. The effects of sample limitations are discussed, especially in order to distinguish between genuine from spurious multifractal behaviour. With the help of an analysis of the CALNET catalogue, Hooge et al. points out, that the origin of the celebrated Gutenberg-Richter law could be related to a non-classical Self-Organized Criticality generated by a first order phase transition in a multifractal earthquake process. They also analyze multifractal seismic fields which are obtained by raising earthquake amplitudes to various powers and summing them on a grid. In contrast, Kagan, analyzing several earthquake catalogues discussed the various laws associated with earthquakes. Giving theoretical and empirical arguments, he proposes an additive (monofractal) model of earthquake stress, emphasizing the relevance of (asymmetric) stable Cauchy probability distributions to describe earthquake stress distributions. This would yield a linear model for self-organized critical earthquakes. References: Kolmogorov, A.N.: Local structure of turbulence in an incompressible liquid for very large Reynolds number, Proc. Acad. Sci. URSS Geochem. Sect., 30, 299-303, 1941. Perrin, J.: Les Atomes, NRF-Gallimard, Paris, 1913. Richardson, L.F.: Weather prediction by numerical process. Cambridge Univ. Press 1922 (republished by Dover, 1965). Richardson, L.F.: Atmospheric diffusion on a distance neighbour graph. Proc. Roy. of London A110, 709-737, 1923. Richardson, L.F.: The problem of contiguity: an appendix of deadly quarrels. General Systems Yearbook, 6, 139-187, 1963. Schertzer, D., Lovejoy, S.: Nonlinear Variability in Geophysics, Kluwer, 252 pp, 1991.

This study collected and analyzed dynamic spatial data of eight traditional villages scattered in different regions of China. A multi-temporal analysis of morphological metrics of spatial patterns and a regression analysis of the morphological evolution were used to analyze and contrast the historical spatial processes of different villages. These were then compared using patch texture and rural macro-morphology perspectives. This led to an assessment of the general laws and trends associated with rural spatial processes. (1) There has been a significant shift in the stability of rural spatial development since the founding of the People’s Republic of China (PRC). (2) Most small and medium-sized villages have maintained a relatively stable spatial texture, while large villages have changed significantly. (3) The mean and variance of the patch area, and the Euclidean nearest-neighbor distance, are correlated in some cases. (4) The mode of rural expansion may be relevant to limitations in the total area of growth. (5) The fractal dimension of the rural macro-morphology may follow a morphological order of oscillation around the equilibrium level. (6) The common mean value of the projected area of rural building patches is expected to be 100 m2.

Shockable ventricular arrhythmias (VAs) such as ventricular tachycardia (VT) and ventricular fibrillation (VFib) are the life-threatening conditions requiring immediate attention. Cardiopulmonary resuscitation (CPR) and defibrillation are the significant immediate recommended treatments for these shockable arrhythmias to obtain the return of spontaneous circulation. However, accurate classification of these shockable VAs from nonshockable ones is the key step during defibrillation by automated external defibrillator (AED). Therefore, in this work, we have proposed a novel algorithm for an automated differentiation of shockable and nonshockable VAs from electrocardiogram (ECG) signal. The ECG signals are segmented into 5, 8 and 10[Formula: see text]s. These segmented ECGs are subjected to four levels of discrete wavelet transformation (DWT). Various nonlinear features such as approximate entropy ([Formula: see text], signal energy ([Formula: see text]), Fuzzy entropy ([Formula: see text]), Kolmogorov Sinai entropy ([Formula: see text], permutation entropy ([Formula: see text]), Renyi entropy ([Formula: see text]), sample entropy ([Formula: see text]), Shannon entropy ([Formula: see text]), Tsallis entropy ([Formula: see text]), wavelet entropy ([Formula: see text]), fractal dimension ([Formula: see text]), Kolmogorov complexity ([Formula: see text]), largest Lyapunov exponent ([Formula: see text]), recurrence quantification analysis (RQA) parameters ([Formula: see text]), Hurst exponent ([Formula: see text]), activity entropy ([Formula: see text]), Hjorth complexity ([Formula: see text]), Hjorth mobility ([Formula: see text]), modified multi scale entropy ([Formula: see text]) and higher order statistics (HOS) bispectrum ([Formula: see text]) are obtained from the DWT coefficients. Later, these features are subjected to sequential forward feature selection (SFS) method and selected features are then ranked using seven ranking methods namely, Bhattacharyya distance, entropy, Fuzzy maximum relevancy and minimum redundancy (mRMR), receiver operating characteristic (ROC), Student’s [Formula: see text]-test, Wilcoxon and ReliefF. These ranked features are supplied independently into the [Formula: see text]-Nearest Neighbor (kNN) classifier. Our proposed system achieved maximum accuracy, sensitivity and specificity of (i) 97.72%, 94.79% and 98.74% for 5[Formula: see text]s, (ii) 98.34%, 95.49% and 99.14% for 8[Formula: see text]s and (iii) 98.32%, 95.16% and 99.20% for 10[Formula: see text]s of ECG segments using only ten features. The integration of the proposed algorithm with ECG acquisition systems in the intensive care units (ICUs) can help the clinicians to decipher the shockable and nonshockable life-threatening arrhythmias accurately. Hence, doctors can use the CPR or AED immediately and increase the chance of survival during shockable life-threatening arrhythmia intervals.

We consider the equiprobable distribution of spanning trees on the square lattice. All bonds of each tree can be oriented uniquely with respect to an arbitrary chosen site called the root. The problem of predecessors is to find the probability that a path along the oriented bonds passes sequentially fixed sites i and j. The conformal field theory for the Potts model predicts the fractal dimension of the path to be 5/4. Using this result, we show that the probability in the predecessors problem for two sites separated by large distance r decreases as P(r) ∼ r −3/4. If sites i and j are nearest neighbors on the square lattice, the probability P(1) = 5/16 can be found from the analytical theory developed for the sandpile model. The known equivalence between the loop erased random walk (LERW) and the directed path on the spanning tree states that P(1) is the probability for the LERW started at i to reach the neighboring site j. By analogy with the self-avoiding walk, P(1) can be called the return probability. Extensive Monte-Carlo simulations confirm the theoretical predictions.