Fractal Analysis Techniques Research Articles

Monitoring of Wild Pseudomonas Biofilm Strain Conditions Using Statistical Characterization of Scanning Electron Microscopy Images

The present paper proposes a novel method of quantification of the variation in biofilm architecture, in correlation with the alteration of growth conditions that include, variations of substrate and conditioning layer. The polymeric biomaterial serving as substrates are widely used in implants and indwelling medical devices, while the plasma proteins serve as the conditioning layer. The present method uses descriptive statistics of FESEM images of biofilms obtained during a variety of growth conditions. We aim to explore here the texture and fractal analysis techniques, to identify the most discriminatory features which are capable of predicting the difference in biofilm growth conditions. We initially extract some statistical features of biofilm images on bare polymer surfaces, followed by those on the same substrates adsorbed with two different types of plasma proteins, viz. Bovine serum albumin (BSA) and Fibronectin (FN), for two different adsorption times. The present analysis has the potential to act as a futuristic technology for developing a computerized monitoring system in hospitals with automated image analysis and feature extraction, which may be used to predict the growth profile of an emerging biofilm on surgical implants or similar medical applications.

Burr height monitoring while drilling CFRP/titanium/aluminium stacks

In the aerospace industry, deburring operations are often difficult to achieve and can be very costly. Hence, burrs generated during the machining should be studied. In this research, the drilling operations were performed and analysed for a stack composed of carbon fibre reinforced polymer (CFRP), titanium and aluminium alloys, using three cutting feeds and three cutting speeds for each material. A monitoring method is presented to predict the burr heights in the titanium and aluminium layers. The cutting force signals obtained during the drilling of the CFRP layer were analysed using the regularization fractal analysis, resulting in an estimation of the fractal dimension. This fractal analysis was optimized in order to monitor the clearance tool wear and the burr heights. The burr heights, measured at the outlet of the titanium and aluminium alloys, were observed in terms of the thrust force, the torque, the hole diameter and circularity, and the clearance tool wear. This fractal analysis technique can be implemented for an on-line control to predict the generated burr heights in the metallic layers while drilling the previous CFRP layer.

Exploring the efficiency of applying fractal analysis for the process of decorative stone quality control

The technique of fractal analysis of regularities in the fracturing formation for various deposits or their sections, which is based on the comparison of values of fractal dimensionality of the roses of fracturing, was developed. The groups of labradorite deposits were distinguished by index of fractal dimensionality, which allows developing standard technological solutions for each group in order to enhance the effectiveness of quality and productivity control over technological complexes. A map of spatial variability in fractal dimensionality of fracturing in the labradorite deposits of Ukraine was produced, the use of which will make it possible to increase efficiency of discovering new labradorite deposits, which will meet certain quality requirements The construction of this map will allow enhancing efficiency of the interpretation of conditions for the formation of particular deposits. The patterns of change in fractal dimensionality at the different structural levels were established and the methods for their prediction were developed, which will make it possible, by the results of exploring fractal dimensionality at one of the structural level, to predict their values for others to optimize the process of control over geological exploration and extraction operations. As a result of the performed experimental studies, the influence of fractal dimensionality of fracturing in the blast-hole drilling zone on the productivity of the process was proved. We created objective function of optimal process to control technological processes, based on geostructural and technological indices that were evaluated by generalizing index of fractal dimensionality. The objective function of optimal process of drilling the fractured array, which includes indices of fractal dimensionality of the drilling zone, was proposed.

Physical characterization of freeze-dried foam prepared from aloe vera gel and guar gum

Background: Foams are colloidal dispersions of a gas suspended in a dispersing phase, which consisting of a semi-freeze-dried or viscous liquid phase. The physical properties of food foams are the result of the bubble characteristics and their spatial arrangement. Objectives: The aim of this work was to obtain foams of A. vera gel and guar gum and describe the changes in their physical properties and microstructure during freeze-drying using the fractal dimension concept and image analysis techniques. Methods: The porosity, density, and volume expansion factor of the fresh foams that were based on the A. vera foams were determined. The kinetics of foam texture, color, porosity and microstructure of the freeze-dried foams were obtained. The fractal texture dimension of surface (FDSDBC) and microstructure (FDESEM) of the foams were determined as indicators of structural changes after freeze-drying. The guar gum concentrations used to obtain the A. vera prefoam were expressed in w/w as F1 (control simple without gum), F2 (2%), F3 (4%) and F4 (6%). Results: We obtained stable freeze-dried foams of Aloe vera gel and guar gum. The porosity, density and volume expansion factor of the fresh and freeze-dried foams were affected by the addition of the guar gum. Changes in the topology of the freeze-dried foam surface during the drying process resulted in a high rugosity compared with the original smooth surface. The microstructure of the dried foam samples suggested a relationship between the gum concentration of the prefoam A. vera gel mixture and the physical properties before and after freeze-drying, such as an increase in the microstructural alterations and surface roughness during freeze-drying. The roughness of the freeze-dried foam surface, described by the FDSDBC represented the macroscopic physical changes of the samples and correlated with the changes in the foam microstructure, which were described by the fractal dimension of the Environmental Scanning Electron Microscopy ESEM microphotographs (FDESEM). Conclusions: The digital analysis of the structure and porosity of the freeze-dried foam can be used to quantify the effect of gum concentrations on the morphological features and physical properties of foams during freeze-drying.

Complexity analysis of human physiological signals based on case studies

This work focuses on methods for investigation of physiological time series based on complexity analysis. It is a part of a wider programme to determine non-invasive markers for healthy ageing. We consider two case studies investigated with actigraphy: (a) sleep and alternations with insomnia, and (b) ageing effects on mobility patterns. We illustrate, using these case studies, the application of fractal analysis to the investigation of regulation patterns and control, and change of physiological function. In the first case study, fractal analysis techniques were implemented to study the correlations present in sleep actigraphy for individuals suffering from acute insomnia in comparison with healthy controls. The aim was to investigate if complexity analysis can detect the onset of adverse health-related events. The subjects with acute insomnia displayed significantly higher levels of complexity, possibly a result of too much activity in the underlying regulatory systems. The second case study considered mobility patterns during night time and their variations with age. It showed that complexity metrics can identify change in physiological function with ageing. Both studies demonstrated that complexity analysis can be used to investigate markers of health, disease and healthy ageing.

Towards an Automated Zebrafish-based Toxicity Test Model Using Machine Learning

Abstract Zebrafish animal is considered as one of the most suitable animals to test toxicity of compounds due many features such as transparency and a large number of embryos produced in each mating. The main problem of the zebrafish-based toxicity test is the manual inspection of thousands of animals images in different phases and this is not feasible enough for the analysis, i.e. it is slow and may be inaccurate process. To help addressing this problem, in this paper, an automated classification of alive (healthy) and coagulant (died because of toxic compounds) zebrafish embryos are proposed. The embryos’ images are used to extract some features using the Segmentation-based Fractal Texture Analysis (SFTA) technique. The Rotation Forest classifier is then used to match between testing and training features (i.e. to classify alive and coagulant embryos). The experiments have proved that choosing threshold value of SFTA technique and the size of the rotation forest classifier have a great impact on the classification accuracy. With accuracy around 99.98%, the experimental results have showed that the proposed model is a very promising step toward a fully automated toxicity test during drug discovery.

Stock Market Reaction during the Global Financial Crisis in India: Fractal Analysis

The Bombay Stock Exchange is the most popular and also the oldest stock exchange in Asia. It has the major number of listed companies in the world. In September 2008, the Sensex experienced huge falls, along with other markets around the world. Financial markets have become ever larger and financial crises have become more threatening to society. The devastating consequences of these crises stimulated the development of methods for predicting financial turmoil. New approaches to stock market prediction are considered on the basis of the intensity of stock index fluctuations estimated by fractal analysis techniques. Fractal analysis is used to analyse the financial time series. This article examined the fractal dimension in S&P BSE Sensex for pre- and post-recession periods—2004–2008 and 2008–2012 respectively.

Complexity analysis of sleep and alterations with insomnia based on non-invasive techniques

For the first time, fractal analysis techniques are implemented to study the correlations present in sleep actigraphy for individuals suffering from acute insomnia with comparisons made against healthy subjects. Analysis was carried out for 21 healthy individuals with no diagnosed sleep disorders and 26 subjects diagnosed with acute insomnia during night-time hours. Detrended fluctuation analysis was applied in order to look for 1/f-fluctuations indicative of high complexity. The aim is to investigate whether complexity analysis can differentiate between people who sleep normally and people who suffer from acute insomnia. We hypothesize that the complexity will be higher in subjects who suffer from acute insomnia owing to increased night-time arousals. This hypothesis, although contrary to much of the literature surrounding complexity in physiology, was found to be correct-for our study. The complexity results for nearly all of the subjects fell within a 1/f-range, indicating the presence of underlying control mechanisms. The subjects with acute insomnia displayed significantly higher correlations, confirmed by significance testing-possibly a result of too much activity in the underlying regulatory systems. Moreover, we found a linear relationship between complexity and variability, both of which increased with the onset of insomnia. Complexity analysis is very promising and could prove to be a useful non-invasive identifier for people who suffer from sleep disorders such as insomnia.

Evaluation of primary phase morphology of cooling slope cast Al-Si-Mg alloy samples using image texture analysis

Rheopressure die casting is one of the newest casting processes of present era for manufacturing of near-net-shaped cast components with improved mechanical properties and high-dimensional accuracy. Rheopressure die casting demands especially prepared semi-solid alloy slurry having nearly globular primary Al phase. In this study, a cooling slope has been employed to produce semi-solid slurry of Al-Si-Mg (A356) alloy and successively cast in a metallic mould. Image texture analysis techniques have been implemented for accurate evaluation of the primary phase morphology of cast samples. In this research, efforts have been made to apply fractal analysis and run-length statistical analysis techniques for automatic characterization of optical micrographs of cast samples produced at different processing conditions.

Multifractal analysis of the rainfall time distribution on the metropolitan area of Barcelona (Spain)

In most of the studies on scale properties in the rainfall process, multifractal behavior has been investigated without taking into account the different rain generation mechanisms involved. However, it is known that rain processes are related to certain scales, determined by climatological characteristics as well as regional and local meteorological features. One of the implications derived from these correspondences is the possibility that the multifractal parameters of the rainfall could depend on the dominant precipitation generation mechanism. Fractal analysis techniques have been applied in this work to rainfall data recorded in the metropolitan area of Barcelona in the period 1994–2001, as well as to a selection of synoptic rainfall events registered in the same city in the period 1927–1992. The multifractal parameters obtained have been significantly different in each case probably showing the influence of the rain generation mechanisms involved. This influence has been revealed also in the analysis of the effects of seasonality on the multifractal behavior of rainfall in Barcelona.

Quantitating the subtleties of microglial morphology with fractal analysis

It is well established that microglial form and function are inextricably linked. In recent years, the traditional view that microglial form ranges between “ramified resting” and “activated amoeboid” has been emphasized through advancing imaging techniques that point to microglial form being highly dynamic even within the currently accepted morphological categories. Moreover, microglia adopt meaningful intermediate forms between categories, with considerable crossover in function and varying morphologies as they cycle, migrate, wave, phagocytose, and extend and retract fine and gross processes. From a quantitative perspective, it is problematic to measure such variability using traditional methods, but one way of quantitating such detail is through fractal analysis. The techniques of fractal analysis have been used for quantitating microglial morphology, to categorize gross differences but also to differentiate subtle differences (e.g., amongst ramified cells). Multifractal analysis in particular is one technique of fractal analysis that may be useful for identifying intermediate forms. Here we review current trends and methods of fractal analysis, focusing on box counting analysis, including lacunarity and multifractal analysis, as applied to microglial morphology.

A new definition of left ventricular compaction/noncompaction - the new gold-standard?

Background Abundant, abnormal myocardial trabeculae define left ventricular noncompaction (LVNC) but measurement is difficult and at least 5 techniques are described. We hypothesized that part of the reason for difficulties was that LV trabeculae were fractal in nature and beyond the simple geometry of 1 or 2 dimensional (2D) measurement. We designed and validated a new, rapid, clinically applicable method of measuring LV trabeculae based on fractal analysis. Methods We developed a fractal analysis technique for measuring LV trabeculation using CMR volume stack images. With no gold-standard for LV trabeculae, we validated the method on the actual compaction process itself

International Real Estate Review

Over the last decade, numerous factors including robust economic growth, population pressure, and the mounting need for office space among growth sectors such as information technology have placed significant upward pressure on Indian realty prices. The easing of government restrictions on foreign investments and venture capital into Indian real estate have provided an additional fillip to the real estate market in the country, and the confluence of such factors appears to have contributed to a speculative bubble in Indian real estate equities in the latter part of the decade. By using this bubble period as a case study, we test for the existence of long memory among real estate equities. For the January 2006-December 2008 period, we employ three self-affine fractal analysis techniques (classical rescaled range, roughness-length, and the variogram/structure function methods) to estimate the Hurst exponent, and find significant evidence of long memory in the Bombay Stock Exchange (BSE) Realty Index. Return persistence is further confirmed by the more powerful Lo¡¦s modified rescaled range analysis (MRSA), which is robust to short-term dependence. In addition to potential regulatory policy implications for this emerging market, our results have ramifications for modeling and forecasting returns, as well as for technical trading rules.

Evaluation of a fractal analysis technique for corrosion studies

Corrosion tests were performed to obtain electrochemical noise (EN) data during general and pitting corrosion in NaCl solutions for type 316 and 403 stainless steels. The data were analyzed by the Hurst parameter (HP) based on the rescaled range analysis. A correlation of the HP with the noise resistance was found in general corrosion, and the variability in published HP data is in part due to the difference in the value of noise resistance. The variability is also attributed to the difference in the amount of high frequency components in EN data. The HP is, however, a useful parameter for assessing the effectiveness of an inhibitor based on the characteristics of EN spectra, but not for identifying changes in the mode of corrosion in the case where the level of EN is low.

A Study of the Returns Behavior of Small Capitalization REITs

We analyze the daily returns on 63 real estate investment trusts (REITs) that comprise five US Small Cap REIT indices, and test for weak-form efficiency by estimating the Hurst exponent and fractal dimension. Fourteen of the 63 firms (or roughly 22% of the firms studied) fail to exhibit weak-form efficiency, based on Classical Rescaled Range Analysis. Two additional self-affine fractal analysis techniques (Roughness-Length and Variogram analyses) provide some support for this finding. In particular, it is found that a majority of the series for which weak-form efficiency is rejected are anti-persistent, with estimated Hurst exponents below 0.50.These results are further confirmed by Lo’s (1991) modified rescaled range analysis, which reveals significant memory at long lags. Overall, the results suggest inefficient pricing for a significant subset of REITs, with important implications for trading and for the modeling of REIT returns. .Some aspects of their returns behavior warrant further study.

Fractal MapReduce decomposition of sequence alignment

BackgroundThe dramatic fall in the cost of genomic sequencing, and the increasing convenience of distributed cloud computing resources, positions the MapReduce coding pattern as a cornerstone of scalable bioinformatics algorithm development. In some cases an algorithm will find a natural distribution via use of map functions to process vectorized components, followed by a reduce of aggregate intermediate results. However, for some data analysis procedures such as sequence analysis, a more fundamental reformulation may be required.ResultsIn this report we describe a solution to sequence comparison that can be thoroughly decomposed into multiple rounds of map and reduce operations. The route taken makes use of iterated maps, a fractal analysis technique, that has been found to provide a "alignment-free" solution to sequence analysis and comparison. That is, a solution that does not require dynamic programming, relying on a numeric Chaos Game Representation (CGR) data structure. This claim is demonstrated in this report by calculating the length of the longest similar segment by inspecting only the USM coordinates of two analogous units: with no resort to dynamic programming.ConclusionsThe procedure described is an attempt at extreme decomposition and parallelization of sequence alignment in anticipation of a volume of genomic sequence data that cannot be met by current algorithmic frameworks. The solution found is delivered with a browser-based application (webApp), highlighting the browser's emergence as an environment for high performance distributed computing.AvailabilityPublic distribution of accompanying software library with open source and version control at http://usm.github.com. Also available as a webApp through Google Chrome's WebStore http://chrome.google.com/webstore: search with "usm".

Reproducibility of 2D and 3D Fractal Analysis Techniques for the Assessment of Spatial Heterogeneity of Regional Blood Flow in Rectal Cancer

To characterize the two-dimensional (2D) and three-dimensional (3D) fractal properties of rectal cancer regional blood flow assessed by using volumetric helical perfusion computed tomography (CT) and to determine its reproducibility. Institutional review board approval and informed consent were obtained. Ten prospective patients (eight men, two women; mean age, 72.3 years) with rectal adenocarcinoma underwent two repeated volumetric helical perfusion CT studies (four-dimensional adaptive spiral mode, 11.4-cm z-axis coverage) without intervening treatment within 24 hours, with regional blood flow derived by using deconvolution analysis. Two-dimensional and 3D fractal analyses of the rectal tumor were performed, after segmentation from surrounding structures by using thresholding, to derive fractal dimension and fractal abundance. Reproducibility was quantitatively assessed by using Bland-Altman statistics. Two-dimensional and 3D lacunarity plots were also generated, allowing qualitative assessment of reproducibility. Statistical significance was at 5%. Mean blood flow was 63.50 mL/min/100 mL ± 8.95 (standard deviation). Good agreement was noted between the repeated studies for fractal dimension; mean difference was -0.024 (95% limits of agreement: -0.212, 0.372) for 2D fractal analysis and -0.024 (95% limits of agreement: -0.307, 0.355) for 3D fractal analysis. Mean difference for fractal abundance was -0.355 (95% limits of agreement: -0.869, 1.579) for 2D fractal analysis and -0.043 (95% limits of agreement: -1.154, 1.239) for 3D fractal analysis. The 95% limits of agreement were narrower for 3D than 2D analysis. Lacunarity plots also visually confirmed close agreement between repeat studies. Regional blood flow in rectal cancer exhibits fractal properties. Good reproducibility was achieved between repeated studies with 2D and 3D fractal analysis.

Correlation between Fractal Dimension and Impact Strength for Wood Plastic Composites

Polylactide (PLA)-based wood plastic composites (WPCs) were manufactured by extrusion blending followed by injection molding. The fracture surfaces created from the impact test were recorded with SEM. Fractal analysis has been used to calculate the fractal dimension of the fracture surfaces with four different fractal analysis techniques. Then, the correlation between the fractal dimension of the fracture surfaces and its impact strength of the PLA-based WPCs was investigated by the linear regression. The results showed that there is a positive correlation between the impact strength and the fractal dimension.

Fractal analysis of space-time variations in the epicentral field of earthquakes for several areas in the Baikal Rift Zone

Fractal analysis techniques were used to study space-time variations in the epicentral field of earthquakes for several areas in the Baikal Rift Zone (BRZ). In each area the epicentral field is found to be a system consisting of several subsystems in the shape of maxima of increased fractal dimension D s , which occurred approximately at the same locations with constant or variable periodicity. We detected simultaneity and migration in the appearance of some maxima of D s . Most local areas in the regions under study typically have an unformed type of epicentral field, to use A.V. Solonenko’s terminology, and this makes it difficult to predict the time of earthquake occurrence at a specified location using simple statistical methods. We used the variations in D s in different regions to study the behavior of the present-day seismotectonic process in the BRZ as a whole.

Monetary policy regimes in macroeconomic data: An application of fractal analysis

Macromonetary data are examined for behavioral stability over Alan Greenspan's tenure as chairman of the Federal Reserve System. Strong evidence of stochastic dependence is found using Lo's modified rescaled range tests, though not consistently over the earlier, as opposed to the later, subsample. This finding is suggestive of a change in fundamentals such as monetary policy. Then, five self-affine fractal analysis techniques for estimating the Hurst exponent, Mandelbrot-Lévy characteristic exponent, and fractal dimension are employed to explore the data's fractal properties. Techniques are rescaled-range, power-spectral density, roughness-length, variogram, and wavelet analysis. Formal hypothesis tests provide further evidence of a change in monetary policy between the 1989–1996 and 1997–2006 subperiods. This change is manifested both in the behavior and distribution of month-to-month changes in monetary aggregates, ratios, and multipliers, and in the behavior and distribution of macroeconomic data. Most series become significantly less antipersistent after the breakpoint than before. Strong evidence is presented that U.S. monetary policy became actively interventionist after December 1996, and that the effectiveness of the Federal Reserve System has been lowered compared to the earlier period.