Human brain response is the result of the overall ability of the brain in analyzing different internal and external stimuli and thus making the proper decisions. During the last decades scientists have discovered more about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research, there were fewer efforts which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling and prediction of the human EEG signal, as an alert state of overall human brain activity monitoring, upon receiving external stimuli, based on fractional diffusion equations. The results of this modeling show very good agreement with the real human EEG signal and thus this model can be used for many types of applications such as prediction of seizure onset in patient with epilepsy.
Fractal dimensions (FDs) are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi's fractal dimension was measured in circumferential direction (FDC) with respect to optic disk (OD), in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES) database and compared against spectrum fractal dimension (SFD) and box-counting (BC) dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H = 5.80, P = 0.016, α = 0.05) compared with SFD (H = 0.51, P = 0.475, α = 0.05) and BC (H = 0.41, P = 0.520, α = 0.05) with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed.
Coronary Artery Disease (CAD), caused by the buildup of plaque on the inside of the coronary arteries, has a high mortality rate. To efficiently detect this condition from echocardiography images, with lesser inter-observer variability and visual interpretation errors, computer based data mining techniques may be exploited. We have developed and presented one such technique in this paper for the classification of normal and CAD affected cases. A multitude of grayscale features (fractal dimension, entropies based on the higher order spectra, features based on image texture and local binary patterns, and wavelet based features) were extracted from echocardiography images belonging to a huge database of 400 normal cases and 400 CAD patients. Only the features that had good discriminating capability were selected using t-test. Several combinations of the resultant significant features were used to evaluate many supervised classifiers to find the combination that presents a good accuracy. We observed that the Gaussian Mixture Model (GMM) classifier trained with a feature subset made up of nine significant features presented the highest accuracy, sensitivity, specificity, and positive predictive value of 100%. We have also developed a novel, highly discriminative HeartIndex, which is a single number that is calculated from the combination of the features, in order to objectively classify the images from either of the two classes. Such an index allows for an easier implementation of the technique for automated CAD detection in the computers in hospitals and clinics.
The fractal dimension is a global measure of complexity and is useful for quantifying anatomical structures, including the retinal vascular network. A previous study found a linear declining trend with aging on the retinal vascular fractal dimension (DF); however, it was limited to the older population (49 years and older). This study aimed to investigate the possible models of the fractal dimension changes from young to old subjects (10-73 years). A total of 215 right-eye retinal samples, including those of 119 (55%) women and 96 (45%) men, were selected. The retinal vessels were segmented using computer-assisted software, and non-vessel fragments were deleted. The fractal dimension was measured based on the log-log plot of the number of grids versus the size. The retinal vascular DF was analyzed to determine changes with increasing age. Finally, the data were fitted to three polynomial models. All three models are statistically significant (Linear: R2 = 0.1270, 213 d.f., p
Understanding the relationship between microbial community and mechanism of aerobic granulation could enable wider applications of granules for high-strength wastewater treatment. The majority of granulation studies principally determine the engineering aspects of granules formation with little emphasis on the microbial diversity. In this study, three identical reactors namely R1, R2 and R3 were operated using POME at volumetric loadings of 1.5, 2.5 and 3.5 kg COD m(-3) d(-1), respectively. Aeration was provided at a volumetric flow rate of 2.5 cms(-1). Aerobic granules were successfully developed in R2 and R3 while bioflocs dominated R1 until the end of experiments. Fractal dimension (D(f)) averaged at 1.90 suggesting good compactness of granules. The PCR-DGGE results indicated microbial evolutionary shift throughout granulation despite different operating OLRs based on decreased Raup and Crick similarity indices upon mature granule formation. The characteristics of aerobic granules treating high strength agro-based wastewater are determined at different volumetric loadings.
Due to their high ionic conductivity, solid polymer electrolyte (SPE) systems have attracted wide spread attention as the most appropriate choice to fabricate all-solid-state electrochemical devices, namely batteries, sensors and fuel cells. In this work, ion conductive polymer electrolyte membranes have been prepared for battery fabrication. However, fractals were found to grow in these polymer electrolyte membranes weeks after they were prepared. It was believed that the formation of fractal aggregates in these membranes were due to ionic movement. The discovery of fractal growth pattern can be used to understand the effects of such phenomenon in the polymer electrolyte membranes. Digital images of the fractal growth patterns were taken and a simulation model was developed based on the Brownian motion theory and a fractal dialect known as L-system. A computer coding has been designed to simulate and visualize the fractal growth.
Studies conducted on the various geometric properties of skeletons of water bodies have shown highly promising results. However, these studies were made under the assumption that water bodies were static objects and that they remained constant over time. Water bodies are actually dynamic objects; they go through significant spatio-temporal changes due to drought and flood. In this study, the characterization of skeletons of simulated drought and flood of water bodies was performed. It was observed that as the drought level increased from 1 to 9, the average length of the skeletons decreased due to reduction in the size of the water bodies and increase in the number of water bodies. As the drought level increased from 9 to 15, the average length of the skeletons increased further due to vanishing of small water bodies. Flood caused an increase in the average length of the skeletons due to merging of adjacent water bodies. Power law relationships were observed between the average length of the skeletons of the simulated drought/flood and the level of drought/flood. The scaling exponent of these power laws which was named as a fractal dimension, indicated the rate of change of the average length of the skeletons of simulated drought/flood of water bodies over varying levels of drought/flood. However, errors observed in the goodness of fit of the plots indicated that monofractals were not sufficient to characterise the skeletons of simulated drought and flood of water bodies. Multifractals and lacunarity analysis were required for more accurate characterisation.
This paper introduces a method for modification of the formula of the fractal box counting dimension. The method is based on the utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features e.g. sea surface and look-alikes in RADARSAT-1 SAR data. The result showed that the new formula of the fractal box counting dimension was able to discriminate between oil spills and look-alike areas. The low wind area had the highest fractal dimension peak of 2.9, as compared to the oil slick and the surrounding rough sea. The maximum error standard deviation of the low wind area was 0.68 which performed with a 2.9 fractal dimension value.
Alumina powder was synthesized from an aluminum precursor and studied using small angle neutron scattering (SANS) technique and complemented with transmission electron microscope (TEM). XRD measurement confirmed that the alumina produced was of high purity and highly crystalline D-phase. SANS examination indicates the formation of mass fractals microstructures with fractal dimension of about 2.8 on the alumina powder.
Training methodology of the Back Propagation Network (BPN) is well documented. One aspect of BPN that requires investigation is whether or not the BPN would get trained for a given training data set and architecture. In this paper the behavior of the BPN is analyzed during its training phase considering convergent and divergent training data sets. Evolution of the weights during the training phase was monitored for the purpose of analysis. The evolution of weights was plotted as return map and was characterized by means of fractal dimension. This fractal dimensional analysis of the weight evolution trajectories is used to provide a new insight to understand the behavior of BPN and dynamics in the evolution of weights.