Narrow Results

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be plagued by the maladaptive behavior of the players, we find that diversity among the players improves the system efficiency, though it slows the convergence to the steady state. Diversity causes a mild spread of resources at the transient state, but reduces the uneven distribution of resources in the steady state.

The chaotic complexity properties of semiconductor lasers in the chaotic synchronization systems are investigated numerically, based on the information theory based quantifier, the permutation entropy (PE). We find that, on the one hand, the degree of complexity for the master laser increases with the feedback strength firstly and then saturate at higher feedback strength, but are hardly affected by the feedback delay. On the other hand, for the slave laser, the complexity degree is closer to that for the master laser when the high quality chaos synchronization is obtained, which shows that, the PE method is a successful quantifier to evaluate the degree of complexity for the chaotic signals in chaos synchronization systems, and can be considered as a complementary tool to observe the synchronization quality.

Combat data collected from World War II and a cellular automaton combat model called MANA are shown to display fractal properties. This strongly supports our earlier hypotheses as to the nature of combat attrition data. It also provides a method by which we can judge a combat model's ability to produce realistic synthetic combat data. The data appear to display properties extremely similar to those of the fractal cascade models used to describe turbulent dynamics. Interestingly, the fractal parameters appear to depend on how the model is set up, implying that they are determined by the boundary and initial conditions. Examination of the dynamical rules used in the MANA model simulation suggests that the model entities need to respond to changes in the level of order on the battlefield grid for fractal behavior to occur. Such data imply that the entropy of the battlefield is dependent on the scale at which it is examined. We speculate that such formations in a military case effectively act to isolate the highest level of command from disorder in the lowest. If disorder within a force grows to the point where that force can no longer maintain a fractal-like distribution, the force distribution may tend to become uniformly random, effectively destroying its viability as a combat unit.

We have questioned whether a complex behavior, such as fish swimming, can be better described quantitatively as a sequence of discrete events or states than with classical kinematic measures which can be compromised by inherent variability. Here, the different states, expressed as combinations of symbols, were defined on the basis of the animal's location (A: periphery, and B: inner part of the aquarium) and speed (Fast and Slow). We observed that the distributions of time intervals spent in the successive states were not gaussian. Rather, they were fit by power laws associated with an underlying Lévy-like process which has more long intervals, primarily due to prolonged periods of relative inactivity. Furthermore, our data suggest that the swimming behavior can be attributed to interactions between two intrinsic systems. One is represented by the matrix of transition of probabilities between states and controls their sequential organization while the second, which is defined by interval distributions, determines the time spent in each state. This kinetic model detects subtle effects of low doses of neuroactive compounds, and identifies their specific locus of action. We propose that this paradigm can be applied to characterize normal behavior and its modifications by genetic or pharmacological manipulations.

Infantile hypertrophic pyloric stenosis (IHPS) is a common surgical condition of unknown etiology. The oral mucosal vascular networks of IHPS patients (n=25) and their unaffected parents showed lower blood vessel-free areas, as well as higher box-counting dimensions at two box size scales [D(1–46), D(1–15)], and relative Lempel-Ziv values (P<0.000001), as compared to those of gender- and age-matched controls. These findings may provide a useful phenotypical marker for identifying couples potentially at risk for the birth of an affected infant, while supporting the importance of a genetic component in this condition.

Multiscale sample entropy (MSE) of human electroencephalogram (EEG) data from patients under different pathological conditions of Alzheimer's disease (AD) was evaluated to measure the complexity of the signal. Quantifying the complexity level with respect to various temporal scales, MSE analysis provides a dynamical description of AD development. When compared to EEG data from normal subjects, EEG data from subjects with mild cognitive impairment (MCI) showed nearly the same complexity profile, but a scale discrepancy which may occur from a spectral abnormality. EEG data from severe AD patients showed a loss of complexity over the wide range of time scales, indicating a destruction of nonlinear structures in brain dynamics. We compare the MSE method and spectral analysis to propose that nonlinear dynamical approach combining a multiscale method is crucial for revealing AD mechanisms.

The heart beat data recorded from samples before and during meditation are analyzed using two different scaling analysis methods. These analyses revealed that meditation severely affects the long range correlation of heart beat of a normal heart. Moreover, it is found that meditation induces periodic behavior in the heart beat. The complexity of the heart rate variability is quantified using multiscale entropy analysis and recurrence analysis. The heart beat during meditation is found to be more complex.

The complexity of the Portevin-Le Chatelier effect in Al-2.5%Mg polycrystalline samples subjected to uniaxial tensile tests is quantified. Multiscale entropy analysis is carried out on the stress time series data observed during jerky flow to quantify the complexity of the distinct spatiotemporal dynamical regimes. It is shown that for the static type C band, the entropy is very low for all the scales compared to the hopping type B and the propagating type A bands. The results are interpreted considering the time and length scales relevant to the effect.

Fractal Dimensions (FD) are one of the popular measures used for characterizing signals. They have been used as complexity measures of signals in various fields including speech and biomedical applications. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties on FD and interpret results in terms of classical signal processing concepts such as amplitude, frequency, number of harmonics, noise power and signal bandwidth. We have used Higuchi's method for estimating FDs. This study may help in gaining a better understanding of the FD complexity measure itself, and for interpreting changing structural complexity of signals in terms of FD. Our results indicate that FD is a useful measure in quantifying structural changes in signal properties.

The object under study is a particular closed and simple curve on the square lattice ℤ² related with the Fibonacci sequence F_n. It belongs to a class of curves whose length is 4F_3n+1, and whose interiors tile the plane by translation. The limit object, when conveniently normalized, is a fractal line for which we compute first the fractal dimension, and then give a complexity measure.

This paper analyzes the complexity of stock exchanges through fractal theory. Closing price indices of four stock exchanges with different industry sectors are selected. Degree of complexity is assessed through Higuchi’s fractal dimension. Various window sizes are considered in evaluating the fractal dimension. It is inferred that the data considered as a whole represents random walk for all the four indices. Analysis of financial data through windowing procedure exhibits multi-fractality. Attempts to apply moving averages to reduce noise in the data revealed lower estimates of fractal dimension, which was verified using fractional Brownian motion. A change in the normalization factor in Higuchi’s algorithm did improve the results. It is quintessential to focus on rural development to realize a standard and steady growth of economy. Tools must be devised to settle the issues in this regard. Micro level institutions are necessary for the economic growth of a country like India, which would induce a sporadic development in the present global economical scenario.

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to $1/f$ noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Analyzing the influence of external stimuli on human eye movements is an important challenge in vision research. In this paper, we investigate the plasticity of eye movements due to the applied auditory stimuli (music). For this purpose, we use fractal theory, which provides us with tools such as fractal dimension as an indicator of process complexity. This study, for the first time, reveals the correlation between fractal dynamics of eye movements and fractal dynamics of auditory stimuli. Based on the performed analysis, the fractal structure of the eye movements shifts toward the fractal structure of the applied auditory stimuli, where the greater variation in fractal dynamics of auditory stimuli causes greater variation in the fractal dynamics of eye movements. The observed behavior is explained through the nervous system. As a rehabilitation purpose, the employed methodology in this research can be investigated in case of patients with vision problems, where the applied music could potentially improve their vision.

It is known that aging affects neuroplasticity. On the other hand, neuroplasticity can be studied by analyzing the electroencephalogram (EEG) signal. An important challenge in brain research is to study the variations of neuroplasticity during aging for patients suffering from epilepsy. This study investigates the variations of the complexity of EEG signal during aging for patients with epilepsy. For this purpose, we employed fractal dimension as an indicator of process complexity. We classified the subjects in different age groups and computed the fractal dimension of their EEG signals. Our investigations showed that as patients get older, their EEG signal will be more complex. The method of investigation that has been used in this study can be further employed to study the variations of EEG signal in case of other brain disorders during aging.

One of the important research areas in behavioral neuroscience is to investigate the brain response to different types of stimuli. Speech-evoked Auditory Brainstem Response (s-ABR) is a tool to study the brainstem processing of speech sounds. During years, scientists have employed different techniques to analyze the influence of auditory stimulation on s-ABR signal in different conditions. One important category of works, which aroused the attention of scientists, has been the analysis of the variations of s-ABR signal in binaural and monaural stimulations. In this research, we analyze the variations of s-ABR signal due to auditory stimulation in the form of speech syllable, in binaural and monaural (right or left ear) listening conditions. For this purpose, we have employed fractal analysis in order to analyze the complexity of s-ABR signal in three stimulation conditions (both ears, right ear, left ear). The results of our analysis showed that s-ABR signal in case of binaural stimulation shows significant lower complexity compared to monaural stimulation. In comparison of s-ABR signals between left ear and right ear using fractal dimension, no significant difference was observed.

Analysis of human behavior is one of the major research topics in neuroscience. It is known that human behavior is related to his brain activity. In this way, the analysis of human brain activity is the root for analysis of his behavior. Electroencephalography (EEG) as one of the most famous methods for measuring brain activity generates a chaotic signal, which has fractal characteristic. This study reveals the relation between the fractal structure (complexity) of human EEG signal and the applied visual stimuli. For this purpose, we chose two types of visual stimuli, namely, living and non-living visual stimuli. We demonstrate that the fractal structure of human EEG signal changes significantly between living versus non-living visual stimuli. The capability observed in this research can be applied to other kinds of stimuli in order to classify the brain response based on the types of stimuli.

Analysis of human behavior is one of the major research topics in neuroscience. It is known that human behavior is related to his brain activity. In this way, the analysis of human brain activity is the root for analysis of his behavior. Electroencephalography (EEG) as one of the most famous methods for measuring of the brain activity generates a chaotic signal, which has fractal characteristic. This study reveals the relation between the fractal structure (complexity) of human EEG signal and the applied auditory stimuli. For this purpose, we chose a range of auditory stimuli with different rhythmic patterns. We demonstrated that the fractal structure of human EEG signal changes significantly based on different rhythmic patterns. The capability observed in this research can be applied to other kinds of stimuli in order to classify the brain response based on the types of stimuli.

Analysis of human movements is an important category of research in biomedical engineering, especially for the rehabilitation purpose. The movement of limbs is investigated usually by analyzing the movement signals. Less efforts have been made to investigate how neural that correlate to the movements, are represented in the human brain. In this research, for the first time we decode the limb movements by fractal analysis of Electroencephalogram (EEG) signals. We investigated how the complexity of EEG signal changes in different limb movements in motor execution (ME), and motor imagination (MI) sessions. The result of our analysis showed that the EEG signal experiences greatest level of complexity in elbow flexion and hand-close movements in ME, and MI sessions respectively. On the other hand, the lowest level of complexity of EEG signal belongs to hand-open and rest condition in ME, and MI sessions, respectively. Employing fractal theory in analysis of bio signals is not limited to EEG signal, and can be further investigated in other types of human’s bio signals in different conditions. The result of these investigations can vastly been employed for the rehabilitation purpose.

Analysis of cutting forces in machining operation is an important issue. The cutting force changes randomly in milling operation where it makes a signal by plotting over time span. An important type of analysis belongs to the study of how cutting forces change along different axes. Since cutting force has fractal characteristics, in this paper for the first time we analyze the variations of complexity of cutting force signal along different axes using fractal theory. For this purpose, we consider two cutting depths and do milling operation in dry and wet machining conditions. The obtained cutting force time series was analyzed by computing the fractal dimension. The result showed that in both wet and dry machining conditions, the feed force (along $x$-axis) has greater fractal dimension than radial force (along $y$-axis). In addition, the radial force (along $y$-axis) has greater fractal dimension than thrust force (along $z$-axis). The method of analysis that was used in this research can be applied to other machining operations to study the variations of fractal structure of cutting force signal along different axes.

Analysis of the brain response to different types of external stimuli has always been one of the major research areas in behavioral neuroscience. The electroencephalography (EEG) technique combined with different signal analysis approaches has been especially successful in revealing the detailed dynamic properties of the neural response to exogenous stimulation. In this analysis, we evaluated the nonlinear structure of the EEG signal using fractal theory in rest and visual stimulation (checkerboard reversal at 8, 14 and 28Hz). Our analysis showed a significant influence of stimulation on the fractal structure of EEG signal. On comparison between different conditions, 14-Hz steady-state visual evoked potentials (SSVEPs), previously shown to trigger an optimal brain response, exhibited the greatest influence on the complexity of the EEG signal. On the other hand, we observed the lowest complexity of EEG signal in the post-stimulation rest period. Statistical analysis confirmed significant differences in the fractal structure of the EEG signal between rest and different stimulation conditions. These findings demonstrate for the first time a direct relationship between the efficiency of brain processing and the complexity of the measured EEG signal, which could be employed for objective assessment and classification in various experimental paradigms.