Chaos theory: the transforming role of functional systems

The review of applications of chaos theory in physiology shows, that this theory makes possible to get quantitative measure of degree of the order for such processes as neuronal activity, heart rate, electroencephalogram etc. The basic concepts of chaos theory--fractal dimension. Liapunov exponents, entropy, some algorithms for obtaining of quantitative characteristics of degree of the order for different processes--have been considered in this paper. The main areas for application chaos theory in physiology and medicine have been revealed and some examples of practical and theoretical achievements in this new region of investigation are given, as well as existing limitations and problems with results interpretation. Entirely new possibilities for understanding of the order in physiological processes are shown when estimation is made from the point of view of the functional system theory.     

Assessing marine ecosystem acoustic diversity across ocean basins

Concurrent with the elevation of the concern over the state of sound in the ocean, advances in terrestrial acoustic monitoring techniques have produced concepts and tools that may be applicable to the underwater world. Several index values that convey information related to acoustic diversity with a single numeric measurement made from acoustic recordings have been proposed for rapidly assessing community biodiversity. Here we apply the acoustic biodiversity index method to low frequency recordings made from three different ocean basins to assess its appropriateness for characterizing species richness in the marine environment. Initial results indicated that raw acoustic entropy (H) values did not correspond to biological patterns identified from individual signal detections and classification. Noise from seismic airgun activity masked the weaker biological signals and confounded the entropy calculation. A simple background removal technique that subtracted an average complex spectrum characteristic of seismic exploration signals from the average spectra of each analysis period that contained seismic signals was applied to compensate for salient seismic airgun signals present in all locations. The noise compensated (H_N) entropy index was more reflective of biological patterns and holds promise for the use of rapid acoustic biodiversity in the marine environment as an indicator of habitat biodiversity and health.     

Recent developments in quantitative graph theory: information inequalities for networks

In this article, we tackle a challenging problem in quantitative graph theory. We establish relations between graph entropy measures representing the structural information content of networks. In particular, we prove formal relations between quantitative network measures based on Shannon's entropy to study the relatedness of those measures. In order to establish such information inequalities for graphs, we focus on graph entropy measures based on information functionals. To prove such relations, we use known graph classes whose instances have been proven useful in various scientific areas. Our results extend the foregoing work on information inequalities for graphs.     

Thermodynamic study of motor behaviour optimization

Our work is aimed at studying the optimization of a complex motor behaviour from a global perspective. First, free climbing as a sport will be briefly introduced while emphasizing in particular its psychomotor aspect called route finding. The basic question raised here is how does the optimization of a sensorimotoricity-environment system take place. The material under study is the free climber's trajectory, viewed as the signature of climbing behaviour (i.e., the spatial dimension). The concepts of learning, optimization, constraint, and degrees of freedom of a system will be discussed using the synergistic approach to the study of movement (Bernstein, 1967; Kelso, 1977). Measures of a trajectory's length and convex hull can be used to define an index whose equation resembles that of an entropy. This index is a measure of the trajectory's overall complexity. Some important concepts related to the thermodynamics of curves will also be discussed. The optimization process will be studied by examining the changes in entropy over time for a set of trajectories generated during the learning of a route (ten successive repetitions of the same climb). It will be shown that the entropy of the trajectories decreases as learning progresses, that each level of expertise has its own characteristic entropy curve, and that for the subjects tested, the mean entropy of skilled climbers is lower than that of average climbers. Basing our analysis on the concepts of degrees of freedom and constraint equations, an attempt is made to relate trajectory entropy to system entropy. Based on the postulate that trajectory entropy is equal to the difference in entropy between the unconstrained and constrained system, a model of motor optimization is proposed. This model is illustrated by an entropy graph reflecting a dynamic release process. In the light of our results, two opposing views will be examined: movement construction vs. movement emergence.     

Resilience of protein-protein interaction networks as determined by their large-scale topological features

The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.     

Sample entropy analysis of cervical neoplasia gene-expression signatures

Background  

We introduce Approximate Entropy as a mathematical method of analysis for microarray data. Approximate entropy is applied here as a method to classify the complex gene expression patterns resultant of a clinical sample set. Since Entropy is a measure of disorder in a system, we believe that by choosing genes which display minimum entropy in normal controls and maximum entropy in the cancerous sample set we will be able to distinguish those genes which display the greatest variability in the cancerous set. Here we describe a method of utilizing Approximate Sample Entropy (ApSE) analysis to identify genes of interest with the highest probability of producing an accurate, predictive, classification model from our data set.     

Collective decision‐making and fission–fusion dynamics: a conceptual framework

Sociality exists in an extraordinary range of ecological settings. For individuals to accrue the benefits associated with social interactions, they are required to maintain a degree of spatial and temporal coordination in their activities, and make collective decisions. Such coordination and decision‐making has been the focus of much recent research. However, efforts largely have been directed toward understanding patterns of collective behaviour in relatively stable and cohesive groups. Less well understood is how fission–fusion dynamics mediate the process and outcome of collective decisions making. Here, we aim to apply established concepts and knowledge to highlight the implications of fission–fusion dynamics for collective decisions, presenting a conceptual framework based on the outcome of a small‐group discussion INCORE meeting (funded by the European Community's Sixth Framework Programme). First, we discuss how the degree of uncertainty in the environment shapes social flexibility and therefore the types of decisions individuals make in different social settings. Second, we propose that the quality of social relationships and the energetic needs of each individual influence fission decisions. Third, we explore how these factors affect the probability of individuals to fuse. Fourth, we discuss how group size and fission–fusion dynamics may affect communication processes between individuals at a local or global scale to reach a consensus or to fission. Finally, we offer a number of suggestions for future research, capturing emerging ideas and concepts on the interaction between collective decisions and fission–fusion dynamics.     

Evolutionary convergences and parallelisms: &;their theoretical differences and the difficulty &;of discriminating them in a practical &;phylogenetic context

The importance of evolutionary parallelisms and their differences from evolutionary convergences have been historically underappreciated, as recently noticed in Gould's last book `The structure of evolutionary history'. In that book, Gould make an effort to distinguish and to reinterpret these concepts in the light of the new discoveries of the last decades on developmental biology and genetics, presenting the elegant metaphor of `Pharaonic bricks versus Corinthian columns'. In this paper I will briefly discuss these concepts, and will argue that, despite the advances that have been made to define them in theory, it is rather hard to differentiate them in a practical phylogenetic context. In order to do so, I will provide some few examples from my own empirical studies on the last years of one of the most morphologically and taxonomically diverse groups of Vertebrates, the catfishes.     

A synergic approach to plant pattern generation

The paper shows convergences between the results found in various models of phyllotaxis. It shows that a synergic approach is needed to deal with the problems of phyllotaxis. An algorithm, called the phi-model, based on the observation of the meaningful and symmetry-generating presence of the golden ratio phi in all types of spiral patterns, and consequently in all types of regular patterns in phyllotaxis, is proposed. The model is suggested by a property of the allometry-type model for pattern recognition in phyllotaxis. It extends recent morphological models developed around the idea of packing efficiency of plant primordia, models that yield the noble numbers, among which are the divergence angles of spiral patterns. The phi-model also gives the noble numbers and moreover orders them in a way that establishes connections with the morphogenetic principles used in models for pattern generation; the order has to do with the relative frequencies of the spiral patterns in nature. The phi-model is a link between the two entropy models in phyllotaxis and offers a nice correspondence with the minimal entropy model generated by a systemic and holistic approach. This latter type of approach is put forward as being able to give a general framework in which to organize the concepts, results, and models in phyllotaxis in a way that produces a synergy of efforts. The necessity of doing so is seen clearly when one considers that phyllotaxis-like patterns are encountered in other fields of research, so that the problem appears to transcend the strict botanical substratum.     

Comparison of walking parameters obtained from the young,elderly and adults with support

Data mining techniques are highly useful in the study of various medical signals and images in order to obtain useful information to better predict the diagnosis or prognosis or treatment options for the patient. Study of the human walking pattern helps us understand the variability of motion during activities such as high performance walking and normal walking. A comparison of the parameters quantifying this variability in motion in normal young and elderly subjects and the subjects who need support will aid in better understanding of the relationship among walking patterns, age and disabilities. In this study, we measured the tri-axial acceleration along three directions: anteroposterior, lateral and vertical. We also measured gyrational pitch, roll and yaw. These parameters were obtained using sensors attached to the back, left thigh and right thigh of the three classes of subjects (normal, elderly and adults with support) during the three types of exercises: 10-m normal walk, 10-m high performance walk and stepping. These recorded signals were then subjected to wavelet packet decomposition, and three entropies, namely approximate entropy and two bispectral entropies, were obtained from the resultant wavelet coefficients. On analysing these entropies, we could observe the following: (1) the entropy steadily decreases with the increase in age and with the presence of impairments, and (2) the entropy decreases among all the three types of exercises, namely normal walking and high performance walking. We feel that the results of this work can help in the design of supporting devices for elderly subjects.     

Micropatterned substratum adhesiveness: a model for morphogenetic cues controlling cell behavior.

It is generally considered that tracks of cell adhesiveness are important in controlling cell migration during the development and regeneration of many tissues. In order to investigate this experimentally, a number of techniques have in the past been employed to make patterns of differential adhesiveness for in vitro studies. However, practical limitations on patterning resolution and the introduction of residual topography to the experimental substrata have restricted their usefulness. Here we describe a simplified photolithographic technique for patterning cell adhesiveness which allows a high degree of flexibility and precision. We have quantified, using adhesion and spreading characteristics of BHK cells, the differential adhesiveness that can be created on patterned surfaces, how this alters with the duration of exposure to serum proteins, and how this, in turn, relates to the persistence of cell patterning despite increases in cell density. We believe that this technique will prove extremely useful for the detailed in vitro examination of the mechanisms controlling cell behavior as it offers a degree of precision and ease of fabrication that has previously been unavailable.     

Eukaryotic DNA methylation: facts and problems

Patterns of DNA methylation in complex genomes like those of mammalian cells have been viewed as indicators of different levels of genetic activities. It is as yet unknown how these complicated patterns are generated and maintained during cell replication. There is evidence from many different biological systems that the sequence-specific methylation of promoters in higher eukaryotes is one of the important factors in controlling gene activity at a long-term level. In general, the fifth nucleotide 5-methyldeoxycytidine can be considered as a modulator of protein-DNA interactions. The degree and direction of this modulation has to be assessed experimentally in each individual instance. The establishment of de novo patterns of DNA methylation is characterized by the gradual non-random spreading of DNA methylation by an essentially unknown mechanism. In this review, some of the general concepts of DNA methylation in mammalian systems are presented, and research currently performed in the authors' laboratory has been summarized.     

Effects of dilation and translation on a perceptron-type learning rule for higher order Hopfield neural networks

In this paper, we will take a further look at a generalized perceptron-like learning rule which uses dilation and translation parameters in order to enhance the recall performance of higher order Hopfield neural networks without significantly increasing their complexity. We will practically study the influence of these parameters on the perceptron learning and recall process, using a generalized version of the Hebbian learning rule for initialization. Our analysis will be based on a pattern recognition problem with random patterns. We will see that in case of a highly correlated set of patterns, there can be gained some improvements concerning the learning and recall performance. On the other hand, we will show that the dilation and translation parameters have to be chosen carefully for a positive result.     

Symmetry and asymmetry in the probability field

The concepts of right-hand entropy and left-hand entropy as a measure of the symmetry in a probability field are defined. Likewise the concept of the asymmetry as a very important property of the same probability field is emphasized. Thus, it is shown that some schemes, which are indistinguishable by means of Shannon's entropy, may be recognized by using these new concepts.     

Ventricular fibrillation: the current methods for analysing the degree of irregularity of the process

Ventricular fibrillation has traditionally been described as "chaotic" and in recent years there has been discussions that fibrillation may be an instance of deterministic chaos in the context of nonlinear dynamical systems theory. The current paper summarizes modern methods of mathematical analysis of the degree of electrical irregularities of the heart during VF. The traditional methods of Fourier analysis of electrocardiographic data as well as concepts of chaos theory--fractal dimension, entropy, reconstruction of attractors and some new methods such as spatial coherence have been considered. The results are discussed in context of mathematical models and hypothesis of mechanisms of VF.     

Investigating Neuromagnetic Brain Responses against Chromatic Flickering Stimuli by Wavelet Entropies

Background

Photosensitive epilepsy is a type of reflexive epilepsy triggered by various visual stimuli including colourful ones. Despite the ubiquitous presence of colorful displays, brain responses against different colour combinations are not properly studied.

Methodology/Principal Findings

Here, we studied the photosensitivity of the human brain against three types of chromatic flickering stimuli by recording neuromagnetic brain responses (magnetoencephalogram, MEG) from nine adult controls, an unmedicated patient, a medicated patient, and two controls age-matched with patients. Dynamical complexities of MEG signals were investigated by a family of wavelet entropies. Wavelet entropy is a newly proposed measure to characterize large scale brain responses, which quantifies the degree of order/disorder associated with a multi-frequency signal response. In particular, we found that as compared to the unmedicated patient, controls showed significantly larger wavelet entropy values. We also found that Renyi entropy is the most powerful feature for the participant classification. Finally, we also demonstrated the effect of combinational chromatic sensitivity on the underlying order/disorder in MEG signals.

Conclusions/Significance

Our results suggest that when perturbed by potentially epileptic-triggering stimulus, healthy human brain manages to maintain a non-deterministic, possibly nonlinear state, with high degree of disorder, but an epileptic brain represents a highly ordered state which making it prone to hyper-excitation. Further, certain colour combination was found to be more threatening than other combinations.     

Predictability of Road Traffic and Congestion in Urban Areas

Mitigating traffic congestion on urban roads, with paramount importance in urban development and reduction of energy consumption and air pollution, depends on our ability to foresee road usage and traffic conditions pertaining to the collective behavior of drivers, raising a significant question: to what degree is road traffic predictable in urban areas? Here we rely on the precise records of daily vehicle mobility based on GPS positioning device installed in taxis to uncover the potential daily predictability of urban traffic patterns. Using the mapping from the degree of congestion on roads into a time series of symbols and measuring its entropy, we find a relatively high daily predictability of traffic conditions despite the absence of any priori knowledge of drivers'' origins and destinations and quite different travel patterns between weekdays and weekends. Moreover, we find a counterintuitive dependence of the predictability on travel speed: the road segment associated with intermediate average travel speed is most difficult to be predicted. We also explore the possibility of recovering the traffic condition of an inaccessible segment from its adjacent segments with respect to limited observability. The highly predictable traffic patterns in spite of the heterogeneity of drivers'' behaviors and the variability of their origins and destinations enables development of accurate predictive models for eventually devising practical strategies to mitigate urban road congestion.