Manifestation of Chaos in Real Complex Systems: Case of Parkinson's Disease

In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve as a reliable quantitative estimation of the state of a complex system and help to estimate the deviation of this state from its normal condition. As the IMC we suggest the statistical spectrum of the non-Markovity parameter (NMP) and its frequency behavior. Our preliminary studies of real complex systems in cardiology, neurophysiology and seismology have shown that the NMP has diverse frequency dependence. It testifies to the competition between Markovian and non-Markovian, random and regular processes and makes a crossover from one relaxation scenario to the other possible. On this basis we can formulate the new concept in the study of the manifestation of chaoticity. We suggest the statistical theory of discrete non-Markov stochastic processes to calculate the NMP and the quantitative evaluation of the IMC in real complex systems. With the help of the IMC we have found out the evident manifestation of chaosity in a normal (healthy) state of the studied system, its sharp reduction in the period of crises, catastrophes and various human diseases. It means that one can appreciably improve the state of a patient (of any system) by increasing the IMC of the studied live system. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treating various human diseases, Parkinson's disease in particular.Comment: 20 pages, 8 figures, 3 tables. To be published in "The Logistic Map and the Route to Chaos: From the Beginnings to the Modern Applications", eds. by M. Ausloos, M. Dirickx, pp. 175-196, Springer-Verlag, Berlin (2006

Multibody simulation benchmark for dynamic vehicle-track interaction in switches and crossings: results and method statements

A Benchmark of railway multibody dynamics software application to switches and crossings (S&C) is presented, comparing all major commercially available software and a few independent codes. Two different representative S&C have been implemented, using the Manchester Benchmark passenger vehicle. The final results show that all software offer a reliable and efficient way to understand the kinematic and dynamics forces between the wheels and the track elements. The highest challenges are found when modelling a combination of multiple rails in simultaneous contact with a wheel (check-stock or switch-stock), large longitudinal variations in rail shape (crossings) and high lateral steering forces (diverging cases in tight radius). In those cases, the codes able to account for the exact relative motion of each wheels with respect to each rails independently are the most apt. The most significant variations between software are found in the contact prediction with an influence on the detailed contact tangential and normal forces. The user variability is found to be very small, with the most time-consuming and error prone being the task of handling the input data for the variable rails definition. All software could benefit from improvements to assist the user and ensure higher reliability and efficiency generally

Compromised junctional integrity phenocopies age-dependent renal dysfunction in Drosophila Snakeskin mutants

Transporting epithelia provide a protective barrier against pathogenic insults while allowing the controlled exchange of ions, solutes and water with the external environment. In invertebrates, these functions depend on formation and maintenance of ‘tight’ septate junctions (SJs). However, the mechanism by which SJs affect transport competence and tissue homeostasis, and how these are modulated by ageing, remain incompletely understood. Here, we demonstrate that the Drosophila renal (Malpighian) tubules undergo an age-dependent decline in secretory capacity, which correlates with mislocalisation of SJ proteins and progressive degeneration in cellular morphology and tissue homeostasis. Acute loss of the septate junction protein Snakeskin in adult tubules induces progressive changes in cellular and tissue architecture, including altered expression and localisation of junctional proteins with concomitant loss of cell polarity and barrier integrity, demonstrating that compromised junctional integrity is sufficient to replicate these ageing-related phenotypes. Taken together, our work demonstrates a crucial link between epithelial barrier integrity, tubule transport competence, renal homeostasis and organismal viability, as well as providing novel insights into the mechanisms underpinning age-onset and renal disease

The groupoid approach to Leavitt path algebras

When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The main result that makes this possible is that the Leavitt path algebra of a graph is graded isomorphic to the Steinberg algebra of the graph’s boundary path groupoid. This expository paper has three parts: Part 1 is on the Steinberg algebra of a groupoid, Part 2 is on the path space and boundary path groupoid of a graph, and Part 3 is on the Leavitt path algebra of a graph. It is a self-contained reference on these topics, intended to be useful to beginners and experts alike. While revisiting the fundamentals, we prove some results in greater generality than can be found elsewhere, including the uniqueness theorems for Leavitt path algebras

Low level methylmercury exposure affects neuropsychological function in adults

BACKGROUND: The neurotoxic effects of methylmercury (MeHg) have been demonstrated in both human and animal studies. Both adult and fetal brains are susceptible to the effects of MeHg toxicity. However, the specific effects of adult exposures have been less well-documented than those of children with prenatal exposures. This is largely because few studies of MeHg exposures in adults have used sensitive neurological endpoints. The present study reports on the results of neuropsychological testing and hair mercury concentrations in adults (>17 yrs) living in fishing communities of Baixada Cuiabana (Mato Grosso) in the Pantanal region of Brazil. METHODS: A cross-sectional study was conducted in six villages on the Cuiaba River. Participants included 129 men and women older than 17 years of age. They were randomly selected in proportion to the age range and number of inhabitants in each village. Questionnaire information was collected on demographic variables, including education, occupation, and residence history. Mercury exposure was determined by analysis of hair using flameless atomic absorption spectrophotometry. The neurocognitive screening battery included tests from the Wechsler Memory Scale and the Wechsler Adult Intelligence Scale, Concentrated Attention Test of the Toulouse-Pierron Factorial Battery, the Manual Ability Subtests of the Tests of Mechanical Ability, and the Profile of Mood States. RESULTS: Mercury exposures in this population were associated with fish consumption. The hair mercury concentration in the 129 subjects ranged from 0.56 to 13.6 μg/g; the mean concentration was 4.2 ± 2.4 micrograms/g and the median was 3.7 μg/g. Hair mercury levels were associated with detectable alterations in performance on tests of fine motor speed and dexterity, and concentration. Some aspects of verbal learning and memory were also disrupted by mercury exposure. The magnitude of the effects increased with hair mercury concentration, consistent with a dose-dependent effect. CONCLUSIONS: This study suggests that adults exposed to MeHg may be at risk for deficits in neurocognitive function. The functions disrupted in adults, namely attention, fine-motor function and verbal memory, are similar to some of those previously reported in children with prenatal exposures

Nonlinear analysis of periodic waves in a neural field model

Various types of brain activity, including motor, visual, and language, are accompanied by the propagation of periodic waves of electric potential in the cortex, possibly providing the synchronization of the epicenters involved in these activities. One example is cortical electrical activity propagating during sleep and described as traveling waves [Massimini et al., J. Neurosci. 24, 6862-6870 (2004)]. These waves modulate cortical excitability as they progress. Clinically related examples include cortical spreading depression in which a wave of depolarization propagates not only in migraine but also in stroke, hemorrhage, or traumatic brain injury [Whalen et al., Sci. Rep. 8, 1-9 (2018)]. Here, we consider the possible role of epicenters and explore a neural field model with two nonlinear integrodifferential equations for the distributions of activating and inhibiting signals. It is studied with symmetric connectivity functions characterizing signal exchange between two populations of neurons, excitatory and inhibitory. Bifurcation analysis is used to investigate the emergence of periodic traveling waves and of standing oscillations from the stationary, spatially homogeneous solutions, and the stability of these solutions. Both types of solutions can be started by local oscillations indicating a possible role of epicenters in the initiation of wave propagation

Modeling of post-stroke stimulation of cortical tissue

Following a stroke, cortical networks in the penumbra area become fragmented and partly deactivated. We develop a model to study the propagation of waves of electric potential in the cortical tissue with integro-differential equations arising in neural field models. The wave speed is characterized by the tissue excitability and connectivity determined through parameters of the model. Post-stroke tissue damage in the penumbra area creates a hypoconnectivity and decreases the speed of wave propagation. It is proposed that external stimulation could restore the wave speed in the penumbra area under certain conditions of the parameters. Model guided cortical stimulation could be used to improve the functioning of cortical networks. © 201