Complex evolution of a multi-particle system

This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.

Analysis of the respiratory dynamics during normal breathing by means of pseudo phase plots and pressure-volume loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure–volume curves and the pseudophaseplane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Accessing complexity from genome information

This paper studies the information content of the chromosomes of 24 species. In a first phase, a scheme inspired in dynamical system state space representation is developed. For each chromosome the state space dynamical evolution is shed into a two dimensional chart. The plots are then analyzed and characterized in the perspective of fractal dimension. This information is integrated in two measures of the species’ complexity addressing its average and variability. The results are in close accordance with phylogenetics pointing quantitative aspects of the species’ genomic complexity.

Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Urban land use change analysis and modelling: a case study of Setubal-Sesimbra, Portugal

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.

Electrical ageing studies of polymeric insulation for power cables (estudo do envelhecimento eléctrico do isolante polimérico de cabos eléctricos

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Física - Física Aplicada pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Analysis of the Respiratory Dynamics During Normal Breathing by Means of Pseudophase Plots and Pressure–Volume Loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure-volume curves and the pseudophase-plane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Study of the electromyographic signal dynamic behavior in Amyotrophic Lateral Sclerosis (ALS)

Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease characterized by motor neurons degeneration, which reduces muscular force, being very difficult to diagnose. Mathematical methods are used in order to analyze the surface electromiographic signal’s dynamic behavior (Fractal Dimension (FD) and Multiscale Entropy (MSE)), evaluate different muscle group’s synchronization (Coherence and Phase Locking Factor (PLF)) and to evaluate the signal’s complexity (Lempel-Ziv (LZ) techniques and Detrended Fluctuation Analysis (DFA)). Surface electromiographic signal acquisitions were performed in upper limb muscles, being the analysis executed for instants of contraction for ipsilateral acquisitions for patients and control groups. Results from LZ, DFA and MSE analysis present capability to distinguish between the patient group and the control group, whereas coherence, PLF and FD algorithms present results very similar for both groups. LZ, DFA and MSE algorithms appear then to be a good measure of corticospinal pathways integrity. A classification algorithm was applied to the results in combination with extracted features from the surface electromiographic signal, with an accuracy percentage higher than 70% for 118 combinations for at least one classifier. The classification results demonstrate capability to distinguish members between patients and control groups. These results can demonstrate a major importance in the disease diagnose, once surface electromyography (sEMG) may be used as an auxiliary diagnose method.

Nonlinear behavior of gelatin networks reveals a hierarchical structure

We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (Rc) and the fractal dimension (df) of the gel networks. The fractal dimension df obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels.

Kinematics and dynamic complexity of postural transitions in frail elderly subjects.

The aim of this study was to propose a methodology allowing a detailed characterization of body sit-to-stand/stand-to-sit postural transition. Parameters characterizing the kinematics of the trunk movement during sit-to-stand (Si-St) postural transition were calculated using one initial sensor system fixed on the trunk and a data logger. Dynamic complexity of these postural transitions was estimated by fractal dimension of acceleration-angular velocity plot. We concluded that this method provides a simple and accurate tool for monitoring frail elderly and to objectively evaluate the efficacy of a rehabilitation program.

Multi-parametric evaluation of sit-to-stand and stand-to-sit transitions in elderly people.

The aim of this study was to extract multi-parametric measures characterizing different features of sit-to-stand (Si-St) and stand-to-sit (St-Si) transitions in older persons, using a single inertial sensor attached to the chest. Investigated parameters were transition's duration, range of trunk tilt, smoothness of transition pattern assessed by its fractal dimension, and trunk movement's dynamic described by local wavelet energy. A measurement protocol with a Si-St followed by a St-Si postural transition was performed by two groups of participants: the first group (N=79) included Frail Elderly subjects admitted to a post-acute rehabilitation facility and the second group (N=27) were healthy community-dwelling elderly persons. Subjects were also evaluated with Tinetti's POMA scale. Compared to Healthy Elderly persons, frail group at baseline had significantly longer Si-St (3.85±1.04 vs. 2.60±0.32, p=0.001) and St-Si (4.08±1.21 vs. 2.81±0.36, p=0.001) transition's duration. Frail older persons also had significantly decreased smoothness of Si-St transition pattern (1.36±0.07 vs. 1.21±0.05, p=0.001) and dynamic of trunk movement. Measurements after three weeks of rehabilitation in frail older persons showed that smoothness of transition pattern had the highest improvement effect size (0.4) and discriminative performance. These results demonstrate the potential interest of such parameters to distinguish older subjects with different functional and health conditions.

Early disturbances of gamma band dynamics in mild cognitive impairment.

Recent studies have indicated that gamma band oscillations participate in the temporal binding needed for the synchronization of cortical networks involved in short-term memory and attentional processes. To date, no study has explored the temporal dynamics of gamma band in the early stages of dementia. At baseline, gamma band analysis was performed in 29 cases with mild cognitive impairment (MCI) during the n-back task. Based on phase diagrams, multiple linear regression models were built to explore the relationship between the cognitive status and gamma oscillation changes over time. Individual measures of phase diagram complexity were made using fractal dimension values. After 1 year, all cases were assessed neuropsychologically using the same battery. A total of 16 MCI patients showed progressive cognitive decline (PMCI) and 13 remained stable (SMCI). When adjusted for gamma values at lag -2, and -3 ms, PMCI cases displayed significantly lower average changes in gamma values than SMCI cases both in detection and 2-back tasks. Gamma fractal dimension of PMCI cases displayed significantly higher gamma fractal dimension values compared to SMCI cases. This variable explained 11.8% of the cognitive variability in this series. Our data indicate that the progression of cognitive decline in MCI is associated with early deficits in temporal binding that occur during the activation of selective attention processes.

Environmental stress and atavism in ammonoid evolution

The most common trends observed in ammonoid evolution during ecologically stable periods are characterized by an increase of shell curvature (e.g. evolute to involute), by the development of more complex ornamentation (flexuosity of ribbing, appearance of nodes and spines) and by a long term increase of the suture line's fractal dimension. Major evolutionary jumps in ammonoids occur during severe extinction events, and are characterized by the sudden appearance of simple, primitive-looking forms which are similar to remote ancestors of their more complex immediate progenitors. Such forms are interpreted as atavistic. According to this hypothesis, homeomorphic species generated during such sublethal stress events can be separated by several millions of years.