O bilhar stadium dependente do tempo: aceleração de Fermi e o fenômeno de retardo de velocidade

Pós-graduação em Física - IGCE

Movimento orbital de satélites artificiais: efeitos ressonantes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Statistical and dynamical properties of a dissipative kicked rotator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter epsilon and experiences a transition from integrable (epsilon = 0) to nonintegrable (epsilon not equal 0). For small values of epsilon, the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter epsilon increases and reaches a critical value epsilon(c), all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large epsilon, the survival probability decays exponentially when it turns into a slower decay as the control parameter epsilon is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity.

Chaotic encryption method based on life-like cellular automata

A chaotic encryption algorithm is proposed based on the "Life-like" cellular automata (CA), which acts as a pseudo-random generator (PRNG). The paper main focus is to use chaos theory to cryptography. Thus, CA was explored to look for this "chaos" property. This way, the manuscript is more concerning on tests like: Lyapunov exponent, Entropy and Hamming distance to measure the chaos in CA, as well as statistic analysis like DIEHARD and ENT suites. Our results achieved higher randomness quality than others ciphers in literature. These results reinforce the supposition of a strong relationship between chaos and the randomness quality. Thus, the "chaos" property of CA is a good reason to be employed in cryptography, furthermore, for its simplicity, low cost of implementation and respectable encryption power. (C) 2012 Elsevier Ltd. All rights reserved.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

Influence of delay time on regularity estimation for voice pathology detection

The employment of nonlinear analysis techniques for automatic voice pathology detection systems has gained popularity due to the ability of such techniques for dealing with the underlying nonlinear phenomena. On this respect, characterization using nonlinear analysis typically employs the classical Correlation Dimension and the largest Lyapunov Exponent, as well as some regularity quantifiers computing the system predictability. Mostly, regularity features highly depend on a correct choosing of some parameters. One of those, the delay time �, is usually fixed to be 1. Nonetheless, it has been stated that a unity � can not avoid linear correlation of the time series and hence, may not correctly capture system nonlinearities. Therefore, present work studies the influence of the � parameter on the estimation of regularity features. Three � estimations are considered: the baseline value 1; a � based on the Average Automutual Information criterion; and � chosen from the embedding window. Testing results obtained for pathological voice suggest that an improved accuracy might be obtained by using a � value different from 1, as it accounts for the underlying nonlinearities of the voice signal.

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Non uniform embedding based on relevance analysis with reduced computational complexity: application to the detection of pathologies from biosignal recordings

Nonlinear analysis tools for studying and characterizing the dynamics of physiological signals have gained popularity, mainly because tracking sudden alterations of the inherent complexity of biological processes might be an indicator of altered physiological states. Typically, in order to perform an analysis with such tools, the physiological variables that describe the biological process under study are used to reconstruct the underlying dynamics of the biological processes. For that goal, a procedure called time-delay or uniform embedding is usually employed. Nonetheless, there is evidence of its inability for dealing with non-stationary signals, as those recorded from many physiological processes. To handle with such a drawback, this paper evaluates the utility of non-conventional time series reconstruction procedures based on non uniform embedding, applying them to automatic pattern recognition tasks. The paper compares a state of the art non uniform approach with a novel scheme which fuses embedding and feature selection at once, searching for better reconstructions of the dynamics of the system. Moreover, results are also compared with two classic uniform embedding techniques. Thus, the goal is comparing uniform and non uniform reconstruction techniques, including the one proposed in this work, for pattern recognition in biomedical signal processing tasks. Once the state space is reconstructed, the scheme followed characterizes with three classic nonlinear dynamic features (Largest Lyapunov Exponent, Correlation Dimension and Recurrence Period Density Entropy), while classification is carried out by means of a simple k-nn classifier. In order to test its generalization capabilities, the approach was tested with three different physiological databases (Speech Pathologies, Epilepsy and Heart Murmurs). In terms of the accuracy obtained to automatically detect the presence of pathologies, and for the three types of biosignals analyzed, the non uniform techniques used in this work lightly outperformed the results obtained using the uniform methods, suggesting their usefulness to characterize non-stationary biomedical signals in pattern recognition applications. On the other hand, in view of the results obtained and its low computational load, the proposed technique suggests its applicability for the applications under study.

Guided Migration and Collective Behavior: Cell Dynamics during Cancer Progression

This dissertation focuses on gaining understanding of cell migration and collective behavior through a combination of experiment, analysis, and modeling techniques. Cell migration is a ubiquitous process that plays an important role during embryonic development and wound healing as well as in diseases like cancer, which is a particular focus of this work. As cancer cells become increasingly malignant, they acquire the ability to migrate away from the primary tumor and spread throughout the body to form metastatic tumors. During this process, changes in gene expression and the surrounding tumor environment can lead to changes in cell migration characteristics. In this thesis, I analyze how cells are guided by the texture of their environment and how cells cooperate with their neighbors to move collectively. The emergent properties of collectively moving groups are a particular focus of this work as collective cell dynamics are known to change in diseases such as cancer. The internal machinery for cell migration involves polymerization of the actin cytoskeleton to create protrusions that---in coordination with retraction of the rear of the cell---lead to cell motion. This actin machinery has been previously shown to respond to the topography of the surrounding surface, leading to guided migration of amoeboid cells. Here we show that epithelial cells on nanoscale ridge structures also show changes in the morphology of their cytoskeletons; actin is found to align with the ridge structures. The migration of the cells is also guided preferentially along the ridge length. These ridge structures are on length scales similar to those found in tumor microenvironments and as such provide a system for studying the response of the cells' internal migration machinery to physiologically relevant topographical cues. In addition to sensing surface topography, individual cells can also be influenced by the pushing and pulling of neighboring cells. The emergent properties of collectively migrating cells show interesting dynamics and are relevant for cancer progression, but have been less studied than the motion of individual cells. We use Particle Image Velocimetry (PIV) to extract the motion of a collectively migrating cell sheet from time lapse images. The resulting flow fields allow us to analyze collective behavior over multiple length and time scales. To analyze the connection between individual cell properties and collective migration behavior, we compare experimental flow fields with the migration of simulated cell groups. Our collective migration metrics allow for a quantitative comparison between experimental and simulated results. This comparison shows that tissue-scale decreases in collective behavior can result from changes in individual cell activity without the need to postulate the existence of subpopulations of leader cells or global gradients. In addition to tissue-scale trends in collective behavior, the migration of cell groups includes localized dynamic features such as cell rearrangements. An individual cell may smoothly follow the motion of its neighbors (affine motion) or move in a more individualistic manner (non-affine motion). By decomposing individual motion into both affine and non-affine components, we measure cell rearrangements within a collective sheet. Finally, finite-time Lyapunov exponent (FTLE) values capture the stretching of the flow field and reflect its chaotic character. Applying collective migration analysis techniques to experimental data on both malignant and non-malignant human breast epithelial cells reveals differences in collective behavior that are not found from analyzing migration speeds alone. Non-malignant cells show increased cooperative motion on long time scales whereas malignant cells remain uncooperative as time progresses. Combining multiple analysis techniques also shows that these two cell types differ in their response to a perturbation of cell-cell adhesion through the molecule E-cadherin. Non-malignant MCF10A cells use E-cadherin for short time coordination of collective motion, yet even with decreased E-cadherin expression, the cells remain coordinated over long time scales. In contrast, the migration behavior of malignant and invasive MCF10CA1a cells, which already shows decreased collective dynamics on both time scales, is insensitive to the change in E-cadherin expression.

Guided Migration and Collective Behavior: Cell Dynamics during Cancer Progression

This dissertation focuses on gaining understanding of cell migration and collective behavior through a combination of experiment, analysis, and modeling techniques. Cell migration is a ubiquitous process that plays an important role during embryonic development and wound healing as well as in diseases like cancer, which is a particular focus of this work. As cancer cells become increasingly malignant, they acquire the ability to migrate away from the primary tumor and spread throughout the body to form metastatic tumors. During this process, changes in gene expression and the surrounding tumor environment can lead to changes in cell migration characteristics. In this thesis, I analyze how cells are guided by the texture of their environment and how cells cooperate with their neighbors to move collectively. The emergent properties of collectively moving groups are a particular focus of this work as collective cell dynamics are known to change in diseases such as cancer. The internal machinery for cell migration involves polymerization of the actin cytoskeleton to create protrusions that---in coordination with retraction of the rear of the cell---lead to cell motion. This actin machinery has been previously shown to respond to the topography of the surrounding surface, leading to guided migration of amoeboid cells. Here we show that epithelial cells on nanoscale ridge structures also show changes in the morphology of their cytoskeletons; actin is found to align with the ridge structures. The migration of the cells is also guided preferentially along the ridge length. These ridge structures are on length scales similar to those found in tumor microenvironments and as such provide a system for studying the response of the cells' internal migration machinery to physiologically relevant topographical cues. In addition to sensing surface topography, individual cells can also be influenced by the pushing and pulling of neighboring cells. The emergent properties of collectively migrating cells show interesting dynamics and are relevant for cancer progression, but have been less studied than the motion of individual cells. We use Particle Image Velocimetry (PIV) to extract the motion of a collectively migrating cell sheet from time lapse images. The resulting flow fields allow us to analyze collective behavior over multiple length and time scales. To analyze the connection between individual cell properties and collective migration behavior, we compare experimental flow fields with the migration of simulated cell groups. Our collective migration metrics allow for a quantitative comparison between experimental and simulated results. This comparison shows that tissue-scale decreases in collective behavior can result from changes in individual cell activity without the need to postulate the existence of subpopulations of leader cells or global gradients. In addition to tissue-scale trends in collective behavior, the migration of cell groups includes localized dynamic features such as cell rearrangements. An individual cell may smoothly follow the motion of its neighbors (affine motion) or move in a more individualistic manner (non-affine motion). By decomposing individual motion into both affine and non-affine components, we measure cell rearrangements within a collective sheet. Finally, finite-time Lyapunov exponent (FTLE) values capture the stretching of the flow field and reflect its chaotic character. Applying collective migration analysis techniques to experimental data on both malignant and non-malignant human breast epithelial cells reveals differences in collective behavior that are not found from analyzing migration speeds alone. Non-malignant cells show increased cooperative motion on long time scales whereas malignant cells remain uncooperative as time progresses. Combining multiple analysis techniques also shows that these two cell types differ in their response to a perturbation of cell-cell adhesion through the molecule E-cadherin. Non-malignant MCF10A cells use E-cadherin for short time coordination of collective motion, yet even with decreased E-cadherin expression, the cells remain coordinated over long time scales. In contrast, the migration behavior of malignant and invasive MCF10CA1a cells, which already shows decreased collective dynamics on both time scales, is insensitive to the change in E-cadherin expression.

Short Lyapunov time: a method for identifying confined chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Liapunov exponent as a tool for exploring phase space

We have used the Liapunov exponent to explore the phase space of a dynamical system. Considering the planar, circular restricted three-body problem for a mass ratio mu = 10(-3) (close to the Jupiter/Sun case), we have integrated similar to 16,000 starting conditions for orbits started interior to that of the perturber and we have estimated the maximum Liapunov characteristic exponent for each starting condition. Despite the fact that the integrations, in general, are for only a few thousand orbital periods of the secondary, a comparative analysis of the Liapunov exponents for various values of the 'cut-off' gives a good overview of the structure of the phase space. It provides information about the diffusion rates of the various chaotic regions, the location of the regular regions associated with primary resonances and even details such as the location of secondary resonances that produce chaotic regions inside the regular regions of primary resonances.

Didanosine-loaded Chitosan Microspheres Optimized By Surface-response Methodology: A Modified Maximum Likelihood Classification" Approach Formulation For Reverse Transcriptase Inhibitors."

Didanosine-loaded chitosan microspheres were developed applying a surface-response methodology and using a modified Maximum Likelihood Classification. The operational conditions were optimized with the aim of maintaining the active form of didanosine (ddI), which is sensitive to acid pH, and to develop a modified and mucoadhesive formulation. The loading of the drug within the chitosan microspheres was carried out by ionotropic gelation technique with sodium tripolyphosphate (TPP) as cross-linking agent and magnesium hydroxide (Mg(OH)2) to assure the stability of ddI. The optimization conditions were set using a surface-response methodology and applying the Maximum Likelihood Classification, where the initial chitosan concentration, TPP and ddI concentration were set as the independent variables. The maximum ddI-loaded in microspheres (i.e. 1433mg of ddI/g chitosan), was obtained with 2% (w/v) chitosan and 10% TPP. The microspheres depicted an average diameter of 11.42μm and ddI was gradually released during 2h in simulated enteric fluid.