Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Dynamical Stability and Predictability of Football Players: The Study of One Match

The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

Blood culture as a parameter of treatment effectiveness in experimental histoplasmosis of the hamster

The aim of this study was to determine the value of blood culture as a parameter of treatment effectiveness in experimental histoplasmosis. A total of thirty five hamsters, weighing approximately 120g, were inoculated intracardiacly with 0.1 ml of a suspension containing 4 x 10(7) cells/ml of the yeast phase of H. capsulatum. Treatments were started one week after the infection and lasted for 3 weeks. The azoles, (itraconazole, saperconazole and fluconazole) were administered once a day by gavage, at a dose of 8 mg/kg; Amphotericin B was given intraperitonealy every other day at a dose of 6mg/kg. Blood samples (1 ml) were obtained by heart punction from the 4th day after infection and were seeded in Sabouraud honey-agar and BHI-agar. The hamsters that survived were killed one week after treatment completion and the following criteria were considered for treatment evaluation: 1) rate of spontaneous death, at the end of the experience; 2) microscopic examination of Giemsa smears from liver and spleen and 3) determination of CFU in spleen cultures. Amphotericin B was the most effective drug, with negative blood cultures at day 20, negative spleen cultures in all cases and all the animals survived until the end of the study. Fluconazole was the less effective drug, blood cultures were positive during the whole experience, spleen cultures showed a similar average of CFU when compared with the control animals and 42.8% of these animals died. Saperconazole and itraconazole showed a similar activity, with survival of all hamsters and negative blood cultures at 23 and 26 days respectively. Blood culture seems to be valuable parameter for treatments' evaluation in experimental histoplasmosis of the hamster.

Isoenzyme profile as parameter to differentiate pathogenic strains of Entamoeba histolytica in Brazil

The isoenzyme profiles (IP) of 33 strains of Entamoeba histolytica isolated from patients and carriers of two regions in Brazil (Amazonia and Southeast) were determined. The enzymes phosphoglucomutase, glucose-phosphate isomerase, hexokinase and malic enzyme were considered. IP of the strains was correlated with culture conditions, time of maintenance in laboratory and clinical history of patients. The strains were maintained under polyxenic, monoxenic and axenic culture conditions: 27 polyxenic, 1 polyxenic and monoxenic, 1 polyxenic, monoxenic and axenic and 4 axenic only. The patients were symptomatic and asymptomatic. The symptomatic patients presented either non dysenteric (NDC) or dysenteric colitis (DC), associated or not with hepatic abscess (HA). One patient presented anal amoeboma (AM). The analysis of IP for isolates maintained in polyxenic culture showed non pathogenic IP (I) for strains from carriers and patients with NDC, while the strains isolated from patients presenting DC, HA and AM resulted in isolates II or XIX pathogenic IP. This parameter was not able to differentiate strains from carriers from symptomatic patients when these strains were found in axenic or monoxenic culture. All these strains displayed pathogenic IP (II), demonstrating the inability of this parameter to classifying for virulence since it showed identical IP for strains isolated from carriers or symptomatic patients.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Multidimensional Scaling Visualization using Parametric Similarity Indices

In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define a given PSI for tracking pieces of data. We then compare the windows for different values of the parameter, and we generate the corresponding MDS maps of ‘points’. Third, we use Procrustes analysis to linearly transform the MDS charts for maximum superposition and to build a global MDS map of “shapes”. This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, the Minkowski distance and four entropy-based indices are tested. The proposed approach is applied to the Dow Jones Industrial Average stock market index and the Europe Brent Spot Price FOB time-series.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Entropy Analysis of Industrial Accident Data Series

Complex industrial plants exhibit multiple interactions among smaller parts and with human operators. Failure in one part can propagate across subsystem boundaries causing a serious disaster. This paper analyzes the industrial accident data series in the perspective of dynamical systems. First, we process real world data and show that the statistics of the number of fatalities reveal features that are well described by power law (PL) distributions. For early years, the data reveal double PL behavior, while, for more recent time periods, a single PL fits better into the experimental data. Second, we analyze the entropy of the data series statistics over time. Third, we use the Kullback–Leibler divergence to compare the empirical data and multidimensional scaling (MDS) techniques for data analysis and visualization. Entropy-based analysis is adopted to assess complexity, having the advantage of yielding a single parameter to express relationships between the data. The classical and the generalized (fractional) entropy and Kullback–Leibler divergence are used. The generalized measures allow a clear identification of patterns embedded in the data.

Dynamical Analysis of Non-Repetitive Trajectories in Robotic Manipulation

A new method for the study and optimization of manu«ipulator trajectories is developed. The novel feature resides on the modeling formulation. Standard system desciptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyze. Moreover, the derived algorithms are suited to "deterministic" tasks, such as those appearing in a repetitivework, and are not well adapted to a "random" operation that occurs in intelligent systems interacting with a non-structured and changing environment. These facts motivate the development of alternative models based on distinct concepts. The proposed embedding of statistics and Fourier trasnform gives a new perspective towards the calculation and optimization of the robot trajectories in manipulating tasks.

Prognostic Value of a New Cardiopulmonary Exercise Testing Parameter in Chronic Heart Failure: Oxygen Uptake Efficiency at Peak Exercise - Comparison with Oxygen Uptake Efficiency Slope

INTRODUCTION: A growing body of evidence shows the prognostic value of oxygen uptake efficiency slope (OUES), a cardiopulmonary exercise test (CPET) parameter derived from the logarithmic relationship between O(2) consumption (VO(2)) and minute ventilation (VE) in patients with chronic heart failure (CHF). OBJECTIVE: To evaluate the prognostic value of a new CPET parameter - peak oxygen uptake efficiency (POUE) - and to compare it with OUES in patients with CHF. METHODS: We prospectively studied 206 consecutive patients with stable CHF due to dilated cardiomyopathy - 153 male, aged 53.3±13.0 years, 35.4% of ischemic etiology, left ventricular ejection fraction 27.7±8.0%, 81.1% in sinus rhythm, 97.1% receiving ACE-Is or ARBs, 78.2% beta-blockers and 60.2% spironolactone - who performed a first maximal symptom-limited treadmill CPET, using the modified Bruce protocol. In 33% of patients an cardioverter-defibrillator (ICD) or cardiac resynchronization therapy device (CRT-D) was implanted during follow-up. Peak VO(2), percentage of predicted peak VO(2), VE/VCO(2) slope, OUES and POUE were analyzed. OUES was calculated using the formula VO(2) (l/min) = OUES (log(10)VE) + b. POUE was calculated as pVO(2) (l/min) / log(10)peakVE (l/min). Correlation coefficients between the studied parameters were obtained. The prognosis of each variable adjusted for age was evaluated through Cox proportional hazard models and R2 percent (R2%) and V index (V6) were used as measures of the predictive accuracy of events of each of these variables. Receiver operating characteristic (ROC) curves from logistic regression models were used to determine the cut-offs for OUES and POUE. RESULTS: pVO(2): 20.5±5.9; percentage of predicted peak VO(2): 68.6±18.2; VE/VCO(2) slope: 30.6±8.3; OUES: 1.85±0.61; POUE: 0.88±0.27. During a mean follow-up of 33.1±14.8 months, 45 (21.8%) patients died, 10 (4.9%) underwent urgent heart transplantation and in three patients (1.5%) a left ventricular assist device was implanted. All variables proved to be independent predictors of this combined event; however, VE/VCO2 slope was most strongly associated with events (HR 11.14). In this population, POUE was associated with a higher risk of events than OUES (HR 9.61 vs. 7.01), and was also a better predictor of events (R2: 28.91 vs. 22.37). CONCLUSION: POUE was more strongly associated with death, urgent heart transplantation and implantation of a left ventricular assist device and proved to be a better predictor of events than OUES. These results suggest that this new parameter can increase the prognostic value of CPET in patients with CHF.

Price-setting dynamical duopoly with incomplete information

We consider a price competition in a duopoly with substitutable goods, linear and symmetric demand. There is a firm (F 1) that chooses first the price p 1 of its good; the other firm (F 2) observes p 1 and then chooses the price p 2 of its good. The conclusions of this price-setting dynamical duopoly are substantially altered by the presence of either differentiated goods or asymmetric information about rival’s production costs. In this paper, we consider asymmetric information about rival’s production costs. We do ex-ante and ex-post analyses of firms’ profits and market prices. We compare the ex-ante firms’ expected profits with the ex-post firms’ profits.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.