L. Guzmán-Vargas

The Dynamic Consequences of Cooperation and Competition in Small-World Networks

We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.

Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine

In this work we present a local stability analysis of the thermo-economic model of an irreversible heat engine working at maximum power conditions. The thermo-economic model is based on the maximization of a benefit function which is defined by the ratio of the power output and the total cost involved in the plant’s performance. Our study shows that, after a small perturbation, the system decays exponentially to the steady state determined by two different relaxation times. In particular, we show that the relaxation times are function of the temperature ratio τ = T2/T1 (T1 > T2), the cost function ƒ and the parameter R (a parameter related to the degree of internal irreversibilities). We observe that the stability of the system improves as τ increases whereas for changes in ƒ and R, the stability properties are characterized by a rapid decay along the fast eigendirection as ƒ increases and R decreases. Finally, we discuss our results in the context of energetic properties.

Fluctuations in the Energetic Properties of a Spark-Ignition Engine Model with Variability

We study the energetic functions obtained in a simulated spark-ignited engine that incorporates cyclic variability through a quasi-dimensional combustion model. Our analyses are focused on the effects of the fuel-air equivalence ratio of the mixture simultaneously over the cycle-to-cycle fluctuations of heat release (QR) and the performance outputs, such as the power (P) and the efficiency (QR). We explore the fluctuant behavior for QR, P and n related to random variations of the basic physical parameters in an entrainment or eddy-burning combustion model. P and n show triangle shaped first return maps, while QR exhibits a structured map, especially at intermediated fuel-air ratios. Structure disappears to a considerable extent in the case of heat release and close-to-stoichiometry fuel-air ratios. By analyzing the fractal dimension to explore the presence of correlations at different scales, we find that whereas QR displays short-range correlations for intermediate values of the fuel ratio, both P and n are characterized by a single scaling exponent, denoting irregular fluctuations. A novel noisy loop-shaped P vs. n plot for a large number of engine cycles is obtained. This plot, which evidences different levels of irreversibilities as the fuel ratio changes, becomes the observed loop P vs. n curve when fluctuations are disregarded, and thus, only the mean values for efficiency and power are considered.

Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis

We study the correlation properties of word lengths in large texts from 30 ebooks in the English language from the Gutenberg Project (www.gutenberg.org) using the natural visibility graph method (NVG). NVG converts a time series into a graph and then analyzes its graph properties. First, the original sequence of words is transformed into a sequence of values containing the length of each word, and then, it is integrated. Next, we apply the NVG to the integrated word-length series and construct the network. We show that the degree distribution of that network follows a power law, P ( k ) ∼ k - γ , with two regimes, which are characterized by the exponents γ s ≈ 1 . 7 (at short degree scales) and γ l ≈ 1 . 3 (at large degree scales). This suggests that word lengths are much more strongly correlated at large distances between words than at short distances between words. That finding is also supported by the detrended fluctuation analysis (DFA) and recurrence time distribution. These results provide new information about the universal characteristics of the structure of written texts beyond that given by word frequencies.

Effects of Direct Fuel Injection Strategies on Cycle-by-Cycle Variability in a Gasoline Homogeneous Charge Compression Ignition Engine: Sample Entropy Analysis

In this study we summarize and analyze experimental observations of cyclic variability in homogeneous charge compression ignition (HCCI) combustion in a single-cylinder gasoline engine. The engine was configured with negative valve overlap (NVO) to trap residual gases from prior cycles and thus enable auto-ignition in successive cycles. Correlations were developed between different fuel injection strategies and cycle average combustion and work output profiles. Hypothesized physical mechanisms based on these correlations were then compared with trends in cycle-by-cycle predictability as revealed by sample entropy. The results of these comparisons help to clarify how fuel injection strategy can interact with prior cycle effects to affect combustion stability and so contribute to design control methods for HCCI engines.

Evolution in time and scales of the stability of heart interbeat rate

We approach heart interbeat rate by observing the evolution of its stability on scales and time, using tools for the analysis of frequency standards. In particular, we employ the dynamic Allan variance, which is used to characterize the time-varying stability of an atomic clock, to analyze heart interbeat time series for normal subjects and patients with congestive heart failure (CHF). Our stability analysis shows that healthy dynamics is characterized by at least two stability regions along different scales. In contrast, diseased patients exhibit at least three different stability regions; over short scales the fluctuations resembled white-noise behavior whereas for large scales a drift is observed. The inflection points delimiting the first two stability regions for both groups are located around the same scales. Moreover, we find that CHF patients show lower variation of the stability in time than healthy subjects.

Global Stability Analysis of a Curzon-Ahlborn Heat Engine under Different Regimes of Performance

We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability.

Scaling differences of heartbeat excursions between wake and sleep periods.

We study the statistical properties of excursions in heart interbeat time series. An excursion is defined as the time employed by a walker to return to its mean value. We consider the homeostatic property of the heartbeat dynamics as a departing point to characterize the dynamics of excursions in beat-to-beat fluctuations. Scaling properties of excursions during wake and sleep periods from two groups are compared: 16 healthy subjects and 11 patients with congestive heart failure (CHF). We find that the cumulative distributions of excursions for both groups follow stretched exponential functions given by g(τ)~e(-aτ(b)) with different fitting parameters a and b, leading to different decaying rates. Our results show that the average characteristic scale associated with the excursion distributions is greater for healthy data compared to CHF patients whereas sleep-wake transitions are more significant for healthy data. Next, we explore changes in the distributions of excursions when considering (i) a shifted mean value to define an excursion and (ii) the sum of the kth excursion successor. Besides, the presence of temporal correlations in the excursions sequences is evaluated by means of the detrended fluctuation analysis. We observe the presence of long-range correlations for healthy subjects, whereas for the CHF group, correlations are described by two regimes; over short scales the fluctuations are close to uncorrelated noise, and for large scales the fluctuations reveal long-range correlations. Finally, we apply a stability analysis of excursions based on the Allan variance which reveals that healthy dynamics is more stable than heart failure excursions.

A comparative study of power law scaling in large word-length sequences

A study of the correlation of lengths of words in large literary texts is presented. We use the statistical tools based on Allan factor and fractal dimension for estimating the fractal indices associated with the presence of correlations in the original sequences. We found that there is a scaling behavior at large scales for Allan factor with an exponent value, which reveals positive correlations. By means of the fractal dimension, we confirmed the presence of memory in the sequences of lengths of words. In addition, when considering a random rearrangement of the lengths of words in the original text, the fractal exponents are consistent with an uncorrelated process.

Evaluating the Irregularity of Natural Languages

In the present work, we quantify the irregularity of different European languages belonging to four linguistic families (Romance, Germanic, Uralic and Slavic) and an artificial language (Esperanto). We modified a well-known method to calculate the approximate and sample entropy of written texts. We find differences in the degree of irregularity between the families and our method, which is based on the search of regularities in a sequence of symbols, and consistently distinguishes between natural and synthetic randomized texts. Moreover, we extended our study to the case where multiple scales are accounted for, such as the multiscale entropy analysis. Our results revealed that real texts have non-trivial structure compared to the ones obtained from randomization procedures.