Relating size and functionality in human social networks through complexity.

Extensive empirical evidence suggests that there is a maximal number of people with whom an individual can maintain stable social relationships (the Dunbar number). We argue that this arises as a consequence of a natural phase transition in the dynamic self-organization among N individuals within a social system. We present the calculated size dependence of the scaling properties of complex social network models to argue that this collective behavior is an enhanced form of collective intelligence. Direct calculation establishes that the complexity of social networks as measured by their scaling behavior is nonmonotonic, peaking around 150, thereby providing a theoretical basis for the value of the Dunbar number. Thus, we establish a theory-based bridge spanning the gap between sociology and psychology.

Critical slowing down in networks generating temporal complexity.

We study a nonlinear Langevin equation describing the dynamic variable X(t), the mean field (order parameter) of a finite size complex network at criticality. The conditions under which the autocorrelation function of X shows any direct connection with criticality are discussed. We find that if the network is prepared in a state far from equilibrium, X(0)=1, the autocorrelation function is characterized by evident signs of critical slowing down as well as by significant aging effects, while the preparation X(0)=0 does not generate evident signs of criticality on X(t), in spite of the fact that the same initial state makes the fluctuating variable η(t)≡sgn(X(t)) yield significant aging effects. These latter effects arise because the dynamics of η(t) are directly dependent on crucial events, namely the re-crossings of the origin, which undergo a significant aging process with the preparation X(0)=0. The time scale dominated by temporal complexity, aging, and ergodicity breakdown of η(t) is properly evaluated by adopting the method of stochastic linearization which is used to explain the exponential-like behavior of the equilibrium autocorrelation function of X(t).

Imitation versus payoff: Duality of the decision-making process demonstrates criticality and consensus formation.

We consider a dual model of decision making, in which an individual forms its opinion based on contrasting mechanisms of imitation and rational calculation. The decision-making model (DMM) implements imitating behavior by means of a network of coupled two-state master equations that undergoes a phase transition at a critical value of a control parameter. The evolutionary spatial game, being a generalization of the prisoner's dilemma game, is used to determine in objective fashion the cooperative or anticooperative strategy adopted by individuals. Interactions between two sources of dynamics increases the domain of initial states attracted to phase transition dynamics beyond that of the DMM network in isolation. Additionally, on average the influence of the DMM on the game increases the final observed fraction of cooperators in the system.

Chipping away at memory.

Inverse power-law behavior is known to be characteristic of adaptation, learning, and memory. Herein, we propose a phenomenological model of forgetting based on renewal theory that introduces a new psychophysical concept, chipping; discrete events that chip away at chunks of memory and thereby produce forgetting. The neural mechanism producing these chips is the 1/f-noise that is generically produced in complex neuronal networks.

Dynamics of electroencephalogram entropy and pitfalls of scaling detection.

In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein we study the time evolution of diffusion entropy to elucidate the scaling of EEG time series. For a cohort of 20 awake healthy volunteers with closed eyes, we find that the diffusion entropy of EEG increments (obtained from EEG waveforms by differencing) exhibits three features: short-time growth, an alpha wave related oscillation whose amplitude gradually decays in time, and asymptotic saturation which is achieved after approximately 1 s. This analysis suggests a linear, stochastic Ornstein-Uhlenbeck Langevin equation with a quasiperiodic forcing (whose frequency and/or amplitude may vary in time) as the model for the underlying dynamics. This model captures the salient properties of EEG dynamics. In particular, both the experimental and simulated EEG time series exhibit short-time scaling which is broken by a strong periodic component, such as alpha waves. The saturation of EEG diffusion entropy precludes the existence of asymptotic scaling. We find that the crossover between two scaling regions seen in detrended fluctuation analysis (DFA) of EEG increments does not originate from the underlying dynamics but is merely an artifact of the algorithm. This artifact is rooted in the failure of the "trend plus signal" paradigm of DFA.

Sun-climate complexity linking.

It is known that Earth's short-term temperature anomalies share the same complexity index mu as solar flares. We show that this property is not accidental and is a consequence of the phenomenon of information transfer based on the crucial role of non-Poisson renewal events in complex networks.

Noni as an anxiolytic and sedative: a mechanism involving its gamma-aminobutyric acidergic effects.

Noni (Morinda citrifolia) is increasing in worldwide popularity as a food or dietary supplement with versatile health benefits. The aim of this study was to investigate the effects of Noni fruit on anxiety symptoms in vitro. To this end, a competitive GABAa receptor-binding assay was developed. Our preliminary study indicates that the methanol crude extract of Noni fruit showed significant affinity to the gamma-aminobutyric acid A (GABAa) inhibitory neurotransmitter receptors, and displayed 75% binding inhibition of the agonist radioligand [3H] muscimol at a concentration of 100 microg/ml. Further experiments demonstrated that the MeOH extract, and its BuOH and H2O partitions, exhibited IC50 values of 22.8, 27.2, and 17.1 microg/ml, respectively, in the GABAa-binding assay. Experimental results with Noni fruit indicate the presence of competitive ligand(s), which may bind to the GABAa receptor as an agonist, and thus induce its anxiolytic and sedative effects. The study provides an in vitro rationale for one of Noni's versatile and traditional uses. In addition, an HPLC fingerprint profile of the methanolic extract of Noni fruit has been established for quality control purpose.

Wavelet assessment of cerebrospinal compensatory reserve and cerebrovascular reactivity.

We introduce a wavelet transfer model to relate spontaneous arterial blood pressure (ABP) fluctuations to intracranial pressure (ICP) fluctuations. We employ a complex continuous wavelet transform to develop a consistent mathematical framework capable of parametrizing both cerebral compensatory reserve and cerebrovascular reactivity. The frequency-dependent gain and phase of the wavelet transfer function are introduced because of the non-stationary character of the ICP and ABP time series. The gain characterizes the dampening of spontaneous ABP fluctuations and is interpreted as a novel measure of cerebrospinal compensatory reserve. For a group of 12 patients who died as a result of cerebral lesions (Glasgow Outcome Scale (GOS) = 1) the average gain in the low-frequency (0.02- 0.07 Hz) range was 0.51 +/- 0.13 and significantly exceeded that of 17 patients with GOS = 2 having an average gain of 0.26 +/- 0.11 with p = 1x10(-4) (Kruskal-Wallis test). A time-averaged synchronization index (which may vary from 0 to 1) defined in terms of the wavelet transfer function phase yields information about the stability of the phase difference of the ABP and ICP signals and is used as a cerebrovascular reactivity index. A low value of synchronization index reflects a normally reactive vascular bed, while a high value indicates pathological entrainment of ABP and ICP fluctuations. Such entrainment is strongly pronounced in patients with fatal outcome (for this group the low-frequency synchronization index was 0.69 +/- 0.17). The gain and synchronization parameters define a cerebral hemodynamic state space (CHS) in which the patients with GOS = 1 are to large extent partitioned away from those with GOS = 2. The concept of CHS elucidates the interplay of vascular and compensatory mechanisms.

Wavelet mapping of sleep spindles in young patients with epilepsy.

Using the wavelet mapping of sleep spindles we investigated influence of focal epilepsy on spindle generation. We found that the maximum of sleep spindle intensity is usually localized away from the epileptic focus. We discuss the possibility of the application of wavelet mapping for localization of epileptic foci prior to epileptic neurosurgery.

Seasonality of birth and conception to teenagers in Texas.

We study the births to teenagers during the years 1964-2000 and analyze separately the three main racial/ethnic groups in Texas (White, Hispanic, and African American), as well as married and unmarried teens during the years 1994-2000. By using traditional statistical methods of analysis and a filter based on the multiresolution wavelet analysis, we draw inferences about the times of the year when adolescent females of different racial/ethnic and marital groups have the highest probability for pregnancy ending in live birth. Multiple factors influencing teen pregnancy are identified and associated with temporal features of social, cultural, educational, and familial processes. In particular, we detect links between unmarried teen conception times and school terms, and weekly birth patterns associated with scheduled c-sections that differ according to racial/ethnic groups.

Canonical and noncanonical equilibrium distribution.

We address the problem of the dynamical foundation of noncanonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of noncanonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the noncanonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Lévy statistics are the best description of the dynamics and that the Lévy distribution is the correct basin of attraction. We also show that the correct path to noncanonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics.

Fractal probability measures of learning.

Herein we introduce a technique for determining the fractal dimension of time series obtained from complex systems, in particular brain-wave data in which the fractal dimension is arguably a measure of awareness and learning. The technique is based on determining the probability distribution for the degree of irregularity in random time series and has been shown to be superior in terms of efficiency and reliability to more commonly used methods that rely on the correlation function. We speculate that the scaling behavior of the probability measure is an indicator of an allometric relation between learning and brain-wave activity.

Non-normal Statistics of DNA Sequences of Prokaryotes.

The √ n-rule of Schrödinger in his discussion of DNA is based onnormal statistics and equilibrium physics. Herein the kurtosis is used tomeasure the deviation from normality of the stistics of non-equilibrium DNAsequences. A pattern for this deviation from normality is identified andthis signature is found in prokaryotes. The signature is explained by atheory of DNA sequences that involves finite length DNA walks withdynamically generated long-range correlations.

Random stride intervals with memory.

The stride interval in normal human gait is not strictly constant, butfluctuates from step to step in a random manner. Herein we show thatcontrary to the traditional assumption of uncorrelated random errors,these fluctuations have long-time memory. However, rather than being amonofractal process as found earlier, there exists a multiplicative timescale that characterizes the process in addition to the fractal dimension.Further, these long-time correlations are interpreted in terms of anallometric control process.

Fractal fluctuations in cardiac time series.

Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.

Molecular evolution modeled as a fractal renewal point process in agreement with the dispersion of substitutions in mammalian genes.

A fractal renewal point process (FRPP) is used to model molecular evolution in agreement with the relationship between the variance and the mean numbers of nonsynonymous and synonymous substitutions in mammals. Like other episodic models such as the doubly stochastic Poisson process, this model accounts for the large variances observed in amino acid substitution rates, but unlike certain other episodic models, it also accounts for the increase in the index of dispersion with the mean number of substitutions in Ohta's (1995) data. We find that this correlation is significant for nonsynonymous substitutions at the 1% level and for synonymous substitutions at the 10% level, even after removing lineage effects and when using Bulmer's (1989) unbiased estimator of the index of dispersion. This model is simpler than most other overdispersed models of evolution in the sense that it is fully specified by a single interevent probability distribution. Interpretations in terms of chaotic dynamics and in terms of chance and selection are discussed.

Molecular evolution modeled as a fractal Poisson process in agreement with mammalian sequence comparisons.

The fractal doubly stochastic Poisson process (FDSPP) model of molecular evolution, like other doubly stochastic Poisson models, agrees with the high estimates for the index of dispersion found from sequence comparisons. Unlike certain previous models, the FDSPP also predicts a positive geometric correlation between the index of dispersion and the mean number of substitutions. Such a relationship is statistically proven herein using comparisons between 49 mammalian genes. There is no characteristic rate associated with molecular evolution according to this model, but there is a scaling relationship in rates according to a fractal dimension of evolution. The FDSPP is a suitable replacement for the homogeneous Poisson process in tests of the lineage dependence of rates and in estimating confidence intervals for divergence times. As opposed to other fractal models, this model can be interpreted in terms of Darwinian selection and drift.