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.

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.

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.

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).

Applications of nonlinear dynamics to clinical cardiology.

(1) Nonlinear mechanisms may apply both to the understanding of SA-AV node interactions and to bifurcations leading to certain types of AV block. (2) The fractal His-Purkinje system serves as the structural substrate for the generation of the broadband, inverse power-law spectrum of the stable ventricular depolarization (QRS) waveform. (3) Fractal anatomy is also seen in multiple other systems: pulmonary, hepatobiliary, renal, etc. Fractal morphogenesis may reflect a type of critical phenomenon that results in the generation of these irregular, but self-similar structures. (4) Self-similar (fractal) scaling may underlie the 1/f-like spectra seen in multiple systems (e.g., interbeat interval variability, daily neutrophil fluctuations). This fractal scaling may provide a mechanism for the "constrained randomness" that appears to underlie physiological variability and adaptability. (5) Behavior consistent with subharmonic bifurcations is seen in cardiac electrophysiology (e.g., sick sinus syndrome) and hemodynamic perturbations (e.g., swinging heart phenomenon in pericardial tamponade). (6) Ventricular tachyarrhythmias associated with sudden cardiac death (e.g., torsades de pointes, ventricular fibrillation) appear to reflect relatively periodic, not chaotic (turbulent) processes resulting from disruption of the physiologic fractal depolarization sequence. (7) Spectral analysis of Holter monitor data may help in the detection of patients at high risk for sudden death.

Beyond the principle of similitude: renormalization in the bronchial tree.

The average dimensions (diameter, length, and volume) of the airways in the mammalian bronchial tree, long thought to be exponential functions of the generation number, are shown to be power laws in generation number modulated by a harmonic variation. These data are satisfactorily described by means of a functional scaling relation--renormalization group property--between successive generations for the average variable of interest. This type of scaling may provide a mechanism for the morphogenesis of complex but highly stable structures.

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.

The momentum of human behavior in a natural setting.

Adults with mental retardation in a group home received popcorn or coffee reinforcers for sorting plastic dinnerware. In Part 1 of the experiment, reinforcers were dispensed according to a variable-interval 60-s schedule for sorting dinnerware of one color and according to a variable-interval 240-s schedule for sorting dinnerware of a different color in successive components of a multiple schedule. Sorting rates were similar in baseline, but when a video program was shown concurrently, sorting of dinnerware was more resistant to distraction when correlated with a higher rate of reinforcement. In Part 2 of the experiment, popcorn or coffee reinforcers were contingent upon sorting both colors of dinnerware according to variable-interval 60-s schedules, but additional reinforcers were given independently of sorting according to a variable-time 30-s schedule during one dinnerware-color component. Baseline sorting rate was lower but resistance to distraction by the video program was greater in the component with additional variable-time reinforcers. These results demonstrate that resistance to distraction depends on the rate of reinforcers obtained in the presence of component stimuli but is independent of baseline response rates and response-reinforcer contingencies. Moreover, these results are similar to those obtained in laboratory studies with pigeons, demonstrating that the determination of resistance to change by stimulus-reinforcer relations is not confined to controlled laboratory settings or unique to the pigeon.

Analysis of demand conditions associated with reluctant speech.

An analysis of five demand conditions affecting the reluctant speech of a preschool child was conducted in the classroom. Results indicated that demand conditions that did not permit escape from academic demand tasks, ignored mute responses, prompted answers and enthusiastically praised verbal responses resulted in higher rates of speech. Further, replication of these procedures across escape conditions resulted in increased speech rates that approximated those of a non-mute peer in the same classroom. Follow-up data at 8 months indicated that in the classroom the subject spoke more often to more people using a greater number of words, subsequent to analysis and intervention. The classroom teacher also reported a marked improvement in speech rate and quality and considered the time spent in analysis worthwhile. The study provides a model for further analysis of conditions associated with reluctant speech.

Dentaline: an out of hours emergency dental service in Kent.

Following wide consultation in 1991 on how to meet the requirement for out-of-hours emergency service provision, Kent Family Health Services Authority established three emergency dental clinics. The sites chosen were in or adjacent to District General Hospital Accident and Emergency Departments. Local dentists were contracted to provide a service each evening and also weekend and bank holiday mornings. Activity is reported for the three and a quarter year period from October 1991 to December 1994 with 300 dentists operating a rota to attend the clinics to provide 'occasional treatment' for all-comers. Drugs, if required, are dispensed directly and, where appropriate, NHS charges levied. On average, each operator works once every 3 months.

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.

Behavioral momentum in the treatment of noncompliance.

Behavioral momentum refers to the tendency for behavior to persist following a change in environmental conditions. The greater the rate of reinforcement, the greater the behavioral momentum. The intervention for noncompliance consisted of issuing a sequence of commands with which the subject was very likely to comply (i.e., high-probability commands) immediately prior to issuing a low-probability command. In each of five experiments, the high-probability command sequence resulted in a "momentum" of compliant responding that persisted when a low-probability request was issued. Results showed the antecedent high-probability command sequence increased compliance and decreased compliance latency and task duration. "Momentum-like" effects were shown to be distinct from experimenter attention and to depend on the contiguity between the high-probability command sequence and the low-probability command.

Surgical nurse principles of audit and clinical practice.

Health-care providers and purchasers have been concerned with developing methods to assure the quality of the service provided in clinical contexts. Crucial to this is the integration of multidisciplinary clinical audit techniques which facilitate good practice.

Immediate postoperative recovery: measurement and care.

When considering the postoperative care of surgical patients, there are three time periods that are important for both the patient's wellbeing and the planning of nursing care. These are termed the immediate recovery period, the intermediate stage of dependency, and the more long-term process of returning to normality. This article concentrates on the first of these stages.

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.

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.