plex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference ⌬ between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index ␥ ϭ ͗sin⌬͘ 2 ϩ ͗cos⌬͘ 2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the groupaveraged index ␥ has two distinct peaks, one at 0.11 Hz [␥ ϭ 0.59 Ϯ 0.09] and another at 0.33 Hz (␥ ϭ 0.55 Ϯ 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 Ϯ 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced. cerebral blood flow; transcranial Doppler sonography; wavelets; synchronization THE STATISTICAL PROPERTIES of physiological fluctuations, such as those found in the time series for heartbeat dynamics (10, 28), respiration (1, 27, 40), human locomotion (11, 39), and posture control (4), have been the focus of interdisciplinary research for more than two decades. This research has underscored the significance of nonlinear and nonstationary aspects of intrinsic variability of many physiological phenomena. Such variability seems to indicate the adaptability of the underlying control systems. The change of paradigm, associated with how we view the dynamics of physiologic phenomena, has not, to date, significantly influenced the interpretation of fluctuations in cerebral hemodynamics. In particular, the mathematical analysis of the fluctuations in either intracranial pressure or cerebral blood flow (CBF) velocity (CBFV) in major arteries is largely confined to traditional spectral methods.A healthy human brain is perfused with blood flowing laminarly through cerebral vessels, providing brain tissue with substrates such as oxygen and glucose. It turns out that CBF...

We study a fully connected network ͑cluster͒ of interacting two-state units as a model of cooperative decision making. Each unit in isolation generates a Poisson process with rate g. We show that when the number of nodes is finite, the decision-making process becomes intermittent. The decision-time distribution density is characterized by inverse power-law behavior with index = 1.5 and is exponentially truncated. We find that the condition of perfect consensus is recovered by means of a fat tail that becomes more and more extended with increasing number of nodes N. The intermittent dynamics of the global variable are described by the motion of a particle in a double well potential. The particle spends a portion of the total time S at the top of the potential barrier. Using theoretical and numerical arguments it is proved that S ϰ ͑1 / g͒ln͑constϫ N͒. The second portion of its time, K , is spent by the particle at the bottom of the potential well and it is given by K = ͑1 / g͒exp͑constϫ N͒. We show that the time K is responsible for the Kramers fat tail. This generates a stronger ergodicity breakdown than that generated by the inverse power law without truncation. We establish that the condition of partial consensus can be transmitted from one cluster to another provided that both networks are in a cooperative condition. No significant information transmission is possible if one of the two networks is not yet self-organized. We find that partitioning a large network into a set of smaller interacting clusters has the effect of converting the fat Kramers tail into an inverse power law with = 1.5.

We study a decision making model in a condition where it is equivalent to the two-dimensional Ising model, and we show that at the onset of phase transition it generates temporal complexity, namely, nonstationary and nonergodic fluctuations. We argue that this is a general property of criticality, thereby opening the door to the application of the recently discovered phenomenon of complexity matching: For an efficient transfer of information to occur, a perturbing complex network must share the same temporal complexity as the perturbed complex network.

According to an increasing number of researchers intelligence emerges from criticality as a consequence of locality breakdown and long-range correlation, well known properties of phase transition processes. We study a model of interacting units, as an idealization of real cooperative systems such as the brain or a flock of birds, for the purpose of discussing the emergence of long-range correlation from the coupling of any unit with its nearest neighbors. We focus on the critical condition that has been recently shown to maximize information transport and we study the topological structure of the network of dynamically linked nodes. Although the topology of this network depends on the arbitrary choice of correlation threshold, namely the correlation intensity selected to establish a link between two nodes; the numerical calculations of this paper afford some important indications on the dynamically induced topology. The first important property is the emergence of a perception length as large as the flock size, thanks to some nodes with a large number of links, thus playing the leadership role. All the units are equivalent and leadership moves in time from one to another set of nodes, thereby insuring fault tolerance. Then we focus on the correlation threshold generating a scale-free topology with power index ν ≈ 1 and we find that if this topological structure is selected to establish consensus through the linked nodes, the control parameter necessary to generate criticality is close to the critical value corresponding to the all-to-all coupling condition. We find that criticality in this case generates also a third state, corresponding to a total lack of consensus. However, we make a numerical analysis of the dynamically induced network, and we find that it consists of two almost independent structures, each of which is equivalent to a network in the all-to-all coupling condition. This observation confirms that cooperation makes the system evolve toward favoring consensus topological structures. We argue that these results are compatible with both Hebbian learning and fault tolerance.

A series of authored and edited monographs that utilize quantitative and computational methods to model, analyze, and interpret large-scale social phenomena. Titles within the series contain methods and practices that test and develop theories of complex social processes through bottom-up modeling of social interactions. Of particular interest is the study of the co-evolution of modern communication technology and social behavior and norms, in connection with emerging issues such as trust, risk, security, and privacy in novel socio-technical environments.Computational Social Sciences is explicitly transdisciplinary: quantitative methods from fields such as dynamical systems, artificial intelligence, network theory, agent-based modeling, and statistical mechanics are invoked and combined with state-of-the-art mining and analysis of large data sets to help us understand social agents, their interactions on and offline, and the effect of these interactions at the macro level. Topics include, but are not limited to social networks and media, dynamics of opinions, cultures and conflicts, socio-technical co-evolution, and social psychology. Computational Social Sciences will also publish monographs and selected edited contributions from specialized conferences and workshops specifically aimed at communicating new findings to a large transdisciplinary audience. A fundamental goal of the series is to provide a single forum within which commonalities and differences in the workings of this field may be discerned, hence leading to deeper insight and understanding.