Malgorzata Turalska

Role of committed minorities in times of crisis

The surprising social phenomena of the Arab Spring and the Occupy Wall Street movement posit the question of whether the active role of committed groups may produce political changes of significant importance. Under what conditions are the convictions of a minority going to dominate the future direction of a society? We address this question with the help of a Cooperative Decision Making model (CDMM) which has been shown to generate consensus through a phase-transition process. We observe that in a system of a finite size the global consensus state is not permanent and times of crisis occur when there is an ambiguity concerning a given social issue. The correlation function within the cooperative system becomes similarly extended as it is observed at criticality. This combination of independence (free will) and long-range correlation makes it possible for very small but committed minorities to produce substantial changes in social consensus.

Cooperation-induced topological complexity: a promising road to fault tolerance and Hebbian learning

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.

Generation of very low frequency cerebral blood flow fluctuations in humans

BACKGROUND Slow oscillations of cerebral blood flow induced by synchronous variations of arterial blood pressure (ABP) are often used for clinical assessment of cerebral autoregulation. In the alternative scenario, spontaneous cerebral vasocycling may produce waves in cerebral blood flow that are, to a large extent, independent of ABP fluctuations. We use wavelet analysis to test the latter hypothesis. METHODS The wavelet variability V(f), defined as the time averaged moduli of frequency dependent wavelet coefficients, is employed to analyze the relation between dynamics of arterial blood pressure and that of cerebral blood flow velocity in middle cerebral artery (MCA). FINDINGS In the very low frequency (VLF, 0.02-0.07 Hz) band the variability in traumatic brain injury (TBI) patients with low intracranial pressure (V(ABP) = 0.36 +/- 0.28) is significantly smaller than that of the volunteers (V(ABP) = 0.70 +/- 0.25) with p = 7 x 10(-5). Interestingly, the corresponding variabilities of MCA flow velocity for both cohorts are comparable. V(MCA) = 0.83 +/- 0.65 of the brain injury patients is not statistically different from that of the volunteers V(MCA) = 1.06 +/- 0.41 (p = 0.11). CONCLUSIONS In TBI patients without cerebral hypertension, the VLF oscillations must have been spontaneously generated within intracranial volume to compensate for the reduced ABP variability. Vasomotion is identified as a plausible physiological mechanism underlying such oscillations. We argue that vasomotion may be beneficial for brain tissue oxygenation especially during periods of critically low perfusion.

Fractional Dynamics of Individuals in Complex Networks

The dependence of the behavior of a single individual on the global dynamics of the social network to which it belongs is an open problem in sociology. We demonstrate that for a dynamical network belonging to the Ising universality class this problem can be approached analytically through a subordination procedure. The analysis leads to a linear fractional differential equation of motion for the average trajectory of the individual, whose analytic solution for the probability of changing states is a Mittag-Leffler function. Consequently, the analysis provides a linear description of the average dynamics of an individual, without linearization of the complex network dynamics.