Monte Carlo study of the growth of striped domains

We analyze the dynamical scaling behavior in a two-dimensional spin model with competing interactions after a quench to a striped phase. We measure the growth exponents studying the scaling of the interfaces and the scaling of the shrinking time of a ball of one phase plunged into the sea of another phase. Our results confirm the predictions found in previous papers. The correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. Our simulations show anisotropic features for the correlations both in the case of single-spin-flip and spin-exchange dynamics.Comment: 15 pages, ReVTe

Natural clustering: the modularity approach

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally in the case of clustering algorithms that are rooted in Statistical Mechanics and use the analogy with a physical system.Comment: 11 pages, 5 figure enlarged versio

Redundant variables and Granger causality

We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under-estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations.Comment: 4 pages, 5 figures. Accepted for publication in Physical Review

Conserved Ising Model on the Human Connectome

Dynamical models implemented on the large scale architecture of the human brain may shed light on how function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the \it{critical state}) the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of an homeostatic principle imposed to neural activity

Clinical correlates of mathematical modeling of cortical spreading depression: Single‐cases study

Introduction: Considerable connections between migraine with aura and cortical spreading depression (CSD), a depolarization wave originating in the visual cortex and traveling toward the frontal lobe, lead to the hypothesis that CSD is underlying migraine aura. The highly individual and complex characteristics of the brain cor‐ tex suggest that the geometry might impact the propagation of cortical spreading depression. Methods: In a single‐case study, we simulated the CSD propagation for five migraine with aura patients, matching their symptoms during a migraine attack to the CSD wavefront propagation. This CSD wavefront was simulated on a patient‐specific tri‐ angulated cortical mesh obtained from individual MRI imaging and personalized dif‐ fusivity tensors derived locally from diffusion tensor imaging data. Results: The CSD wave propagation was simulated on both hemispheres, despite in all but one patient the symptoms were attributable to one hemisphere. The CSD wave diffused with a large wavefront toward somatosensory and prefrontal regions, devoted to pain processing. Discussion: This case‐control study suggests that the cortical geometry may con‐ tribute to the modality of CSD evolution and partly to clinical expression of aura symptoms. The simulated CSD is a large and diffuse phenomenon, possibly capa‐ ble to activate trigeminal nociceptors and to involve cortical areas devoted to pain processing

Expanding the Transfer Entropy to Identify Information Subgraphs in Complex Systems

We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion are associated to informational circuits present in the system, with an informational character which can be associated to the sign of the contribution. For the sake of computational complexity, we adopt the assumption of Gaussianity and use the corresponding exact formula for the conditional mutual information. We report the application of the proposed methodology on two EEG data sets

Anisotropic dynamical scaling in a spin model with competing interactions

Results are presented for the kinetics of domain growth of a two-dimensional Ising spin model with competing interactions quenched from a disordered to a striped phase. The domain growth exponent are $\beta=1/2$ and $\beta=1/3$ for single-spin-flip and spin-exchange dynamics, as found in previous simulations. However the correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. In the case of single-spin-flip dynamics an anisotropic version of the Ohta-Jasnow-Kawasaki theory for the pair scaling function can be used to fit our data.Comment: 4 pages, REVTeX fil

Clustering data by inhomogeneous chaotic map lattices

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system corresponds to a macroscopic attractor independent of the initial conditions. The mutual information between couples of maps serves to partition the data set in clusters, without prior assumptions about the structure of the underlying distribution of the data. Experiments on simulated and real data sets show the effectiveness of the proposed algorithm.Comment: 8 pages, 6 figures. Revised version accepted for publication on Physical Review Letter

Phase shifts of synchronized oscillators and the systolic/diastolic blood pressure relation

We study the phase-synchronization properties of systolic and diastolic arterial pressure in healthy subjects. We find that delays in the oscillatory components of the time series depend on the frequency bands that are considered, in particular we find a change of sign in the phase shift going from the Very Low Frequency band to the High Frequency band. This behavior should reflect a collective behavior of a system of nonlinear interacting elementary oscillators. We prove that some models describing such systems, e.g. the Winfree and the Kuramoto models offer a clue to this phenomenon. For these theoretical models there is a linear relationship between phase shifts and the difference of natural frequencies of oscillators and a change of sign in the phase shift naturally emerges.Comment: 8 figures, 9 page