Spectral dimension reduction of complex dynamical networks

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes' dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.Comment: 16 pages, 8 figure

Fluid-driven seismicity in a stable tectonic context: The Remiremont fault zone, Vosges, France

Some relocated seismic events, which have small magnitudes (ML < 4.8), are found to align along a 40 km-long fault zone flanking the southern Vosges Massif to the west. It joins to the south with the epicentral area of the historical 1682 earthquake (Io = VIII MSK). The Remiremont cluster was preceded by a period of seismic coalescence and triggered outward of bilateral seismic migration. The 1984 seismic crisis developed along a well defined 3 km-long vertical plane. In both cases, migration rates of the order of 5–10 km/yr over 30 km-long distances are determined. This pattern requires some mechanism of stress interaction which must act over distances of the order of 1 to 20 km within years. Given the low tectonic activity and the magnitudes of the events the stress transfer cannot result from co-seismic elastic loading or from transient strain at depth. We suggest that the seismic activity reflect rupture of asperities driven by fluid-flow in a zone of relatively high permeability

Structural relaxation around substitutional Cr3+ in MgAl2O4

The structural environment of substitutional Cr3+ ion in MgAl2O4 spinel has been investigated by Cr K-edge Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES) spectroscopies. First-principles computations of the structural relaxation and of the XANES spectrum have been performed, with a good agreement to the experiment. The Cr-O distance is close to that in MgCr2O4, indicating a full relaxation of the first neighbors, and the second shell of Al atoms relaxes partially. These observations demonstrate that Vegard's law is not obeyed in the MgAl2O4-MgCr2O4 solid solution. Despite some angular site distortion, the local D3d symmetry of the B-site of the spinel structure is retained during the substitution of Cr for Al. Here, we show that the relaxation is accomodated by strain-induced bond buckling, with angular tilts of the Mg-centred tetrahedra around the Cr-centred octahedron. By contrast, there is no significant alteration of the angles between the edge-sharing octahedra, which build chains aligned along the three four-fold axes of the cubic structure.Comment: 7 pages, 4 figure

Speed and Atmosphere Influences on Nanotribological Properties of NbSe2

Nanotribological properties of NbSe2 are studied using an atomic friction force microscope. The friction force is measured as a function of normal load and scan speeds ranging from 10 nm s−1 to 40 μm s−1 under two atmospheres (air and argon). At low speed, no effect of atmosphere is noticed and a linear relationship between the friction and normal forces is observed leading to a friction coefficient close to 0.02 for both atmospheres. At high speed, the tip/surface contact obeys the JKR theory and the tribological properties are atmosphere dependent: the shear stress measured in air environment is three times lower than the one measured under argon atmosphere. A special attention is paid to interpret these results through numerical data obtained from a simple athermal model based on Tomlinson approach

Complex networks as an emerging property of hierarchical preferential attachment

Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.Comment: 12 pages, 7 figure

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework, we provide a detailed analysis of the stationary state that covers, for a given structure, every dynamic regimes easily tuned by the rewiring rate. This analysis is suitable for the characterization of the phase transition and leads to three main contributions. (i) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (ii) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (iii) We reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon : observables for different degree classes have a different scaling with the infection rate. This leads to the successive activation of the degree classes beyond the epidemic threshold.Comment: 14 pages, 11 figure

Assessment of Olfactory Perception in Individuals with Motion Sickness

BACKGROUND: Individuals who experience motion sickness (MS) frequently mention the presence of smells in the environment as a factor favoring the occurrence of MS symptoms. The aim of the present work was to compare olfactory function in MS sensitive (MS+) and insensitive (MS-) subjects. METHODS: Olfactory testing included determination of odor detection thresholds, subjective evaluation of the quality (intensity, hedonicity, and familiarity) of three different odorants (limonene, isovaleric acid, and petrol) as well as measures of skin conductance responses to these three odorants. RESULTS: Results showed no difference in olfactory sensitivity between MS+ and MS- subjects. However, findings of both subjective (odor quality self-rating) and objective (psychophysiological responses) measures did reveal that the affective response to petrol odor was significantly different in MS+ and in MS- subjects. Indeed, on a scale from 0 (unpleasant) to 10 (pleasant) MS+ subjects rated petrol odor as more unpleasant (mean = 2.52) than MS- subjects (mean = 4.15) and rise-time of skin conductance responses to petrol odor was significantly longer in MS+ (mean = 5.98 s) compared to MS- subjects (mean = 3.22 s). DISCUSSION: Our study delves further into the knowledge of the relationship between motion sickness and olfaction by demonstrating a modified olfactory perception in motion sickness sensitive subjects at both the psychophysical and psychophysiological levels

The Influence of Odors on Time Perception

International audienceThe effect of an olfactory stimulation on the perception of time was investigated through two different experiments based on temporal bisection tasks. In experiment 1, the durations to be classified as either short or long were centered on 400 ms while in Experiment 2 there were centered on 2000 ms. The participants were different in the two experiments (36 subjects in each one). In each experiment, half of the subjects learnt the anchor durations when smelling an unpleasant odor (decanoic acid) and the other half when smelling no odor. After the learning phase, both groups were tested with and without odor. The results showed opposite effects depending on the duration range. The subjects underestimated the time in the presence of the unpleasant odor in the short duration range while they overestimated it in the long duration range. The results have been discussed in the framework of the pacemaker-counter clock model and a potential emotional effect induced by the odor on the subjective time perception has also been considered