Foundations & Physics  (FP) Session 3

Abstract: Anomalous diffusion processes, in particular superdiffusive ones, are known to be powerful strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are Lévy Flights, where the walkers are allowed to perform jumps, the “flights”, that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a 1D lattice, “cascades” of n unitary steps instead of a jump in the Lévy case. In analogy with the Lévy approach, the size of such cascades is distributed according to a power-law tailed PDF P(n); on the other hand, at difference with Lévy Flights, we do not require an a priori knowledge of the jump length since, in our model, the walker follows strictly local rules. We thus show that this local mechanism for the walk gives indeed rise to superdiffusion or normal diffusion according to the P(n) power law exponent. We also investigate the interplay with the possibility to be stuck on a node, introducing waiting times that are power-law distributed as well. In this case, the competition of the two processes extends the palette of the reachable diffusion regimes and, again, this switch relies on the two PDF's power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks. Close

Abstract: We will show some of the recent result in our group concerning dynamics in multiplex networks. On the one hand we consider multiplex networks as set of nodes in different layers. At each layer the set of nodes is the same but the connections among the nodes can be different in the layers. Furthermore the connections among the layers is described by a “network of layers”. We have studied different processes across the layers (diffusion) and between the layers (reaction) [1]. In this case Turing patterns appear as an effect of different average connectivities in different layers [2]. We also show that a multiplex construction where the layers correspond to contexts in which agents make different sets of connections can make a model of opinion formation to show stationary states of coexistence that are not observed in simple layers [3]. Finally, as a particular case of multiplex network, one can also analyze networks that change in time, since in this case each layer of the multiplex corresponds to a snapshot of the interaction pattern. For this situation, we have shown that there are different mechanisms that dominate the diffusion of information in the system depending on the relative effect of mobility and diffusion among the nodes [4]. [1] Replicator dynamics with diffusion on multiplex networks. RJ Requejo, A. Diaz-Guilera. Arxiv:1601.05658 (2016) [2] Pattern formation in multiplex networks. NE Kouvaris, S Hata & A. Diaz-Guilera. Scientific Reports 5, Article number: 10840 (2015) [3] Agreement and disagreement on multiplex networks. R Amato, N E Kouvaris, M San Miguel and Albert Díaz-Guilera, in preparation. [4] Tuning Synchronization of Integrate-and-Fire Oscillators through Mobility. L. Prignano, O. Sagarra, and A. Díaz-Guilera Phys. Rev. Lett. 110, 114101 (2013) Close

Abstract: The interplay of multiple types of interactions has been of interest in the social sciences for decades. Recent advances in the complexity sciences allow the analysis of such multilayer networks in a quantitative way. The question to what extent nodes are similarly important in all layers arises naturally. We define the promiscuity of a node as a measure for the variability of its degree across layers. This builds on similar frameworks that investigate such questions in networks with modular structure while taking into account that different layers can vary in their importance themselves. Using those tools on a range of empirical networks from a variety of disciplines including transportation, economic and social interactions, and biological regulation we show that the observed promiscuity distributions are different on the networks of different origins. Transportation networks, for example, where the layers represent different modes of transportation tend to have a majority of low promiscuity nodes. A few hub nodes with high promiscuity enable the transit between different modes of transportation. The representation of global trade as a multilayer network reveals that country’s imports are often very diverse whereas the export of some countries depends extremely on a single commodity. Employing the promiscuity on transcription factor interaction in multiple cell types reveals proteins that are potential biomarkers of cell fate. Despite its simplicity, the presented framework gives novel insights into numerous types of multilayer networks and expands the available toolbox for multilayer network analysis. Close

Abstract: Collective phenomena have investigated in various fields of science, such as material science, biological science and social science. Examples of such phenomena are slacking of granular media, group formation of organisms, jam formation in traffic flow and lane formation of pedestrians. Scientists usually investigate them only using the equation of motion of individuals directly. It is generally difficult to derive the macroscopic laws of collective behaviors from such microscopic models. We challenge to develop a new approach to analyze macroscopic laws of these phenomena. In this paper, we describe collective behaviors in a low-dimensional space of macroscopic states obtained by dimensionality reduction. Such a space is constructed by using Diffusion maps as one of the pattern classification techniques. We obtain a few appropriate coarse-grained variables to distinguish the macroscopic states by the similarity of patterns, and we construct the low-dimensional space. A time development of collective behavior is represented as a trajectory in the space. We apply this method to the optimal velocity model for the analysis of the macroscopic property of traffic jam formation. The phenomena is considered as the dynamical phase transition of a non-equilibrium system. The important property of the transition is bistability of jammed flow and free flow. This property has been investigated by many researchers using the model. However their analysis does not satisfactory explain. Using our method, we clearly reveal a bifurcation structure, which features the bistability. Close

Abstract: The self-assembly of simple molecular units into regular 2d (monolayer) lattice patterns continues to provide an exciting intersection between experiment, theory and computational simulation. We study a simple model of polyominoes with edge specific interactions and introduce a visualisation of the configuration space that allows us to identify all possible ground states and the interactions which stabilise them. By considering temperature induced phase transitions away from ground states, we demonstrate kinetic robustness of particular configurations with respect to local rearrangements. We also present a rigorous sampling algorithm for larger lattices where complete enumeration is computationally intractable and discuss common features of the configuration space across different polyomino shapes. Close