The emergent cooperative behavior of mobile physical entities exchanging information with their neighborhood has become an important problem across disciplines, thus requiring a general framework to describe such a variety of situations. We introduce a generic model to tackle this problem by considering the synchronization in time-evolving networks generated by the stochastic motion of self-propelled physical interacting units. This framework generalizes previous approaches and brings a unified picture to understand the role played by the network topology, the motion of the agents, and their mutual interaction. This allows us to identify different dynamic regimes where synchronization can be understood from theoretical considerations. While for noninteracting particles, self-propulsion accelerates synchronization, the presence of excluded volume interactions gives rise to a richer scenario, where self-propulsion has a nonmonotonic impact on synchronization. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening, verifying the dynamic scaling hypothesis, with the same scaling laws as the 2D XY model following a quench. Our results shed light into the generic nature of synchronization in time-dependent networks, providing an efficient way to understand more specific situations involving interacting mobile agents.

We study a two-filament driven lattice gas model with oppositely directed species of particles moving on two parallel filaments with filament-switching processes and particle inflow and outflow at filament ends. The filament-switching process is correlated with the occupation number of the adjacent site such that particles switch filaments with finite probability only when oppositely directed particles meet on the same filament. This model mimics some of the coarse-grained features observed in context of microtubule-(MT) based intracellular transport, wherein cellular cargo loaded and off-loaded at filament ends are transported on multiple parallel MT filaments and can switch between the parallel microtubule filaments. We focus on a regime where the filaments are weakly coupled, such that filament-switching rate of particles scale inversely as the length of the filament. We find that the interplay of (off-) loading processes at the boundaries and the filament-switching process of particles leads to some distinctive features of the system. These features includes occurrence of a variety of phases in the system with inhomogeneous density profiles including localized density shocks, density difference across the filaments, and bidirectional current flows in the system. We analyze the system by developing a mean field (MF) theory and comparing the results obtained from the MF theory with the Monte Carlo (MC) simulations of the dynamics of the system. We find that the steady-state density and current profiles of particles and the phase diagram obtained within the MF picture matches quite well with MC simulation results. These findings maybe useful for studying multifilament intracellular transport.

We derive the constitutive equations of an active polar gel from a model for the dynamics of elastic molecules that link polar elements. Molecular binding kinetics induces the fluidization of the material, giving rise to Maxwell viscoelasticity and, provided that detailed balance is broken, to the generation of active stresses. We give explicit expressions for the transport coefficients of active gels in terms of molecular properties, including nonlinear contributions on the departure from equilibrium. In particular, when activity favors linker unbinding, we predict a decrease of viscosity with activity-active thinning-of kinetic origin, which could explain some experimental results on the cell cortex. By bridging the molecular and hydrodynamic scales, our results could help understand the interplay between molecular perturbations and the mechanics of cells and tissues.

Collective cell migration in spreading epithelia in controlled environments has become a landmark in our current understanding of fundamental biophysical processes in development, regeneration, wound healing or cancer. Epithelial monolayers are treated as thin layers of a viscous fluid that exert active traction forces on the substrate. The model is exactly solvable and shows a broad range of applicabilities for the quantitative analysis and interpretation of force microscopy data of monolayers from a variety of experiments and cell lines. In addition, the proposed model provides physical insights into how the biological regulation of the tissue is encoded in a reduced set of time-dependent physical parameters. In particular the temporal evolution of the effective viscosity entails a mechanosensitive regulation of adhesion. Besides, the observation of an effective elastic tensile modulus can be interpreted as an emergent phenomenon in an active fluid.

In order to assess the effect of hydrodynamics in the assembly of active attractive spheres, we simulate a semi-dilute suspension of attractive self-propelled spherical particles in a quasi-two dimensional geometry comparing the case with and without hydrodynamics interactions. To start with, independent of the presence of hydrodynamics, we observe that depending on the ratio between attraction and propulsion, particles either coarsen or aggregate forming finite-size clusters. Focusing on the clustering regime, we characterize two different cluster parameters, i.e. their morphology and orientational order, and compare the case when active particles behave either as pushers or pullers (always in the regime where inter-particle attractions compete with self-propulsion). Studying cluster phases for squirmers with respect to those obtained for active Brownian disks (indicated as ABPs), we have shown that hydrodynamics alone can sustain a cluster phase of active swimmers (pullers), while ABPs form cluster phases due to the competition between attraction and self-propulsion. The structural properties of the cluster phases of squirmers and ABPs are similar, although squirmers show sensitivity to active stresses. Active Brownian disks resemble weakly pusher squirmer suspensions in terms of cluster size distribution, structure of the radius of gyration on the cluster size and degree of cluster polarity.

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

Identifying and quantifying dissimilarities among graphs is a fundamental and challenging problem of practical importance in many fields of science. Current methods of network comparison are limited to extract only partial information or are computationally very demanding. Here we propose an efficient and precise measure for network comparison, which is based on quantifying differences among distance probability distributions extracted from the networks. Extensive experiments on synthetic and real-world networks show that this measure returns non-zero values only when the graphs are non-isomorphic. Most importantly, the measure proposed here can identify and quantify structural topological differences that have a practical impact on the information flow through the network, such as the presence or absence of critical links that connect or disconnect connected components.

Type 1 diabetes (T1D) is commonly diagnosed in childhood and adolescence, and the developing brain has to cope with its deleterious effects. Although brain adaptation to the disease may not result in evident cognitive dysfunction, the effects of T1D on neurodevelopment could alter the pattern of BOLD fMRI activation. The aim of this study was to explore the neural BOLD activation pattern in patients with T1D versus that of healthy matched controls while performing two visuospatial working memory tasks, which included a pair of assignments administered through a block design. In the first task (condition A), the subjects were shown a trial sequence of 3 or 4 white squares positioned pseudorandomly around a fixation point on a black background. After a fixed delay, a second corresponding sequence of 3 or 4 red squares was shown that either resembled (direct, 50%) or differed from (50%) the previous stimulation order. The subjects were required to press one button if the two spatial sequences were identical or a second button if they were not. In condition B, the participants had to determine whether the second sequence of red squares appeared in inverse order (inverse, 50%) or not (50%) and respond by pressing a button. If the latter sequence followed an order distinct from the inverse sequence, the subjects were instructed to press a different button. Sixteen patients with normal IQ and without diabetes complications and 16 healthy control subjects participated in the study. In the behavioral analysis, there were no significant differences between the groups in the pure visuo-spatial task, but the patients with diabetes exhibited poorer performance in the task with verbal stimuli (p < .001). However, fMRI analyses revealed that the patients with T1D showed significantly increased activation in the prefrontal inferior cortex, subcortical regions and the cerebellum (in general p < .001). These different activation patterns could be due to adaptive compensation mechanisms that are devoted to improving efficiency while solving more complex cognitive tasks.

We introduce a novel random field Ising model, grounded on experimental observations, to assess the importance of metric correlations in cortical circuits in vitro. Metric correlations arise from both the finite axonal length and the heterogeneity in the spatial arrangement of neurons. The experiments consider the response of neuronal cultures to an external electric stimulation for a gradually weaker connectivity strength between neurons, and in cultures with different spatial configurations. The model can be analytically solved in the metric-free, mean-field scenario. The presence of metric correlations precipitates a strong deviation from the mean field. Null models of the same networks that preserve the distribution of connections recover the mean field. Our results show that metric-inherited correlations in spatial networks dominate the connectivity blueprint, mask the actual distribution of connections, and may emerge as the asset that shapes network dynamics.

We show that real multiplex networks are unexpectedly robust against targeted attacks on high-degree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

The heterogeneity of computationally predicted reaction fluxes in metabolic networks within a single flux state can be exploited to detect their significant flux backbone. Here, we disclose the backbone of Escherichia coli, and compare it with the backbones of other bacteria. We find that, in general, the core of the backbones is mainly composed of reactions in energy metabolism corresponding to ancient pathways. In E. coli, the synthesis of nucleotides and the metabolism of lipids form smaller cores which rely critically on energy metabolism. Moreover, the consideration of different media leads to the identification of pathways sensitive to environmental changes. The metabolic backbone of an organism is thus useful to trace simultaneously both its evolution and adaptation fingerprints.

We review some extensions of the continuous time random walk first introduced by Elliott Montroll and George Weiss more than 50 years ago [E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)], extensions that embrace multistate walks and, in particular, the persistent random walk. We generalize these extensions to include fractional random walks and derive the associated master equation, namely, the fractional telegrapher's equation. We dedicate this review to our joint work with George H. Weiss (1930-2017). It saddens us greatly to report the recent death of George Weiss, a scientific giant and at the same time a lovely and humble man.

Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose any desired stochastic behavior (compatible with the continuity equation for the probability function) on both systems by the appropriate choice of time-and site-dependent coins. This implies, in particular, that one can devise quantum walks that show diffusive spreading without losing coherence as well as random walks that exhibit the characteristic fast propagation of a quantum particle driven by a Hadamard coin.

Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion formation model, we show that, in the herding phase, a group of agents become effectively the leaders of the dynamics while the rest of the population follow blindly their opinion. Interestingly, in some cases such herding dynamics accelerates the time to consensus, which then becomes size independent or, on the contrary, makes the consensus nearly impossible. These behaviors have important consequences when an external noise is added to the system that makes consensus (absorbing) states to disappear. We analyze this model, which shows an interesting phase diagram, with a purely diffusive phase, a herding (or two-states) phase, and mixed phases where both behaviors are possible.

We combine experiments and theory to investigate the dynamics and orientational fluctuations of ferromagnetic microellipsoids that form a ribbonlike structure due to attractive dipolar forces. When assembled in the ribbon, the ellipsoids display orientational thermal fluctuations with an amplitude that can be controlled via application of an in-plane magnetic field. We use video microscopy to investigate the orientational dynamics in real time and space. Theoretical arguments are used to derive an analytical expression that describes how the distribution of the different angular configurations depends on the strength of the applied field. The experimental data are in good agreement with the developed model for all the range of field parameters explored. Understanding the role of fluctuations in chains composed of dipolar particles is important not only from a fundamental point of view, but it may also help understanding the stability of such structures against thermal noise, which is relevant in microfluidics and laboratory-on-a-chip applications.

We generalize the Vicsek model to describe the collective behavior of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations promote macroscopic droplets with late time sizes proportional to the system size (indicating phase separation) whereas fast rotations generate patterns consisting of phase synchronized microflocks with a controllable characteristic size proportional to the average single-particle swimming radius. Our results defy the viewpoint that monofrequent rotations form a vapid extension of the Vicsek model and establish a generic route to pattern formation in chiral active matter with possible applications for understanding and designing rotating microflocks.

We derive the three-dimensional telegrapher's equation out of a random walk model. The model is a three-dimensional version of the multistate random walk where the number of different states form a continuum representing the spatial directions that the walker can take. We set the general equations and solve them for isotropic and uniform walks which finally allows us to obtain the telegrapher's equation in three dimensions. We generalize the isotropic model and the telegrapher's equation to include fractional anomalous transport in three dimensions.

Huntington’s disease (HD) is a fatal neurodegenerative disease with motor, cognitive and psychiatric impairment. Dysfunctions in HD models have been related to reduced levels of striatal brain-derived neurotrophic factor (BDNF) and imbalance between its receptors TrkB and p75(NTR). Thus, molecules with activity on the BDNF/TrkB/p75 system can have therapeutic potential. 7,8-Dihydroxyflavone (7,8-DHF) was described as a TrkB agonist in several models of neuro-degenerative diseases, however, its TrkB activation profile needs further investigation due to its pleiotropic properties and divergence from BDNF effect. To investigate this, we used in vitro and in vivo models of HD to dissect TrkB activation upon 7,8-DHF treatment. 7,8-DHF treatment in primary cultures showed phosphorylation of TrkBY816 but not TrkBY515 with activation of the PLCγ1 pathway leading to morphological and functional improvements. Chronic administration of 7,8-DHF delayed motor deficits in R6/1 mice and reversed deficits on the Novel Object Recognition Test (NORT) at 17 weeks. Morphological and biochemical analyses revealed improved striatal levels of enkephalin, and prevention of striatal volume loss. We found a TrkBY816 but not TrkBY515 phosphorylation recovery in striatum concordant with in vitro results. Additionally, 7,8-DHF normalized striatal levels of induced and neuronal nitric oxide synthase (iNOS and nNOS, respectively) and ameliorated the imbalance of p75/TrkB. Our results provide new insights into the mechanism of action of 7,8-DHF suggesting that its effect through the TrkB receptor in striatum is via selective phosphorylation of its Y816 residue and activation of PLCγ1 pathway, but pleiotropic effects of the drug also contribute to its therapeutic potential.

Redundancy constitutes a fundamental and intrinsic aspect of healthy vasculatures. Built-in redundancy might also be a desirable feature in man-made microfluidic devices. We show that redundant and non-redundant networks, built to have identical resistances to flow when unobstructed, allow for very different flows when they are occluded; redundant ones —densely occluded at a certain bifurcation level— allowing for larger flows than non-redundant ones —obstructed above relatively small thresholds. We also show that redundancy protects vessels against the large shear-rate gradients that occlusions would cause if it were not present. Our study allows one to quantify a network tolerance against blockage, provides guidance in the tailoring of microfluidic devices, and offers novel insights into why nature has selected intrinsic redundancy over thicker vessels to assure blood supply at key places of the organisms.

Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a ‘multitasking’ behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields.

We present a model that takes into account the coupling between evolutionary game dynamics and social influence. Importantly, social influence and game dynamics take place in different domains, which we model as different layers of a multiplex network. We show that the coupling between these dynamical processes can lead to cooperation in scenarios where the pure game dynamics predicts defection. In addition, we show that the structure of the network layers and the relation between them can further increase cooperation. Remarkably, if the layers are related in a certain way, the system can reach a polarized metastable state. These findings could explain the prevalence of polarization observed in many social dilemmas.

Phase-field models have been extensively used to study interfacial phenomena, from solidification to vesicle dynamics. In this article, we analyze a phase-field model that captures the relevant physical features that characterize biological membranes. We show that the Helfrich theory of elasticity of membranes can be applied to phase-field models, allowing to derive the expressions of the stress tensor, lateral stress profile and elastic moduli. We discuss the relevance and interpretations of these magnitudes from a phase-field perspective. Taking the sharp-interface limit we show that the membrane macroscopic equilibrium equation can be derived from the equilibrium condition of the phase-field interface. We also study two dynamic models that describe the behaviour of a membrane. From the study of the relaxational behaviour of the membrane we characterize the relevant dynamics of each model, and discuss their applications.

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.

Contribution to the Topical Issue “Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook”, edited by Ryszard Kutner and Jaume Masoliver.

We present a hydrodynamic model of spreading epithelial monolayers described as polar viscous fluids, with active contractility and traction on a substrate. The combination of both active forces generates an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. Our viscous fluid model provides a comprehensive understanding of a variety of observations on the slow dynamics of epithelial monolayers, remarkably those that seemed to be characteristic of elastic media. The model also makes simple predictions to test the non-elastic nature of the mechanical waves, and provides new insights into collective cell dynamics, explaining plithotaxis as a result of strong flow-polarity coupling, and quantifying the non-locality of force transmission. In addition, we study the nonlinear regime of waves deriving an exact map of the model into the complex Ginzburg–Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the chaotic dynamics often observed in epithelia.

We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motor displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean-field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynamic coupling as well as on system size. We quantify the phase diagram for the different phases that characterize the collective motion of hydrodynamically coupled motors and show that sustained oscillations can be reached for biologically relevant parameters, hence, demonstrating the relevance of hydrodynamic interactions in intracellular transport.