Edmilson Roque

Low dimensional dynamics of large networks is the focus of many theoretical works, but controlled laboratory experiments are comparatively very few. Here, we discuss experimental observations on a mean-field coupled network of hundreds of semiconductor lasers, which collectively display effectively low-dimensional mixed mode oscillations and chaotic spiking typical of slow-fast systems. We demonstrate that such a reduced dimensionality originates from the slow-fast nature of the system and of the existence of a critical manifold of the network where most of the dynamics takes place. Experimental measurement of the bifurcation parameter for different network sizes corroborate the theory.

We consider random holomorphic dynamical systems on the Riemann sphere whose choices of maps are related to Markov chains. Our motivation is to generalize the facts which hold in i.i.d. random holomorphic dynamical systems. In particular, we focus on the function ##IMG## [http://ej.iop.org/images/0951-7715/32/10/3742/nonab231eieqn001.gif] which represents the probability of tending to infinity. We show some sufficient conditions which make ##IMG## [http://ej.iop.org/images/0951-7715/32/10/3742/nonab231eieqn002.gif] continuous on the whole space and we characterize the Julia sets in terms of the function ##IMG## [http://ej.iop.org/images/0951-7715/32/10/3742/nonab231eieqn003.gif] under certain assumptions.

Author(s): Paulo Cesar Ventura da Silva, Fátima Velásquez-Rojas, Colm Connaughton, Federico Vazquez, Yamir Moreno, and Francisco A. Rodrigues

One of the major issues in theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as indiv...

[Phys. Rev. E] Published Thu Sep 05, 2019

In this paper, we introduce a network-based methodology to study how clusters represented by political entities evolve over time. We constructed networks of voting data from the Brazilian Chamber of Deputies, where deputies are nodes and edges are represented by voting similarity among deputies. The Brazilian Chamber of deputies is characterized by a multi-party political system. Thus, we would expect a broad spectrum of ideas to be represented. Our results, however, revealed that plurality of ideas is not present at all: the effective number of communities representing ideas based on agreement/disagreement in propositions is about 3 over the entire studied time span. The obtained results also revealed different patterns of coalitions between distinct parties. Finally, we also found signs of early party isolation before presidential impeachment proceedings effectively started. We believe that the proposed framework could be used to complement the study of political dynamics and even applied in similar social networks where individuals are organized in a complex manner.

Author(s): Anna Paola Muntoni, Rafael Díaz Hernández Rojas, Alfredo Braunstein, Andrea Pagnani, and Isaac Pérez Castillo

The problem of efficiently reconstructing tomographic images can be mapped into a Bayesian inference problem over the space of pixels densities. Solutions to this problem are given by pixels assignments that are compatible with tomographic measurements and maximize a posterior probability density. T...

[Phys. Rev. E] Published Wed Sep 04, 2019

We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We show how quotient entropy can be explicitly computed by symbolic coding. To do so, we make use of the relationship between the category of dynamical systems and the category of graphs, a connection mediated by Markov partitions and topological Markov chains.

A synchrony subspace of R^n is defined by setting certain components of the vectors equal according to an equivalence relation. Synchrony subspaces invariant under a given set of square matrices form a lattice. Applications of these invariant synchrony subspaces include equitable and almost equitable partitions of the vertices of a graph used in many areas of graph theory, balanced and exo-balanced partitions of coupled cell networks, and coset partitions of Cayley graphs. We study the basic properties of invariant synchrony subspaces and provide many examples of the applications. We also present what we call the split and cir algorithm for finding the lattice of invariant synchrony subspaces. Our theory and algorithm is further generalized for non-square matrices. This leads to the notion of tactical decompositions studied for its application in design theory.

Author(s): Tiago P. Peixoto

We present a scalable nonparametric Bayesian method to perform network reconstruction from observed functional behavior, that at the same time infers the communities present in the network. We show that the joint reconstruction with community detection has a synergistic effect, where the edge correl...

[Phys. Rev. Lett.] Published Mon Aug 19, 2019

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such topological features are also important for their role in the dynamical processes occurring in networked systems. In this paper, we argue that the dynamical activity of the nodes may strongly reshape their relevance inside the network making centrality measures in many cases misleading. We show that when the dynamics taking place at the local level of the node is slower than the global one between the nodes, then the system may lose track of the structural features. On the contrary, when that ratio is reversed only global properties such as the shortest distances can be recovered. From the perspective of networks inference, this constitutes an uncertainty principle, in the sense that it limits the extraction of multi-resolution information about the structure, particularly in the presence of noise. For illustration purposes, we show that for networks with different time-scale structures such as strong modularity, the existence of fast global dynamics can imply that precise inference of the community structure is impossible.

Author(s): Shanwu Li, Eurika Kaiser, Shujin Laima, Hui Li, Steven L. Brunton, and J. Nathan Kutz

Vortex-induced vibrations (VIVs) have been observed on a long-span suspension bridge. The nonstationary wind in the field characterized by the time-varying mean wind speed is likely to lead to time-varying aerodynamics of the wind-bridge system during VIVs, which is different from VIVs induced by st...

[Phys. Rev. E 100, 022220] Published Wed Aug 21, 2019

Author(s): A. V. Andreev, N. S. Frolov, A. N. Pisarchik, and A. E. Hramov

In this paper we study a chimera state in complex networks of bistable Hodgkin-Huxley neurons with excitatory coupling, that manifests as a termination of spiking activity of a part of interacting neurons. We provide a detailed investigation of this phenomenon in scale-free, small-world and random n...

[Phys. Rev. E] Published Wed Aug 14, 2019

Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent type of method for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between connectivity patterns in different layers. Finally, we explain how to use correlated models for edge prediction in multilayer networks. By taking into account edge correlations, prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously-purchased grocery products.

Heterogeneity is among the most important features characterizing real-world networks. Empirical evidence in support of this fact is unquestionable. Existing theoretical frameworks justify heterogeneity in networks as a convenient way to enhance desirable systemic features, such as robustness, synchronizability and navigability. Information theory is one of the most fundamental theoretical frameworks of network science and machine learning. However, the current information theory frameworks for understading networks, based on maximum entropy network ensembles, are not able to explain the emergence of heterogeneity in complex networks. Here, we fill this gap of knowledge by developing a classical information theoretical framework for networks based on finding a trade-off between the information content of a compressed representation of the ensemble and the information content of the actual network ensemble. We show that among all degree distributions that can be used to generate random networks, the one emerging from the principle of maximum entropy is a power law. We also study spatially embedded networks finding that the interactions between nodes naturally lead to nonuniform distributions of points in the space. The pertinent features of real-world air transportation networks are well described by the proposed framework.

Community structure and interaction delays are common features of ensembles of network coupled oscillators, but their combined effect on the emergence of synchronization has not been studied in detail. We study the transitions between macroscopic states in coupled oscillator systems with community structure and time delays. We show that the combination of these two properties gives rise to non-monotonic transitions, whereby increasing the global coupling strength can both inhibit and promote synchronization, yielding both desynchronization and synchronization transitions. For relatively wide parameter choices we also observe asymmetric suppression of synchronization, where communities compete to suppress one another's synchronization properties until one or more win, totally suppressing the others to effective incoherence. Using the ansatz of Ott and Antonsen we provide analytical descriptions for these transitions that confirm numerical simulations.

Contagion processes are strongly linked to the network structures on which they propagate, and learning these structures is essential for understanding and intervention on complex network processes such as epidemics and (mis)information propagation. However, using contagion data to infer network structure is a challenging inverse problem. In particular, it is imperative to have appropriate measures of uncertainty in network structure estimates, however these are largely ignored in most machine-learning approaches. We present a probabilistic framework that uses samples from the distribution of networks that are compatible with the dynamics observed to produce network and uncertainty estimates. We demonstrate the method using the well known independent cascade model to sample from the distribution of networks P(G) conditioned on the observation of a set of infections C. We evaluate the accuracy of the method by using the marginal probabilities of each edge in the distribution, and show the bene ts of quantifying uncertainty to improve estimates and understanding, particularly with small amounts of data.

Let $G=(V, E)$ be a finite weighted graph, and $\Omega\subseteq V$ be a domain such that $\Omega^\circ\neq\emptyset$. In this paper, we study the following initial boundary problem for the non-homogenous wave equation \begin{equation*} \left\{ \begin{aligned} &\partial_t^2 u(t,x)-\Delta_\Omega u(t,x)=f(t,x),\qquad&&(t,x)\in[0,\infty)\times \Omega^\circ,\\ &u(0,x)=g(x),\qquad&& x\in\Omega^\circ,\\ &\partial_tu(0,x)=h(x),\qquad&& x\in\Omega^\circ,\\ &u(t,x)=0,\qquad&&(t,x)\in[0,\infty)\times\partial \Omega, \end{aligned} \right. \end{equation*} where $\Delta_\Omega$ denotes the Dirichlet Laplacian on $\Omega^\circ$. Using Rothe's method, we prove that the above wave equation has a unique solution.

We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for the nonhomogeneous heat equation in $\Omega\times (0,\infty)$ where $\Omega$ is a bounded domain in $\mathbb{R}^2$ with smooth boundary $\partial\Omega$ from overposed lateral data on a sparse subset of $\partial\Omega\times(0,\infty)$. Specifically, we shall require a small finite number $N$ of measurement points on $\partial\Omega$ and prove a uniqueness result; namely the recovery of the pair $(p,q)$ within a given class, by a judicious choice of $N=2$ points. Naturally, with this paucity of overposed data, the problem is severely ill-posed. Nevertheless we shall show that provided the data noise level is low, effective numerical reconstructions may be obtained.

We construct an epidemic model for the transmission of dengue fever with early-life stage in the vector dynamics and age-structure within hosts. The early-life stage of the vector is modeled via a general function that supports multiple vector densities. The {\it basic reproductive number} and {\it vector demographic threshold} are computed to study the local and global stability of the infection-free state. A numerical framework is implemented and simulations are performed.

Author(s): Shibabrat Naik and Stephen Wiggins

We present a method based on a Lagrangian descriptor for revealing the high-dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include a normally hyperbolic invariant manifold and its stable and unstable manifold...

[Phys. Rev. E 100, 022204] Published Mon Aug 05, 2019

Nature Physics, Published online: 05 August 2019; doi:10.1038/s41567-019-0598-1

Modelling and microscopy of thousands of cells together reveal the coupling through which the cell cycle influences the circadian clock. This coupling may explain why mammalian tissues growing at different rates have shifted circadian rhythms.

Author(s): Mohammad Salahshour

We consider a population of individuals living in an uncertain environment. Individuals are able to make noisy observations of the environment and communicate using signals. We show that the model shows an order-disorder transition from an ordered phase in low communication noise in which a consensu...

[Phys. Rev. Lett. 123, 068101] Published Tue Aug 06, 2019

Author(s): Patrick A. K. Reinbold and Roman O. Grigoriev

In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially complicates construction of an accurate model for such systems usin...

[Phys. Rev. E] Published Mon Aug 05, 2019

The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.

Synchronization among rhythmic elements is modeled by coupled phase-oscillators each of which has the so-called natural frequency. A symmetric natural frequency distribution induces a continuous or discontinuous synchronization transition from the nonsynchronized state, for instance. It has been numerically reported that asymmetry in the natural frequency distribution brings new types of bifurcation diagram having, in the order parameter, oscillation or a discontinuous jump which emerges from a partially synchronized state. We propose a theoretical classification method of five types of bifurcation diagrams including the new ones, paying attention to the generality of the theory. The oscillation and the jump from partially synchronized states are discussed respectively by the linear analysis around the nonsynchronized state and by extending the amplitude equation up to the third leading term. The theoretical classification is examined by comparing with numerically obtained one.

This paper considers the problem of estimating a power-law degree distribution of an undirected network. Even though power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating them (e.g. linear regression on double-logarithmic axes, maximum likelihood estimation with uniformly sampled nodes) suffer from the large variance introduced by the lack of data-points from the tail portion of the power-law degree distribution. As a solution, we present a novel maximum likelihood estimation approach that exploits the friendship paradox to sample more efficiently from the tail of the degree distribution. We analytically show that the proposed method results in a smaller bias, variance and a Cramer-Rao lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes (which is the most commonly used method in literature). Detailed simulation results are presented to illustrate the performance of the proposed method under different conditions and how it compares with alternative methods.

The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex dissipative chaotic systems, however, are widely assumed to have a linear response even if the microscopic variables do not, but the mechanism for this is not well-understood.

We present a comprehensive picture for the linear response of macroscopic observables in high-dimensional coupled deterministic dynamical systems, where the coupling is via a mean field and the microscopic subsystems may or may not obey linear response theory. We derive stochastic reductions of the dynamics of these observables from statistics of the microscopic system, and provide conditions for linear response theory to hold in finite dimensional systems and in the thermodynamic limit. In particular, we show that for large systems of finite size, linear response is induced via self-generated noise.

We present examples in the thermodynamic limit where the macroscopic observable satisfies LRT, although the microscopic subsystems individually violate LRT, as well a converse example where the macroscopic observable does not satisfy LRT despite all microscopic subsystems satisfying LRT when uncoupled. This latter, maybe surprising, example is associated with emergent non-trivial dynamics of the macroscopic observable. We provide numerical evidence for our results on linear response as well as some analytical intuition.

The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex dissipative chaotic systems, however, are widely assumed to have a linear response even if the microscopic variables do not, but the mechanism for this is not well-understood.

We present a comprehensive picture for the linear response of macroscopic observables in high-dimensional coupled deterministic dynamical systems, where the coupling is via a mean field and the microscopic subsystems may or may not obey linear response theory. We derive stochastic reductions of the dynamics of these observables from statistics of the microscopic system, and provide conditions for linear response theory to hold in finite dimensional systems and in the thermodynamic limit. In particular, we show that for large systems of finite size, linear response is induced via self-generated noise.

We present examples in the thermodynamic limit where the macroscopic observable satisfies LRT, although the microscopic subsystems individually violate LRT, as well a converse example where the macroscopic observable does not satisfy LRT despite all microscopic subsystems satisfying LRT when uncoupled. This latter, maybe surprising, example is associated with emergent non-trivial dynamics of the macroscopic observable. We provide numerical evidence for our results on linear response as well as some analytical intuition.

We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with a biased diffusion process among different layers. A parameter $\alpha$ is introduced to control the bias of the diffusion process, such that each individual prefers to move to one layer with more infected (or recovered) neighbors for larger values of $\alpha$. Using stochastic simulations and mean-field theory, we show that the type of phase transition from a disease-free phase to an endemic phase depends on the value of $\alpha$. When $\alpha$ is small enough, the system undergoes a usual continuous phase transition as an effective spreading rate $\beta$ increases, as in single-layer networks. Interestingly, when $\alpha$ exceeds a critical value the system shows either a hybrid two-step phase transition or a one-step discontinuous phase transition as $\beta$ increases. The former contains a continuous transition between the disease-free phase and a low-prevalence endemic phase, and a discontinuous transition between the low-prevalence endemic phase and a high-prevalence endemic phase. For the latter, only a discontinuous transition occurs from the disease-free phase directly to the high-prevalence endemic phase. Moreover, we show that the discontinuous transition is always accompanied by a spontaneous symmetry breaking in occupation probabilities of individuals in each layer.

This project examined perceptions of the vegan lifestyle using surveys and social media to explore barriers to choosing veganism. A survey of 510 individuals indicated that non-vegans did not believe veganism was as healthy or difficult as vegans. In a second analysis, Instagram posts using #vegan suggest content is aimed primarily at the female vegan community. Finally, sentiment analysis of roughly 5 million Twitter posts mentioning 'vegan' found veganism to be portrayed in a more positive light compared to other topics. Results suggest non-vegans' lack of interest in veganism is driven by non-belief in the health benefits of the diet.