arXiv subjects

Tiago Pereira

Publications and source records attributed to Tiago Pereira.

At least 37 records · Page 2Linked to original sources

arXiv2021

Chimera states through invariant manifold theory

We establish the existence of chimera states, simultaneously supporting synchronous and asynchronous dynamics, in a network consisting of two symmetrically linked star subnetworks consisting of identical oscillators with shear and Kuramoto--Sakaguchi coupling. We show that the chimera states may be metastable or asymptotically stable. If the intra-star coupling strength is of order $\varepsilon$, the chimera states persist on time scales at least of order $1/\varepsilon$ in general, and on time-scales at least of order $1/\varepsilon^2$ if the intra-star coupling is of Kuramoto--Sakaguchi type. If the intra-star coupling configuration is sparse, the chimeras are asymptotically stable. The analysis relies on a combination of dimensional reduction using a Möbius symmetry group and techniques from averaging theory and normal hyperbolicity.

math.DS↗

arXiv2021

Smart testing and critical care bed sharing for COVID-19 control

During the early months of the current COVID-19 pandemic, social-distancing measures effectively slowed disease transmission in many countries in Europe and Asia, but the same benefits have not been observed in some developing countries such as Brazil. In part, this is due to a failure to organise systematic testing campaigns at nationwide or even regional levels. To gain effective control of the pandemic, decision-makers in developing countries, particularly those with large populations, must overcome difficulties posed by an unequal distribution of wealth combined with low daily testing capacities. The economic infrastructure of the country, often concentrated in a few cities, forces workers to travel from commuter cities and rural areas, which induces strong nonlinear effects on disease transmission. In the present study, we develop a smart testing strategy to identify geographic regions where COVID-19 testing could most effectively be deployed to limit further disease transmission. The strategy uses readily available anonymised mobility and demographic data integrated with intensive care unit (ICU) occupancy data and city-specific social-distancing measures. Taking into account the heterogeneity of ICU bed occupancy in differing regions and the stages of disease evolution, we use a data-driven study of the Brazilian state of Sao Paulo as an example to show that smart testing strategies can rapidly limit transmission while reducing the need for social-distancing measures, thus returning life to a so-called new normal, even when testing capacity is limited.

physics.soc-ph↗

arXiv2019

Effective networks: a model to predict network structure and critical transitions from datasets

Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in network behaviour, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behaviour for parameter ranges for which no data on the system is available. In this paper, we address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics at each node and a statistical description of their interactions. We illustrate this approach by reconstructing the dynamics and structure of realistic neuronal interaction networks of the cat cerebral cortex. We reconstruct the community structure by analysing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

nlin.AO↗

arXiv2019

Consequences of delays and imperfect implementation of isolation in epidemic control

For centuries isolation has been the main control strategy of unforeseen epidemic outbreaks. When implemented in full and without delay, isolation is very effective. However, flawless implementation is seldom feasible in practice. We present an epidemic model called SIQ with an isolation protocol, focusing on the consequences of delays and incomplete identification of infected hosts. The continuum limit of this model is a system of Delay Differential Equations, the analysis of which reveals clearly the dependence of epidemic evolution on model parameters including disease reproductive number, isolation probability, speed of identification of infected hosts and recovery rates. Our model offers estimates on minimum response capabilities needed to curb outbreaks,and predictions of endemic states when containment fails. Critical response capability is expressed explicitly in terms of parameters that are easy to obtain, to assist in the evaluation of funding priorities involving preparedness and epidemics management.

q-bio.PE↗

arXiv2018

SIQ: a delay differential equations model for disease control via isolation

Infectious diseases are among the most prominent threats to mankind. When preventive health care cannot be provided, a viable means of disease control is the isolation of individuals, who may be infected. To study the impact of isolation, we propose a system of Delay Differential Equations and offer our model analysis based on the geometric theory of semi-flows. Calibrating the response to an outbreak in terms of the fraction of infectious individuals isolated and the speed with which this is done, we deduce the minimum response required to curb an incipient outbreak, and predict the ensuing endemic state should the infection continue to spread.

math.DS↗

arXiv2017

Heterogeneously Coupled Maps: hub dynamics and emergence across connectivity layers

The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact with few others. The local dynamics on each node is chaotic, coupled with other nodes according to the network structure. Such high-dimensional systems are hard to understand in full, nevertheless we are able to describe the system over exponentially large time scales. In particular, we show that the dynamics of hub nodes can be very well approximated by a low-dimensional system. This allows us to establish the emergence of macroscopic behaviour such as coherence of dynamics among hubs of the same connectivity layer (i.e. with the same number of connections), and chaotic behaviour of the poorly connected nodes. The HCM we study provide a paradigm to explain why and how the dynamics of the network can change across layers.

math.DS↗

arXiv2017

The Effects of Structural Perturbations on the Synchronizability of Diffusive Networks

We investigate the effects of structural perturbations of both, undirected and directed diffusive networks on their ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.

math.DS↗

arXiv2017

Coupling functions: Universal insights into dynamical interaction mechanisms

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

nlin.AO↗

arXiv2017

Synchronization in Networks with Strongly Delayed Couplings

We investigate the stability of synchronization in networks of dynamical systems with strongly delayed connections. We obtain strict conditions for synchronization of periodic and equilibrium solutions. In particular, we show the existence of a critical coupling strength $κ_{c}$, depending only on the network structure, isolated dynamics and coupling function, such that for large delay and coupling strength $κ<κ_{c}$, the network possesses stable synchronization. The critical coupling $κ_{c}$ can be chosen independently of the delay for the case of equilibria, while for the periodic solution, $κ_{c}$ depends essentially on the delay and vanishes as the delay increases. We observe that, for random networks, the synchronization interval is maximal when the network is close to the connectivity threshold. We also derive scaling of the coupling parameter that allows for a synchronization of large networks for different network topologies.

math.DS↗

arXiv2017

Why Is Non-thermal Line Broadening of Spectral Lines in The Lower Transition Region of the Sun Independent of Spatial Resolution?

Spectral observations of the solar transition region (TR) and corona show broadening of spectral lines beyond what is expected from thermal and instrumental broadening. The remaining non-thermal broadening is significant (5-30 km/s) and correlated with the intensity. Here we study spectra of the TR Si IV 1403 Angstrom line obtained at high resolution with the Interface Region Imaging Spectrograph (IRIS). We find that the large improvement in spatial resolution (0.33 arcsec) of IRIS compared to previous spectrographs (2 arcsec) does not resolve the non-thermal line broadening which in most regions remains at pre-IRIS levels of about 20 km/s. This invariance to spatial resolution indicates that the processes behind the broadening occur along the line-of-sight (LOS) and/or on spatial scales (perpendicular to the LOS) smaller than 250 km. Both effects appear to play a role. Comparison with IRIS chromospheric observations shows that, in regions where the LOS is more parallel to the field, magneto-acoustic shocks driven from below impact the TR and can lead to significant non-thermal line broadening. This scenario is supported by MHD simulations. While these do not show enough non-thermal line broadening, they do reproduce the long-known puzzling correlation between non-thermal line broadening and intensity. This correlation is caused by the shocks, but only if non-equilibrium ionization is taken into account. In regions where the LOS is more perpendicular to the field, the prevalence of small-scale twist is likely to play a significant role in explaining the invariance and correlation with intensity.

astro-ph.SR↗

arXiv2017

Self-Synchronization in Duty-cycled Internet of Things (IoT) Applications

In recent years, the networks of low-power devices have gained popularity. Typically these devices are wireless and interact to form large networks such as the Machine to Machine (M2M) networks, Internet of Things (IoT), Wearable Computing, and Wireless Sensor Networks. The collaboration among these devices is a key to achieving the full potential of these networks. A major problem in this field is to guarantee robust communication between elements while keeping the whole network energy efficient. In this paper, we introduce an extended and improved emergent broadcast slot (EBS) scheme, which facilitates collaboration for robust communication and is energy efficient. In the EBS, nodes communication unit remains in sleeping mode and are awake just to communicate. The EBS scheme is fully decentralized, that is, nodes coordinate their wake-up window in partially overlapped manner within each duty-cycle to avoid message collisions. We show the theoretical convergence behavior of the scheme, which is confirmed through real test-bed experimentation.

cs.DC↗

arXiv2017

Robustness of ergodic properties of nonautonomous piecewise expanding maps

Recently, there has been an increasing interest on nonautonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map $F$ results in statistical behaviour close to that of $F$. We show this fact in the case of piecewise regular expanding maps. In particular, we impose conditions on perturbations of this class of maps that include situations slightly more general than what has been considered so far, and prove that these are stochastically stable in the usual sense. We then prove that the evolution of a given distribution of mass under composition of time dependent perturbations (arbitrarily - rather than randomly - chosen at each step) close to a given map $F$ remains close to the invariant mass distribution of $F$. Moreover, for almost every point, Birkhoff averages along trajectories do not fluctuate wildly. This result complements recent results on memory loss for nonautonomous dynamical systems.

math.DS↗

arXiv2017

Setting Up Pepper For Autonomous Navigation And Personalized Interaction With Users

In this paper we present our work with the Pepper robot, a service robot from SoftBank Robotics. We had two main goals in this work: improving the autonomy of this robot by increasing its awareness of the environment; and enhance the robot ability to interact with its users. To achieve this goals, we used ROS, a modern open-source framework for developing robotics software, to provide Pepper with state of the art localization and navigation capabilities. Furthermore, we contribute an architecture for effective human interaction based on cloud services. Our architecture improves Pepper speech recognition capabilities by connecting it to the IBM Bluemix Speech Recognition service and enable the robot to recognize its user via an in-house face recognition web-service. We show examples of our successful integration of ROS and IBM services with Pepper's own software. As a result, we were able to make Pepper move autonomously in a environment with humans and obstacles. We were also able to have Pepper execute spoken commands from known users as well as newly introduced users that were enrolled in the robot list of trusted users via a multi-modal interface.

cs.RO↗

arXiv2017

Spectra of Laplacian matrices of weighted graphs: structural genericity properties

This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity) and its associated eigenvector, the so-called Fiedler vector. Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only non-zero entries. These structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems.

math-ph↗

arXiv2017

Synchronization of Chaos

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronization, a classical paradigm of order. We survey the main theory behind complete, generalized and phase synchronization phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.

nlin.CD↗

arXiv2015

Persistence of Network Synchronization under Nonidentical Coupling Functions

We investigate the persistence of synchronization in networks of diffusively coupled oscillators when the coupling functions are nonidentical. Under mild conditions, we uncover the influence of the network interaction structure on the mismatches of the coupling function. We show that Erdös-Rényi random graphs support large perturbations in the coupling function. In contrast scale-free graphs do not allow large perturbations in the coupling function, that is, as the network size n goes to infinity it forces the coupling functions to be identical.

math.DS↗

arXiv2015

Fast Fermi Acceleration and Entropy Growth

Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time, the energy is no longer conserved, which makes the acceleration possible. One of the main problems is how to generate a sustained and robust energy growth. We show that the non-ergodicity of any chaotic Hamiltonian system must universally lead to the exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of a Geometric Brownian Motion with a positive drift and relate it to the entropy increase.

nlin.CD↗

arXiv2015

Sync: Persistence in Two Diffusively Coupled Oscillators

We address the problem of stability of synchronization in two diffu- sively coupled oscillators under small perturations. We have two cases, namely, when the perturation becomes of a linear operator and the case of non-linear operator. We use the Lyapunov second method to guar- antee the global analysis for the first case. For the second, we use the Hartman-Grobman theorem, providing local analysis.

math.DS↗