Causality, influence, and computation in possibly disconnected synchronous dynamic networks

In this work, we study the propagation of influence and computation in dynamic distributed computing systems that are possibly disconnected at every instant. We focus on a synchronous message-passing communication model with broadcast and bidirectional links. Our network dynamicity assumption is a worst-case dynamicity controlled by an adversary scheduler, which has received much attention recently. We replace the usual (in worst-case dynamic networks) assumption that the network is connected at every instant by minimal temporal connectivity conditions. Our conditions only require that another causal influence occurs within every time window of some given length. Based on this basic idea, we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate termination criteria in networks in which an upper bound on any of these metrics is known. We exploit our termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental counting and all-to-all token dissemination (or gossip) problems

Characterization of the Community Structure of Large Scale Functional Brain Networks During Ketamine-Medetomidine Anesthetic Induction

One of the central questions in neuroscience is to understand the way communication is organized in the brain, trying to comprehend how cognitive capacities or physiological states of the organism are potentially related to brain activities involving interactions of several brain areas. One important characteristic of the functional brain networks is that they are modularly structured, being this modular architecture regarded to account for a series of properties and functional dynamics. In the neurobiological context, communities may indicate brain regions that are involved in one same activity, representing neural segregated processes. Several studies have demonstrated the modular character of organization of brain activities. However, empirical evidences regarding to its dynamics and relation to different levels of consciousness have not been reported yet. Within this context, this research sought to characterize the community structure of functional brain networks during an anesthetic induction process. The experiment was based on intra-cranial recordings of neural activities of an old world macaque of the species Macaca fuscata during a Ketamine-Medetomidine anesthetic induction process. Networks were serially estimated in time intervals of five seconds. Changes were observed within about one and a half minutes after the administration of the anesthetics, revealing the occurrence of a transition on the community structure. The awake state was characterized by the presence of large clusters involving frontal and parietal regions, while the anesthetized state by the presence of communities in the primary visual and motor cortices, being the areas of the secondary associative cortex most affected. The results report the influence of general anesthesia on the structure of functional clusters, contributing for understanding some new aspects of neural correlates of consciousness.Comment: 24 pages, 8 figures. arXiv admin note: text overlap with arXiv:1604.0000

A Faster Counting Protocol for Anonymous Dynamic Networks

We study the problem of counting the number of nodes in a slotted-time communication network, under the challenging assumption that nodes do not have identifiers and the network topology changes frequently. That is, for each time slot links among nodes can change arbitrarily provided that the network is always connected. Tolerating dynamic topologies is crucial in face of mobility and unreliable communication whereas, even if identifiers are available, it might be convenient to ignore them in massive networks with changing topology. Counting is a fundamental task in distributed computing since knowing the size of the system often facilitates the design of solutions for more complex problems. Currently, the best upper bound proved on the running time to compute the exact network size is double-exponential. However, only linear complexity lower bounds are known, leaving open the question of whether efficient Counting protocols for Anonymous Dynamic Networks exist or not. In this paper we make a significant step towards answering this question by presenting a distributed Counting protocol for Anonymous Dynamic Networks which has exponential time complexity. Our algorithm ensures that eventually every node knows the exact size of the system and stops executing the algorithm. Previous Counting protocols have either double-exponential time complexity, or they are exponential but do not terminate, or terminate but do not provide running-time guarantees, or guarantee only an exponential upper bound on the network size. Other protocols are heuristic and do not guarantee the correct count

Causal coupling inference from multivariate time series based on ordinal partition transition networks

Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Finally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data