The emergence of coherence in complex networks of heterogeneous dynamical systems

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength, all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.Comment: 4 pages, 1 figure. Published versio

Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators

The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a given population are heterogeneous in that their natural frequencies are drawn from a given distribution, and each population has its own such distribution. The coupling among the oscillators is global, however, we permit the coupling strengths between the members of different populations to be separately specified. We determine the critical condition for the onset of coherent collective behavior, and develop the illustrative case in which the oscillator frequencies are drawn from a set of (possibly different) Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in which the collective dynamics of several interacting populations of oscillators (such as excitatory and inhibitory neurons and glia) are of interest.Comment: The original was replaced with a version that has been accepted to Phys. Rev. E. The new version has the same content, but the title, abstract, and the introductory text have been revise

The onset of synchronization in large networks of coupled oscillators

We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix. We show how, with an additional assumption, a mean field approximation recently proposed is recovered from our results. We test our theory with numerical simulations, and find that it describes the transition when our assumptions are satisfied. We find that our theory describes the transition well in situations in which the mean field approximation fails. We study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two figures and improved the discussion of the range of validity of perturbative approache

Spatial patterns of desynchronization bursts in networks

We adapt a previous model and analysis method (the {\it master stability function}), extensively used for studying the stability of the synchronous state of networks of identical chaotic oscillators, to the case of oscillators that are similar but not exactly identical. We find that bubbling induced desynchronization bursts occur for some parameter values. These bursts have spatial patterns, which can be predicted from the network connectivity matrix and the unstable periodic orbits embedded in the attractor. We test the analysis of bursts by comparison with numerical experiments. In the case that no bursting occurs, we discuss the deviations from the exactly synchronous state caused by the mismatch between oscillators

The theory of chaotic attractors

James Yorke won the 2003 Japan Prize for his work in the field of chaos theory. This book was compiled by four of his best-known collaborators in honor of his 60th birthday and contains papers by various authors on chaos and chaotic attractors. The papers are organized around the topics of "natural" invariant measure and fractal dimension of the associated chaotic attractors. A few of the papers are written by Yorke and collaborators, but the editors say they have chosen the collection primarily for the papers' historical importance and their accessibility to students. The book begins with the famous paper "Deterministic Nonperiodic Flow" by Edward Lorenz. Anyone who doubts the importance of interdisciplinary institutes or of "linking" figures like Yorke should read Gleick's [4] account of Yorke's role in the dissemination of this paper to the mathematics community. The shocking aspect of the story is that the paper had been in print a full 9 years before most mathematicians were aware of it. Lorenz had found a three-dimensional ODE (a reduction of a model for Rayleigh-Benard instability in hydrodynamics) containing a limit set A that appeared to have the following properties: (1) The orbit of almost every initial condition in a neighborhood of A has its limit points in A (hence, it is an attractor). (2) The limit set is not periodic or asymptotically periodic. (3) The orbits show sensitive dependence on initial conditions. (Hence, by (2) and (3), the limit set A is chaotic.) (4) The limit set A contains a dense orbit (hence, it is indecomposable). Although several properties of a chaotic attractor are listed here, there is no universally accepted definition. Some prefer a more mathematical (technical) statement; others want conditions that could be verified by experimentalists. In a paper which appears in this volume, Milnor gives a definition of "attractor" in which condition (1) is replaced with the requirement that the basin of attraction should have positive measure. He also requires that no smaller closed subset has the same basin, up to measure zero. This definition has withstood the test of time, and a definition of "chaotic attractor" based on it appears in [2]. Milnor's paper also provides an insightful survey of the subject and many important examples. The editors present an excellent selection of key works in the development of the statistical or measure-theoretic approach to chaotic attractors. The important work of Yorke was early in this development. To get a true feeling for his many contributions to nonlinear dynamics, a book would have to touch on almost all aspects of (low-dimensional) chaos, where he has seen new, sometimes startling, connections and in doing so has opened avenues of investigation and introduced innovative techniques

Systematic Review and Meta-Analysis Toward Synthesis of Thresholds of Ocean Acidification Impacts on Calcifying Pteropods and Interactions With Warming

Interpreting the vulnerability of pelagic calcifiers to ocean acidification (OA) is enhanced by an understanding of their critical thresholds and how these thresholds are modified by other climate change stressors (e.g., warming). To address this need, we undertook a three-part data synthesis for pteropods, one of the calcifying zooplankton group. We conducted the first meta-analysis and threshold analysis of literature characterizing pteropod responses to OA and warming by synthetizing dataset comprising of 2,097 datapoints. Meta-analysis revealed the extent to which responses among studies conducted on differing life stages and disparate geographies could be integrated into a common analysis. The results demonstrated reduced calcification, growth, development, and survival to OA with increased magnitude of sensitivity in the early life stages, under prolonged duration, and with the concurrent exposure of OA and warming, but not species-specific sensitivity. Second, breakpoint analyses identified OA thresholds for several endpoints: dissolution (mild and severe), calcification, egg development, shell growth, and survival. Finally, consensus by a panel of pteropod experts was used to verify thresholds and assign confidence scores for five endpoints with a sufficient signal: noise ratio to develop life-stage specific, duration-dependent thresholds. The range of aragonite saturation state from 1.5–0.9 provides a risk range from early warning to lethal impacts, thus providing a rigorous basis for vulnerability assessments to guide climate change management responses, including an evaluation of the efficacy of local pollution management. In addition, meta-analyses with OA, and warming shows increased vulnerability in two pteropod processes, i.e., shell dissolution and survival, and thus pointing toward increased threshold sensitivity under combined stressor effect

Can older people remember medication reminders presented using synthetic speech?

Reminders are often part of interventions to help older people adhere to complicated medication regimes. Computer-generated (synthetic) speech is ideal for tailoring reminders to different medication regimes. Since synthetic speech may be less intelligible than human speech, in particular under difficult listening conditions, we assessed how well older people can recall synthetic speech reminders for medications. 44 participants aged 50-80 with no cognitive impairment recalled reminders for one or four medications after a short distraction. We varied background noise, speech quality, and message design. Reminders were presented using a human voice and two synthetic voices. Data were analyzed using generalized linear mixed models. Reminder recall was satisfactory if reminders were restricted to one familiar medication, regardless of the voice used. Repeating medication names supported recall of lists of medications. We conclude that spoken reminders should build on familiar information and be integrated with other adherence support measures. © The Author 2014. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For Permissions, please email: [email protected] numbered affiliations see end of article

Investigating the effectiveness of many-core network processors for high performance cyber protection systems. Part I, FY2011.

This report documents our first year efforts to address the use of many-core processors for high performance cyber protection. As the demands grow for higher bandwidth (beyond 1 Gbits/sec) on network connections, the need to provide faster and more efficient solution to cyber security grows. Fortunately, in recent years, the development of many-core network processors have seen increased interest. Prior working experiences with many-core processors have led us to investigate its effectiveness for cyber protection tools, with particular emphasis on high performance firewalls. Although advanced algorithms for smarter cyber protection of high-speed network traffic are being developed, these advanced analysis techniques require significantly more computational capabilities than static techniques. Moreover, many locations where cyber protections are deployed have limited power, space and cooling resources. This makes the use of traditionally large computing systems impractical for the front-end systems that process large network streams; hence, the drive for this study which could potentially yield a highly reconfigurable and rapidly scalable solution

Trends in Caffeine Use and Association between Clinical Outcomes and Timing of Therapy in Very Low Birth Weight Infants

Objective: To examine the effect of early initiation of caffeine therapy on neonatal outcomes and characterize the use of caffeine therapy in very low birth weight (VLBW) infants. Study design: We analyzed a cohort of 62 056 VLBW infants discharged between 1997 and 2010 who received caffeine therapy. We compared outcomes in infants receiving early caffeine therapy (initial dose before 3 days of life) and those receiving late caffeine therapy (initial dose at or after 3 days of life) through propensity scoring using baseline and early clinical variables. The primary outcome was the association between the timing of caffeine initiation and the incidence of bronchopulmonary dysplasia (BPD) or death. Results: We propensity score–matched 29 070 VLBW infants at a 1:1. Of infants receiving early caffeine therapy, 3681 (27.6%) died or developed BPD, compared with 4591 infants (34.0%) receiving late caffeine therapy (OR, 0.74; 99% CI, 0.69-0.80). Infants receiving early caffeine had a lower incidence of BPD (23.1% vs 30.7%; OR, 0.68; 95% CI, 0.63-0.73) and a higher incidence of death (4.5% vs 3.7%; OR, 1.23; 95% CI, 1.05-1.43). Infants receiving early caffeine therapy had less treatment of patent ductus arteriosus (OR, 0.60; 95% CI, 0.55-0.65) and a shorter duration of mechanical ventilation (mean difference, 6 days; P \u3c .001). Conclusion: Early caffeine initiation is associated with a decreased incidence of BPD. Randomized trials are needed to determine the efficacy and safety of early caffeine prophylaxis in VLBW infants. (J Pediatr 2014; 164:992-8)

Trends in Caffeine Use and Association between Clinical Outcomes and Timing of Therapy in Very Low Birth Weight Infants

Objective: To examine the effect of early initiation of caffeine therapy on neonatal outcomes and characterize the use of caffeine therapy in very low birth weight (VLBW) infants. Study design: We analyzed a cohort of 62 056 VLBW infants discharged between 1997 and 2010 who received caffeine therapy. We compared outcomes in infants receiving early caffeine therapy (initial dose before 3 days of life) and those receiving late caffeine therapy (initial dose at or after 3 days of life) through propensity scoring using baseline and early clinical variables. The primary outcome was the association between the timing of caffeine initiation and the incidence of bronchopulmonary dysplasia (BPD) or death. Results: We propensity score–matched 29 070 VLBW infants at a 1:1. Of infants receiving early caffeine therapy, 3681 (27.6%) died or developed BPD, compared with 4591 infants (34.0%) receiving late caffeine therapy (OR, 0.74; 99% CI, 0.69-0.80). Infants receiving early caffeine had a lower incidence of BPD (23.1% vs 30.7%; OR, 0.68; 95% CI, 0.63-0.73) and a higher incidence of death (4.5% vs 3.7%; OR, 1.23; 95% CI, 1.05-1.43). Infants receiving early caffeine therapy had less treatment of patent ductus arteriosus (OR, 0.60; 95% CI, 0.55-0.65) and a shorter duration of mechanical ventilation (mean difference, 6 days; P \u3c .001). Conclusion: Early caffeine initiation is associated with a decreased incidence of BPD. Randomized trials are needed to determine the efficacy and safety of early caffeine prophylaxis in VLBW infants. (J Pediatr 2014; 164:992-8)