Explosive Synchronization is Discontinuous

Spontaneous explosive is an abrupt transition to collective behavior taking place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. This explosive transition was conjectured to be discontinuous. Indeed, numerical investigations reveal a hysteresis behavior associated with the transition. Here, we analyze explosive synchronization in star graphs. We show that in the thermodynamic limit the transition to (and out) collective behavior is indeed discontinuous. The discontinuous nature of the transition is related to the nonlinear behavior of the order parameter, which in the thermodynamic limit exhibits multiple fixed points. Moreover, we unravel the hysteresis behavior in terms of the graph parameters. Our numerical results show that finite size graphs are well described by our predictions

Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E \textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment disregarding the intrinsic non-stationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for non-stationary stochastic processes like fBm.Comment: 8 pages, 6 figure

Complex Network Approach to the Statistical Features of the Sunspot Series

Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network which span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15\,--\,1000 days by a power-law regime with scaling exponent $\gamma = 2.04$ of the occurrence time of the two subsequent and successive strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models. The power-law regime suggested by the waiting times does indicate that there are some level of predictable patterns in the minima.Comment: 18 pages, 11 figures. Solar Physics, 201

Reliability-aware and energy-efficient system level design for networks-on-chip

2015 Spring.Includes bibliographical references.With CMOS technology aggressively scaling into the ultra-deep sub-micron (UDSM) regime and application complexity growing rapidly in recent years, processors today are being driven to integrate multiple cores on a chip. Such chip multiprocessor (CMP) architectures offer unprecedented levels of computing performance for highly parallel emerging applications in the era of digital convergence. However, a major challenge facing the designers of these emerging multicore architectures is the increased likelihood of failure due to the rise in transient, permanent, and intermittent faults caused by a variety of factors that are becoming more and more prevalent with technology scaling. On-chip interconnect architectures are particularly susceptible to faults that can corrupt transmitted data or prevent it from reaching its destination. Reliability concerns in UDSM nodes have in part contributed to the shift from traditional bus-based communication fabrics to network-on-chip (NoC) architectures that provide better scalability, performance, and utilization than buses. In this thesis, to overcome potential faults in NoCs, my research began by exploring fault-tolerant routing algorithms. Under the constraint of deadlock freedom, we make use of the inherent redundancy in NoCs due to multiple paths between packet sources and sinks and propose different fault-tolerant routing schemes to achieve much better fault tolerance capabilities than possible with traditional routing schemes. The proposed schemes also use replication opportunistically to optimize the balance between energy overhead and arrival rate. As 3D integrated circuit (3D-IC) technology with wafer-to-wafer bonding has been recently proposed as a promising candidate for future CMPs, we also propose a fault-tolerant routing scheme for 3D NoCs which outperforms the existing popular routing schemes in terms of energy consumption, performance and reliability. To quantify reliability and provide different levels of intelligent protection, for the first time, we propose the network vulnerability factor (NVF) metric to characterize the vulnerability of NoC components to faults. NVF determines the probabilities that faults in NoC components manifest as errors in the final program output of the CMP system. With NVF aware partial protection for NoC components, almost 50% energy cost can be saved compared to the traditional approach of comprehensively protecting all NoC components. Lastly, we focus on the problem of fault-tolerant NoC design, that involves many NP-hard sub-problems such as core mapping, fault-tolerant routing, and fault-tolerant router configuration. We propose a novel design-time (RESYN) and a hybrid design and runtime (HEFT) synthesis framework to trade-off energy consumption and reliability in the NoC fabric at the system level for CMPs. Together, our research in fault-tolerant NoC routing, reliability modeling, and reliability aware NoC synthesis substantially enhances NoC reliability and energy-efficiency beyond what is possible with traditional approaches and state-of-the-art strategies from prior work

Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods

Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.Comment: 24 pages, 10 figure