5,781 research outputs found
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
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
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