556 research outputs found
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Scaling Expected Force: Efficient Identification of Key Nodes in Network-based Epidemic Models
Centrality measures are fundamental tools of network analysis as they
highlight the key actors within the network. This study focuses on a newly
proposed centrality measure, Expected Force (EF), and its use in identifying
spreaders in network-based epidemic models. We found that EF effectively
predicts the spreading power of nodes and identifies key nodes and immunization
targets. However, its high computational cost presents a challenge for its use
in large networks. To overcome this limitation, we propose two parallel
scalable algorithms for computing EF scores: the first algorithm is based on
the original formulation, while the second one focuses on a cluster-centric
approach to improve efficiency and scalability. Our implementations
significantly reduce computation time, allowing for the detection of key nodes
at large scales. Performance analysis on synthetic and real-world networks
demonstrates that the GPU implementation of our algorithm can efficiently scale
to networks with up to 44 million edges by exploiting modern parallel
architectures, achieving speed-ups of up to 300x, and 50x on average, compared
to the simple parallel solution
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Contagion aÌ effet de seuil dans les reÌseaux complexes
Networks arise frequently in the study of complex systems, since interactions among the components of such systems are critical. Networks can act as a substrate for dynamical process, such as the diffusion of information or disease throughout populations. Network structure can determine the temporal evolution of a dynamical process, including the characteristics of the steady state.The simplest representation of a complex system is an undirected, unweighted, single layer graph. In contrast, real systems exhibit heterogeneity of interaction strength and type. Such systems are frequently represented as weighted multiplex networks, and in this work we incorporate these heterogeneities into a master equation formalism in order to study their effects on spreading processes. We also carry out simulations on synthetic and empirical networks, and show that spreading dynamics, in particular the speed at which contagion spreads via threshold mechanisms, depend non-trivially on these heterogeneities. Further, we show that an important family of networks undergo reentrant phase transitions in the size and frequency of global cascades as a result of these interactions.A challenging feature of real systems is their tendency to evolve over time, since the changing structure of the underlying network is critical to the behaviour of overlying dynamical processes. We show that one aspect of temporality, the observed âburstinessâ in interaction patterns, leads to non-monotic changes in the spreading time of threshold driven contagion processes.The above results shed light on the effects of various network heterogeneities, with respect to dynamical processes that evolve on these networks.Les interactions entre les composants des systeÌmes complexes font eÌmerger diffeÌrents types de reÌseaux. Ces reÌseaux peuvent jouer le roÌle dâun substrat pour des processus dynamiques tels que la diffusion dâinformations ou de maladies dans des populations. Les structures de ces reÌseaux deÌterminent lâeÌvolution dâun processus dynamique, en particulier son reÌgime transitoire, mais aussi les caracteÌristiques du reÌgime permanent.Les systeÌmes complexes reÌels manifestent des inteÌractions heÌteÌrogeÌnes en type et en intensiteÌ. Ces systeÌmes sont repreÌseteÌs comme des reÌseaux pondeÌreÌs aÌ plusieurs couches. Dans cette theÌse, nous deÌveloppons une eÌquation maiÌtresse afin dâinteÌgrer ces heÌteÌrogeÌneÌiteÌs et dâeÌtudier leurs effets sur les processus de diffusion. AÌ lâaide de simulations mettant en jeu des reÌseaux reÌels et geÌneÌreÌs, nous montrons que les dynamiques de diffusion sont lieÌes de manieÌre non triviale aÌ lâheÌteÌrogeÌneÌiteÌ de ces reÌseaux, en particulier la vitesse de propagation dâune contagion baseÌe sur un effet de seuil. De plus, nous montrons que certaines classes de reÌseaux sont soumises aÌ des transitions de phase reÌentrantes fonctions de la taille des âglobal cascadesâ.La tendance des reÌseaux reÌels aÌ eÌvoluer dans le temps rend difficile la modeÌlisation des processus de diffusion. Nous montrons enfin que la dureÌe de diffusion dâun processus de contagion baseÌ sur un effet de seuil change de manieÌre non-monotone du fait de la preÌsence deârafalesâ dans les motifs dâinteÌractions. Lâensemble de ces reÌsultats mettent en lumieÌre les effets de lâheÌteÌrogeÌneÌiteÌ des reÌseaux vis-aÌ-vis des processus dynamiques y eÌvoluant
Detecting exploit patterns from network packet streams
Network-based Intrusion Detection Systems (NIDS), e.g., Snort, Bro or NSM, try to detect malicious network activity such as Denial of Service (DoS) attacks and port scans by monitoring network traffic. Research from network traffic measurement has identified various patterns that exploits on today\u27s Internet typically exhibit. However, there has not been any significant attempt, so far, to design algorithms with provable guarantees for detecting exploit patterns from network traffic packets. In this work, we develop and apply data streaming algorithms to detect exploit patterns from network packet streams.
In network intrusion detection, it is necessary to analyze large volumes of data in an online fashion. Our work addresses scalable analysis of data under the following situations. (1) Attack traffic can be stealthy in nature, which means detecting a few covert attackers might call for checking traffic logs of days or even months, (2) Traffic is multidimensional and correlations between multiple dimensions maybe important, and (3) Sometimes traffic from multiple sources may need to be analyzed in a combined manner. Our algorithms offer provable bounds on resource consumption and approximation error. Our theoretical results are supported by experiments over real network traces and synthetic datasets
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Exact and approximate epidemic models on networks: theory and applications
This thesis is concerned with modelling the spread of diseases amongst host populations and the epidemics that result from this process. We are primarily interested in how networks can be used to model the various heterogeneities observable in real-world populations.
Firstly, we start with the full system of Kolmogorov/master equations for a simple Susceptible-Infected-Susceptible (SIS) type epidemic on an arbitrary contact network. From this general framework, we rigorously derive sets of ODEs that describe the exact dynamics of the expected number of individuals and pairs of individuals.
We proceed to use moment closure techniques to close these hierarchical systems of ODEs, by approximating higher order moments in terms of lower order moments. We prove that the simple first order mean-field approximation becomes exact in the limit of a large, fully-connected network. We then investigate how well two different pairwise approximations capture the topological features of theoretical networks generated using different algorithms.
We then introduce the effective degree modelling framework and propose a model for SIS epidemics on dynamic contact networks by accounting for random link activation and deletion. We show that results from the resulting set of ODEs agrees well with results from stochastic simulations, both in describing the evolution of the network and the disease. Furthermore, we derive an analytic calculation of the stability of the disease-free steady state and explore the validity of such a measure in the context of a dynamically evolving contact network.
Finally, we move on to derive a system of ODEs that describes the interacting dynamics of a disease and information relating to the disease. We allow individuals to become responsive in light of received information and, thus, reduce the rate at which they become infected. We consider the effectiveness of different routes of information transmission (such as peer-to-peer communication or mass media campaigns) in slowing or preventing the spread of a disease.
Finally, we use a range of modelling techniques to investigate the spread of disease within sheep flocks. We use field data to construct weighted contact networks for flocks of sheep to account for seasonal changes of the flock structure as lambs are born and eventually become weaned. We construct a range of network and ODE models that are designed to investigate the effect of link-weight heterogeneity on the spread of disease
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Prediction-enhanced Routing in Disruption-tolerant Satellite Networks
This thesis introduces a framework for enhancing DTN (Delay-/Disruption-Tolerant Networking) routing in dynamic LEO satellite constellations based on the prediction of contacts.
The solution is developed with a clear focus on the requirements imposed by the 'Ring Road' use case, mandating a concept for dynamic contact prediction and its integration into a state-of-the-art routing approach.
The resulting system does not restrict possible applications to the 'Ring Road,' but allows for flexible adaptation to further use cases.
A thorough evaluation shows that employing proactive routing in concert with a prediction mechanism offers significantly improved performance when compared to alternative opportunistic routing techniques
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