4,550 research outputs found
On fast-slow consensus networks with a dynamic weight
We study dynamic networks under an undirected consensus communication
protocol and with one state-dependent weighted edge. We assume that the
aforementioned dynamic edge can take values over the whole real numbers, and
that its behaviour depends on the nodes it connects and on an extrinsic slow
variable. We show that, under mild conditions on the weight, there exists a
reduction such that the dynamics of the network are organized by a
transcritical singularity. As such, we detail a slow passage through a
transcritical singularity for a simple network, and we observe that an exchange
between consensus and clustering of the nodes is possible. In contrast to the
classical planar fast-slow transcritical singularity, the network structure of
the system under consideration induces the presence of a maximal canard. Our
main tool of analysis is the blow-up method. Thus, we also focus on tracking
the effects of the blow-up transformation on the network's structure. We show
that on each blow-up chart one recovers a particular dynamic network related to
the original one. We further indicate a numerical issue produced by the slow
passage through the transcritical singularity
Coupled dynamics of node and link states in complex networks: A model for language competition
Inspired by language competition processes, we present a model of coupled
evolution of node and link states. In particular, we focus on the interplay
between the use of a language and the preference or attitude of the speakers
towards it, which we model, respectively, as a property of the interactions
between speakers (a link state) and as a property of the speakers themselves (a
node state). Furthermore, we restrict our attention to the case of two socially
equivalent languages and to socially inspired network topologies based on a
mechanism of triadic closure. As opposed to most of the previous literature,
where language extinction is an inevitable outcome of the dynamics, we find a
broad range of possible asymptotic configurations, which we classify as: frozen
extinction states, frozen coexistence states, and dynamically trapped
coexistence states. Moreover, metastable coexistence states with very long
survival times and displaying a non-trivial dynamics are found to be abundant.
Interestingly, a system size scaling analysis shows, on the one hand, that the
probability of language extinction vanishes exponentially for increasing system
sizes and, on the other hand, that the time scale of survival of the
non-trivial dynamical metastable states increases linearly with the size of the
system. Thus, non-trivial dynamical coexistence is the only possible outcome
for large enough systems. Finally, we show how this coexistence is
characterized by one of the languages becoming clearly predominant while the
other one becomes increasingly confined to "ghetto-like" structures: small
groups of bilingual speakers arranged in triangles, with a strong preference
for the minority language, and using it for their intra-group interactions
while they switch to the predominant language for communications with the rest
of the population.Comment: 21 pages, 15 figure
Multivariate Relations Aggregation Learning in Social Networks
Multivariate relations are general in various types of networks, such as
biological networks, social networks, transportation networks, and academic
networks. Due to the principle of ternary closures and the trend of group
formation, the multivariate relationships in social networks are complex and
rich. Therefore, in graph learning tasks of social networks, the identification
and utilization of multivariate relationship information are more important.
Existing graph learning methods are based on the neighborhood information
diffusion mechanism, which often leads to partial omission or even lack of
multivariate relationship information, and ultimately affects the accuracy and
execution efficiency of the task. To address these challenges, this paper
proposes the multivariate relationship aggregation learning (MORE) method,
which can effectively capture the multivariate relationship information in the
network environment. By aggregating node attribute features and structural
features, MORE achieves higher accuracy and faster convergence speed. We
conducted experiments on one citation network and five social networks. The
experimental results show that the MORE model has higher accuracy than the GCN
(Graph Convolutional Network) model in node classification tasks, and can
significantly reduce time cost.Comment: 11 pages, 6 figure
Complexity and Criticality in financial markets: systemic risk across frequencies and cross sections
Extreme market events and systemic collapses cause most of the popular attention to finance and financial markets. Extreme phenomena and the dynamics of con- nected/interacting systems have been the subject of financial modeling since early derivatives modeling, exposure risk modeling and portfolio construction. In the present work we discuss how traditional methods have for the most part failed to properly model the interconnected global financial and economic system. This led to systemic risk events and simplistic regulation which does not properly account for its implications. Analogously, we discuss how from as early as Mandelbrot’s works on financial prices and fat tails, academics, practitioners and regulators alike were warned of fat tails in financial modeling and in particular market making and derivatives pricing. The improper modeling or dismissal of these lies at the cen- tre of financial downturns ranging from LTCM’s collapse to the quant downturn of August 2007.
The solution I promote in this thesis is that of complexity and criticality. In line with this we propose two lines of work. The former analyses markets as complex networks and their structure through to practical takeaways including a proof of concept for portfolio construction. The latter instead focuses on extreme events in high frequency markets with results for both tail modeling and systemic events and practical insights from those. Recent events have shown how retail investors and their savings are now heavily involved in financial markets. We hope that our contribution of methods of practical use for proper risk modeling will encourage their adoption by practitioners and regulators with the outcome of a more stable and efficient financial system
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
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