arXiv subjects

Giannis Moutsinas

Publications and source records attributed to Giannis Moutsinas.

7 recordsLinked to original sources

arXiv2020

Graph Hierarchy: A novel approach to understanding hierarchical structures in complex networks

Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties and partition and rank the vertices accordingly. Yet trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this paper we introduce a novel framework, a generalisation of trophic levels, which we call hierarchical levels, that can be defined on any simple graph. Within this general framework, we develop additional metrics named influence centrality, a measure of a vertices ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system, both of which have implications for the controllability of complex systems. We discuss how our generalisation relates to previous attempts and what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, we show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model.

physics.soc-ph↗

arXiv2020

Uncertainty of Resilience in Complex Networks with Nonlinear Dynamics

Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is limited. Recent research in predicting the network level resilience pattern has advanced our understanding of the coupling relationship between global network topology and local nonlinear component dynamics. However, when there is uncertainty in the model parameters, our understanding of how this translates to uncertainty in resilience is unclear for a large-scale networked system. Here we develop a polynomial chaos expansion method to estimate the resilience for a wide range of uncertainty distributions. By applying this method to case studies, we not only reveal the general resilience distribution with respect to the topology and dynamics sub-models, but also identify critical aspects to inform better monitoring to reduce uncertainty.

eess.SY↗

arXiv2019

Probabilistic Stability of Traffic Load Balancing on Wireless Complex Networks

Load balancing between adjacent base stations (BSs) is important for balancing load distributions and improving service provisioning. Whilst load balancing between any given pair of BSs is beneficial, cascade load sharing can cause network level instability that is hard to predict. The relationship between each BS's load balancing dynamics and the network topology is not understood. In this seminal work on stability analysis, we consider a frequency re-use network with no interference, whereby load balancing dynamics doesn't perturb the individual cells' capacity. Our novelty is to show an exact analytical and also a probabilistic relationship for stability, relating generalized local load balancing dynamics with generalized network topology, as well as the uncertainty we have in load balancing parameters. We prove that the stability analysis given is valid for any generalized load balancing dynamics and topological cell deployment and we believe this general relationship can inform the joint design of both the load balancing dynamics and the neighbour list of the network.

cs.NI↗

arXiv2019

Uncertainty Quantification in Molecular Signals using Polynomial Chaos Expansion

Molecular signals are abundant in engineering and biological contexts, and undergo stochastic propagation in fluid dynamic channels. The received signal is sensitive to a variety of input and channel parameter variations. Currently we do not understand how uncertainty or noise in a variety of parameters affect the received signal concentration, and nor do we have an analytical framework to tackle this challenge. In this paper, we utilize Polynomial Chaos Expansion (PCE) to show to uncertainty in parameters propagates to uncertainty in the received signal. In demonstrating its applicability, we consider a Turbulent Diffusion Molecular Communication (TDMC) channel and highlight which parameters affect the received signals. This can pave the way for future information theoretic insights, as well as guide experimental design.

physics.comp-ph↗

arXiv2018

Node-Level Resilience Loss in Dynamic Complex Networks

In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well, our understanding of large-scale networked resilience is limited. Recent research in predicting the effective network-level resilience pattern has advanced our understanding of the coupling relationship between topology and dynamics. However, a method to estimate the resilience of an individual node within an arbitrarily large complex network governed by non-linear dynamics is still lacking. Here, we develop a sequential mean-field approach and show that after 1-3 steps of estimation, the node-level resilience function can be represented with up to 98\% accuracy. This new understanding compresses the higher dimensional relationship into a one-dimensional dynamic for tractable understanding, mapping the relationship between local dynamics and the statistical properties of network topology. By applying this framework to case studies in ecology and biology, we are able to not only understand the general resilience pattern of the network, but also identify the nodes at the greatest risk of failure and predict the impact of perturbations. These findings not only shed new light on the causes of resilience loss from cascade effects in networked systems, but the identification capability could also be used to prioritize protection, quantify risk, and inform the design of new system architectures.

nlin.AO↗

arXiv2017

Splitting of separatrices in a family of area-preserving maps that unfolds a fixed point at the resonance of order three

We study the exponentially small splitting of separatrices in an analytic one-parameter family of area-preserving maps that generically unfolds a 1:3 resonance. Near the resonance the normal form theory predicts existence of a small triangle formed by separatrices of a period three hyperbolic point. We prove that in a generic family the separatrices split, provided that the Stokes constant of the map does not vanish. This constant describes the distance between the analytical continuations of invariant manifolds associated with the degenerate saddle of the map at the exact resonance. We provide an asymptotic formula which describes the size of the splitting. The leading term of this asymptotic formula is proportional to the Stokes constant.

math.DS↗

arXiv2017

Unfolding of nilpotent equilibria of degree 4 in Hamiltonian systems with 2 degrees of freedom

We consider Hamiltonian systems of two degrees of freedome having a nilpotent equilibrium point with only one eigenvector. We provide the universal unfolding of such equilibrium, provided a non-degeneracy condition holds. We show that the only co-dimension 1 bifurcations that happen in the unfolding are of two types: the normally hyperbolic or elliptic centre-saddle bifurcations and the supercritical Hamiltonian-Hopf bifurcation.

math.DS↗