14,313 research outputs found
Robustness of Complex Networks To Global Perturbations
This thesis studies the robustness of complex dynamical networks with non-trivial topologies against global perturbations, following Robert May’s seminal work on network stability, in order to find critical stability thresholds of global perturbations and to determine if their impact varies across different network topologies. Numerical analysis is used as the primary research method. Dynamical networks are randomly generated in the form of a coefficient matrix of stable linear differential equations. The networks are then inflicted with global perturbation (i.e., addition of another random matrix with varying magnitudes) and their stabilities are tested for each perturbation magnitude, to determine at what scale of global perturbation they are jarred to instability.
The results show a monotonic decrease of the instability threshold over increasing link density for all network topologies. For a given link density, random regular networks show highest robustness against global perturbation, closely followed by Watts-Strogatz small-world networks and Erdos-Renyi random graphs, and then Barabasi-Albert scalefree networks are least robust among the four topologies tested. Fully connected networks used in May’s original work are found to be consistently unstable in the presence of global perturbation of any magnitude. These findings offer useful implications for the robustness and sustainability/vulnerability of real-world complex networks with nontrivial topologies
Preserving Link Privacy in Social Network Based Systems
A growing body of research leverages social network based trust relationships
to improve the functionality of the system. However, these systems expose
users' trust relationships, which is considered sensitive information in
today's society, to an adversary.
In this work, we make the following contributions. First, we propose an
algorithm that perturbs the structure of a social graph in order to provide
link privacy, at the cost of slight reduction in the utility of the social
graph. Second we define general metrics for characterizing the utility and
privacy of perturbed graphs. Third, we evaluate the utility and privacy of our
proposed algorithm using real world social graphs. Finally, we demonstrate the
applicability of our perturbation algorithm on a broad range of secure systems,
including Sybil defenses and secure routing.Comment: 16 pages, 15 figure
Quantifying Transient Spreading Dynamics on Networks
Spreading phenomena on networks are essential for the collective dynamics of
various natural and technological systems, from information spreading in gene
regulatory networks to neural circuits or from epidemics to supply networks
experiencing perturbations. Still, how local disturbances spread across
networks is not yet quantitatively understood. Here we analyze generic
spreading dynamics in deterministic network dynamical systems close to a given
operating point. Standard dynamical systems' theory does not explicitly provide
measures for arrival times and amplitudes of a transient, spreading signal
because it focuses on invariant sets, invariant measures and other quantities
less relevant for transient behavior. We here change the perspective and
introduce effective expectation values for deterministic dynamics to work out a
theory explicitly quantifying when and how strongly a perturbation initiated at
one unit of a network impacts any other. The theory provides explicit timing
and amplitude information as a function of the relative position of initially
perturbed and responding unit as well as on the entire network topology.Comment: 9 pages and 4 figures main manuscript 9 pages and 3 figures appendi
The Regularizing Capacity of Metabolic Networks
Despite their topological complexity almost all functional properties of
metabolic networks can be derived from steady-state dynamics. Indeed, many
theoretical investigations (like flux-balance analysis) rely on extracting
function from steady states. This leads to the interesting question, how
metabolic networks avoid complex dynamics and maintain a steady-state behavior.
Here, we expose metabolic network topologies to binary dynamics generated by
simple local rules. We find that the networks' response is highly specific:
Complex dynamics are systematically reduced on metabolic networks compared to
randomized networks with identical degree sequences. Already small topological
modifications substantially enhance the capacity of a network to host complex
dynamic behavior and thus reduce its regularizing potential. This exceptionally
pronounced regularization of dynamics encoded in the topology may explain, why
steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure
Pattern invariance for reaction-diffusion systems on complex networks
Given a reaction-diffusion system interacting via a complex network, we
propose two different techniques to modify the network topology while
preserving its dynamical behaviour. In the region of parameters where the
homogeneous solution gets spontaneously destabilized, perturbations grow along
the unstable directions made available across the networks of connections,
yielding irregular spatio-temporal patterns. We exploit the spectral properties
of the Laplacian operator associated to the graph in order to modify its
topology, while preserving the unstable manifold of the underlying equilibrium.
The new network is isodynamic to the former, meaning that it reproduces the
dynamical response (pattern) to a perturbation, as displayed by the original
system. The first method acts directly on the eigenmodes, thus resulting in a
general redistribution of link weights which, in some cases, can completely
change the structure of the original network. The second method uses
localization properties of the eigenvectors to identify and randomize a
subnetwork that is mostly embedded only into the stable manifold. We test both
techniques on different network topologies using the Ginzburg-Landau system as
a reference model. Whereas the correlation between patterns on isodynamic
networks generated via the first recipe is larger, the second method allows for
a finer control at the level of single nodes. This work opens up a new
perspective on the multiple possibilities for identifying the family of
discrete supports that instigate equivalent dynamical responses on a
multispecies reaction-diffusion system
Dynamics of Unperturbed and Noisy Generalized Boolean Networks
For years, we have been building models of gene regulatory networks, where
recent advances in molecular biology shed some light on new structural and
dynamical properties of such highly complex systems. In this work, we propose a
novel timing of updates in Random and Scale-Free Boolean Networks, inspired by
recent findings in molecular biology. This update sequence is neither fully
synchronous nor asynchronous, but rather takes into account the sequence in
which genes affect each other. We have used both Kauffman's original model and
Aldana's extension, which takes into account the structural properties about
known parts of actual GRNs, where the degree distribution is right-skewed and
long-tailed. The computer simulations of the dynamics of the new model compare
favorably to the original ones and show biologically plausible results both in
terms of attractors number and length. We have complemented this study with a
complete analysis of our systems' stability under transient perturbations,
which is one of biological networks defining attribute. Results are
encouraging, as our model shows comparable and usually even better behavior
than preceding ones without loosing Boolean networks attractive simplicity.Comment: 29 pages, publishe
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