333,274 research outputs found
An ensemble perspective on multi-layer networks
We study properties of multi-layered, interconnected networks from an
ensemble perspective, i.e. we analyze ensembles of multi-layer networks that
share similar aggregate characteristics. Using a diffusive process that evolves
on a multi-layer network, we analyze how the speed of diffusion depends on the
aggregate characteristics of both intra- and inter-layer connectivity. Through
a block-matrix model representing the distinct layers, we construct transition
matrices of random walkers on multi-layer networks, and estimate expected
properties of multi-layer networks using a mean-field approach. In addition, we
quantify and explore conditions on the link topology that allow to estimate the
ensemble average by only considering aggregate statistics of the layers. Our
approach can be used when only partial information is available, like it is
usually the case for real-world multi-layer complex systems
Time scale modeling for consensus in sparse directed networks with time-varying topologies
The paper considers the consensus problem in large networks represented by
time-varying directed graphs. A practical way of dealing with large-scale
networks is to reduce their dimension by collapsing the states of nodes
belonging to densely and intensively connected clusters into aggregate
variables. It will be shown that under suitable conditions, the states of the
agents in each cluster converge fast toward a local agreement. Local agreements
correspond to aggregate variables which slowly converge to consensus. Existing
results concerning the time-scale separation in large networks focus on fixed
and undirected graphs. The aim of this work is to extend these results to the
more general case of time-varying directed topologies. It is noteworthy that in
the fixed and undirected graph case the average of the states in each cluster
is time-invariant when neglecting the interactions between clusters. Therefore,
they are good candidates for the aggregate variables. This is no longer
possible here. Instead, we find suitable time-varying weights to compute the
aggregate variables as time-invariant weighted averages of the states in each
cluster. This allows to deal with the more challenging time-varying directed
graph case. We end up with a singularly perturbed system which is analyzed by
using the tools of two time-scales averaging which seem appropriate to this
system
Generalized Master Equations for Non-Poisson Dynamics on Networks
The traditional way of studying temporal networks is to aggregate the
dynamics of the edges to create a static weighted network. This implicitly
assumes that the edges are governed by Poisson processes, which is not
typically the case in empirical temporal networks. Consequently, we examine the
effects of non-Poisson inter-event statistics on the dynamics of edges, and we
apply the concept of a generalized master equation to the study of
continuous-time random walks on networks. We show that the equation reduces to
the standard rate equations when the underlying process is Poisson and that the
stationary solution is determined by an effective transition matrix whose
leading eigenvector is easy to calculate. We discuss the implications of our
work for dynamical processes on temporal networks and for the construction of
network diagnostics that take into account their nontrivial stochastic nature
Distributed Algorithms for Scheduling on Line and Tree Networks
We have a set of processors (or agents) and a set of graph networks defined
over some vertex set. Each processor can access a subset of the graph networks.
Each processor has a demand specified as a pair of vertices , along
with a profit; the processor wishes to send data between and . Towards
that goal, the processor needs to select a graph network accessible to it and a
path connecting and within the selected network. The processor requires
exclusive access to the chosen path, in order to route the data. Thus, the
processors are competing for routes/channels. A feasible solution selects a
subset of demands and schedules each selected demand on a graph network
accessible to the processor owning the demand; the solution also specifies the
paths to use for this purpose. The requirement is that for any two demands
scheduled on the same graph network, their chosen paths must be edge disjoint.
The goal is to output a solution having the maximum aggregate profit. Prior
work has addressed the above problem in a distibuted setting for the special
case where all the graph networks are simply paths (i.e, line-networks).
Distributed constant factor approximation algorithms are known for this case.
The main contributions of this paper are twofold. First we design a
distributed constant factor approximation algorithm for the more general case
of tree-networks. The core component of our algorithm is a tree-decomposition
technique, which may be of independent interest. Secondly, for the case of
line-networks, we improve the known approximation guarantees by a factor of 5.
Our algorithms can also handle the capacitated scenario, wherein the demands
and edges have bandwidth requirements and capacities, respectively.Comment: Accepted to PODC 2012, full versio
Collective intelligence: aggregation of information from neighbors in a guessing game
Complex systems show the capacity to aggregate information and to display
coordinated activity. In the case of social systems the interaction of
different individuals leads to the emergence of norms, trends in political
positions, opinions, cultural traits, and even scientific progress. Examples of
collective behavior can be observed in activities like the Wikipedia and Linux,
where individuals aggregate their knowledge for the benefit of the community,
and citizen science, where the potential of collectives to solve complex
problems is exploited. Here, we conducted an online experiment to investigate
the performance of a collective when solving a guessing problem in which each
actor is endowed with partial information and placed as the nodes of an
interaction network. We measure the performance of the collective in terms of
the temporal evolution of the accuracy, finding no statistical difference in
the performance for two classes of networks, regular lattices and random
networks. We also determine that a Bayesian description captures the behavior
pattern the individuals follow in aggregating information from neighbors to
make decisions. In comparison with other simple decision models, the strategy
followed by the players reveals a suboptimal performance of the collective. Our
contribution provides the basis for the micro-macro connection between
individual based descriptions and collective phenomena.Comment: 9 pages, 9 figure
Riemannian consensus for manifolds with bounded curvature
Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in Euclidean space. In this work we propose Riemannian consensus, a natural extension of existing averaging consensus algorithms to the case of Riemannian manifolds. Unlike previous generalizations, our algorithm is intrinsic and, in principle, can be applied to any complete Riemannian manifold. We give sufficient convergence conditions on Riemannian manifolds with bounded curvature and we analyze the differences with respect to the Euclidean case. We test the proposed algorithms on synthetic data sampled from the space of rotations, the sphere and the Grassmann manifold.This work was supported by the grant NSF CNS-0834470. Recommended by Associate Editor L. Schenato. (CNS-0834470 - NSF
ChoiceRank: Identifying Preferences from Node Traffic in Networks
Understanding how users navigate in a network is of high interest in many
applications. We consider a setting where only aggregate node-level traffic is
observed and tackle the task of learning edge transition probabilities. We cast
it as a preference learning problem, and we study a model where choices follow
Luce's axiom. In this case, the marginal counts of node visits are a
sufficient statistic for the transition probabilities. We show how to
make the inference problem well-posed regardless of the network's structure,
and we present ChoiceRank, an iterative algorithm that scales to networks that
contains billions of nodes and edges. We apply the model to two clickstream
datasets and show that it successfully recovers the transition probabilities
using only the network structure and marginal (node-level) traffic data.
Finally, we also consider an application to mobility networks and apply the
model to one year of rides on New York City's bicycle-sharing system.Comment: Accepted at ICML 201
Cascading failures in spatially-embedded random networks
Cascading failures constitute an important vulnerability of interconnected
systems. Here we focus on the study of such failures on networks in which the
connectivity of nodes is constrained by geographical distance. Specifically, we
use random geometric graphs as representative examples of such spatial
networks, and study the properties of cascading failures on them in the
presence of distributed flow. The key finding of this study is that the process
of cascading failures is non-self-averaging on spatial networks, and thus,
aggregate inferences made from analyzing an ensemble of such networks lead to
incorrect conclusions when applied to a single network, no matter how large the
network is. We demonstrate that this lack of self-averaging disappears with the
introduction of a small fraction of long-range links into the network. We
simulate the well studied preemptive node removal strategy for cascade
mitigation and show that it is largely ineffective in the case of spatial
networks. We introduce an altruistic strategy designed to limit the loss of
network nodes in the event of a cascade triggering failure and show that it
performs better than the preemptive strategy. Finally, we consider a real-world
spatial network viz. a European power transmission network and validate that
our findings from the study of random geometric graphs are also borne out by
simulations of cascading failures on the empirical network.Comment: 13 pages, 15 figure
Enhanced reconstruction of weighted networks from strengths and degrees
Network topology plays a key role in many phenomena, from the spreading of
diseases to that of financial crises. Whenever the whole structure of a network
is unknown, one must resort to reconstruction methods that identify the least
biased ensemble of networks consistent with the partial information available.
A challenging case, frequently encountered due to privacy issues in the
analysis of interbank flows and Big Data, is when there is only local
(node-specific) aggregate information available. For binary networks, the
relevant ensemble is one where the degree (number of links) of each node is
constrained to its observed value. However, for weighted networks the problem
is much more complicated. While the naive approach prescribes to constrain the
strengths (total link weights) of all nodes, recent counter-intuitive results
suggest that in weighted networks the degrees are often more informative than
the strengths. This implies that the reconstruction of weighted networks would
be significantly enhanced by the specification of both strengths and degrees, a
computationally hard and bias-prone procedure. Here we solve this problem by
introducing an analytical and unbiased maximum-entropy method that works in the
shortest possible time and does not require the explicit generation of
reconstructed samples. We consider several real-world examples and show that,
while the strengths alone give poor results, the additional knowledge of the
degrees yields accurately reconstructed networks. Information-theoretic
criteria rigorously confirm that the degree sequence, as soon as it is
non-trivial, is irreducible to the strength sequence. Our results have strong
implications for the analysis of motifs and communities and whenever the
reconstructed ensemble is required as a null model to detect higher-order
patterns
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