59,248 research outputs found
Performance Characterization of Random Proximity Sensor Networks
In this paper, we characterize the localization performance
and connectivity of sensors networks consisting of
binary proximity sensors using a random sensor management
strategy. The sensors are deployed uniformly at random over
an area, and to limit the energy dissipation, each sensor node
switches between an active and idle state according to random
mechanisms regulated by a birth-and-death stochastic process.
We first develop an upper bound for the minimum transmitting
range which guarantees connectivity of the active nodes in the
network with a desired probability. Then, we derive an analytical
formula for predicting the mean-squared localization error of
the active nodes when assuming a centroid localization scheme.
Simulations are used to verify the theoretical claims for various
localization schemes that operate only over connected active
nodes
Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
We report on some recent developments in the search for optimal network
topologies. First we review some basic concepts on spectral graph theory,
including adjacency and Laplacian matrices, and paying special attention to the
topological implications of having large spectral gaps. We also introduce
related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we
discuss two different dynamical feautures of networks: synchronizability and
flow of random walkers and so that they are optimized if the corresponding
Laplacian matrix have a large spectral gap. From this, we show, by developing a
numerical optimization algorithm that maximum synchronizability and fast random
walk spreading are obtained for a particular type of extremely homogeneous
regular networks, with long loops and poor modular structure, that we call
entangled networks. These turn out to be related to Ramanujan and Cage graphs.
We argue also that these graphs are very good finite-size approximations to
Bethe lattices, and provide almost or almost optimal solutions to many other
problems as, for instance, searchability in the presence of congestion or
performance of neural networks. Finally, we study how these results are
modified when studying dynamical processes controlled by a normalized (weighted
and directed) dynamics; much more heterogeneous graphs are optimal in this
case. Finally, a critical discussion of the limitations and possible extensions
of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted
for pub. in JSTA
Bayesian nonparametric sparse VAR models
High dimensional vector autoregressive (VAR) models require a large number of
parameters to be estimated and may suffer of inferential problems. We propose a
new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional
VAR models that can improve estimation efficiency and prediction accuracy. Our
hierarchical prior overcomes overparametrization and overfitting issues by
clustering the VAR coefficients into groups and by shrinking the coefficients
of each group toward a common location. Clustering and shrinking effects
induced by the BNP-Lasso prior are well suited for the extraction of causal
networks from time series, since they account for some stylized facts in
real-world networks, which are sparsity, communities structures and
heterogeneity in the edges intensity. In order to fully capture the richness of
the data and to achieve a better understanding of financial and macroeconomic
risk, it is therefore crucial that the model used to extract network accounts
for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the
paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ----
Supplementary Material available on reques
Exchangeable Random Measures for Sparse and Modular Graphs with Overlapping Communities
We propose a novel statistical model for sparse networks with overlapping
community structure. The model is based on representing the graph as an
exchangeable point process, and naturally generalizes existing probabilistic
models with overlapping block-structure to the sparse regime. Our construction
builds on vectors of completely random measures, and has interpretable
parameters, each node being assigned a vector representing its level of
affiliation to some latent communities. We develop methods for simulating this
class of random graphs, as well as to perform posterior inference. We show that
the proposed approach can recover interpretable structure from two real-world
networks and can handle graphs with thousands of nodes and tens of thousands of
edges
Random consensus protocol in large-scale networks
One of the main performance issues for consensus
protocols is the convergence speed. In this paper, we focus on the
convergence behavior of discrete-time consensus protocols over
large-scale sensor networks with uniformly random deployment,
which are modelled as Poisson random graphs. Instead of
using the random rewiring procedure, we introduce a deterministic
principle to locate certain “chosen nodes” in the network
and add “virtual” shortcuts among them so that the number
of iterations to achieve average consensus drops dramatically.
Simulation results are presented to verify the efficiency of this
approach. Moreover, a random consensus protocol is proposed,
in which virtual shortcuts are implemented by random routes
A Perfect Sampling Method for Exponential Family Random Graph Models
Generation of deviates from random graph models with non-trivial edge
dependence is an increasingly important problem. Here, we introduce a method
which allows perfect sampling from random graph models in exponential family
form ("exponential family random graph" models), using a variant of Coupling
From The Past. We illustrate the use of the method via an application to the
Markov graphs, a family that has been the subject of considerable research. We
also show how the method can be applied to a variant of the biased net models,
which are not exponentially parameterized.Comment: To appear in the Journal of Mathematical Sociology (accepted version
Threshold-Controlled Global Cascading in Wireless Sensor Networks
We investigate cascade dynamics in threshold-controlled (multiplex)
propagation on random geometric networks. We find that such local dynamics can
serve as an efficient, robust, and reliable prototypical activation protocol in
sensor networks in responding to various alarm scenarios. We also consider the
same dynamics on a modified network by adding a few long-range communication
links, resulting in a small-world network. We find that such construction can
further enhance and optimize the speed of the network's response, while keeping
energy consumption at a manageable level
Dynamic Load Balancing Strategies for Graph Applications on GPUs
Acceleration of graph applications on GPUs has found large interest due to
the ubiquitous use of graph processing in various domains. The inherent
\textit{irregularity} in graph applications leads to several challenges for
parallelization. A key challenge, which we address in this paper, is that of
load-imbalance. If the work-assignment to threads uses node-based graph
partitioning, it can result in skewed task-distribution, leading to poor
load-balance. In contrast, if the work-assignment uses edge-based graph
partitioning, the load-balancing is better, but the memory requirement is
relatively higher. This makes it unsuitable for large graphs. In this work, we
propose three techniques for improved load-balancing of graph applications on
GPUs. Each technique brings in unique advantages, and a user may have to employ
a specific technique based on the requirement. Using Breadth First Search and
Single Source Shortest Paths as our processing kernels, we illustrate the
effectiveness of each of the proposed techniques in comparison to the existing
node-based and edge-based mechanisms
Asymptotic properties of random unlabelled block-weighted graphs
We study the asymptotic shape of random unlabelled graphs subject to certain
subcriticality conditions. The graphs are sampled with probability proportional
to a product of Boltzmann weights assigned to their -connected components.
As their number of vertices tends to infinity, we show that they admit the
Brownian tree as Gromov--Hausdorff--Prokhorov scaling limit, and converge in a
strengthened Benjamini--Schramm sense toward an infinite random graph. We also
consider a family of random graphs that are allowed to be disconnected. Here a
giant connected component emerges and the small fragments converge without any
rescaling towards a finite random limit graph
Generating random networks with given degree-degree correlations and degree-dependent clustering
Random networks are widely used to model complex networks and research their
properties. In order to get a good approximation of complex networks
encountered in various disciplines of science, the ability to tune various
statistical properties of random networks is very important. In this manuscript
we present an algorithm which is able to construct arbitrarily degree-degree
correlated networks with adjustable degree-dependent clustering. We verify the
algorithm by using empirical networks as input and describe additionally a
simple way to fix a degree-dependent clustering function if degree-degree
correlations are given.Comment: 4 pages, 3 figure
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