6,998 research outputs found
Networking - A Statistical Physics Perspective
Efficient networking has a substantial economic and societal impact in a
broad range of areas including transportation systems, wired and wireless
communications and a range of Internet applications. As transportation and
communication networks become increasingly more complex, the ever increasing
demand for congestion control, higher traffic capacity, quality of service,
robustness and reduced energy consumption require new tools and methods to meet
these conflicting requirements. The new methodology should serve for gaining
better understanding of the properties of networking systems at the macroscopic
level, as well as for the development of new principled optimization and
management algorithms at the microscopic level. Methods of statistical physics
seem best placed to provide new approaches as they have been developed
specifically to deal with non-linear large scale systems. This paper aims at
presenting an overview of tools and methods that have been developed within the
statistical physics community and that can be readily applied to address the
emerging problems in networking. These include diffusion processes, methods
from disordered systems and polymer physics, probabilistic inference, which
have direct relevance to network routing, file and frequency distribution, the
exploration of network structures and vulnerability, and various other
practical networking applications.Comment: (Review article) 71 pages, 14 figure
Data clustering using a model granular magnet
We present a new approach to clustering, based on the physical properties of
an inhomogeneous ferromagnet. No assumption is made regarding the underlying
distribution of the data. We assign a Potts spin to each data point and
introduce an interaction between neighboring points, whose strength is a
decreasing function of the distance between the neighbors. This magnetic system
exhibits three phases. At very low temperatures it is completely ordered; all
spins are aligned. At very high temperatures the system does not exhibit any
ordering and in an intermediate regime clusters of relatively strongly coupled
spins become ordered, whereas different clusters remain uncorrelated. This
intermediate phase is identified by a jump in the order parameters. The
spin-spin correlation function is used to partition the spins and the
corresponding data points into clusters. We demonstrate on three synthetic and
three real data sets how the method works. Detailed comparison to the
performance of other techniques clearly indicates the relative success of our
method.Comment: 46 pages, postscript, 15 ps figures include
Macrostate Data Clustering
We develop an effective nonhierarchical data clustering method using an
analogy to the dynamic coarse graining of a stochastic system. Analyzing the
eigensystem of an interitem transition matrix identifies fuzzy clusters
corresponding to the metastable macroscopic states (macrostates) of a diffusive
system. A "minimum uncertainty criterion" determines the linear transformation
from eigenvectors to cluster-defining window functions. Eigenspectrum gap and
cluster certainty conditions identify the proper number of clusters. The
physically motivated fuzzy representation and associated uncertainty analysis
distinguishes macrostate clustering from spectral partitioning methods.
Macrostate data clustering solves a variety of test cases that challenge other
methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral
graph theory, dynamic eigenvectors, machine learning, macrostates,
classificatio
Communities in Networks
We survey some of the concepts, methods, and applications of community
detection, which has become an increasingly important area of network science.
To help ease newcomers into the field, we provide a guide to available
methodology and open problems, and discuss why scientists from diverse
backgrounds are interested in these problems. As a running theme, we emphasize
the connections of community detection to problems in statistical physics and
computational optimization.Comment: survey/review article on community structure in networks; published
version is available at
http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd
Clustering in Hilbert space of a quantum optimization problem
The solution space of many classical optimization problems breaks up into
clusters which are extensively distant from one another in the Hamming metric.
Here, we show that an analogous quantum clustering phenomenon takes place in
the ground state subspace of a certain quantum optimization problem. This
involves extending the notion of clustering to Hilbert space, where the
classical Hamming distance is not immediately useful. Quantum clusters
correspond to macroscopically distinct subspaces of the full quantum ground
state space which grow with the system size. We explicitly demonstrate that
such clusters arise in the solution space of random quantum satisfiability
(3-QSAT) at its satisfiability transition. We estimate both the number of these
clusters and their internal entropy. The former are given by the number of
hardcore dimer coverings of the core of the interaction graph, while the latter
is related to the underconstrained degrees of freedom not touched by the
dimers. We additionally provide new numerical evidence suggesting that the
3-QSAT satisfiability transition may coincide with the product satisfiability
transition, which would imply the absence of an intermediate entangled
satisfiable phase.Comment: 11 pages, 6 figure
Multi-view Graph Embedding with Hub Detection for Brain Network Analysis
Multi-view graph embedding has become a widely studied problem in the area of
graph learning. Most of the existing works on multi-view graph embedding aim to
find a shared common node embedding across all the views of the graph by
combining the different views in a specific way. Hub detection, as another
essential topic in graph mining has also drawn extensive attentions in recent
years, especially in the context of brain network analysis. Both the graph
embedding and hub detection relate to the node clustering structure of graphs.
The multi-view graph embedding usually implies the node clustering structure of
the graph based on the multiple views, while the hubs are the boundary-spanning
nodes across different node clusters in the graph and thus may potentially
influence the clustering structure of the graph. However, none of the existing
works in multi-view graph embedding considered the hubs when learning the
multi-view embeddings. In this paper, we propose to incorporate the hub
detection task into the multi-view graph embedding framework so that the two
tasks could benefit each other. Specifically, we propose an auto-weighted
framework of Multi-view Graph Embedding with Hub Detection (MVGE-HD) for brain
network analysis. The MVGE-HD framework learns a unified graph embedding across
all the views while reducing the potential influence of the hubs on blurring
the boundaries between node clusters in the graph, thus leading to a clear and
discriminative node clustering structure for the graph. We apply MVGE-HD on two
real multi-view brain network datasets (i.e., HIV and Bipolar). The
experimental results demonstrate the superior performance of the proposed
framework in brain network analysis for clinical investigation and application
Statistical Traffic State Analysis in Large-scale Transportation Networks Using Locality-Preserving Non-negative Matrix Factorization
Statistical traffic data analysis is a hot topic in traffic management and
control. In this field, current research progresses focus on analyzing traffic
flows of individual links or local regions in a transportation network. Less
attention are paid to the global view of traffic states over the entire
network, which is important for modeling large-scale traffic scenes. Our aim is
precisely to propose a new methodology for extracting spatio-temporal traffic
patterns, ultimately for modeling large-scale traffic dynamics, and long-term
traffic forecasting. We attack this issue by utilizing Locality-Preserving
Non-negative Matrix Factorization (LPNMF) to derive low-dimensional
representation of network-level traffic states. Clustering is performed on the
compact LPNMF projections to unveil typical spatial patterns and temporal
dynamics of network-level traffic states. We have tested the proposed method on
simulated traffic data generated for a large-scale road network, and reported
experimental results validate the ability of our approach for extracting
meaningful large-scale space-time traffic patterns. Furthermore, the derived
clustering results provide an intuitive understanding of spatial-temporal
characteristics of traffic flows in the large-scale network, and a basis for
potential long-term forecasting.Comment: IET Intelligent Transport Systems (2013
A statistical network analysis of the HIV/AIDS epidemics in Cuba
The Cuban contact-tracing detection system set up in 1986 allowed the
reconstruction and analysis of the sexual network underlying the epidemic
(5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168
edges), shedding light onto the spread of HIV and the role of contact-tracing.
Clustering based on modularity optimization provides a better visualization and
understanding of the network, in combination with the study of covariates. The
graph has a globally low but heterogeneous density, with clusters of high
intraconnectivity but low interconnectivity. Though descriptive, our results
pave the way for incorporating structure when studying stochastic SIR epidemics
spreading on social networks
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
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