7,557 research outputs found
Community Structure in the United States House of Representatives
We investigate the networks of committee and subcommittee assignments in the
United States House of Representatives from the 101st--108th Congresses, with
the committees connected by ``interlocks'' or common membership. We examine the
community structure in these networks using several methods, revealing strong
links between certain committees as well as an intrinsic hierarchical structure
in the House as a whole. We identify structural changes, including additional
hierarchical levels and higher modularity, resulting from the 1994 election, in
which the Republican party earned majority status in the House for the first
time in more than forty years. We also combine our network approach with
analysis of roll call votes using singular value decomposition to uncover
correlations between the political and organizational structure of House
committees.Comment: 44 pages, 13 figures (some with multiple parts and most in color), 9
tables, to appear in Physica A; new figures and revised discussion (including
extra introductory material) for this versio
Sequential testing for structural stability in approximate factor models
We develop a monitoring procedure to detect changes in a large approximate
factor model. Letting be the number of common factors, we base our
statistics on the fact that the -th eigenvalue of the
sample covariance matrix is bounded under the null of no change, whereas it
becomes spiked under changes. Given that sample eigenvalues cannot be estimated
consistently under the null, we randomise the test statistic, obtaining a
sequence of \textit{i.i.d} statistics, which are used for the monitoring
scheme. Numerical evidence shows a very small probability of false detections,
and tight detection times of change-points
Randomness and Complexity in Networks
I start by reviewing some basic properties of random graphs. I then consider
the role of random walks in complex networks and show how they may be used to
explain why so many long tailed distributions are found in real data sets. The
key idea is that in many cases the process involves copying of properties of
near neighbours in the network and this is a type of short random walk which in
turn produce a natural preferential attachment mechanism. Applying this to
networks of fixed size I show that copying and innovation are processes with
special mathematical properties which include the ability to solve a simple
model exactly for any parameter values and at any time. I finish by looking at
variations of this basic model.Comment: Survey paper based on talk given at the workshop on ``Stochastic
Networks and Internet Technology'', Centro di Ricerca Matematica Ennio De
Giorgi, Matematica nelle Scienze Naturali e Sociali, Pisa, 17th - 21st
September 2007. To appear in proceeding
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