15,773 research outputs found
Confidence sets for network structure
Latent variable models are frequently used to identify structure in
dichotomous network data, in part because they give rise to a Bernoulli product
likelihood that is both well understood and consistent with the notion of
exchangeable random graphs. In this article we propose conservative confidence
sets that hold with respect to these underlying Bernoulli parameters as a
function of any given partition of network nodes, enabling us to assess
estimates of 'residual' network structure, that is, structure that cannot be
explained by known covariates and thus cannot be easily verified by manual
inspection. We demonstrate the proposed methodology by analyzing student
friendship networks from the National Longitudinal Survey of Adolescent Health
that include race, gender, and school year as covariates. We employ a
stochastic expectation-maximization algorithm to fit a logistic regression
model that includes these explanatory variables as well as a latent stochastic
blockmodel component and additional node-specific effects. Although
maximum-likelihood estimates do not appear consistent in this context, we are
able to evaluate confidence sets as a function of different blockmodel
partitions, which enables us to qualitatively assess the significance of
estimated residual network structure relative to a baseline, which models
covariates but lacks block structure.Comment: 17 pages, 3 figures, 3 table
The Statistics of Supersymmetric D-brane Models
We investigate the statistics of the phenomenologically important D-brane
sector of string compactifications. In particular for the class of intersecting
D-brane models, we generalise methods known from number theory to determine the
asymptotic statistical distribution of solutions to the tadpole cancellation
conditions. Our approach allows us to compute the statistical distribution of
gauge theoretic observables like the rank of the gauge group, the number of
chiral generations or the probability of an SU(N) gauge factor. Concretely, we
study the statistics of intersecting branes on T^2 and T^4/Z_2 and T^6/Z_2 x
Z_2 orientifolds. Intriguingly, we find a statistical correlation between the
rank of the gauge group and the number of chiral generations. Finally, we
combine the statistics of the gauge theory sector with the statistics of the
flux sector and study how distributions of gauge theoretic quantities are
affected.Comment: 62 pages, 31 figures, harvmac; v3: sections 3.2. + 3.7. added, figs.
7,28,29 added, figs. 24,25,26 corrected, refs. added, typos correcte
Compressing networks with super nodes
Community detection is a commonly used technique for identifying groups in a
network based on similarities in connectivity patterns. To facilitate community
detection in large networks, we recast the network to be partitioned into a
smaller network of 'super nodes', each super node comprising one or more nodes
in the original network. To define the seeds of our super nodes, we apply the
'CoreHD' ranking from dismantling and decycling. We test our approach through
the analysis of two common methods for community detection: modularity
maximization with the Louvain algorithm and maximum likelihood optimization for
fitting a stochastic block model. Our results highlight that applying community
detection to the compressed network of super nodes is significantly faster
while successfully producing partitions that are more aligned with the local
network connectivity, more stable across multiple (stochastic) runs within and
between community detection algorithms, and overlap well with the results
obtained using the full network
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