3,613 research outputs found
On A Simpler and Faster Derivation of Single Use Reliability Mean and Variance for Model-Based Statistical Testing
Markov chain usage-based statistical testing has proved sound and effective in providing audit trails of evidence in certifying software-intensive systems. The system end-toend reliability is derived analytically in closed form, following an arc-based Bayesian model. System reliability is represented by an important statistic called single use reliability, and defined as the probability of a randomly selected use being successful. This paper continues our earlier work on a simpler and faster derivation of the single use reliability mean, and proposes a new derivation of the single use reliability variance by applying a well-known theorem and eliminating the need to compute the second moments of arc
failure probabilities. Our new results complete a new analysis that could be shown to be simpler, faster, and more direct while also rendering a more intuitive explanation. Our new
theory is illustrated with three simple Markov chain usage models with manual derivations and experimental results
Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering
Comparing large covariance matrices has important applications in modern
genomics, where scientists are often interested in understanding whether
relationships (e.g., dependencies or co-regulations) among a large number of
genes vary between different biological states. We propose a computationally
fast procedure for testing the equality of two large covariance matrices when
the dimensions of the covariance matrices are much larger than the sample
sizes. A distinguishing feature of the new procedure is that it imposes no
structural assumptions on the unknown covariance matrices. Hence the test is
robust with respect to various complex dependence structures that frequently
arise in genomics. We prove that the proposed procedure is asymptotically valid
under weak moment conditions. As an interesting application, we derive a new
gene clustering algorithm which shares the same nice property of avoiding
restrictive structural assumptions for high-dimensional genomics data. Using an
asthma gene expression dataset, we illustrate how the new test helps compare
the covariance matrices of the genes across different gene sets/pathways
between the disease group and the control group, and how the gene clustering
algorithm provides new insights on the way gene clustering patterns differ
between the two groups. The proposed methods have been implemented in an
R-package HDtest and is available on CRAN.Comment: The original title dated back to May 2015 is "Bootstrap Tests on High
Dimensional Covariance Matrices with Applications to Understanding Gene
Clustering
Modelling the Self-similarity in Complex Networks Based on Coulomb's Law
Recently, self-similarity of complex networks have attracted much attention.
Fractal dimension of complex network is an open issue. Hub repulsion plays an
important role in fractal topologies. This paper models the repulsion among the
nodes in the complex networks in calculation of the fractal dimension of the
networks. The Coulomb's law is adopted to represent the repulse between two
nodes of the network quantitatively. A new method to calculate the fractal
dimension of complex networks is proposed. The Sierpinski triangle network and
some real complex networks are investigated. The results are illustrated to
show that the new model of self-similarity of complex networks is reasonable
and efficient.Comment: 25 pages, 11 figure
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