13,392 research outputs found
The Number of Hierarchical Orderings
An ordered set-partition (or preferential arrangement) of n labeled elements
represents a single ``hierarchy''; these are enumerated by the ordered Bell
numbers. In this note we determine the number of ``hierarchical orderings'' or
``societies'', where the n elements are first partitioned into m <= n subsets
and a hierarchy is specified for each subset. We also consider the unlabeled
case, where the ordered Bell numbers are replaced by the composition numbers.
If there is only a single hierarchy, we show that the average rank of an
element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the
unlabeled case.Comment: 7 page
Inference of Temporally Varying Bayesian Networks
When analysing gene expression time series data an often overlooked but
crucial aspect of the model is that the regulatory network structure may change
over time. Whilst some approaches have addressed this problem previously in the
literature, many are not well suited to the sequential nature of the data. Here
we present a method that allows us to infer regulatory network structures that
may vary between time points, utilising a set of hidden states that describe
the network structure at a given time point. To model the distribution of the
hidden states we have applied the Hierarchical Dirichlet Process Hideen Markov
Model, a nonparametric extension of the traditional Hidden Markov Model, that
does not require us to fix the number of hidden states in advance. We apply our
method to exisiting microarray expression data as well as demonstrating is
efficacy on simulated test data
Towards a genome-wide transcriptogram: the Saccharomyces cerevisiae case
A genome modular classification that associates cellular processes to modules could lead to a method to quantify the differences in gene expression levels in different cellular stages or conditions: the transcriptogram, a powerful tool for assessing cell performance, would be at hand. Here we present a computational method to order genes on a line that clusters strongly interacting genes, defining functional modules associated with gene ontology terms. The starting point is a list of genes and a matrix specifying their interactions, available at large gene interaction databases. Considering the Saccharomyces cerevisiae genome we produced a succession of plots of gene transcription levels for a fermentation process. These plots discriminate the fermentation stage the cell is going through and may be regarded as the first versions of a transcriptogram. This method is useful for extracting information from cell stimuli/responses experiments, and may be applied with diagnostic purposes to different organisms
Optimal Hierarchical Layouts for Cache-Oblivious Search Trees
This paper proposes a general framework for generating cache-oblivious
layouts for binary search trees. A cache-oblivious layout attempts to minimize
cache misses on any hierarchical memory, independent of the number of memory
levels and attributes at each level such as cache size, line size, and
replacement policy. Recursively partitioning a tree into contiguous subtrees
and prescribing an ordering amongst the subtrees, Hierarchical Layouts
generalize many commonly used layouts for trees such as in-order, pre-order and
breadth-first. They also generalize the various flavors of the van Emde Boas
layout, which have previously been used as cache-oblivious layouts.
Hierarchical Layouts thus unify all previous attempts at deriving layouts for
search trees.
The paper then derives a new locality measure (the Weighted Edge Product)
that mimics the probability of cache misses at multiple levels, and shows that
layouts that reduce this measure perform better. We analyze the various degrees
of freedom in the construction of Hierarchical Layouts, and investigate the
relative effect of each of these decisions in the construction of
cache-oblivious layouts. Optimizing the Weighted Edge Product for complete
binary search trees, we introduce the MinWEP layout, and show that it
outperforms previously used cache-oblivious layouts by almost 20%.Comment: Extended version with proofs added to the appendi
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