54,462 research outputs found
Non-Local Probes Do Not Help with Graph Problems
This work bridges the gap between distributed and centralised models of
computing in the context of sublinear-time graph algorithms. A priori, typical
centralised models of computing (e.g., parallel decision trees or centralised
local algorithms) seem to be much more powerful than distributed
message-passing algorithms: centralised algorithms can directly probe any part
of the input, while in distributed algorithms nodes can only communicate with
their immediate neighbours. We show that for a large class of graph problems,
this extra freedom does not help centralised algorithms at all: for example,
efficient stateless deterministic centralised local algorithms can be simulated
with efficient distributed message-passing algorithms. In particular, this
enables us to transfer existing lower bound results from distributed algorithms
to centralised local algorithms
Quantum Geometry and Quantum Gravity
The purpose of this contribution is to give an introduction to quantum
geometry and loop quantum gravity for a wide audience of both physicists and
mathematicians. From a physical point of view the emphasis will be on
conceptual issues concerning the relationship of the formalism with other more
traditional approaches inspired in the treatment of the fundamental
interactions in the standard model. Mathematically I will pay special attention
to functional analytic issues, the construction of the relevant Hilbert spaces
and the definition and properties of geometric operators: areas and volumes.Comment: To appear in the AIP Conference Proceedings of the XVI International
Fall Workshop on Geometry and Physics, Lisbon - Portugal, 5-8 September 200
Mapping Dynamic Histone Acetylation Patterns to Gene Expression in Nanog-depleted Murine Embryonic Stem Cells
Embryonic stem cells (ESC) have the potential to self-renew indefinitely and
to differentiate into any of the three germ layers. The molecular mechanisms
for self-renewal, maintenance of pluripotency and lineage specification are
poorly understood, but recent results point to a key role for epigenetic
mechanisms. In this study, we focus on quantifying the impact of histone 3
acetylation (H3K9,14ac) on gene expression in murine embryonic stem cells. We
analyze genome-wide histone acetylation patterns and gene expression profiles
measured over the first five days of cell differentiation triggered by
silencing Nanog, a key transcription factor in ESC regulation. We explore the
temporal and spatial dynamics of histone acetylation data and its correlation
with gene expression using supervised and unsupervised statistical models. On a
genome-wide scale, changes in acetylation are significantly correlated to
changes in mRNA expression and, surprisingly, this coherence increases over
time. We quantify the predictive power of histone acetylation for gene
expression changes in a balanced cross-validation procedure. In an in-depth
study we focus on genes central to the regulatory network of Mouse ESC,
including those identified in a recent genome-wide RNAi screen and in the
PluriNet, a computationally derived stem cell signature. We find that compared
to the rest of the genome, ESC-specific genes show significantly more
acetylation signal and a much stronger decrease in acetylation over time, which
is often not reflected in an concordant expression change. These results shed
light on the complexity of the relationship between histone acetylation and
gene expression and are a step forward to dissect the multilayer regulatory
mechanisms that determine stem cell fate.Comment: accepted at PLoS Computational Biolog
Locating a robber with multiple probes
We consider a game in which a cop searches for a moving robber on a connected
graph using distance probes, which is a slight variation on one introduced by
Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any
-vertex graph there is a winning strategy for the cop on the graph
obtained by replacing each edge of by a path of length , if
. The present authors showed that, for all but a few small values of
, this bound may be improved to , which is best possible. In this
paper we consider the natural extension in which the cop probes a set of
vertices, rather than a single vertex, at each turn. We consider the
relationship between the value of required to ensure victory on the
original graph and the length of subdivisions required to ensure victory with
. We give an asymptotically best-possible linear bound in one direction,
but show that in the other direction no subexponential bound holds. We also
give a bound on the value of for which the cop has a winning strategy on
any (possibly infinite) connected graph of maximum degree , which is
best possible up to a factor of .Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to
infinite graphs. Accepted for publication in Discrete Mathematic
Analysing multiple types of molecular profiles simultaneously: connecting the needles in the haystack
It has been shown that a random-effects framework can be used to test the
association between a gene's expression level and the number of DNA copies of a
set of genes. This gene-set modelling framework was later applied to find
associations between mRNA expression and microRNA expression, by defining the
gene sets using target prediction information.
Here, we extend the model introduced by Menezes et al (2009) to consider the
effect of not just copy number, but also of other molecular profiles such as
methylation changes and loss-of-heterozigosity (LOH), on gene expression
levels. We will consider again sets of measurements, to improve robustness of
results and increase the power to find associations. Our approach can be used
genome-wide to find associations, yields a test to help separate true
associations from noise and can include confounders.
We apply our method to colon and to breast cancer samples, for which
genome-wide copy number, methylation and gene expression profiles are
available. Our findings include interesting gene expression-regulating
mechanisms, which may involve only one of copy number or methylation, or both
for the same samples. We even are able to find effects due to different
molecular mechanisms in different samples.
Our method can equally well be applied to cases where other types of
molecular (high-dimensional) data are collected, such as LOH, SNP genotype and
microRNA expression data. Computationally efficient, it represents a flexible
and powerful tool to study associations between high-dimensional datasets. The
method is freely available via the SIM BioConductor package
Algorithmic and Statistical Perspectives on Large-Scale Data Analysis
In recent years, ideas from statistics and scientific computing have begun to
interact in increasingly sophisticated and fruitful ways with ideas from
computer science and the theory of algorithms to aid in the development of
improved worst-case algorithms that are useful for large-scale scientific and
Internet data analysis problems. In this chapter, I will describe two recent
examples---one having to do with selecting good columns or features from a (DNA
Single Nucleotide Polymorphism) data matrix, and the other having to do with
selecting good clusters or communities from a data graph (representing a social
or information network)---that drew on ideas from both areas and that may serve
as a model for exploiting complementary algorithmic and statistical
perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors,
"Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201
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