30,576 research outputs found
Probabilistic estimation of microarray data reliability and underlying gene expression
Background: The availability of high throughput methods for measurement of
mRNA concentrations makes the reliability of conclusions drawn from the data
and global quality control of samples and hybridization important issues. We
address these issues by an information theoretic approach, applied to
discretized expression values in replicated gene expression data.
Results: Our approach yields a quantitative measure of two important
parameter classes: First, the probability that a gene is in the
biological state in a certain variety, given its observed expression
in the samples of that variety. Second, sample specific error probabilities
which serve as consistency indicators of the measured samples of each variety.
The method and its limitations are tested on gene expression data for
developing murine B-cells and a -test is used as reference. On a set of
known genes it performs better than the -test despite the crude
discretization into only two expression levels. The consistency indicators,
i.e. the error probabilities, correlate well with variations in the biological
material and thus prove efficient.
Conclusions: The proposed method is effective in determining differential
gene expression and sample reliability in replicated microarray data. Already
at two discrete expression levels in each sample, it gives a good explanation
of the data and is comparable to standard techniques.Comment: 11 pages, 4 figure
Image registration with sparse approximations in parametric dictionaries
We examine in this paper the problem of image registration from the new
perspective where images are given by sparse approximations in parametric
dictionaries of geometric functions. We propose a registration algorithm that
looks for an estimate of the global transformation between sparse images by
examining the set of relative geometrical transformations between the
respective features. We propose a theoretical analysis of our registration
algorithm and we derive performance guarantees based on two novel important
properties of redundant dictionaries, namely the robust linear independence and
the transformation inconsistency. We propose several illustrations and insights
about the importance of these dictionary properties and show that common
properties such as coherence or restricted isometry property fail to provide
sufficient information in registration problems. We finally show with
illustrative experiments on simple visual objects and handwritten digits images
that our algorithm outperforms baseline competitor methods in terms of
transformation-invariant distance computation and classification
Impact of the tick-size on financial returns and correlations
We demonstrate that the lowest possible price change (tick-size) has a large
impact on the structure of financial return distributions. It induces a
microstructure as well as it can alter the tail behavior. On small return
intervals, the tick-size can distort the calculation of correlations. This
especially occurs on small return intervals and thus contributes to the decay
of the correlation coefficient towards smaller return intervals (Epps effect).
We study this behavior within a model and identify the effect in market data.
Furthermore, we present a method to compensate this purely statistical error.Comment: 18 pages, 10 figure
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
Stochastic Galerkin methods for non-affine coefficient representations are
known to cause major difficulties from theoretical and numerical points of
view. In this work, an adaptive Galerkin FE method for linear parametric PDEs
with lognormal coefficients discretized in Hermite chaos polynomials is
derived. It employs problem-adapted function spaces to ensure solvability of
the variational formulation. The inherently high computational complexity of
the parametric operator is made tractable by using hierarchical tensor
representations. For this, a new tensor train format of the lognormal
coefficient is derived and verified numerically. The central novelty is the
derivation of a reliable residual-based a posteriori error estimator. This can
be regarded as a unique feature of stochastic Galerkin methods. It allows for
an adaptive algorithm to steer the refinements of the physical mesh and the
anisotropic Wiener chaos polynomial degrees. For the evaluation of the error
estimator to become feasible, a numerically efficient tensor format
discretization is developed. Benchmark examples with unbounded lognormal
coefficient fields illustrate the performance of the proposed Galerkin
discretization and the fully adaptive algorithm
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