114 research outputs found
Seeing the Forest for the Trees: Using the Gene Ontology to Restructure Hierarchical Clustering
Motivation: There is a growing interest in improving the cluster analysis of expression data by incorporating into it prior knowledge, such as the Gene Ontology (GO) annotations of genes, in order to improve the biological relevance of the clusters that are subjected to subsequent scrutiny. The structure of the GO is another source of background knowledge that can be exploited through the use of semantic similarity. Results: We propose here a novel algorithm that integrates semantic similarities (derived from the ontology structure) into the procedure of deriving clusters from the dendrogram constructed during expression-based hierarchical clustering. Our approach can handle the multiple annotations, from different levels of the GO hierarchy, which most genes have. Moreover, it treats annotated and unannotated genes in a uniform manner. Consequently, the clusters obtained by our algorithm are characterized by significantly enriched annotations. In both cross-validation tests and when using an external index such as proteinâprotein interactions, our algorithm performs better than previous approaches. When applied to human cancer expression data, our algorithm identifies, among others, clusters of genes related to immune response and glucose metabolism. These clusters are also supported by proteinâprotein interaction data. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.Lynne and William Frankel Center for Computer Science; Paul Ivanier center for robotics research and production; National Institutes of Health (R01 HG003367-01A1
Another Proof of the Total Positivity of the Discrete Spline Collocation Matrix
AbstractWe provide a different proof for Morken's result on necessary and sufficient conditions for a minor of the discrete B-spline collocation matrix to be positive and supply intuition for those conditions
Speeding up Simplification of Polygonal Curves using Nested Approximations
We develop a multiresolution approach to the problem of polygonal curve
approximation. We show theoretically and experimentally that, if the
simplification algorithm A used between any two successive levels of resolution
satisfies some conditions, the multiresolution algorithm MR will have a
complexity lower than the complexity of A. In particular, we show that if A has
a O(N2/K) complexity (the complexity of a reduced search dynamic solution
approach), where N and K are respectively the initial and the final number of
segments, the complexity of MR is in O(N).We experimentally compare the
outcomes of MR with those of the optimal "full search" dynamic programming
solution and of classical merge and split approaches. The experimental
evaluations confirm the theoretical derivations and show that the proposed
approach evaluated on 2D coastal maps either shows a lower complexity or
provides polygonal approximations closer to the initial curves.Comment: 12 pages + figure
Relative Convex Hull Determination from Convex Hulls in the Plane
A new algorithm for the determination of the relative convex hull in the
plane of a simple polygon A with respect to another simple polygon B which
contains A, is proposed. The relative convex hull is also known as geodesic
convex hull, and the problem of its determination in the plane is equivalent to
find the shortest curve among all Jordan curves lying in the difference set of
B and A and encircling A. Algorithms solving this problem known from
Computational Geometry are based on the triangulation or similar decomposition
of that difference set. The algorithm presented here does not use such
decomposition, but it supposes that A and B are given as ordered sequences of
vertices. The algorithm is based on convex hull calculations of A and B and of
smaller polygons and polylines, it produces the output list of vertices of the
relative convex hull from the sequence of vertices of the convex hull of A.Comment: 15 pages, 4 figures, Conference paper published. We corrected two
typing errors in Definition 2: has to be defined based on , and
has to be defined based on (not just using ). These errors
appeared in the text of the original conference paper, which also contained
the pseudocode of an algorithm where and appeared as correctly
define
Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case
We provide a quick overview of various calculus tools and of the main results
concerning the heat flow on compact metric measure spaces, with applications to
spaces with lower Ricci curvature bounds.
Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in
metric spaces, a new approach to differentiation and to the theory of Sobolev
spaces over metric measure spaces, the equivalence of the L^2-gradient flow of
a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the
relative entropy functional, a metric version of Brenier's Theorem, and a new
(stronger) definition of Ricci curvature bound from below for metric measure
spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence
and it is strictly connected with the linearity of the heat flow.Comment: To the memory of Enrico Magenes, whose exemplar life, research and
teaching shaped generations of mathematician
Circles in the Water: Towards Island Group Labeling
Many algorithmic results are known for automated label placement on maps. However, algorithms to compute labels for groups of features, such as island groups, are largely missing. In this paper we address this issue by presenting new, efficient algorithms for island label placement in various settings. We consider straight-line and circular-arc labels that may or may not overlap a given set of islands. We concentrate on computing the line or circle that minimizes the maximum distance to the islands, measured by the closest distance. We experimentally test whether the generated labels are reasonable for various real-world island groups, and compare different options. The results are positive and validate our geometric formalizations
Seeing the forest for the trees: using the Gene Ontology to restructure hierarchical clustering
Motivation: There is a growing interest in improving the cluster analysis of expression data by incorporating into it prior knowledge, such as the Gene Ontology (GO) annotations of genes, in order to improve the biological relevance of the clusters that are subjected to subsequent scrutiny. The structure of the GO is another source of background knowledge that can be exploited through the use of semantic similarity
Efficient computation of the outer hull of a discrete path
We present here a linear time and space algorithm for computing the outer hull of any discrete path encoded by its Freeman chain code. The basic data structure uses an enriched version of the data structure introduced by Brlek, Koskas and Provençal: using quadtrees for representing points in the discrete plane â€Ă†with neighborhood links, deciding path intersection is achievable in linear time and space. By combining the well-known wall follower algorithm for traversing mazes, we obtain the desired result with two passes resulting in a global linear time and space algorithm. As a byproduct, the convex hull is obtained as well
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