260 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
On the eigenvalues of non-negative Jacobi matrices
AbstractThe spectrum Ï of a non-negative Jacobi matrix J is characterized. If J is also required to be irreducible, further conditions on Ï are needed, some of which are explored
On the Trade-off between the Number of Nodes and the Number of Trees in a Random Forest
In this paper, we focus on the prediction phase of a random forest and study
the problem of representing a bag of decision trees using a smaller bag of
decision trees, where we only consider binary decision problems on the binary
domain and simple decision trees in which an internal node is limited to
querying the Boolean value of a single variable. As a main result, we show that
the majority function of variables can be represented by a bag of () decision trees each with polynomial size if is a constant, where
and must be odd (in order to avoid the tie break). We also show that a bag
of decision trees can be represented by a bag of decision trees each
with polynomial size if is a constant and a small classification error is
allowed. A related result on the -out-of- functions is presented too
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
In-ovo feeding with creatine monohydrate: implications for chicken energy reserves and breast muscle development during the pre-post hatching period
The most dynamic period throughout the lifespan of broiler chickens is the pre-post-hatching period, entailing profound effects on their energy status, survival rate, body weight, and muscle growth. Given the significance of this pivotal period, we evaluated the effect of in-ovo feeding (IOF) with creatine monohydrate on late-term embryosâ and hatchlingsâ energy reserves and post-hatch breast muscle development. The results demonstrate that IOF with creatine elevates the levels of high-energy-value molecules (creatine and glycogen) in the liver, breast muscle and yolk sac tissues 48 h post IOF, on embryonic day 19 (p < 0.03). Despite this evidence, using a novel automated image analysis tool on day 14 post-hatch, we found a significantly higher number of myofibers with lower diameter and area in the IOF creatine group compared to the control and IOF NaCl groups (p < 0.004). Gene expression analysis, at hatch, revealed that IOF creatine group had significantly higher expression levels of myogenin (MYOG) and insulin-like growth factor 1 (IGF1), related to differentiation of myogenic cells (p < 0.01), and lower expression of myogenic differentiation protein 1 (MyoD), related to their proliferation (p < 0.04). These results imply a possible effect of IOF with creatine on breast muscle development through differential expression of genes involved in myogenic proliferation and differentiation. The findings provide valuable insights into the potential of pre-hatch enrichment with creatine in modulating post-hatch muscle growth and development
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
Recommended from our members
Preconditioning 2D integer data for fast convex hull computations
In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ? n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p Ă q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ? n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ? n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved
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