85 research outputs found
Edge-weighting of gene expression graphs
In recent years, considerable research efforts have been directed to micro-array technologies and their role in providing simultaneous information on expression profiles for thousands of genes. These data, when subjected to clustering and classification procedures, can assist in identifying patterns and providing insight on biological processes. To understand the properties of complex gene expression datasets, graphical representations can be used. Intuitively, the data can be represented in terms of a bipartite graph, with weighted edges corresponding to gene-sample node couples in the dataset. Biologically meaningful subgraphs can be sought, but performance can be influenced both by the search algorithm, and, by the graph-weighting scheme and both merit rigorous investigation. In this paper, we focus on edge-weighting schemes for bipartite graphical representation of gene expression. Two novel methods are presented: the first is based on empirical evidence; the second on a geometric distribution. The schemes are compared for several real datasets, assessing efficiency of performance based on four essential properties: robustness to noise and missing values, discrimination, parameter influence on scheme efficiency and reusability. Recommendations and limitations are briefly discussed
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
The least common multiple of a sequence of products of linear polynomials
Let be the product of several linear polynomials with integer
coefficients. In this paper, we obtain the estimate: as , where is a constant depending on
.Comment: To appear in Acta Mathematica Hungaric
On the Optimal Combination of Tensor Optimization Methods
We consider the minimization problem of a sum of a number of functions having
Lipshitz -th order derivatives with different Lipschitz constants. In this
case, to accelerate optimization, we propose a general framework allowing to
obtain near-optimal oracle complexity for each function in the sum separately,
meaning, in particular, that the oracle for a function with lower Lipschitz
constant is called a smaller number of times. As a building block, we extend
the current theory of tensor methods and show how to generalize near-optimal
tensor methods to work with inexact tensor step. Further, we investigate the
situation when the functions in the sum have Lipschitz derivatives of a
different order. For this situation, we propose a generic way to separate the
oracle complexity between the parts of the sum. Our method is not optimal,
which leads to an open problem of the optimal combination of oracles of a
different order
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