Large-scale comparison of the similarities between two biological sequences is a major issue in computational biology; a fast method, the D(2) statistic, relies on the comparison of the k-tuple content for both sequences. Although it has been known for some years that the D(2) statistic is not suitable for this task, as it tends to be dominated by single-sequence noise, to date no suitable adju...

BACKGROUND Phylogenetic hypotheses are increasingly being used to elucidate historical patterns of diversification rate-variation. Hypothesis testing is often conducted by comparing the observed vector of branching times to a null, pure-birth expectation. A popular method for inferring a decrease in speciation rate, which might suggest an early burst of diversification followed by a decrease in...

Replication of time series in microarray experiments is costly. To analyze time series data with no replicate, many model-specific approaches have been proposed. However, they fail to identify the genes whose expression patterns do not fit the pre-defined models. Besides, modeling the temporal expression patterns is difficult when the dynamics of gene expression in the experiment is poorly unde...

There is a need for a reliable statistical test which is appropriate for assessing cospeciation of more than two phylogenies. We have developed an algorithm using a permutation method that can be used to test for and infer tri-trophic evolutionary relationships of organisms given both their phylogenies and pairwise interactions. An overall statistic has been developed based on the dominant eige...

Replication of time series in microarray experiments is costly. To analyze time series data with no replicate, many model-specific approaches have been proposed. However, they fail to identify the genes whose expression patterns do not fit the pre-defined models. Besides, modeling the temporal expression patterns is difficult when the dynamics of gene expression in the experiment is poorly unde...

In this paper, we study the problem of finding tight bounds on the expected value of the kth order statistic E[xk:n] under moment information on n real-valued random variables. Given means E[xi] = μi and variances V ar[xi] = σ i , we show that the tight upper bound on the expected value of the highest order statistic E[xn:n] can be computed with a bisection search algorithm. An extremal discret...

Title of Document: DETECTING AND CORRECTING ERRORS IN GENOME ASSEMBLIES Poorani Subramanian, Ph.D. 2010 Directed by: Professor James A. Yorke, Department of Mathematics Genome assemblies have various types of deficiencies or misassemblies. This work is aimed at detecting and correcting a type of misassembly that we call Compression/Expansion or CE misassemblies whereby a section of sequence has...

Inhomogeneous lattice paths are introduced as ordered sequences of rectangular Young tableaux thereby generalizing recent work on the Kostka polynomials by Nakayashiki and Yamada and by Lascoux, Leclerc and Thibon. Motivated by these works and by Kashiwara’s theory of crystal bases we define a statistic on paths yielding two novel classes of polynomials. One of these provides a generalization o...

The methods of integral equations numerical solving are proposed. These methods combine both deterministic and statistic operations. Like when using deterministic methods, the problem is reduced to solving a set of algebraic equations. But approximation of the integral by finite sum is performed by means of the Monte Carlo method.

Based on a local spatial/frequency representation,we employ a spectral histogram as a feature statistic for texture classification. The spectral histogram consists of marginal distributions of responses of a bank of filters and encodes implicitly the local structure of images through the filtering stage and the global appearance through the histogram stage. The distance between two spectral his...