O. Michael Melko

Khalifa University of Science and Technology

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Larry Bates

University of Calgary

Luis Weruaga

Khalifa University of Science and Technology

Larr M. Bates

University of Calgary

Arcady Mushegian

U.S. National Science Foundation

Cooperative Institutions

University of Calgary

Khalifa University of Science and Technology

Austrian Academy of Sciences

Universidad Católica San Antonio de Murcia

Universidad Politécnica de Cartagena

U.S. National Science Foundation

Division of Molecular & Cellular Biosciences

University of Cambridge

Stowers Institute for Medical Research

University of Kansas Medical Center

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On curves of constant torsion I

Journal of Geometry (2013)

Larry Bates O. Michael Melko

Constant (computer programming)

Constant curvature

10.1007/s00022-013-0166-2

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Citations (19)

Asymptotic Cramér-Rao Bound for Noise-Compensated Autoregressive Analysis

IEEE Transactions on Circuits and Systems I Regular Papers (2012)

Luis Weruaga O. Michael Melko

Noise-compensated autoregressive (AR) analysis is a problem insufficiently explored with regard to the accuracy of the estimate. This paper studies comprehensively the lower limit of the estimation variance, presenting the asymptotic Cramér-Rao bound (CRB) for Gaussian processes and additive Gaussian noise. This novel result is obtained by using a frequency-domain perspective of the problem as well as an unusual parametrization of an AR model. The Wiener filter rule appears as the distinctive building element in the Fisher information matrix. The theoretical analysis is validated numerically, showing that the proposed CRB is attained by competitive ad hoc estimation methods under a variety of Gaussian color noise and realistic scenarios.

Gaussian Noise

Cramér–Rao bound

10.1109/tcsi.2012.2185277

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Citations (3)

Distribution of words with a predefined range of mismatches to a DNA probe in bacterial genomes

Bioinformatics (2003)

O. Michael Melko Arcady Mushegian

Hybridization of oligonucleotides with longer nucleotide sequences is an essential step in nucleic acid biosynthesis in vitro and in vivo, in oligonucleotide-based diagnostics, and in therapeutic applications of oligonucleotides. A major factor determining sensitivity and selectivity of hybridization is the number of base pair mismatches that occur in an ungapped alignment of the oligonucleotide (probe) and a longer sequence (target).The k-distance match count between the probe and the target is defined as the number of ungapped alignments between the two sequences that have exactly k mismatches, and the k-neighbor match count is defined as the sum of the j-distance match counts for j between 0 and k. We derive a novel formula for the probability of a k-distance match. This formula is based on the assumption that the target is strand-symmetric Bernoulli text (i.e. nucleotides are independently, identically distributed in the target and satisfy Chargaff's second parity rule). Our model predicts that the GC-content in both the probe and the target significantly affects the match count expectation. The ratio of k-neighbor match counts in two distinct genomes for a given probe is a measure of its specificity. We calculated such ratios for pairs of bacterial genomes with different combinations of length, GC-content and phylogenetic distance. Examination of the extreme values of these ratios indicates that probes with a high discriminative power exist for each tested pair.

Bacterial genome size

10.1093/bioinformatics/btg374

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On curves of constant torsion I

arXiv (Cornell University) (2012)

Larr M. Bates O. Michael Melko

We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.

Constant (computer programming)

Constant curvature

Torsion constant

10.48550/arxiv.1206.7086

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On the Cramér-Rao bound of autoregressive estimation in noise

Luis Weruaga O. Michael Melko

The problem of noise-compensated autoregressive estimation has not been sufficiently explored especially with regard to the variance of the estimation. This paper explores this important aspect, presenting the asymptotic Cramer-Rao bound thereto. This valuable result is achieved by using a frequency- domain perspective of the problem as well as an unusual parametrization of an autoregressive model. One interesting finding is that the Fisher information matrix turns out to be built with the Wiener filter rule. Despite the power spectral density of the noise is assumed to be available in advance, the variance of the best estimator thereto is proven to be larger than that of the classical (noiseless) autoregressive estimation. The theoretical analysis has been validated with simulation experiments involving stationary colored noise.

Colors of noise

Wiener filter

Spectral density estimation

10.1109/iscas.2011.5937580

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Citations (1)

ERGODIC THEORY AND ITS APPLICATION TO THE ANALYSIS OF NUCLEIC ACID SEQUENCES

O. Michael Melko

Basic facts about measure-preserving transformations and the ergodic theorem are reviewed with an emphasis on discrete spaces. These ideas are then used to derive an estimate for the number of approximate matches between a fixed word and a long sequence of randomly generated characters over an alphabet. This is followed by a discussion of generalizations, and potential applications to molecular probe design.

Sequence (biology)

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An exotic symplectic $\mathbf{R}^6$

arXiv (Cornell University) (2015)

Larry Bates O. Michael Melko

An explicit example of an exotic symplectic $\mathbf{R}^6$ is given. Together with an earlier known example on $\mathbf{R}^4$, this yields an explicit exotic symplectic form on $\mathbf{R}^{2n}$ for all $n\geq2$.

10.48550/arxiv.1507.08939

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On curves of constant torsion I

arXiv (Cornell University) (2012)

Larr M. Bates O. Michael Melko

Constant curvature

Constant (computer programming)

Torsion constant

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