Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction

On the use of approximate analytical solutions in solving optimum trajectory problems

Method for numerical solutions of nonlinear optimum trajectory problems using approximate analytic metho

Detection of atrial fibrillation episodes in long-term heart rhythm signals using a support vector machine

Atrial fibrillation (AF) is a serious heart arrhythmia leading to a significant increase of the risk for occurrence of ischemic stroke. Clinically, the AF episode is recognized in an electrocardiogram. However, detection of asymptomatic AF, which requires a long-term monitoring, is more efficient when based on irregularity of beat-to-beat intervals estimated by the heart rate (HR) features. Automated classification of heartbeats into AF and non-AF by means of the Lagrangian Support Vector Machine has been proposed. The classifier input vector consisted of sixteen features, including four coefficients very sensitive to beat-to-beat heart changes, taken from the fetal heart rate analysis in perinatal medicine. Effectiveness of the proposed classifier has been verified on the MIT-BIH Atrial Fibrillation Database. Designing of the LSVM classifier using very large number of feature vectors requires extreme computational efforts. Therefore, an original approach has been proposed to determine a training set of the smallest possible size that still would guarantee a high quality of AF detection. It enables to obtain satisfactory results using only 1.39% of all heartbeats as the training data. Post-processing stage based on aggregation of classified heartbeats into AF episodes has been applied to provide more reliable information on patient risk. Results obtained during the testing phase showed the sensitivity of 98.94%, positive predictive value of 98.39%, and classification accuracy of 98.86%.Web of Science203art. no. 76

Detection of Heteroplasmic Single Nucleotide Polymorphisms Using Melt Curve Analysis and Dual Labeled Fluorescent Probes

Plant mitochondrial genomes are strange – they are unusually large, consist of huge amounts of non-coding DNA, and contain of several overlapping regions throughout the genome. The genome is made of several different sized linear and circular molecules and different mitochondria within a cell will have different pieces of the genome. Even if multiple mitochondria contain the same region of the genome, these sequences can differ by single nucleotide polymorphisms (SNPS). This is known as heteroplasmy. Heteroplasmy has been documented in Arabidopsis thaliana using whole-genome sequencing data. While heteroplasmy is well-documented, its existence in the mitochondrial genome is unexpected and it can be hard to quantify the degree to which heteroplasmy exists. This project sought to illustrate the existence of heteroplasmy in A. thaliana using melt-curve analysis and probe detection. Melt curve analysis takes advantage of the fact that DNA denatures at different temperatures depending upon the sequence; while probe detection quantifies different DNA sequences by the degree of fluorescence. The goal of this project was to show that both methods were successful in illustrating heteroplasmy in mitochondria and demonstrate heteroplasmy in DNA where one single base is different in a population. Both methods proved to be successful in illustrating heteroplasmy; however, there were drawbacks to each. Both methods required accurate knowledge of the presence of single nucleotide polymorphisms in the DNA sequences and melt curve analysis had a relatively high limit of detection

Development of a method for optimal maneuver analysis of complex space missions

A system that allows mission planners to find optimal multiple-burn space trajectories easily is described. Previously developed methods with different gravity assumptions perform the optimization function. The power of these programs is extended by a method of costate estimation. A penalty function method of constraining coast arc times to be positive is included. The capability of the method is demonstrated by finding the optimal control for three different space missions. These include a shuttle abort-once-around mission and two- and three-burn geosynchronous satellite-placement missions

Primer vector theory and applications

A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed

Fetal electrocardiograms, direct and abdominal with reference heartbeat annotations

Monitoring fetal heart rate (FHR) variability plays a fundamental role in fetal state assessment. Reliable FHR signal can be obtained from an invasive direct fetal electrocardiogram (FECG), but this is limited to labour. Alternative abdominal (indirect) FECG signals can be recorded during pregnancy and labour. Quality, however, is much lower and the maternal heart and uterine contractions provide sources of interference. Here, we present ten twenty-minute pregnancy signals and 12 five-minute labour signals. Abdominal FECG and reference direct FECG were recorded simultaneously during labour. Reference pregnancy signal data came from an automated detector and were corrected by clinical experts. The resulting dataset exhibits a large variety of interferences and clinically significant FHR patterns. We thus provide the scientific community with access to bioelectrical fetal heart activity signals that may enable the development of new methods for FECG signals analysis, and may ultimately advance the use and accuracy of abdominal electrocardiography methods.Web of Science71art. no. 20

A novel technique for fetal heart rate estimation from Doppler ultrasound signal

<p>Abstract</p> <p>Background</p> <p>The currently used fetal monitoring instrumentation that is based on Doppler ultrasound technique provides the fetal heart rate (FHR) signal with limited accuracy. It is particularly noticeable as significant decrease of clinically important feature - the variability of FHR signal. The aim of our work was to develop a novel efficient technique for processing of the ultrasound signal, which could estimate the cardiac cycle duration with accuracy comparable to a direct electrocardiography.</p> <p>Methods</p> <p>We have proposed a new technique which provides the true beat-to-beat values of the FHR signal through multiple measurement of a given cardiac cycle in the ultrasound signal. The method consists in three steps: the dynamic adjustment of autocorrelation window, the adaptive autocorrelation peak detection and determination of beat-to-beat intervals. The estimated fetal heart rate values and calculated indices describing variability of FHR, were compared to the reference data obtained from the direct fetal electrocardiogram, as well as to another method for FHR estimation.</p> <p>Results</p> <p>The results revealed that our method increases the accuracy in comparison to currently used fetal monitoring instrumentation, and thus enables to calculate reliable parameters describing the variability of FHR. Relating these results to the other method for FHR estimation we showed that in our approach a much lower number of measured cardiac cycles was rejected as being invalid.</p> <p>Conclusions</p> <p>The proposed method for fetal heart rate determination on a beat-to-beat basis offers a high accuracy of the heart interval measurement enabling reliable quantitative assessment of the FHR variability, at the same time reducing the number of invalid cardiac cycle measurements.</p

Domain duplication, divergence, and loss events in vertebrate Msx paralogs reveal phylogenomically informed disease markers

<p>Abstract</p> <p>Background</p> <p>Msx originated early in animal evolution and is implicated in human genetic disorders. To reconstruct the functional evolution of Msx and inform the study of human mutations, we analyzed the phylogeny and synteny of 46 metazoan Msx proteins and tracked the duplication, diversification and loss of conserved motifs.</p> <p>Results</p> <p>Vertebrate Msx sequences sort into distinct Msx1, Msx2 and Msx3 clades. The sister-group relationship between <it>MSX1 </it>and <it>MSX2 </it>reflects their derivation from the 4p/5q chromosomal paralogon, a derivative of the original "MetaHox" cluster. We demonstrate physical linkage between Msx and other MetaHox genes (<it>Hmx</it>, <it>NK1</it>, <it>Emx</it>) in a cnidarian. Seven conserved domains, including two Groucho repression domains (N- and C-terminal), were present in the ancestral Msx. In cnidarians, the Groucho domains are highly similar. In vertebrate Msx1, the N-terminal Groucho domain is conserved, while the C-terminal domain diverged substantially, implying a novel function. In vertebrate Msx2 and Msx3, the C-terminal domain was lost. MSX1 mutations associated with ectodermal dysplasia or orofacial clefting disorders map to conserved domains in a non-random fashion.</p> <p>Conclusion</p> <p>Msx originated from a MetaHox ancestor that also gave rise to Tlx, Demox, NK, and possibly EHGbox, Hox and ParaHox genes. Duplication, divergence or loss of domains played a central role in the functional evolution of Msx. Duplicated domains allow pleiotropically expressed proteins to evolve new functions without disrupting existing interaction networks. Human missense sequence variants reside within evolutionarily conserved domains, likely disrupting protein function. This phylogenomic evaluation of candidate disease markers will inform clinical and functional studies.</p