Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

The Analysis of interval censoring and double censoring via Markov chain Monte Carlo methods

L'Anàlisi de la supervivència s'utilitza en diferents camps per analitzar el temps transcorregut entre dos esdeveniments. El que distingeix l'anàlisi de la supervivència d'altres àrees de l'estadística és que les dades normalment estan censurades. La censura en un interval apareix quan l'esdeveniment final d'interès no és directament observable i només se sap que el temps de fallada està en un interval concret. Un esquema de censura més complex encara apareix quan tant el temps inicial com el temps final estan censurats en un interval. Aquesta situació s'anomena doble censura. En aquest article donem una descripció formal d'un mètode bayesà paramètric per a l'anàlisi de dades censurades en un interval i dades doblement censurades així com unes indicacions clares de la seva utilització o pràctica. La metodologia proposada s'ilustra amb dades d'una cohort de pacients hemofílics que es varen infectar amb el virus VIH a principis dels anys 1980's.

Integration and visualization of systems biology data in context of the genome

Background: High-density tiling arrays and new sequencing technologies are generating rapidly increasing volumes of transcriptome and protein-DNA interaction data. Visualization and exploration of this data is critical to understanding the regulatory logic encoded in the genome by which the cell dynamically affects its physiology and interacts with its environment. Results: The Gaggle Genome Browser is a cross-platform desktop program for interactively visualizing high-throughput data in the context of the genome. Important features include dynamic panning and zooming, keyword search and open interoperability through the Gaggle framework. Users may bookmark locations on the genome with descriptive annotations and share these bookmarks with other users. The program handles large sets of user-generated data using an in-process database and leverages the facilities of SQL and the R environment for importing and manipulating data. A key aspect of the Gaggle Genome Browser is interoperability. By connecting to the Gaggle framework, the genome browser joins a suite of interconnected bioinformatics tools for analysis and visualization with connectivity to major public repositories of sequences, interactions and pathways. To this flexible environment for exploring and combining data, the Gaggle Genome Browser adds the ability to visualize diverse types of data in relation to its coordinates on the genome. Conclusions: Genomic coordinates function as a common key by which disparate biological data types can be related to one another. In the Gaggle Genome Browser, heterogeneous data are joined by their location on the genome to create information-rich visualizations yielding insight into genome organization, transcription and its regulation and, ultimately, a better understanding of the mechanisms that enable the cell to dynamically respond to its environment.

Three-dimensional visualization of human hemoglobin phenotypes with HPLC

Hemoglobinopathies were included in the Brazilian Neonatal Screening Program on June 6, 2001. Automated high-performance liquid chromatography (HPLC) was indicated as one of the diagnostic methods. The amount of information generated by these systems is immense, and the behavior of groups cannot always be observed in individual analyses. Three-dimensional (3-D) visualization techniques can be applied to extract this information, for extracting patterns, trends or relations from the results stored in databases. We applied the 3-D visualization tool to analyze patterns in the results of hemoglobinopathy based on neonatal diagnosis by HPLC. The laboratory results of 2520 newborn analyses carried out in 2001 and 2002 were used. The ""Fast"", ""F1"", ""F"" and ""A"" peaks, which were detected by the analytical system, were chosen as attributes for mapping. To establish a behavior pattern, the results were classified into groups according to hemoglobin phenotype: normal (N = 2169), variant (N = 73) and thalassemia (N = 279). 3-D visualization was made with the FastMap DB tool; there were two distribution patterns in the normal group, due to variation in the amplitude of the values obtained by HPLC for the F1 window. It allowed separation of the samples with normal Hb from those with alpha thalassemia, based on a significant difference (P < 0.05) between the mean values of the ""Fast"" and ""A"" peaks, demonstrating the need for better evaluation of chromatograms; this method could be used to help diagnose alpha thalassemia in newborns.

Visualization of learning in multilayer perceptron networks using principal component analysis

This paper is concerned with the use of scientific visualization methods for the analysis of feedforward neural networks (NNs). Inevitably, the kinds of data associated with the design and implementation of neural networks are of very high dimensionality, presenting a major challenge for visualization. A method is described using the well-known statistical technique of principal component analysis (PCA). This is found to be an effective and useful method of visualizing the learning trajectories of many learning algorithms such as back-propagation and can also be used to provide insight into the learning process and the nature of the error surface.

Histogram-based DNA analysis for the visualization of chromosome, genome and species information

We describe a novel approach to explore DNA nucleotide sequence data, aiming to produce high-level categorical and structural information about the underlying chromosomes, genomes and species. The article starts by analyzing chromosomal data through histograms using fixed length DNA sequences. After creating the DNA-related histograms, a correlation between pairs of histograms is computed, producing a global correlation matrix. These data are then used as input to several data processing methods for information extraction and tabular/graphical output generation. A set of 18 species is processed and the extensive results reveal that the proposed method is able to generate significant and diversified outputs, in good accordance with current scientific knowledge in domains such as genomics and phylogenetics.

Analysis and visualization of seismic data using mutual information

Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.

Inversion prepared coronary MR angiography: direct visualization of coronary blood flow.

PURPOSE: Visualization of coronary blood flow by means of a slice-selective inversion pre-pulse in concert with bright-blood coronary MRA. MATERIALS AND METHODS: Coronary magnetic resonance angiography (MRA) of the right coronary artery (RCA) was performed in eight healthy adult subjects on a 1.5 Tesla MR system (Gyroscan ACS-NT, Philips Medical Systems, Best, NL) using a free-breathing navigator-gated and cardiac-triggered 3D steady-state free-precession (SSFP) sequence with radial k-space sampling. Imaging was performed with and without a slice-selective inversion pre-pulse, which was positioned along the main axis of the coronary artery but perpendicular to the imaging volume. Objective image quality parameters such as SNR, CNR, maximal visible vessel length, and vessel border definition were analyzed. RESULTS: In contrast to conventional bright-blood 3D coronary MRA, the selective inversion pre-pulse provided a direct measure of coronary blood flow. In addition, CNR between the RCA and right ventricular blood pool was increased and the vessels had a tendency towards better delineation. Blood SNR and CNR between right coronary blood and epicardial fat were comparable in both sequences. CONCLUSION: The combination of a free-breathing navigator-gated and cardiac-triggered 3D SSFP sequence with a slice-selective inversion pre-pulse allows for direct and directional visualization of coronary blood flow with the additional benefit of improved contrast between coronary and right ventricular blood pool.

Whole-heart coronary vein imaging: a comparison between non-contrast-agent- and contrast-agent-enhanced visualization of the coronary venous system.

The feasibility of three-dimensional (3D) whole-heart imaging of the coronary venous (CV) system was investigated. The hypothesis that coronary magnetic resonance venography (CMRV) can be improved by using an intravascular contrast agent (CA) was tested. A simplified model of the contrast in T(2)-prepared steady-state free precession (SSFP) imaging was applied to calculate optimal T(2)-preparation durations for the various deoxygenation levels expected in venous blood. Non-contrast-agent (nCA)- and CA-enhanced images were compared for the delineation of the coronary sinus (CS) and its main tributaries. A quantitative analysis of the resulting contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) in both approaches was performed. Precontrast visualization of the CV system was limited by the poor CNR between large portions of the venous blood and the surrounding tissue. Postcontrast, a significant increase in CNR between the venous blood and the myocardium (Myo) resulted in a clear delineation of the target vessels. The CNR improvement was 347% (P < 0.05) for the CS, 260% (P < 0.01) for the mid cardiac vein (MCV), and 430% (P < 0.05) for the great cardiac vein (GCV). The improvement in SNR was on average 155%, but was not statistically significant for the CS and the MCV. The signal of the Myo could be significantly reduced to about 25% (P < 0.001).

Selective three-dimensional visualization of the coronary arterial lumen using arterial spin tagging.

Conventional coronary magnetic resonance angiography (MRA) techniques display the coronary blood-pool along with the surrounding structures, including the myocardium, the ventricular and atrial blood-pool, and the great vessels. This representation of the coronary lumen is not directly analogous to the information provided by x-ray coronary angiography, in which the coronary lumen displayed by iodinated contrast agent is seen. Analogous "luminographic" data may be obtained using MR arterial spin tagging (projection coronary MRA) techniques. Such an approach was implemented using a 2D selective "pencil" excitation for aortic spin tagging in concert with a 3D interleaved segmented spiral imaging sequence with free-breathing, and real-time navigator technology. This technique allows for selective 3D visualization of the coronary lumen blood-pool, while signal from the surrounding structures is suppressed.

Positive contrast visualization of nitinol devices using susceptibility gradient mapping.

MRI visualization of devices is traditionally based on signal loss due to T(2)* effects originating from local susceptibility differences. To visualize nitinol devices with positive contrast, a recently introduced postprocessing method is adapted to map the induced susceptibility gradients. This method operates on regular gradient-echo MR images and maps the shift in k-space in a (small) neighborhood of every voxel by Fourier analysis followed by a center-of-mass calculation. The quantitative map of the local shifts generates the positive contrast image of the devices, while areas without susceptibility gradients render a background with noise only. The positive signal response of this method depends only on the choice of the voxel neighborhood size. The properties of the method are explained and the visualizations of a nitinol wire and two stents are shown for illustration.

Noninvasive visualization of coronary artery endothelial function in healthy subjects and in patients with coronary artery disease.

OBJECTIVES: The goal was to test 2 hypotheses: first, that coronary endothelial function can be measured noninvasively and abnormal function detected using clinical 3.0-T magnetic resonance imaging (MRI); and second, that the extent of local coronary artery disease (CAD), in a given patient, is related to the degree of local abnormal coronary endothelial function. BACKGROUND: Abnormal endothelial function mediates the initiation and progression of atherosclerosis and predicts cardiovascular events. However, direct measures of coronary endothelial function have required invasive assessment. METHODS: The MRI was performed in 20 healthy adults and 17 patients with CAD. Cross-sectional coronary area and blood flow were quantified before and during isometric handgrip exercise, an endothelial-dependent stressor. In 10 severe, single-vessel CAD patients, paired endothelial function was measured in the artery with severe stenosis and the contralateral artery with minimal disease. RESULTS: In healthy adults, coronary arteries dilated and flow increased with stress. In CAD patients, coronary artery area and blood flow decreased with stress (both p </= 0.02). In the paired study, coronary artery area and blood flow failed to increase during exercise in the mildly diseased vessel, but both area (p = 0.01) and blood flow (p = 0.02) decreased significantly in the severely diseased, contralateral artery. CONCLUSIONS: Endothelial-dependent coronary artery dilation and increased blood flow in healthy subjects, and their absence in CAD patients, can now be directly visualized and quantified noninvasively. Local coronary endothelial function differs between severely and mildly diseased arteries in a given CAD patient. This novel, safe method may offer new insights regarding the importance of local coronary endothelial function and improved risk stratification in patients at risk for and with known CAD.

Magnetization transfer-based 3D visualization of foot peripheral nerves.

PURPOSE: To investigate magnetization transfer (MT) effects as a new source of contrast for imaging and tracking of peripheral foot nerves. MATERIALS AND METHODS: Two sets of 3D spoiled gradient-echo images acquired with and without a saturation pulse were used to generate MT ratio (MTR) maps of 260 μm in-plane resolution for eight volunteers at 3T. Scan parameters were adjusted to minimize signal loss due to T2 dephasing, and a dedicated coil was used to improve the inherently low signal-to-noise ratio of small voxels. Resulting MTR values in foot nerves were compared with those in surrounding muscle tissue. RESULTS: Average MTR values for muscle (45.5 ± 1.4%) and nerve (21.4 ± 3.1%) were significantly different (P < 0.0001). In general, the difference in MTR values was sufficiently large to allow for intensity-based segmentation and tracking of foot nerves in individual subjects. This procedure was termed MT-based 3D visualization. CONCLUSION: The MTR serves as a new source of contrast for imaging of peripheral foot nerves and provides a means for high spatial resolution tracking of these structures. The proposed methodology is directly applicable on standard clinical MR scanners and could be applied to systemic pathologies, such as diabetes.

AssociationViewer: a scalable and integrated software tool for visualization of large-scale variation data in genomic context.

SUMMARY: We present a tool designed for visualization of large-scale genetic and genomic data exemplified by results from genome-wide association studies. This software provides an integrated framework to facilitate the interpretation of SNP association studies in genomic context. Gene annotations can be retrieved from Ensembl, linkage disequilibrium data downloaded from HapMap and custom data imported in BED or WIG format. AssociationViewer integrates functionalities that enable the aggregation or intersection of data tracks. It implements an efficient cache system and allows the display of several, very large-scale genomic datasets. AVAILABILITY: The Java code for AssociationViewer is distributed under the GNU General Public Licence and has been tested on Microsoft Windows XP, MacOSX and GNU/Linux operating systems. It is available from the SourceForge repository. This also includes Java webstart, documentation and example datafiles.