Computing and Visualizing Solution Sets of Interval Linear Systems

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

Reliable selfing rate estimates from imperfect population genetic data.

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.

Studies on the propagation of errors in physical oceanographic computations

The results of an investigation on the limits of the random errors contained in the basic data of Physical Oceanography and their propagation through the computational procedures are presented in this thesis. It also suggest a method which increases the reliability of the derived results. The thesis is presented in eight chapters including the introductory chapter. Chapter 2 discusses the general theory of errors that are relevant in the context of the propagation of errors in Physical Oceanographic computations. The error components contained in the independent oceanographic variables namely, temperature, salinity and depth are deliniated and quantified in chapter 3. Chapter 4 discusses and derives the magnitude of errors in the computation of the dependent oceanographic variables, density in situ, gt, specific volume and specific volume anomaly, due to the propagation of errors contained in the independent oceanographic variables. The errors propagated into the computed values of the derived quantities namely, dynamic depth and relative currents, have been estimated and presented chapter 5. Chapter 6 reviews the existing methods for the identification of level of no motion and suggests a method for the identification of a reliable zero reference level. Chapter 7 discusses the available methods for the extension of the zero reference level into shallow regions of the oceans and suggests a new method which is more reliable. A procedure of graphical smoothening of dynamic topographies between the error limits to provide more reliable results is also suggested in this chapter. Chapter 8 deals with the computation of the geostrophic current from these smoothened values of dynamic heights, with reference to the selected zero reference level. The summary and conclusion are also presented in this chapter.

Synthesis of computations and experiments for obtaining pulsatile gas flow rates from dynamic pressure difference measurements across an orifice-plate meter

The use of conventional orifice-plate meter is typically restricted to measurements of steady flows. This study proposes a new and effective computational-experimental approach for measuring the time-varying (but steady-in-the-mean) nature of turbulent pulsatile gas flows. Low Mach number (effectively constant density) steady-in-the-mean gas flows with large amplitude fluctuations (whose highest significant frequency is characterized by the value fF) are termed pulsatile if the fluctuations have a direct correlation with the time-varying signature of the imposed dynamic pressure difference and, furthermore, they have fluctuation amplitudes that are significantly larger than those associated with turbulence or random acoustic wave signatures. The experimental aspect of the proposed calibration approach is based on use of Coriolis-meters (whose oscillating arm frequency fcoriolis >> fF) which are capable of effectively measuring the mean flow rate of the pulsatile flows. Together with the experimental measurements of the mean mass flow rate of these pulsatile flows, the computational approach presented here is shown to be effective in converting the dynamic pressure difference signal into the desired dynamic flow rate signal. The proposed approach is reliable because the time-varying flow rate predictions obtained for two different orifice-plate meters exhibit the approximately same qualitative, dominant features of the pulsatile flow.

Distributed, layered and reliable computing nets to represent neuronal receptive fields

Abstract. Receptive fields of retinal and other sensory neurons show a large variety of spatiotemporal linear and non linear types of responses to local stimuli. In visual neurons, these responses present either asymmetric sensitive zones or center-surround organization. In most cases, the nature of the responses suggests the existence of a kind of distributed computation prior to the integration by the final cell which is evidently supported by the anatomy. We describe a new kind of discrete and continuous filters to model the kind of computations taking place in the receptive fields of retinal cells. To show their performance in the analysis of diferent non-trivial neuron-like structures, we use a computer tool specifically programmed by the authors to that efect. This tool is also extended to study the efect of lesions on the whole performance of our model nets.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

ICTM: an interval tessellation-based model for reliable topographic segmentation

This work introduces a tessellation-based model for the declivity analysis of geographic regions. The analysis of the relief declivity, which is embedded in the rules of the model, categorizes each tessellation cell, with respect to the whole considered region, according to the (positive, negative, null) sign of the declivity of the cell. Such information is represented in the states assumed by the cells of the model. The overall configuration of such cells allows the division of the region into subregions of cells belonging to a same category, that is, presenting the same declivity sign. In order to control the errors coming from the discretization of the region into tessellation cells, or resulting from numerical computations, interval techniques are used. The implementation of the model is naturally parallel since the analysis is performed on the basis of local rules. An immediate application is in geophysics, where an adequate subdivision of geographic areas into segments presenting similar topographic characteristics is often convenient.

Tissue Microarray Is A Reliable Method For Immunohistochemical Analysis Of Pleomorphic Adenoma.

To determine the most adequate number and size of tissue microarray (TMA) cores for pleomorphic adenoma immunohistochemical studies. Eighty-two pleomorphic adenoma cases were distributed in 3 TMA blocks assembled in triplicate containing 1.0-, 2.0-, and 3.0-mm cores. Immunohistochemical analysis against cytokeratin 7, Ki67, p63, and CD34 were performed and subsequently evaluated with PixelCount, nuclear, and microvessel software applications. The 1.0-mm TMA presented lower results than 2.0- and 3.0-mm TMAs versus conventional whole section slides. Possibly because of an increased amount of stromal tissue, 3.0-mm cores presented a higher microvessel density. Comparing the results obtained with one, two, and three 2.0-mm cores, there was no difference between triplicate or duplicate TMAs and a single-core TMA. Considering the possible loss of cylinders during immunohistochemical reactions, 2.0-mm TMAs in duplicate are a more reliable approach for pleomorphic adenoma immunohistochemical study.

Serum Bdnf Levels Are Not Reliable Correlates Of Neurodegeneration In Ms Patients.

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A reliable measure of similarity based on dependency for short time series: an application to gene expression networks

Background: Microarray techniques have become an important tool to the investigation of genetic relationships and the assignment of different phenotypes. Since microarrays are still very expensive, most of the experiments are performed with small samples. This paper introduces a method to quantify dependency between data series composed of few sample points. The method is used to construct gene co-expression subnetworks of highly significant edges. Results: The results shown here are for an adapted subset of a Saccharomyces cerevisiae gene expression data set with low temporal resolution and poor statistics. The method reveals common transcription factors with a high confidence level and allows the construction of subnetworks with high biological relevance that reveals characteristic features of the processes driving the organism adaptations to specific environmental conditions. Conclusion: Our method allows a reliable and sophisticated analysis of microarray data even under severe constraints. The utilization of systems biology improves the biologists ability to elucidate the mechanisms underlying celular processes and to formulate new hypotheses.

Validation of dot blot hybridization and denaturing high performance liquid chromatography as reliable methods for TP53 codon 72 genotyping in molecular epidemiologic studies

Background: Mutations in TP53 are common events during carcinogenesis. In addition to gene mutations, several reports have focused on TP53 polymorphisms as risk factors for malignant disease. Many studies have highlighted that the status of the TP53 codon 72 polymorphism could influence cancer susceptibility. However, the results have been inconsistent and various methodological features can contribute to departures from Hardy-Weinberg equilibrium, a condition that may influence the disease risk estimates. The most widely accepted method of detecting genotyping error is to confirm genotypes by sequencing and/or via a separate method. Results: We developed two new genotyping methods for TP53 codon 72 polymorphism detection: Denaturing High Performance Liquid Chromatography (DHPLC) and Dot Blot hybridization. These methods were compared with Restriction Fragment Length Polymorphism (RFLP) using two different restriction enzymes. We observed high agreement among all methodologies assayed. Dot-blot hybridization and DHPLC results were more highly concordant with each other than when either of these methods was compared with RFLP. Conclusions: Although variations may occur, our results indicate that DHPLC and Dot Blot hybridization can be used as reliable screening methods for TP53 codon 72 polymorphism detection, especially in molecular epidemiologic studies, where high throughput methodologies are required.

Measurements on trapped laser-cooled ions using quantum computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.

Concussion in contact sports: Reliable change indices of impairment and recovery

This paper reports a follow-up study to an article on the sensitivity of three tests of speed of information processing to impairment after concussion (Hinton-Bayre, Geffen, BL McFarland, 1997). Group analyses showed that practice effects can obscure the effects of concussion on information processing, thereby making the assessment of functional impairment and recovery after injury unreliable. A Reliable Change Index (RCI) was used to assess individual variations following concussion. It was found that 16 of the 20 concussed professional rugby league players were impaired 1-3 days following injury. It was also demonstrated that 7 players still displayed cognitive deficits at 1-2 weeks, before returning to preseason levels at 3-5 weeks. The RCI permits comparisons between different tests, players, and repeated assessments, thereby providing a quantitative basis for decisions regarding return to play.

General scales of community reaction to noise (dissatisfaction and perceived affectedness) are more reliable than scales of annoyance

General measures of reaction to noise, which assess the respondent's perceived affectedness or dissatisfaction, appear to be more valid and internally consistent than more narrow measures, such as specific assessment of noise annoyance. However, the test-retest reliability of general and specific measures has yet to be compared. As a part of the large-scale Sydney Airport Health Study, 97 respondents participated in the same interview twice, several weeks apart. Test-retest reliabilities were found to be significant (p

Developing a reliable audit instrument to measure the physical environment for physical activity

Background: The physical environment plays an important role in influencing participation in physical activity, although which factors of the physical environment have the greatest effect on patterns of activity remain to be determined. We describe the development of a comprehensive instrument to measure the physical environmental factors that may influence walking and cycling in local neighborhoods and report on its reliability. Methods: Following consultation with experts from a variety of fields and a literature search, we developed a Systematic Pedestrian and Cycling Environmental Scan (SPACES) instrument and used it to collect data over a total of 1987 kilometers of roads in metropolitan Perth, Western Australia. The audit instrument is available from the first author on request. Additional environmental information was collected using desktop methods and geographic information systems (GIS) technology. We assessed inter- and intra-rater reliability of the instrument among the 16 observers who collected the data. Results: The observers reported that the audit instrument was easy to use. Both inter- and intra-rater reliability of the environmental scan instrument were generally high. Conclusions: Our instrument provides a reliable, practical, and easy to-use method for collecting detailed street-level data on physical environmental factors that are potential influences on walking in local neighborhoods.