Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Computing”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,747 records · Page 97Linked to original sources

Relax, a flexible program for the back calculation of NOESY spectra based on complete-relaxation-matrix formalism.

RELAX is a flexible program for the quantitative analysis of NOESY spectra. It allows the simultaneous application of different models describing the internal and overall motion of the molecule under investigation for individual spin pairs or groups of spins. A correction for anisotropy effects due to the deviation of the molecule from a spherical shape is calculated automatically from the trial structure. The program can deal with completely relaxed spectra as well as spectra recorded with a short relaxation delay. An execution-time-controlled splitting of the relaxation matrix reduces the computation time significantly without any loss of accuracy. This is especially important for large molecules or medium distance cutoffs.

Actins↗

[Significance of optic formula selection for postoperative refraction after cataract operation].

BACKGROUND: Prediction of postoperative patient refraction is of paramount importance in modern cataract surgery. The choice of the IOL calculation formula plays a major role here. The influence of popular calculation formulas is evaluated in a prospective study. MATERIALS AND METHODS: We performed cataract surgery on 539 eyes with PC-IOL implantation in the capsular bag. The IOL power was computed using 10 different calculation formulas with the help of a personal computer. Patient refraction was examined two days and six months after surgery. RESULTS: The mean difference between desired and obtained refraction was -0.11 +/- 0.88 dpt 83% of all patients were in a +/- 1 D interval of desired refraction with a median visual acuity of 20/25. The formula used contributes a major part to the precision of calculation despite all problems due to errors of measurement. The theoretical formulas with variable "pseudophacic anterior chamber depth" are superior to the older ones. Standard deviation of the worst formula tested is 25% higher than that of the best one. With the best formula tested there would have been a good result (error < or = 1 D) in 82% of the cases, with the worst one in only 72%. CONCLUSIONS: The use of older formulas like SRK and Binkhorst should be discontinued and only the newer theoretical formulas (e.g. SRK/T, Holladay, Haigis etc.) be used. This is especially true for short and long eyes. For owners of a personal computer calculation and optimization of those more complex formulas should not be a problem.

Aged↗

Qualitative and quantitative accuracy of CAOS in a standardized in vitro spine model.

Pedicle breach with screw implantation is relatively common. For clinical application of computer-assisted orthopaedic surgery, it is important to quantitatively know the accuracy and localization of any guidance modality. We ascertained the accuracy of computed tomography and C-arm-based navigated drilling versus conventional fluoroscopy using an artificial thoracic and lumbar spine model. The 3.2-mm diameter transpedicle drilling target was the center of a 4-mm steel ball fixed in the anterior left pedicle axis. After drilling, we used computed tomography to verify the position of the steel ball and the canal and visually explored for cortex perforation. Quantitative vector calculation showed computed tomography-based navigation had the greatest accuracy (median, d(thoracic) = 1.4 mm; median, d(lumbar) = 1.8 mm) followed by C-arm navigation (median, d(thoracic) = 2.6 mm; median, d(lumbar) = 2 mm) and the conventional procedure (median, d(thoracic) = 2.2 mm; median, d(lumbar) = 2.7 mm). Visual examination showed a decreased perforation rate in navigated drillings. We found no correlation between pedicle breaches and inaccurate drilling. The data suggest computer-assisted orthopaedic surgery cannot provide sub-millimeter accuracy, and complete prevention of pedicle perforation is not realistic.

Fluoroscopy↗

Wave propagation simulation in normal and infarcted myocardium: computational and modelling issues.

Simulation of propagating action potentials (PAP) in normal and abnormal myocardium is used for the understanding of mechanisms responsible for eliciting dangerous arrhythmias. One- and two-dimensional models dealing with PAP properties are reviewed in this paper viewed both from the computational and mathematical aspects. These models are used for linking theoretical and experimental results. The discontinuous nature of the PAP is demonstrated through the combination of experimental and theoretically derived results. In particular it can be shown that for increased intracellular coupling resistance the PAP upstroke phase properties (Vmax, dV/dtmax and tau foot) change considerably, and in some cases non-monotonically with increased coupling resistance. It is shown that tau foot) is a parameter that is very sensitive to the cell's distance to the stimulus site, the stimulus strength and the coupling resistance. In particular it can be shown that in a one-dimensional structure the tau foot value can increase dramatically for lower coupling resistance values near the stimulus site and subsequently can be reduced as we move to distances larger than five resting length constants from the stimulus site. The tau foot variability is reduced with increased coupling resistance, rendering the lower coupling resistance structures, under abnormal excitation sequences, more vulnerable to conduction block and arrhythmias. Using the theory of discontinuous propagation of the PAP in the myocardium it is demonstrated that for specific abnormal situations in the myocardium, such as infarcted tissue, one- and two-dimensional models can reliably simulate propagation characteristics and explain complex phenomena such as propagation at bifurcation sites and mechanisms of block and re-entry. In conclusion it is shown that applied mathematics and informatics can help in elucidating electrophysiologically complex mechanisms such as arrhythmias and conduction disturbances in the myocardium.

Action Potentials↗

[Status of neurophysiologic research in psychiatry].

Neurophysiological studies in psychiatry have two trends: study of the mechanisms of normal and abnormal brain actvity and the use of the neurophysiological techniques to diagnose brain function in different mental pathology. The essential progress of both trends is based on the wide use of computers and mathematical analysis during recent decade. The drawback of the present state of clinical neurophysiology is its inadequate interrelation with the trends and concepts of experimental neurophysiology.

Brain↗

[Mathematical model of the digestion process regulation and its computer presentation].

The article presents a mathematic model, which describes regulation of the digestion process. The simulation was based on data on mutual influence of the factors participating in digestion regulation, which were acquired from analysis of over 1200 sources of experimental observations on digestion in dogs published in Russia and abroad, and on own experimental studies. The simulation includes 67 factors and about 400 interactions observed between them. The computer implementation of this simulation demonstrated descriptive coincidence of patterns of the variables respective to the factors of the model with experimental research data; the coincidence was observed in individual patterns and in combined patterns, as well as in coordinated responses in time.

Animals↗

Gaining more flexibility in Cox proportional hazards regression models with cubic spline functions.

The Cox proportional hazards model is the most popular model for the analysis of survival data. The use of cubic spline functions allows investigation of non-linear effects of continuous covariates and flexible assessment of time-by-covariate interactions. Two main advantages are provided--no particular functional form has to be specified and standard computer software packages like SAS or BMDP can be used. A SAS macro which implements the method is presented.

Antimetabolites, Antineoplastic↗

A surface-based approach to DNA computation.

A scalable approach to DNA-based computations is described. Complex combinatorial mixtures of DNA molecules encoding all possible answers to a computational problem are synthesized and attached to the surface of a solid support. This set of molecules is queried in successive MARK (hybridization) and DESTROY (enzymatic digestion) operations. Determination of the sequence of the DNA molecules remaining on the surface after completion of these operations yields the answer to the computational problem. Experimental demonstrations of aspects of the strategy are presented.

Automation↗

Modelling 'evo-devo' with RNA.

The folding of RNA sequences into secondary structures is a simple yet biophysically grounded model of a genotype-phenotype map. Its computational and mathematical analysis has uncovered a surprisingly rich statistical structure characterized by shape space covering, neutral networks and plastogenetic congruence. I review these concepts and discuss their evolutionary implications.

Algorithms↗

Statistical properties of neutral evolution.

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered. Fluctuations from one branch of the evolutionary tree to another are strong, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are in part due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results can improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences. In particular, we compute the minimal sequence similarity below which no information about the evolutionary divergence of the compared sequences can be obtained.

Amino Acid Substitution↗

A computerized system for the continuous recording and analysis of feeding, drinking, diuresis, and locomotor activity.

A system has been designed to study the intake of liquids and solid foods in rats that allows for the analysis of feeding and drinking episodes over time. In addition, it monitors locomotor activity and diuresis. This system is particularly useful for the study of the differential effects of drugs on various parameters of feeding and drinking. Because it allows for the monitoring of all behaviors for periods of 24 consecutive hours without disturbing the animals, it can be applied to the study of light/dark cycles of ingestive behavior. The apparatus consists of rat cages (equipped with photocells, bottles, electronic balances, and a funnel to collect urine), computer interfaces, an AT-compatible microcomputer for data collection, and a VAX system for analysis.

Animals↗

Computer-assisted design of surface coils used in magnetic resonance imaging. II. Rotational discrimination nonlinear regression analysis and the design of surface coils.

For a number of reasons, it is desirable to fabricate coils which, for a known current, shall produce predetermined values of the magnetic field intensity at a number of points within a nuclear magnetic resonance imager. The calculation of the magnetic field intensity at a set of points involves the integration of the Biot-Savart equation for all components of the segments of conductor which make up the coil. This process in itself is a rather formidable task. When this process is parameterized in terms of coil diameter, coil spacing, etc. the problem is to determine the values of these parameters to match values of magnetic field intensities which are desired. The problem thereby increases in complexity to the point where, by ordinary methods, the problem becomes intractable. A generalized solution technique has been developed on a digital computer to implement the rotational discrimination nonlinear regression techniques of Faris, Law and Letcher to find the best solution to this problem. The problem is posed by integrating the Biot-Savart equation. This produces algebraic expressions for incorporation into the optimization program which is executed on a computer in a conversational mode. This technique was employed to specify the dimensions of a rectangular surface coil for the investigation of the whole human spine.

Equipment Design↗

SEGMENT: identifying compositional domains in DNA sequences.

MOTIVATION: DNA sequences are formed by patches or domains of different nucleotide composition. In a few simple sequences, domains can simply be identified by eye; however, most DNA sequences show a complex compositional heterogeneity (fractal structure), which cannot be properly detected by current methods. Recently, a computationally efficient segmentation method to analyse such nonstationary sequence structures, based on the Jensen-Shannon entropic divergence, has been described. Specific algorithms implementing this method are now needed. RESULTS: Here we describe a heuristic segmentation algorithm for DNA sequences, which was implemented on a Windows program (SEGMENT). The program divides a DNA sequence into compositionally homogeneous domains by iterating a local optimization procedure at a given statistical significance. Once a sequence is partitioned into domains, a global measure of sequence compositional complexity (SCC), accounting for both the sizes and compositional biases of all the domains in the sequence, is derived. SEGMENT computes SCC as a function of the significance level, which provides a multiscale view of sequence complexity.

Algorithms↗

Uniformity of the fluid flow velocities within hollow fiber membranes of blood oxygenation devices.

A finite volume-based computational model was developed to investigate the uniformity of the fluid flow across the hollow fiber membranes in blood oxygenation devices. A two-dimensional annular cross section of a blood oxygenation device including about 3,300 hollow fiber membranes was used in the computation model. The equations governing the steady incompressible laminar flow in the blood oxygenation device were solved numerically and the results were compared with those obtained from the equivalent porous medium approximation. For the porous medium approximation, the Ergun equation was used for evaluating the permeability. The simulation results showed that the fluid molecules spend about six times longer in the fiber bundle region than that in its equivalent porous medium approximation model. The computational model also provides a more detailed fluid flow pattern in the membrane compartment of the blood oxygenator.

Artificial Organs↗

Structural equation modeling: reviewing the basics and moving forward.

This tutorial begins with an overview of structural equation modeling (SEM) that includes the purpose and goals of the statistical analysis as well as terminology unique to this technique. I will focus on confirmatory factor analysis (CFA), a special type of SEM. After a general introduction, CFA is differentiated from exploratory factor analysis (EFA), and the advantages of CFA techniques are discussed. Following a brief overview, the process of modeling will be discussed and illustrated with an example using data from a HIV risk behavior evaluation of homeless adults (Stein & Nyamathi, 2000). Techniques for analysis of nonnormally distributed data as well as strategies for model modification are shown. The empirical example examines the structure of drug and alcohol use problem scales. Although these scales are not specific personality constructs, the concepts illustrated in this article directly correspond to those found when analyzing personality scales and inventories. Computer program syntax and output for the empirical example from a popular SEM program (EQS 6.1; Bentler, 2001) are included.

Adult↗

Uniforming of outpatient health care statistics.

In the process of developing the health care information system, the Public Health Institute of the Republic of Slovenia harmonized the outpatient health care statistics at the national level. This paper presents the goals, contents, methodology and a brief analysis of the new data structure. The main functions of the ZUBSTAT computer program, user training methods, and planned further activities in this field are described.

Adolescent↗

Cross-correlation for flow cytometric histogram background subtractions.

Background subtraction is a widely encountered problem in flow cytometry applications for which the currently available analysis techniques are unsatisfactory. The 99% division line method, also referred to as the threshold or marker method, is widely used because it is computationally simple but it has poor accuracy and tends to underestimate the percentage of positive cells when there is overlap between histograms. Model-based approaches are preferred when there are overlapping peaks, but these methods require curve fitting and strong assumptions regarding the shape of the underlying distributions. This report assesses a mathematically rigorous, computationally facile, non-parametric technique called cross correlation for the background subtraction problem. A metric, positivity, derived from cross correlation is shown to overcome the disadvantages of both the 99% division line and model-based methods without compromise.

Flow Cytometry↗

Methods for projecting the incidence and prevalence of chronic diseases in aging populations: application to Alzheimer's disease.

Projections of the incidence and prevalence of disease are important for public health planning. This paper describes methods for projecting the incidence and prevalence of a chronic disease in ageing populations. The approach uses age-specific disease incidence rates together with assumptions about survival to reconstruct disease prevalence. The methods can be used to evaluate the potential impact of public health interventions that may prevent disease or prolong survival. We used the methods to project the future prevalence of Alzheimer's disease in the United States. We found that the prevalence of Alzheimer's disease will nearly quadruple over the next 50 years. Although projections of the absolute prevalence are sensitive to assumptions about the age-specific incidence rates of disease, the proportionate growth is relatively insensitive. The increase in prevalence results from the ageing of the U.S. population. In order to perform the calculations, we have assembled U.S. Census population projections and U.S. mortality rates into computer software that is available from the authors at www.jhsph.edu/Departments/Biostats/software.h tml.

Aged↗