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 271 records · Page 15Linked to original sources
PubMed1994

Rapid numerical integration algorithm for finding the equilibrium state of a system of coupled binding reactions.

We have adapted a simple method of numerical integration to predict the equilibrium state of a population of components undergoing reversible association according to the Law of Mass Action. Its particular application is to populations of protein molecules in aqueous solution. The method is based on Euler integration but employs an adaptive step size: the time increment being reduced if it would make the concentration of any component negative and increased while the concentration of any component changes at greater than a specified rate. Parameters of the algorithm have been optimized empirically using a model set of binding equilibria with dissociation constants ranging from 10(-5) M to 10(-9) M. The method obtains the solution to a set of binding equilibria more rapidly than the conventional initial value methods (simple Euler, 4th order Runge-Kutta and variable-step Runge-Kutta methods were tested) for the same accuracy. A computer code in standard C is presented.

Algorithms↗
PubMed1999

Bayesian inference on biopolymer models.

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/

Bayes Theorem↗
PubMed2000

Mathematica packages for simulation of experimental genetics.

UNLABELLED: This note describes add-on packages for the Mathematica software system (Wolfram 1996) which allow simulation and analysis of both Mendelian and complex genetic traits in experimental crosses of plants or animals. AVAILABILITY: The add-on packages are freely available at http://www.mathsource.com/cgi-bin/msitem?0209-30 4. SUPPLEMENTARY INFORMATION: A tutorial notebook file is included with the packages at the mathsource site.

Animals↗
PubMed1986

Steady-state modelling of metabolic pathways: a guide for the prospective simulator.

Steady-state modelling and control analysis by means of computer simulation provides valuable insight into the behavior of metabolic pathways. This review, which is aimed at the newcomer to this field, discusses the objectives of steady-state modelling and the steady-state properties of the four basic metabolic structures, namely linear and branched chains, loops and cycles. It is shown how the model definition in terms of stoichiometric reactions and rate equations leads to a set of balance equations from which the conservation constraints and flux relationships can be deduced, either informally or through a rigorous analysis of the stoichiometric matrix. The initial analysis of a steady-state metabolic model is summarized in an algorithm. Key references to the literature on metabolic modelling are given.

Computer Simulation↗
PubMed1990

The development of a high-order Taylor expansion solution to the chemical rate equation for the simulation of complex biochemical systems.

A numerical method for evaluating chemical rate equations is presented. This method was developed by expressing the system of coupled, first-degree, ordinary differential chemical rate equations as a single tensor equation. The tensorial rate equation is invariant in form for all reversible and irreversible reaction schemes that can be expressed as first- and second-order reaction steps, and can accommodate any number of reactive components. The tensor rate equation was manipulated to obtain a simple formula (in terms of rate constants and initial concentrations) for the power coefficients of the Taylor expansion of the chemical rate equation. The Taylor expansion formula was used to develop a FORTRAN algorithm for analysing the time development of chemical systems. A computational experiment was performed with a Michaelis-Menten scheme in which step size and expansion order (to the 100th term) were varied; the inclusion of high-order terms of the Taylor expansion was shown to reduce truncation and round-off errors associated with Runge-Kutta methods and lead to increased computational efficiency.

Algorithms↗
PubMed1990

POLCA, a library running in a modern environment, implements a protocol for averaging randomly oriented images.

The library POLCA implements the averaging of biological structures whose images are recorded in digital form from electron micrographs. The averaging protocol is based upon a method developed about ten years ago, which allows one to operate on a sequence of objects oriented and displaced at random within their frame; the relative rotations and the displacements of the structures are detected with the use of correlation algorithms and modified to make all objects appear the same, apart from their noisy components. The average image is then obtained by a simple addition and the signal-to-noise ratio is improved by a factor equal to the square root of the number of objects used to calculate the average. With respect to the original implementation of the method, two novel features characterize the library: the first one deals with the functions that are cross-correlated to determine the relative rotations of the structures; the functions used here are the inverse transforms of the amplitude spectra (IAS functions), which give rise to sharp maxima when they are cross-correlated. The second peculiarity is the systematic adoption, in the transformations of coordinates and in other circumstances, of an interpolation technique based upon the Fourier series kernel. POLCA is written in C and runs on a VME machine under the UNIX V/68 operating system. A programming style has been adopted to exploit fully the machine resources.

Algorithms↗
PubMed1991

Building structural models of peptides: a semi-automatic software.

We present a software package that allows the construction and display of structural models of proteins starting from the amino acid sequence written in the one-letter code of standard data bank format. The software includes a very fast and efficient algorithm aimed at finding the global energy minimum of the potential function describing the molecular interactions. The whole package is conceived to have maximum flexibility. Completely automatic procedures are envisaged for standard problems. For non-standard problems, the construction procedure can be interactively adopted to meet with different options.

Algorithms↗
PubMed1991

Parallel computation and FASTA: confronting the problem of parallel database search for a fast sequence comparison algorithm.

We have parallelized the FASTA algorithm for biological sequence comparison using Linda, a machine-independent parallel programming language. The resulting parallel program runs on a variety of different parallel machines. A straight-forward parallelization strategy works well if the amount of computation to be done is relatively large. When the amount of computation is reduced, however, disk I/O becomes a bottleneck which may prevent additional speed-up as the number of processors is increased. The paper describes the parallelization of FASTA, and uses FASTA to illustrate the I/O bottleneck problem that may arise when performing parallel database search with a fast sequence comparison algorithm. The paper also describes several program design strategies that can help with this problem. The paper discusses how this bottleneck is an example of a general problem that may occur when parallelizing, or otherwise speeding up, a time-consuming computation.

Algorithms↗
PubMed1989

Local convolution in ectomography.

In tomographic imaging, using limited angular sampling, details outside the imaged section are displaced along circles of blur. In ectomography, these are eliminated by a spatial convolution process. It is shown that the convolution function has to be as long as the projected dimension of the imaged object perpendicular to the section and twice the dimension parallel to the section.

Image Processing, Computer-Assisted↗
PubMed1990

Approximation of surfaces in quantitative 3-D reconstructions.

In serial section reconstructions a series of planar profiles are taken representing curves on the surface of the structure to be reconstructed. For a number of quantitative serial section methods, approximation of a surface is done by the formation of tiles between points of adjacent profiles. As generally proposed, finding this approximation has been difficult due to the inordinately large number of possible solutions resulting from different combinations of tiles between points. Current algorithms have either applied heuristic criteria to force the formation of only one solution or have searched all acceptable combinations for one that minimizes some cost function. The algorithm presented has been developed to choose the tiling which minimizes the estimated error when the tile approximation of the surface is used in subsequent quantitative algorithm such as the calculation of surface area.

Algorithms↗
PubMed1994

Semi-automated measurement of true chord length distributions and moments by video microscopy and image analysis.

The distribution of the lengths of airspace chords in pulmonary parenchyma characterizes many architectural features of the alveoli and alveolar ducts. Laborious to obtain manually, the distributions and density functions may be acquired semi-automatically by video microscopy, digitization and image processing. The accuracy of the estimation is influenced by the microscopical methods and also by the techniques used (i) to convert the digitized greyscale picture to a two-valued image, (ii) to collect the chord lengths and (iii) to compensate for finite field widths. The last problem arises because some chords are completely visible within a field while others are only partially seen, since one of the two air-tissue boundaries lies outside the field of view. This error systematically biases the observed distribution. This paper contains solutions to hardware, software and analytic problems encountered while developing the capability to measure airspace chord length density functions semi-automatically. Formulas for estimating the true chord length density function from samples of observed chord lengths are presented. Also given are formulas for the estimation of the first and second moments of the true chord length distribution from the means of observed chord lengths. These techniques of image preparation and analysis should be suitable for characterizing particle, grain or cell size distributions, especially where many profiles fall partially outside the field of view.

Animals↗
PubMed1995

Image quality in digital chromosome analysis systems.

This paper reports on an investigation into the differences in image quality of different components used in a digital image processing system for chromosome analysis. As chromosome aberrations are important tools in the cloning of genes, it is important to know if the introduction of computerized analysis systems increases the risk of missing small aberrations. In this investigation the number of visible bands on a number of chromosomes has been used as a measure of quality. The images compared are microscope ocular images, photographs from a microscope built-in camera, digital images from a high and from a standard resolution camera, presented both on screen and print-out on paper. The main conclusions are that: (1) the view in the microscope ocular gives the best resolution, (2) there are risks of losing vital information using the digital image processing system for chromosome analysis, and (3) this risk is significantly reduced when using a high resolution camera.

Chromosome Banding↗
PubMed1998

Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution.

An implementation of classical molecular dynamics on parallel computers of increased efficiency has enabled a simulation of protein folding with explicit representation of water for 1 microsecond, about two orders of magnitude longer than the longest simulation of a protein in water reported to date. Starting with an unfolded state of villin headpiece subdomain, hydrophobic collapse and helix formation occur in an initial phase, followed by conformational readjustments. A marginally stable state, which has a lifetime of about 150 nanoseconds, a favorable solvation free energy, and shows significant resemblance to the native structure, is observed; two pathways to this state have been found.

Carrier Proteins↗