Tasks which are too complex to compute.
Explore the source record for details and available documents.
Mathematical Computing↗
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.
Proline in alpha-helix: stability and conformation studied by dynamics simulation.
Free-energy simulations have been used to estimate the change in the conformational stability of short polyalanine alpha-helices when one of the alanines is replaced by a proline residue. For substituting proline in the middle of the helix the change in free energy of folding (delta delta G degrees) was calculated as 14 kJ/mol (3.4 kcal/mol), in excellent agreement with the one available experimental value. The helix containing proline was found to be strongly kinked; the free energy for reducing the angle of the kink from 40 degrees to 15 degrees was calculated, and found to be small. A tendency to alternate hydrogen bonding schemes was observed in the proline-containing helix. These observations for the oligopeptide agree well with the observation of a range of kink angles (18-35 degrees) and variety of hydrogen bonding schemes, in the rare instances where proline occurs in helices in globular proteins. For substituting proline at the N-terminus of the helix the change in free energy of folding (delta delta G degrees) was calculated as -4 kJ/mol in the first helical position (N1) and +6 kJ/mol in the second helical position (N2). The observed frequent occurrence of proline in position N1 in alpha-helices in proteins therefore has its origin in stability differences of secondary structure. The conclusion reached here that proline may be a better helix former in position N1 than (even) alanine, and thus be a helix initiator may be testable experimentally by measurements of fraction helical conformation of individual residues in oligopeptides of appropriate sequence. The relevance of these results in regards to the frequent occurrence of proline-containing helices in certain membrane proteins is discussed.
Alanine↗
On alleged gains in power from lower P-values.
Explore the source record for details and available documents.
Computer Simulation↗
A parallel implementation of the ALOPEX process.
Optimization techniques have found many applications in science, engineering, and industry. In all applications, the best value of a "cost function" is sought in a well-defined domain; this cost function in general depends on many parameters. An iterative optimization technique has been developed (ALOPEX) that uses feedback in order to optimize the response of a system. The cost function for this process is problem dependent and therefore quite flexible. The method has been applied successfully to different optimization problems such as pattern recognition, receptive field studies in the visual system of animals, curve fitting, etc. We present two special purpose hardware implementations for ALOPEX. The first method takes time O(logN + logm) and uses O(mN2) processing elements. The second method takes O(logN + m) time and uses O(N2) processing elements. Our basic architecture is a binary tree with N2 leaves (equal to the length of the vectors) and therefore had depth O(logN). Different implications of the two approaches will be discussed including similarities with the biological visual process.
Algorithms↗
Estimation and inference in pharmacokinetic models: the effectiveness of model reformulation and resampling methods for functions of parameters.
It is well known that high parameter estimate correlations and asymptotic variance estimates can cause estimation and inference problems in the analysis of pharmacokinetic models. In this paper we show that analysis of three important functions of pharmacokinetic parameters, the half-life, mean residence time, and the area under the curve, can sometimes be greatly improved by reformulating the model to address collinearity and by using the bootstrap to form confidence intervals. The resultant estimators can be more accurate than the original ones, and resultant confidence intervals can be narrower. Of the three measures, the half-life estimator is much better behaved than the estimators of mean residence time and area under the curve under collinearity, suggesting that it (or measures like it) should be used more often.
Analysis of Variance↗
Performance of various mathematical methods for computer-aided processing of radioimmunoassay results.
Interpolation and regression methods are available for computer aided determination of radioimmunological end results. We compared the performance of 6 algorithms (weighted and unweighted linear logit log regression; quadratic logit log regression, smoothing spline interpolation with a large and small smoothing factor, respectively, and polygonal interpolation and the manual curve fitting on the basis of three radioimmunoassays with different reference curve characteristics (digoxin, estriol, human chorionic somatomammotrophin (HCS)). Great store was set by the accuracy of the approximation at the intermediate points on the curve, i.e. those points that lie midway between two standard concentrations. These concentrations were obtained by weighing and inserted as unknown samples. In the case of digoxin and estriol the polygonal interpolation provided the best results, while the weighted logit log regression proved superior in the case of HCS.
Computers↗
Interactive statistical analysis of survival data.
This paper describes a SAS macro which facilitates the interactive analysis of right-censored survival data. Such data commonly occur in medical studies. The program produces Kaplan-Meier survival curves on a wide variety of graphics devices. The program also performs log-rank and generalized Wilcoxon significance tests among all plotted curves and for each pairwise contrast if desired. Because the program is intelligent and does not prompt the user for information that it can independently obtain, it is quite easy to use.
Computer Graphics↗
Balancing allocation of subjects in biomedical research: a minimization strategy based on ranks.
A new method for ensuring the comparability of groups of experimental subjects is proposed. All subjects are ranked on each measured pretreatment variable and differences between groups in the means and the standard deviations of these ranks are minimized by systematically exchanging subjects when those exchanges yield less imbalance between groups. This method was designed for small studies in which pretreatment data from all subjects are known before the start of the experiment. A series of computer simulations suggests that this procedure is effective in balancing groups on several variables although the amount of computer time required becomes excessive as the number of subjects is increased.
Computer Simulation↗
A new method for aligning histological serial sections for three-dimensional reconstruction.
A new method for aligning histological serial sections for three-dimensional reconstruction by computer is introduced. This method is particularly suited for embedding structures in celloidine or paraplast. Prior to sectioning, at least three reference markers are affixed to the preparation in a direction perpendicular to the section plane, for easy identification on the finished sections. An algorithm translates and rotates the serial sections until all the reference markers are congruent. The main advantage of this method, however, is its capability to eliminate deformations caused by compression or stretching during sectioning by the determination of correction factors.
Algorithms↗
Automatic geometrical registration of fluorescein retinal angiograms.
Changes in retinal microvascular perfusion revealed by fluorescein angiography have been reported in patients undergoing coronary artery surgery. Quantification of these changes is important and current techniques depend on careful visual inspection of the angiograms by humans. Computer image processing methods can be used to identify and highlight differences, but geometrical registration of the images is a prerequisite to the comparisons. Automatic methods for locating and matching reference points have therefore been developed. In combination with an iterative process which used least-squares error to calculate the transformation coefficients, subsets of reference points were selected and used to register successfully 20 image pairs.
Coronary Artery Bypass↗
Tooth surface fitting and three-dimensional display using hidden surface removal technique.
Bi-cubic parametric spline surface is applied for surface-fitting of the external surface and canal of tooth based on its crown-to-root, cross-sectional data obtained by X-ray scanning. For three-dimensional display of the fitted surfaces, a technique for fast removal of the hidden surfaces is also reported. The selection of the accumulated chord length or coordinate component as parameter make it possible to fit any kind of surface smoothly. For displaying or plotting a well-fitted surface, a method capable of discriminating the grades for sequential removal of the hidden surfaces is developed for substantial reduction of computing time.
Algorithms↗
Algorithms for the computation of spatial statistics.
Algorithms are described for the calculation of spatial statistics. The statistics are the functions K(t), G(y), F(x), and K12(t). They can be used to determine (a) which type of spatial process ('random', 'clustered', 'regular', etc.) best fits a data set and whether the spatial pattern changes with distance, and (b) whether two types of events are correlated with each other, and if so, at which distances the correlation occurs. These functions provide a powerful tool for analysing the spatial distribution of biomedical and biological phenomena. An interactive, command-driven program that incorporates these algorithms is described.
Algorithms↗
A program for simulation of nerve equations with branching geometries.
A computer program has been developed for simulation of electrical activity in neurons with complex branching morphology, multiple channel types, and inhomogeneous channel distribution. The program is based around an interpreter and screen editor for flexible specification of nerve properties and analysis of simulation results. Efficient simulation of the nerve specification is accomplished with procedure calls to fast, compiled routines for integration of the nerve equations.
Cell Membrane↗
A mathematical model for the computational determination of parameter values of anthropomorphic segments.
Explore the source record for details and available documents.
Adult↗
High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach.
Two modified DLT algorithms are presented that improve the accuracy of three-dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods. The improvement in the linear modified DLT (MDLT) algorithm is achieved by satisfying certain orthogonality conditions in the form of a non-linear constraint, thereby effectively eliminating a redundant DLT parameter. In the non-linear MDLT algorithm, the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized. The highest reconstruction accuracy of 0.733 mm rms mean error was obtained with the non-linear MDLT algorithm. This corresponds to a spatial resolution of about one part in 2860 or 0.035% overall accuracy. The accuracy obtainable with the linear MDLT was found to be slightly less and about 0.041% (0.833 mm rms mean error).
Algorithms↗
Intersection of shaped radiation beams with arbitrary image sections.
Display of the intersection of a shaped radiation beam with an arbitrarily oriented image plane is a very useful tool in three-dimensional external beam radiation treatment planning. Coverage of the tumor (or target) region can be graphically investigated, as well as the radiation received by the surrounding healthy tissues. An algorithm is presented that obtains and displays these intersections by projecting contour points defining the beam's aperture on the plane. A general procedure is given, as well as provisions for special cases in which a straightforward projection is not sufficient.
Algorithms↗
VARCOV II: a computer program for the multivariate analysis of growth and response curves.
A FORTRAN computer program written to perform a multivariate analysis of growth and response curves is described. The underlying statistical methodology is particularly applicable with incomplete observations, and may offer improved power performance to the distribution-free methods described previously.
Analysis of Variance↗
CONFREG: a BASIC program for calculating and plotting confidence regions based on correlational analyses.
Many observations encountered in biological and medical research are randomly distributed in bivariate scales, and thus not susceptible to simple regression analyses. Since such data are depicted by ellipses in scatter diagrams, a computer program to calculate the confidence regions for the means or the total data of bivariate samples was written in BASIC for correlational analyses. The program, based on the principal axes algorithm, plots the calculated confidence regions as an elliptic area, using the fitted equations for its major and minor axes. The program displays the sample parameters required to perform comparisons between different groups of experimental conditions.
Animals↗