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New joint prediction algorithm (Q7-JASEP) improves the prediction of protein secondary structure.

The classical problem of secondary structure prediction is approached by a new joint algorithm (Q7-JASEP) that combines the best aspects of six different methods. The algorithm includes the statistical methods of Chou-Fasman, Nagano, and Burgess-Ponnuswamy-Scheraga, the homology method of Nishikawa, the information theory method of Garnier-Osgurthope-Robson, and the artificial neural network approach of Qian-Sejnowski. Steps in the algorithm are (i) optimizing each individual method with respect to its correlation coefficient (Q7) for assigning a structural type from the predictive score of the method, (ii) weighting each method, (iii) combining the scores from different methods, and (iv) comparing the scores for alpha-helix, beta-strand, and coil conformational states to assign the secondary structure at each residue position. The present application to 45 globular proteins demonstrates good predictive power in cross-validation testing (with average correlation coefficients per test protein of Q7, alpha = 0.41, Q7, beta = 0.47, Q7,c = 0.41 for alpha-helix, beta-strand, and coil conformations). By the criterion of correlation coefficient (Q7) for each type of secondary structure, Q7-JASEP performs better than any of the component methods. When all protein classes are included for training and testing (by cross-validation), the results here equal the best in the literature, by the Q7 criterion. More generally, the basic algorithm can be applied to any protein class and to any type of structure/sequence or function/sequence correlation for which multiple predictive methods exist.

Algorithms

An algorithm for the treatment of pain in advanced cancer.

An algorithm is presented that has been developed over the past three years to provide pain relief in advanced cancer. The hospital records of 92 patients were reviewed to evaluate the validity of the algorithm. The algorithm is as follows: the 24 hour oral consumption of opioids was converted to sustained release morphine. If ineffective usually over 360 mg daily the total 24 hour oral dose was divided by 6 to convert to I.V. If this was ineffective, usually over 10 mg/hr of morphine, the intravenous dose was divided by 10 and infused epidurally. Local anesthetic was added for plexus involvement. After four days, the patient was weaned from local anesthetic solution. If sharp pain or pain to movement persisted, 6% phenol in 1 to 2 ml aliquots was injected every 8-12 hours to a total of 5-8 ml. While the conversion from intravenous to epidural morphine was 10:1 that from epidural to intravenous was only 1:3. Intravenous dose converts directly to the subcutaneous. The conversion from intravenous to oral is 1:3. There view showed that the dosages at which the conversions were made varied considerably. The reasons for the wide variation are presented. In summary the algorithm is a good practical guide for treatment of cancer pain.

Adult

The enhancement of radiographic images from a multiwire camera using a maximum entropy algorithm.

The multiwire camera (MWC) produces high speed, quantitative autoradiography of radiolabelled substances in two-dimensional systems. While greatly superior to film-based systems in respect of speed and quantitativity the MWC has significantly poorer spatial resolution (particularly for high energy beta-emitting radiolabels) and the performance is ultimately limited by the noise induced in the images by Poisson statistics and counter background. Processing the MWC images with a maximum entropy algorithm significantly improves the performance of the system in these respects. The algorithm has been tested using one-dimensional data taken from images of known tritium, 14C and 125I distributions. Processed images are visually more acceptable with improved quantitative accuracy and spatial resolution. Quantitative accuracy, calculated as the root mean square deviation between an image and the known sample activities, is 10-40% lower for processed images compared with original camera images. Spatial resolution, calculated from slopes in the images representing edges of activity in the sources, is improved by 20-40% for the processed images. The algorithm is used to improve a two-dimensional image from a biological study. The source distribution consisted of a set of circular dots of varying activity. The dots with lowest activity were barely discernible in the raw MWC image but are clearly resolved after processing. The algorithm used is simple and effective and executes acceptably quickly on a personal computer. It should prove useful in any context where the imaging performance of a system is limited by Poisson statistics.

Algorithms

A two-dimensional pencil-beam algorithm for calculation of arc electron dose distributions.

A two-dimensional pencil-beam algorithm is presented for the calculation of arc electron dose distributions in any plane that is perpendicular to the axis of rotation. The dose distributions are calculated by modelling the arced beam as a single broad beam defined by the irradiated surface of the patient. The algorithm is two-dimensional in that the anatomical cross section of the patient and the skin collimators are assumed identical in parallel planes outside the plane of calculation. The broad beam is modelled as a collection of strip beams, each strip beam being characterised by its planar fluence, mean projected angular direction and a root-mean-square spread about the mean direction. Using these parameters, the dose distribution is calculated using pencil-beam theory. Examples of strip-beam parameters and resulting dose distributions for patient geometries are presented. Features of the algorithm, which include (1) incorporation of pencil-beam theory for the calculation of dose in heterogeneous tissue, (2) run times of only about twice that of comparable-sized fixed electron fields and (3) the input requirement of only a single depth dose and four off-axis dose profiles of measured data, make the algorithm practical for clinical use.

Algorithms

Effect of dimensionality of heterogeneity corrections on the implementation of a three-dimensional electron pencil-beam algorithm.

Electron beam dose distributions were calculated on a three-dimensional grid using three pencil-beam algorithms, each taking into account irregularities in field shape. The algorithms differ in that patient anatomy in either one, two, or three dimensions is used in the calculation of dose to a point. Algorithms were optimized for speed by such techniques as precalculation and storage of several quantities, reordering of pencil-beam and grid-point loops, selection of cut-off values for some calculated quantities, and invoking error function symmetries. Execution times for optimized versions of each of the algorithms as implemented on a three-dimensional treatment planning system were comparable for both the one- and two-dimensional heterogeneity correction requires an additional calculational loop over fan lines. Execution times for the three-dimensional heterogeneity correction were approximately a factor of four longer than those for the two-dimensional correction. For certain geometries, three-dimensional heterogeneity corrections were necessary to calculate dose distributions accurately, in spite of the additional cost in calculation times.

Algorithms

An algorithm for maximizing the probability of complication-free tumour control in radiation therapy.

New radiobiological models are used to describe tumour and normal tissue reactions and to account for their dependence on the irradiated volume and inhomogeneities of the delivered dose distribution and cell sensitivity. The probability of accomplishing complication-free tumour control is maximized by an iterative algorithm. The algorithm is demonstrated by applying it to a one-dimensional (1D) tumour model but also to a more clinically relevant 2D case. The new algorithm is n-dimensional so it could simultaneously optimize the dose delivery in a 3D volume and in principle also select the ideal beam orientations, beam modalities (photons, electrons, neutrons, etc) and optimal spectral distributions of the corresponding modalities. To make calculation time reasonable, 2D-3D problems are most practical, and suitable beam orientations are preselected by the choice of irradiation kernel. The energy deposition kernel should therefore be selected in order to avoid irradiation through organs at risk. Clinically established dose response parameters for the tissues of interest are used to make the optimization as relevant as possible to the clinical problems at hand. The algorithm can be used even with a poorly selected kernel because it will always, as far as possible, avoid irradiating organs at risk. The generated dose distribution will be optimal with respect to the spatial distribution and assumed radiobiological properties of the tumour and normal tissues at risk for the kernel chosen. More specifically the probability of achieving tumour control without fatal complications in normal tissues is maximized. In the clinical examples a reduced tumour dose is seen at the border to sensitive organs at risk, but instead an increased dose just inside the tumour border is generated. The increased tumour dose has the effect that the dose fall-off is as steep as possible at the border to organs at risk.

Algorithms

DNAMAT: an efficient graphic matrix sequence homology algorithm and its application to structural analysis.

We present a fast algorithm to produce a graphic matrix representation of sequence homology. The algorithm is based on lexicographical ordering of fragments. It preserves most of the options of a simple naive algorithm with a significant increase in speed. This algorithm was the bais for a program, called DNAMAT, that has been extensively tested during the last three years at the Weizmann Institute of Science and has proven to be very useful. In addition we suggest a way to extend our approach to analyse a series of related DNA or RNA sequences, in order to determine certain common structural features. The analysis is done by 'summing' a set of dot-matrices to produce an overall matrix that displays structural elements common to most of the sequences. We give an example of this procedure by analysing tRNA sequences.

Algorithms

Graphics of RNA secondary structure; towards an object-oriented algorithm.

We present a new algorithm for the display of RNA secondary structure. The principle of the algorithm is entirely different from those currently in use in that our algorithm is 'object oriented' while current algorithms are 'procedural'. The circular RNA molecule of chrysanthemum stunt viroid was used as input data for demonstrating the operation of the program. The major interest of this method will be found in its potential use in simulation graphics of RNA folding processes.

Algorithms

An algorithm for searching restriction maps.

This paper presents an algorithm that searches a DNA restriction enzyme map for regions that approximately match a shorter 'probe' map. Both the map and the probe consist of a sequence of address-enzyme pairs denoting restriction sites, and the algorithm penalizes a potential match for undetected or missing sites and for discrepancies in the distance between adjacent sites. The algorithm was designed specifically for comparing relatively short DNA sequences with a long restriction map, a problem that will become increasing common as large physical maps are generated. The algorithm has been used to extract information from a restriction map of the entire Escherichia coli genome.

Algorithms

An algorithm to fit the Gompertz function to growth curves.

An algorithm to fit the Gompertz growth function is presented. This algorithm is easy to program on a microcomputer. The algorithm is based on employing a searching technique to solve a set of equations derived from the Gompertz function. Its application may prove valuable when access to a computer mainframe is difficult. Such a method may be useful in construction of a specific growth curve in biology, or as a managerial tool in livestock enterprise, as well as in the clinical treatment of tumors. Demonstration of the successful application of this algorithm in experimental livestock growth data are presented.

Algorithms

dGAMLSS: an exact, distributed algorithm to fit Generalized Additive Models for Location, Scale, and Shape for privacy-preserving population reference charts.

MOTIVATION: There is growing interest in estimating population reference ranges across age and sex to better identify atypical clinically-relevant measurements throughout the lifespan. For this task, the World Health Organization recommends using Generalized Additive Models for Location, Scale, and Shape (GAMLSS), which can model non-linear growth trajectories under complex distributions that address the heterogeneity in human populations.Fitting GAMLSS models requires large, generalizable sample sizes, especially for accurate estimation of extreme quantiles, but obtaining such multi-site data can be challenging due to privacy concerns and practical considerations. In settings where patient data cannot be shared, privacy-preserving distributed algorithms for federated learning can be used, but no such algorithm exists for GAMLSS. RESULTS: We propose distributed GAMLSS (dGAMLSS), a distributed algorithm that can fit GAMLSS models across multiple sites without sharing patient-level data. This includes specific considerations for the fitting of smooth functions at varying levels of communication efficiency. We demonstrate the effectiveness of dGAMLSS in constructing population reference charts across clinical, genomics, and neuroimaging settings and show that dGAMLSS is able to reproduce pooled reference charts and inference down to numerical differences. AVAILABILITY AND IMPLEMENTATION: An R package providing examples of the dGAMLSS algorithm, as well as functions for sharing and aggregating site-specific parameters, is available at https://github.com/hufengling/dGAMLSS.

Algorithms

Trials, tribulations, and triumphs of the EM algorithm in pedigree analysis.

The EM algorithm is an iterative method for finding maximum-likelihood estimates. Its advantages often include numerical stability, simplicity of computer implementation, and natural incorporation of parameter constraints. However, the EM algorithm must be tailored to each specific problem. Smith (1957) and Ott (1977, 1979) have accomplished this for a variety of problems in human pedigree analysis. The present paper clarifies their theory by presenting it from a modern perspective. Five practical numerical examples are also given in an attempt to assess the value of the EM algorithm in realistic genetic modelling. These examples deal with racial admixture, linkage homogeneity, classical segregation analysis, a Mendelian latent trait model for schizophrenia, and a heterozygote detection assay for Ataxia-telangiectasia. Comparison with a quasi-Newton method of optimization reveals that the EM algorithm generally converges more slowly, but also more stably.

Algorithms

Design and prospective evaluation of an algorithm for penetrating truncal injuries.

The major aim was to develop a branch-chain decision tree for penetrating truncal injury and to subject this to a prospective trial of its feasibility to track management decisions. In contrast to the conventional trauma study which focuses on highly selected, well-defined surgical problems, this algorithmic approach was designed to look at the whole gamut of problems of unselected patients with penetrating injury as they enter the ED. The branch-chain algorithm primarily focuses on priorities, order of procedures, and the immediate therapeutic options. The algorithm was used to track clinical management of 280 consecutive patients with penetrating truncal injuries; 31 were dead on arrival, 12 were alive on admission but died during their hospitalization. Of 209 patients whose management was in satisfactory compliance, four (2%) died; eight (20%) of 40 patients who had major deviations from the algorithm died (p less than .01).

Algorithms

Rapid automated algorithm for aligning and reslicing PET images.

A computer algorithm for the three-dimensional (3D) alignment of PET images is described. To align two images, the algorithm calculates the ratio of one image to the other on a voxel-by-voxel basis and then iteratively moves the images relative to one another to minimize the variance of this ratio across voxels. Since the method relies on anatomic information in the images rather than on external fiducial markers, it can be applied retrospectively. Validation studies using a 3D brain phantom show that the algorithm aligns images acquired at a wide variety of positions with maximum positional errors that are usually less than the width of a voxel (1.745 mm). Simulated cortical activation sites do not interfere with alignment. Global errors in quantitation from realignment are less than 2%. Regional errors due to partial volume effects are largest when the gantry is rotated by large angles or when the bed is translated axially by one-half the interplane distance. To minimize such partial volume effects, the algorithm can be used prospectively, during acquisition, to reposition the scanner gantry and bed to match an earlier study. Computation requires 3-6 min on a Sun SPARCstation 2.

Algorithms

An algorithm for associating the features of two images.

In this paper we describe an algorithm that operates on the distances between features in the two related images and delivers a set of correspondences between them. The algorithm maximizes the inner product of two matrices, one of which is the desired 'pairing matrix' and the other a 'proximity matrix' with elements exp (-rij2/2 sigma 2), where rij is the distance between two features, one in each image, and sigma is an adjustable scale parameter. The output of the algorithm may be compared with the movements that people perceive when viewing two images in quick succession, and it is found that an increase in sigma affects the computed correspondences in much the same way as an increase in interstimulus interval alters the perceived displacements. Provided that sigma is not too small the algorithm will recover the feature mappings that result from image translation, expansion or shear deformation--transformations of common occurrence in image sequences--even when the displacements of individual features depart slightly from the general trend.

Algorithms

The use of adaptive algorithms for obtaining optimal electrical shimming in magnetic resonance imaging (MRI).

A method of determining the dc coil current values to electrically shim the static magnetic fields used in magnetic resonance imaging (MRI) using modified steepest descent adaptive algorithm is described. Using a 32 cm diameter by a 40 cm long water phantom as the test volume, the algorithm achieved field homogeneities of 0.2 parts per million (ppm) peak-to-peak within a 20 cm diameter spherical imaging volume, and 1.3 ppm peak-to-peak within the entire phantom. The algorithm achieved an inhomogeneity variance of 0.18 ppm2. The shim system was successfully modeled as a sum of adaptive linear combiners. The model contains 13 parameters that can be varied, 12 shim coil currents, and the receiver mixer frequency. The model was then used to predict key adaptive algorithm parameters. Experimental verification of these parameters lends support to the accuracy of the model.

Algorithms

A comparison of the noise sensitivity of nine QRS detection algorithms.

The noise sensitivities for nine different QRS detection algorithms were measured for a normal, single-channel lead II, synthesized ECG corrupted with five different types of synthesized noise. The noise types were electromyographic interference, 60 Hz powerline interference, baseline drift due to respiration, abrupt baseline shift, and a composite noise constructed from all of the other noise types. The percentage of QRS complexes detected, the number of false positives, and the detection delay were measured. None of the algorithms were able to detect all QRS complexes without any false positives for all of the noise types at the highest noise level. Algorithms based on amplitude and slope had the highest performance for EMG-corrupted ECG. An algorithm using a digital filter had the best performance for the composite noise corrupted data.

Algorithms

A semiclosed-loop algorithm for the control of blood glucose levels in diabetics.

In this paper, a theoretical analysis of the control of plasma glucose levels in diabetic individuals is undertaken using a simple mathematical model of the dynamics of glucose and insulin interaction in the blood system. Mathematical optimization techniques are applied to the mathematical model to derive insulin infusion programs for the control of blood levels in diabetic individuals. Based on the results of the mathematical optimization, a semiclosed-loop algorithm is proposed for continuous insulin delivery to diabetic patients. The algorithm is based on three hourly plasma glucose samples. A theoretical evaluation of the effectiveness of this algorithm shows that it is superior to two existing algorithms in controlling hyperglycemia. A glucose infusion term representing the effect of glucose intake resulting from a meal is then introduced into the model equations. Various insulin infusion programs for the control of plasma glucose levels following a meal are then assessed. The theoretical results suggest that the most effective short-term control is achieved by an insulin infusion program which incorporates an injection to coincide with the meal.

Algorithms