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Software manipulations to speed up a real-valued fast Fourier transform algorithm.

It is described how a real-valued fast Fourier transform (RFFT) algorithm can be converted quite easily into a computer program in which loops, evaluation of subscripts, exchange of data, and logical operations are completely avoided. The resulting program runs considerably faster than the original algorithm. The actual saving of execution time depends upon both the computer system and the length of the RFFT. In the majority of the investigated cases the execution time was reduced by a factor between 1.8 and 5. The described technique can be recommended especially for critical real-time tasks and for applications requiring a huge amount of RFFT evaluations. Other algorithms as for example the complex-valued FFT, the inverse RFFT or correlation algorithms can be treated in a similar way.

Algorithms

The influence of different generations of computer algorithms on diabetes control.

With all control schedules, the management of diabetes is possible using Skyler's algorithm. In general, those control algorithms which do not allow the individual adaptation to changing conditions lead to overinsulinisation. So-called meal-related algorithms do usually minimise the fluctuations in blood sugar. The introduction of self-adapting algorithms, detecting peripheral insulin resistance, may further improve metabolic diabetes control.

Algorithms

A computer algorithm to determine the nadir and rise time in nocturnal cortisol secretion.

The nadir concentration value and the time of the circadian rise are two important characteristics of the nocturnal cortisol secretory pattern. A computer algorithm has been developed which objectively determines these parameters, supplementing the subjective evaluating methods previously used. The algorithm smooths the cortisol values and incorporates the intra-assay variability when calculating the nadir and rise. It was tested on 156 nights of cortisol data for healthy control and depressed subjects. The algorithm results closely matched the nadir and rise time subjectively determined by the investigators. With careful screening of the computer generated results, the algorithm decreases the reliance on subjective methods to determine the actual nocturnal cortisol nadir and rise time.

Adolescent

Random search algorithm (RONSC) for optimization of radiation therapy with both physical and biological end points and constraints.

A new algorithm for the optimization of 3-dimensional radiotherapy plans is presented. The RONSC algorithm (Random Optimization with Non-linear Score functions and Constraints) is based on the idea of random search in the space of feasible solutions. RONSC takes advantage of some specific properties of the dose distribution and derivable information such as dose-volume histograms and calculated estimates of tumor control and normal tissue complication probabilities. The performance of the algorithm for clinical and test cases is discussed and compared with the performance of the simulated annealing algorithm, which is also based on the idea of random search.

Algorithms

Searching protein sequence libraries: comparison of the sensitivity and selectivity of the Smith-Waterman and FASTA algorithms.

The sensitivity and selectivity of the FASTA and the Smith-Waterman protein sequence comparison algorithms were evaluated using the superfamily classification provided in the National Biomedical Research Foundation/Protein Identification Resource (PIR) protein sequence database. Sequences from each of the 34 superfamilies in the PIR database with 20 or more members were compared against the protein sequence database. The similarity scores of the related and unrelated sequences were determined using either the FASTA program or the Smith-Waterman local similarity algorithm. These two sets of similarity scores were used to evaluate the ability of the two comparison algorithms to identify distantly related protein sequences. The FASTA program using the ktup = 2 sensitivity setting performed as well as the Smith-Waterman algorithm for 19 of the 34 superfamilies. Increasing the sensitivity by setting ktup = 1 allowed FASTA to perform as well as Smith-Waterman on an additional 7 superfamilies. The rigorous Smith-Waterman method performed better than FASTA with ktup = 1 on 8 superfamilies, including the globins, immunoglobulin variable regions, calmodulins, and plastocyanins. Several strategies for improving the sensitivity of FASTA were examined. The greatest improvement in sensitivity was achieved by optimizing a band around the best initial region found for every library sequence. For every superfamily except the globins and immunoglobulin variable regions, this strategy was as sensitive as a full Smith-Waterman. For some sequences, additional sensitivity was achieved by including conserved but nonidentical residues in the lookup table used to identify the initial region.

Algorithms

Nonparametric comparison of entire ROC curves for computerized ECG left ventricular hypertrophy algorithms using data from the Framingham Heart Study.

A computer program may be capable of several different statements for left ventricular hypertrophy (eg, possible LVH, probable LVH, consistent with LVH), but such statements resulting from discretized levels of sensitivity/specificity would represent only isolated points on a receiver-operating characteristic (ROC) curve, which is a plot of all levels of sensitivity versus specificity. Even if two algorithms use the same discrete scales, their performances may not readily be compared. The authors present a comparison methodology for ROC curves using ROC area as a nonparametric measure of the ability of the algorithm to separate the two populations; the ROC area ranges from 0.5 (no ability) to 1.0 (perfect separation) and is unbiased if the normal versus abnormal populations have no common values for the measurement. The methodology compares the performance of ECG algorithms on the same population of cases by testing for significant differences of ROC areas and incorporating correlation of the algorithms in a nonparametric way. To illustrate this methodology, they use ECG and echocardiographic data from the Framingham Heart Study.

Algorithms

An algorithmic approach to diagnosis of hypoglycemia.

An algorithm has been devised to facilitate the diagnostic approach to the causes of hypoglycemia. This systematic approach enables the physician to reach the final diagnosis in a logical way without subjecting the child to unnecessary and possibly hazardous investigations. The algorithm is based on the following measurements as required by each patient: concentrations of blood glucose, lactate, ketone bodies, and glucose-regulating hormones. These measurements are performed with the patient in the fasting state and after loading tests (glycerol and galactose) as needed. If indicated, an enzymatic test is performed to establish the final diagnosis. Eighteen children aged 1 month to 7 years who had persistent or recurrent hypoglycemia have been examined according to this algorithm. The correct diagnosis was arrived at in 17 patients. The diagnosis was not reached in one neonate who had glucose-6-phosphatase deficiency and initially did not have lactic acidosis; once lactic acidosis developed, his illness fitted perfectly into the algorithm.

Algorithms

Developing a clinical algorithm for early management of cervical spine injury in child trauma victims.

To define a subset of injured children for whom emergency cervical spine radiography may be unnecessary, we performed a retrospective chart and radiologic review. Two entry methods were used: All injured children, from birth through 16 years, who had received cervical spine radiographs at The Children's Memorial Hospital from September 1983, to September 1984, were included. All patients from birth to 16 years with proven or suspected cases of cervical spine injury who had received cervical spine radiographs and who had been treated at either the Children's Memorial Hospital or the Northwestern University Spine Trauma Unit during period 1974 to 1984 also were included. Each child's chart was reviewed, and 84 clinical variables were recorded. All radiographs were reviewed by a pediatric neuroradiologist. Of 206 children studied, 59 had cervical spine injuries. A clinical algorithm was derived using the following eight variables: neck pain; neck tenderness; limitation of neck mobility; history of trauma to the neck; and abnormalities of reflexes, strength, sensation, or mental status. The following decision rule was selected: Positive findings in any of these eight variables mandates cervical spine radiography. This algorithm correctly identified 58 of 59 children with cervical spine injury, yielding a sensitivity of 98% and specificity of 54%. Cervical spine radiographs could have been avoided in 79 children (38% of the entire sample). This algorithm performed better than did models derived from logistic regression analysis of the same data. Validation trials are required prior to the implementation of this or other clinical decision algorithms in practice.

Accidents

Development of a decision algorithm for a semiautomatic defibrillator.

A decision algorithm was developed for a semiautomatic defibrillator. The function of the algorithm is to evaluate the ECG of a patient and determine whether a defibrillation shock should be delivered. The development process included establishment of defibrillation criteria, creation of ECG databases, algorithm design, development of test protocols, and clinical testing. The result was an algorithm with sensitivity and specificity sufficiently accurate to allow a defibrillation shock to be delivered safely outside the hospital.

Algorithms

Resuscitation algorithm for management of acute emergencies.

Assuming that unrecognized or inadequately corrected hypovolemia results in higher mortality and morbidity rates, we developed a systematic approach to resuscitation that would: 1) identify criteria to aid in the recognition of hypovolemia and ensure the expeditious correction of this defect without interfering with diagnostic workup and management; 2) define criteria to prevent fluid overload which may jeopardize the patient's course, and 3) express these criteria in an explicit, systematic, patient care algorithm, ie, protocol, useful to both the resident and the practicing physician. We are now conducting prospective clinical trials with one service using the algorithm and the others acting as the control group. Preliminary results comparing patient outcomes suggest that the algorithm improves patient care by shortening resuscitation time and results in fewer hospital days, intensive care unit days, febrile days, and days on mechanical ventilation as well as reduced mortality. The algorithm provides a systematic plan to organize patient care so that the most urgently needed procedures are not delayed or overlooked.

Algorithms

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