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A modified EM algorithm for estimation in generalized mixed models.

Application of the EM algorithm for estimation in the generalized mixed model has been largely unsuccessful because the E-step cannot be determined in most instances. The E-step computes the conditional expectation of the complete data log-likelihood and when the random effect distribution is normal, this expectation remains an intractable integral. The problem can be approached by numerical or analytic approximations; however, the computational burden imposed by numerical integration methods and the absence of an accurate analytic approximation have limited the use of the EM algorithm. In this paper, Laplace's method is adapted for analytic approximation within the E-step. The proposed algorithm is computationally straightforward and retains much of the conceptual simplicity of the conventional EM algorithm, although the usual convergence properties are not guaranteed. The proposed algorithm accommodates multiple random factors and random effect distributions besides the normal, e.g., the log-gamma distribution. Parameter estimates obtained for several data sets and through simulation show that this modified EM algorithm compares favorably with other generalized mixed model methods.

Algorithms↗

Evaluation of an algorithm for integrated management of childhood illness in an area of Kenya with high malaria transmission.

In 1993, the World Health Organization completed the development of a draft algorithm for the integrated management of childhood illness (IMCI), which deals with acute respiratory infections, diarrhoea, malaria, measles, ear infections, malnutrition, and immunization status. The present study compares the performance of a minimally trained health worker to make a correct diagnosis using the draft IMCI algorithm with that of a fully trained paediatrician who had laboratory and radiological support. During the 14-month study period, 1795 children aged between 2 months and 5 years were enrolled from the outpatient paediatric clinic of Siaya District Hospital in western Kenya; 48% were female and the median age was 13 months. Fever, cough and diarrhoea were the most common chief complaints presented by 907 (51%), 395 (22%), and 199 (11%) of the children, respectively; 86% of the chief complaints were directly addressed by the IMCI algorithm. A total of 1210 children (67%) had Plasmodium falciparum infection and 1432 (80%) met the WHO definition for anaemia (haemoglobin < 11 g/dl). The sensitivities and specificities for classification of illness by the health worker using the IMCI algorithm compared to diagnosis by the physician were: pneumonia (97% sensitivity, 49% specificity); dehydration in children with diarrhoea (51%, 98%); malaria (100%, 0%); ear problem (98%, 2%); nutritional status (96%, 66%); and need for referral (42%, 94%). Detection of fever by laying a hand on the forehead was both sensitive and specific (91%, 77%). There was substantial clinical overlap between pneumonia and malaria (n = 895), and between malaria and malnutrition (n = 811). Based on the initial analysis of these data, some changes were made in the IMCI algorithm. This study provides important technical validation of the IMCI algorithm, but the performance of health workers should be monitored during the early part of their IMCI training.

Algorithms↗

Learning algorithms based on linearization.

The aim of this article is to investigate a mechanical description of learning. A framework for local and simple learning algorithms based on interpreting a neural network as a set of configuration constraints is proposed. For any architectural design and learning task, unsupervised and supervised algorithms can be derived, optionally using unconstrained and hidden neurons. Unlike algorithms based on the gradient in weight space, the proposed tangential correlation (TC) algorithms move along the gradient in state space. This results in optimal scaling properties and simple expressions for the weight updates. The number of synapses is much larger than the number of neurons. A constraint for neural states does not impose a unique constraint for synaptic weights. Which weights to assign credit to can be selected from a parametrization of all weight changes equivalently satisfying the state constraints. At the heart of the parametrization are minimal weight changes. Two supervised algorithms (differing by their parametrizations) operating on a three-layer perceptron are compared with standard backpropagation. The successful training of fixed points of recurrent networks is demonstrated. The unsupervised learning of oscillations with variable frequencies is performed on standard and more sophisticated recurrent networks. The results presented here can be useful both for the analysis and for the synthesis of learning algorithms.

Algorithms↗

Identification and estimation algorithm for stochastic neural system.

An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.

Animals↗

Analysis of a cooperative stereo algorithm.

Marr and Poggio (1976) recently described a cooperative algorithm that solves the correspondence problem for stereopsis. This article uses a probabilistic technique to analyze the convergence of that algorithm, and derives the conditions governing the stability of the solution state. The actual results of applying the algorithm to random-dot stereograms are compared with the probabilistic analysis. A satisfactory mathematical analysis of the asymptotic behaviour of the algorithm is possible for a suitable choice of the parameter values and loading rules, and again the actual performance of the algorithm under these conditions is compared with the theoretical predictions. Finally, some problems raised by the analysis of this type of "cooperative" algorithm are briefly discussed.

Depth Perception↗

Sensitivity and specificity of a dual-chamber arrhythmia recognition algorithm for implantable devices.

Present ventricular rate-based arrhythmia detection algorithms lack specificity. Using a training set of 109 endocardial electrogram recordings, a sensitive and specific dual-chamber arrhythmia recognition algorithm has been developed. The algorithm uses atrial and ventricular rates, irregularity, degree of beat-to-beat similarity, and measure of electrogram complex distinctiveness to arrive at a diagnostic conclusion. A test set of 121 endocardial electrogram recordings obtained during provocative electrophysiology studies was then used for blinded validation of the algorithm. In normal rhythm, 1:1 tachycardia, atrial tachycardia, atrial flutter, atrial fibrillation, ventricular tachycardia, and ventricular fibrillation, the percentages of sensitivity/specificity were, respectively, 100/99, 100/99, 80/99, 89/98, 91/97, 92/100, and 100/98. Although ventricular rate alone can usually distinguish normal rhythm, ventricular tachycardia, and ventricular fibrillation, it is confounded by atrial arrhythmias and 1:1 tachycardias. When tested on a database, a ventricular rate-only algorithm resulted in sensitivity/specificity of 100/65, 90/78, and 100/99%, respectively, for these three rhythms. Therefore, the dual-chamber algorithm based on both temporal and morphologic measures provides better distinction of normal rhythm and ventricular tachycardia than existing methods, without sacrificing sensitivity.

Arrhythmias, Cardiac↗

Byte structure variable length coding (BS-VLC): a new specific algorithm applied in the compression of trajectories generated by molecular dynamics

Molecular dynamics is a well-known technique very much used in the study of biomolecular systems. The trajectory files produced by molecular dynamics simulations are extensive, and the classical lossless algorithms give poor efficiencies in their compression. In this work, a new specific algorithm, named byte structure variable length coding (BS-VLC), is introduced. Trajectory files, obtained by molecular dynamics applied to trypsin and a trypsin:pancreatic trypsin inhibitor complex, were compressed using four classical lossless algorithms (Huffman, adaptive Huffman, LZW, and LZ77) as well as the BS-VLC algorithm. The results obtained show that BS-VLC nearly triplicates the compression efficiency of the best classical lossless algorithm, preserving a near lossless behavior. Compression efficiencies close to 50% can be obtained with a high degree of precision, and the maximum efficiency possible (75%), within this algorithm, can be performed with good precision.

Journal Article↗

Potential effect of self-care algorithms on the number of physician visits.

To assess the potential effect of self-care algorithms on the number of physician visits, actual visits from the Seattle Virus Watch were compared retrospectively with those recommended by clinical algorithms for common illnesses from the book, Take Care of Yourself, by Vickery and Fries. From a total of 3929 illnesses, records indicating the presence of the index symptom for eight algorithms were identified, determining whether the criteria for seeing a physician were met and whether a physician visit was recorded. The number of visits observed was compared to the number of visits recommended by the algorithms. Strict adherence would have increased the number of visits over that observed for five, remained the same for two, and decreased for one of the algorithms. These results indicate that adherence to some commonly promulgated self-care algorithms may increase rather than decrease the number of physician visits.

Activities of Daily Living↗

Clinical algorithms for prehospital cardiac care.

Algorithms for the prehospital management of cardiac arrhythmias were developed and their use by and value to paramedics evaluated. The algorithms, in booklet form, were distributed to half of the Philadelphia paramedic platoons; paramedics in the other platoons followed a narrative protocol that reflected identical contents. An arrhythmia recognition test given 18 months after the algorithm booklets were introduced showed that paramedics who received the booklets scored significantly higher in identifying life-threatening arrhythmias (p = 0.029) than did their counterparts without the booklets. Survival data for 459 patients in ventricular fibrillation treated by paramedics were collected 1 year before and 7 months after the introduction of the algorithm booklets. The paramedics using the algorithms improved their survival rate from 11.25 to 15.1 per cent, while the survival rate for patients treated by paramedics using the narrative protocols decreased from 12.4 to 7.7 per cent. The likelihood of obtaining a ratio of survival odds of this magnitude when there is no true difference is 0.092. Time-to-death was significantly different (p = 0.04) for the two groups of patients. Thus, the use of algorithm booklets as an inexpensive educational aid for paramedics is recommended.

Allied Health Personnel↗

Cluster diversity and entropy on the percolation model: the lattice animal identification algorithm

We present an algorithm to identify and count different lattice animals (LA's) in the site-percolation model. This algorithm allows a definition of clusters based on the distinction of cluster shapes, in contrast with the well-known Hoshen-Kopelman algorithm, in which the clusters are differentiated by their sizes. It consists in coding each unit cell of a cluster according to the nearest neighbors (NN) and ordering the codes in a proper sequence. In this manner, a LA is represented by a specific code sequence. In addition, with some modification the algorithm is capable of differentiating between fixed and free LA's. The enhanced Hoshen-Kopelman algorithm [J. Hoshen, M. W. Berry, and K. S. Minser, Phys. Rev. E 56, 1455 (1997)] is used to compose the set of NN code sequences of each cluster. Using Monte Carlo simulations on planar square lattices up to 2000x2000, we apply this algorithm to the percolation model. We calculate the cluster diversity and cluster entropy of the system, which leads to the determination of probabilities associated with the maximum of these functions. We show that these critical probabilities are associated with the percolation transition and with the complexity of the system.

Journal Article↗

Higher-order force gradient symplectic algorithms

We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 10(3), 10(4), 10(4), and 10(5) better.

Journal Article↗

The use of a computerized algorithm to determine single cardiac cell volumes.

Single cardiac muscles cell volume data have been difficult to obtain, especially because the shape of a cell is quite complex. With the aid of a surface reconstruction method, a cell volume estimation algorithm has been developed that can be used on serial of cells. The cell surface is reconstructed by means of triangular tiles so that the cell is represented as a polyhedron. When this algorithm was tested on computer generated surfaces of a known volume, the difference was less than 1.6%. Serial sections of two phantoms of a known volume were also reconstructed and a comparison of the mathematically derived volumes and the computed volume estimations gave a per cent difference of between 2.8% and 4.1%. Finally cell volumes derived using conventional methods and volumes calculated using the algorithm were compared. The mean atrial muscle cell volume derived using conventional methods was 7752.7 +/- 644.7 micrometers3, while the mean computerized algorithm estimated atrial muscle cell volume was 7110.6 +/- 625.5 micrometers3. For AV bundle cells the mean cell volume obtained by conventional methods was 484.4 +/- 88.8 micrometers3 and the volume derived from the computer algorithm was 506.0 +/- 78.5 micrometers3. The differences between the volumes calculated using conventional methods and the algorithm were not significantly different.

Animals↗

In vivo comparison of different algorithms for the artificial beta-cell.

Using an extracorporeal artificial beta-cell in chronically diabetic dogs, the effects of four different mathematical models of glucose-controlled insulin dosage were compared: the Biostator algorithm (quadratic equation), Toronto algorithm (hyperbolic tangent function), Karlsburg algorithm (modified first-order derivative controller), and Ilmenau algorithm (second-order linear difference equation). The constants of all formulas implemented for the artificial beta-cell were obtained by regression analysis of paired blood glucose and plasma insulin data from normal control animals. Thus, they were biologically equivalent for all formulas. The patterns of blood glucose, insulin doses, and plasma insulin before, during, and after an intravenous glucose infusion test performed during the glucose-controlled insulin infusion showed no significant differences between the experimental groups subjected to the different algorithms. However, in no case were really normal blood glucose response curves restored by the artificial beta-cell. This might be due, first, to the fact that the algorithm parameters were not adapted to the actual individual insulin responsiveness, second, to the unphysiological peripheral venous route of insulin administration, and, third, to the lack of appropriate adaptation of the animals to normoglycemia.

Animals↗

Failure of third-generation implantable cardioverter defibrillators to abort shock therapy for nonsustained ventricular tachycardia due to shortcomings of the VF confirmation algorithm.

Unnecessary shocks by ICDs for rhythms other than sustained VT or VF have been described as the most frequent adverse event in ICD patients. To avoid unnecessary shocks for self-terminating arrhythmias, the third-generation Jewel PCD defibrillators 7202, 7219, and 7220 Plus use a specially designed VF confirmation algorithm after charge end. The purpose of this study was to determine the ability of this VF confirmation algorithm to recognize nonsustained VT, and to analyze the reasons for failure of the PCD device to abort shock therapy for nonsustained VT despite use of this VF confirmation algorithm. Analysis of stored electrograms of electrical events triggering high voltage capacitor charging in the programmed VF zone of the device showed 36 spontaneous episodes of nonsustained VT (227 +/- 21 beats/min) during 18 +/- 7 months follow-up in 15 patients who had a Jewel PCD implanted at our hospital. Intracardiac electrogram recordings and simultaneously retrieved marker channels demonstrated that the ICD shock was appropriately aborted according to the VF confirmation algorithm in 24 (67%) of 36 episodes of nonsustained VT. Twelve episodes (33%) of nonsustained VT, however, were followed by spontaneous ICD shock in 6 (40%) of the 15 study patients. The only reason for all 12 shocks for sustained VT was the inability of the device to recognize the absence of VT after charge end due to shortcomings of the VF confirmation algorithm: 11 of the 12 shocks for nonsustained VT were triggered by the occurrence of paced beats during the VF confirmation period and 1 shock for nonsustained VT was triggered by the occurrence of 2 premature beats after charge end. Thus, better VF confirmation algorithms need to be incorporated in future PCD devices to avoid unnecessary shocks for nonsustained VT.

Defibrillators, Implantable↗

Two-film brachytherapy reconstruction algorithm.

We have developed a new isocentric two-film reconstruction algorithm for brachytherapy seed and needle implants. The algorithm has no requirements that the two films be orthogonal, symmetric, or even be taken in a transverse plane. In addition, there is no requirement that the two films even have the same number of images. We have found removal of these usual constraints useful for head and neck implants where images are often obscured by patient anatomy. The inherent image matching ambiguities associated with traditional two-film techniques are minimized by considering the image end points, rather than just the image centroids. For two films, the new algorithm, which considers all image combinations at one time, matches all the end-point images on one film with those on the other, and then reconstructs the end-point positions of the seeds. The algorithm minimizes the difference between the actual images and the projected images from the reconstructed seeds. The new two-film image matching problem is shown to be equivalent to the well-known assignment problem. For an implant of N seeds, this equivalence allows the two-film problem to be solved by an algorithm (ACM algorithm 548) that scales with a polynomial power of N, rather than N! as is usually assumed. An implant of N seeds can be matched and reconstructed in approximately (N/20)2s on a VAX 11/780.

Brachytherapy↗

An excitation-pattern algorithm for the estimation of (2f1-f2) and (f2-f1) cancellation level and phase.

An excitation-pattern algorithm is described which provides an estimate of cancellation level and phase for the (2f1-f2) and (f2-f1) distortion products. An experiment is first conducted to demonstrate the need for such an algorithm for (f2-f1) level predictions. The results of this experiment, which employed three pairs of primaries having complementary input levels (L1 = 65, L2 = 85 dB; L1 = 85, L2 = 65 dB), do not agree with the predictions of another similar algorithm [E. Zwicker, J. Acoust. Soc. Am. 69, 1410-1413 (1981)]. A new excitation-pattern algorithm is then described. The predicted level behavior for (f2-f1) and (2f1-f2) is more accurate for the proposed algorithm. In addition, an accurate phase estimate is also provided by the new algorithm.

Acoustic Stimulation↗

Greedy Algorithms for Finding a Small Set of Primers Satisfying Cover and Length Resolution Conditions in PCR Experiments.

Selecting a good collection of primers is very important for polymerase chain reaction (PCR) experiments. Most existing algorithms for primer selection are concerned with computing a primer pair for each DNA sequence. In generalizing the arbitrarily primed PCR, etc., to the case that all DNA sequences of target objects are already known, like about 6000 ORFs of yeast, we may design a small set of primers so that all the targets are PCR amplified and resolved electrophoretically in a series of experiments. This is quite useful because deceasing the number of primers greatly reduces the cost of experiments. Pearson et al. (ISMB 1995: 285-291, 1995; Discrete Appl. Math. 71: 231-246, 1996) consider finding a minimum set of primers covering all given DNA sequences, but their method does not meet necessary biological conditions such as primer amplification and electrophoresis resolution. In this paper, based on the modeling and computational complexity analysis by Doi, we propose algorithms for this primer selection problem. These algorithms do not necessarily minimize the number of primers, but, since basic versions of these problems are shown to be computationally intractable, especially even for approximability with the length resolution condition, this is inevitable. In the algorithms, the amplification condition by a primer pair and the length resolution condition by electrophoresis are incorporated. These algorithms are based on the theoretically well-founded greedy algorithm for the set cover in computer science. Preliminary computational results are presented to show the validity of this approach. The number of computed primers is much less than a half of the number of targets, and hence is less than one forth of the number needed in the multiplex PCR.

Journal Article↗

A Greedy Algorithm for Minimizing the Number of Primers in Multiple PCR Experiments.

The selection of a suitable set of primers is very important for polymerase chain reaction (PCR) experiments. Most existing algorithms for primer selection are concerned with producing a primer pair for each DNA sequence. However, when all the DNA sequences of the target objects are already known, like the approximately 6,000 yeast ORFs, we may want to design a small set of primers to PCR amplify all the targets, which can then be resolved electrophoretically in a series of experiments. This would be quite useful, because decreasing the number of primers greatly reduces the cost of an experiment. This paper extends the problem of primer selection for a single experiment presented in Doi and Imai (Genome Informatics, 8:43-52, 1997) to primer selection for multiple PCR experiments, and proposes algorithms for the extended problem. The algorithms design primer sets one at a time. We extend the greedy algorithm for one PCR experiment in (Genome Informatics, 8:43-52, 1997) by handling amplified segments in DNA sequences that have been identified by primer pairs already selected and by changing the priorities in the greedy algorithm. This algorithm is applied to real yeast data. The number of primers equaled 85% of the number of identified DNA sequences, which represented more than 90% of all the target DNA sequences. This is 42% the number of primers needed for multiplex PCR. Furthermore, the length of each primer is less than half the length of multiplex PCR primers so the cost of producing the primers is reduced to 20% of the cost in the multiplex PCR case.

Journal Article↗