Mathematical analyses of the interference phenomenon of tobacco mosaic virus: experimental tests.
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Computers↗
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Results for “Mathematical Computing”
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Computing probabilities of homozygosity by descent.
A person is autozygous at a locus if the person inherits the same allele twice identical by descent along two distinct paths from the same ancestor. Autozygosity is a common cause of recessive diseases in inbred populations. Homozygosity mapping uses this fact to locate the genes that cause recessive diseases. The probability of autozygosity can be used to estimate the probability of a true positive and of a false positive in homozygosity mapping. Thompson [1994] and Guo [1997] therefore studied the problem of computing the prior, unconditional (multilocus) probability of autozygosity (MPA). I consider a different quantity: the interval probability of autozygosity (IPA). The two measures are identical in the single-locus case. IPA has two notable advantages over MPA: 1. IPA does not include the possibility of heterozygous regions between the homozygous markers. 2. IPA can be computed in time that is polynomial in the pedigree size. My polynomial-time algorithm for the single-locus case solves a problem mentioned by Guo. I implemented a program to compute the IPA. The contribution of this work is the application of basic, abstract methods from computer science to address a problem in genetics.
Algorithms↗
Bootstrapping the lexicon: a computational model of infant speech segmentation.
Prelinguistic infants must find a way to isolate meaningful chunks from the continuous streams of speech that they hear. BootLex, a new model which uses distributional cues to build a lexicon, demonstrates how much can be accomplished using this single source of information. This conceptually simple probabilistic algorithm achieves significant segmentation results on various kinds of language corpora - English, Japanese, and Spanish; child- and adult-directed speech, and written texts; and several variations in coding structure - and reveals which statistical characteristics of the input have an influence on segmentation performance. BootLex is then compared, quantitatively and qualitatively, with three other groups of computational models of the same infant segmentation process, paying particular attention to functional characteristics of the models and their similarity to human cognition. Commonalities and contrasts among the models are discussed, as well as their implications both for theories of the cognitive problem of segmentation itself, and for the general enterprise of computational cognitive modeling.
Algorithms↗
MBEToolbox: a MATLAB toolbox for sequence data analysis in molecular biology and evolution.
BACKGROUND: MATLAB is a high-performance language for technical computing, integrating computation, visualization, and programming in an easy-to-use environment. It has been widely used in many areas, such as mathematics and computation, algorithm development, data acquisition, modeling, simulation, and scientific and engineering graphics. However, few functions are freely available in MATLAB to perform the sequence data analyses specifically required for molecular biology and evolution. RESULTS: We have developed a MATLAB toolbox, called MBEToolbox, aimed at filling this gap by offering efficient implementations of the most needed functions in molecular biology and evolution. It can be used to manipulate aligned sequences, calculate evolutionary distances, estimate synonymous and nonsynonymous substitution rates, and infer phylogenetic trees. Moreover, it provides an extensible, functional framework for users with more specialized requirements to explore and analyze aligned nucleotide or protein sequences from an evolutionary perspective. The full functions in the toolbox are accessible through the command-line for seasoned MATLAB users. A graphical user interface, that may be especially useful for non-specialist end users, is also provided. CONCLUSION: MBEToolbox is a useful tool that can aid in the exploration, interpretation and visualization of data in molecular biology and evolution. The software is publicly available at http://web.hku.hk/~jamescai/mbetoolbox/ and http://bioinformatics.org/project/?group_id=454
Algorithms↗
Parallel computing applied to breeding value estimation in dairy cattle.
Continuous genetic evaluation of dairy cattle with test-day models is desired in Finland. However, the computing time for the genetic evaluation is 4 d and exceeds the minimum of a weekend. Three parallel implementations of the preconditioned conjugate gradient iterative solver were programmed and compared to identify the best strategy for solving mixed model equations using parallel computing. The programs were used to solve two random regression test-day models with approximately 7.28 and 49.9 million unknowns. The latter model will be used in the Finnish dairy cattle evaluation. Computing times for the smaller model with the four processors available were 52, 32, and 27% of the single processor program when the complexity of the parallel program was increased. In practice, the best program required the most programming because the other parallel programs could not solve the larger model because of excess memory requirements. Parallel computing with four processors reduced the time to obtain solutions of Finnish dairy cattle evaluations to under 2 d. Benefit from parallel computing will be increased if amount of computing memory is increased.
Animals↗
Mathematical curves for the description of input and output variables of the daily production process in aviary housing systems for laying hens.
The objectives of this study were 1) to compute appropriate mathematical curves that describe the daily production process by the input variables daily feed consumption, water consumption, ambient temperature, and output variables hen-day egg production, egg weight, second grade eggs, floor eggs, cumulative mortality, body weight, and flock uniformity; and 2) to obtain insights into the daily variations in these variables, in order to support the poultry farmer with an aviary housing system in his daily management. Literature and research data attained from six unmolted flocks that were housed in aviary systems were used to formulate the mathematical curves. The curves were a function of the number of days in the laying period. Curves for cumulative mortality, hen-day egg production, egg weight, body weight, and percentage of floor eggs described individual flock results well (0.72 < R2adj < 1.00). The coefficients of determination for feed consumption, water consumption, flock uniformity, and percentage of second grade eggs were in general low (0.33 < R2adj < 0.54), which implies that the form of the curve differs between flocks. Egg weight, body weight, cumulative mortality, and hen-day egg production had the lowest minimum coefficients of variation (0.8 to 1.9), followed by feed consumption, water consumption, and flock uniformity (2.8 to 3.6). Ambient temperature, percentage floor eggs, and percentage of second grade eggs had the highest minimum coefficients of variation (4.8 to 9.1).
Animals↗
[Simulation of the hippocampal theta rhythm].
Centre of Theoretical and Computational Neuroscience, University of Plymouth, UK Basing on the hypothesis about the mechanisms of the theta rhythm generation, the article presents mathematical and computational models of theta activity in the hippocampus. The problem of the theta rhythm modeling is nontrivial because the slow theta oscillations (about 5 Hz) should be generated by a neural system composed of frequently firing neural populations. We studied a model of neural pacemakers in the septum. In this model, the pacemaker follows the frequency of the external signal if this frequency does not deviate too far from the natural frequency of the pacemaker, otherwise the pacemaker returns to the frequency of its own oscillations. These results are in agreement with the experimental records of medial septum neurons. Our model of the septal pacemaker of the theta rhythm is based on the hypothesis that the hippocampal theta appears as a result of the influence of the assemblies of neurons in the medial septum which are under control of pacemaker neurons. Though the model of the pacemaker satisfies many experimental facts, the synchronization of activity in different neural assemblies of the model is not as strong as it should be. Another model of the theta generation is based on the anatomical data about the existence of the inhibitory GABAergic loop between the medial septum and the hippocampus. This model shows stable oscillations at the frequency of the theta rhythm in a broad range of parameter values. It also provides explanation to the experimental data about the variation of the frequency and the amplitude of the theta rhythm under different external stimulations of the system. The role of the theta rhythm for information processing in the hippocampus is discussed.
Computer Simulation↗
Computer packages C.A.MAN (computer assisted mixture analysis) and Dismap.
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Algorithms↗
[Computing the confidence limits for a percentage of a binomial population].
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Humans↗
[Mathematical analysis of curves of labelled mitoses].
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Cells, Cultured↗
Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors.
Multivariable regression models are powerful tools that are used frequently in studies of clinical outcomes. These models can use a mixture of categorical and continuous variables and can handle partially observed (censored) responses. However, uncritical application of modelling techniques can result in models that poorly fit the dataset at hand, or, even more likely, inaccurately predict outcomes on new subjects. One must know how to measure qualities of a model's fit in order to avoid poorly fitted or overfitted models. Measurement of predictive accuracy can be difficult for survival time data in the presence of censoring. We discuss an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities. Both types of predictive accuracy should be unbiasedly validated using bootstrapping or cross-validation, before using predictions in a new data series. We discuss some of the hazards of poorly fitted and overfitted regression models and present one modelling strategy that avoids many of the problems discussed. The methods described are applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes. Methods are illustrated with a survival analysis in prostate cancer using Cox regression.
Clinical Trials as Topic↗
A general statistical analysis for fMRI data.
We propose a method for the statistical analysis of fMRI data that seeks a compromise between efficiency, generality, validity, simplicity, and execution speed. The main differences between this analysis and previous ones are: a simple bias reduction and regularization for voxel-wise autoregressive model parameters; the combination of effects and their estimated standard deviations across different runs/sessions/subjects via a hierarchical random effects analysis using the EM algorithm; overcoming the problem of a small number of runs/session/subjects using a regularized variance ratio to increase the degrees of freedom.
Algorithms↗
Voxel-based morphometry using the RAVENS maps: methods and validation using simulated longitudinal atrophy.
Statistical analysis of anatomical maps in a stereotaxic space has been shown to be a useful tool in population-based studies for quantifying local anatomical differences or changes, without a priori assumptions about the location and extent of the regions of interest. This paper presents an extension and validation of a previously published methodology, referred to as RAVENS, for characterizing regional atrophy in the brain. A new method for elastic, volume-preserving spatial normalization, which allows for accurate quantification of very localized atrophy, is used. The RAVENS methodology was tested on images with simulated atrophy within two gyri: precentral and superior temporal. It was found to accurately determine the regions of atrophy, despite their localized nature and the interindividual variability of cortical structures. Moreover, it was found to perform substantially better than the voxel-based morphology method of SPM'99. Improved sensitivity was achieved at the expense of human effort involved in defining a number of sulcal curves that serve as constraints on the 3D elastic warping.
Atrophy↗
An immune algorithm for resolution of multicomponent overlapping chromatograms.
A novel immune algorithm for resolution and quantitative determination of the components in overlapping chromatograms was proposed by imitating biological immune systems. The algorithm takes an overlapping chromatogram as its input and subtracts the chromatograms of standard samples from the input by iteration of a network. When the residual does not change, the network will converge and chromatographic information of the components in overlapping chromatogram will be obtained. Both simulated and experimental data sets were investigated by the method. Results showed that both resolved results and recoveries of quantitative determination are satisfactory. Comparing with conventional least-square method, the immune algorithm is fast in calculation.
Algorithms↗
Computer-assisted assessment of one-handed knot tying skills performed within various contexts: a construct validity study.
BACKGROUND: The widespread use of computer-assisted assessment of technical proficiency in surgical residents shows the need for further investigations of the construct validity of these devices (eg, hand motion analysis) before implementation into competency testing. METHODS: Thirty general surgery residents performed 1-handed knot tying in 2 contexts: superficial and deep. The Imperial College Surgical Assessment Device (ICSAD) was used to evaluate performance. It was hypothesized that senior residents (postgraduate year [PGY] 4-5) would perform better then junior residents (PGY 1-3) and that the superficial version of the skill would be easier than the deep. RESULTS: Technical efficiency scores were better for seniors than for juniors (P < .001) and on the superficial versus the deep model (P < .001). Both groups were equally affected by the contextual changes to the skill, suggesting a consistent impact on the skill-specific movement patterns. CONCLUSIONS: Additional evidence for the validity of ICSAD as a competency assessment tool has been shown. First, it distinguished senior and junior residents. Second, it discerned differences on the same skill performed in 2 different contexts.
Clinical Competence↗
A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone.
Targeted remodeling is activated by fatigue microcracks and plays an important role in maintaining bone integrity. It is widely believed that fluid flow-induced shear stress plays a major role in modulating the mechanotransduction process. Therefore, it is likely that fluid flow-induced shear stress plays a major role in the initiation of the repair of fatigue damage. Since no in vivo measurements of fluid flow within bone exist, computational and mathematical models must be employed to investigate the fluid flow field and the shear stress occurring within cortical bone. We developed a computational fluid dynamic model of cortical bone to examine the effect of a fatigue microcrack on the fluid flow field. Our results indicate that there are alterations in the fluid flow field as far as 150 microm away from the crack, and that at distances farther than this, the fluid flow field is similar to the fluid flow field of intact bone. Through the crack and immediately above and below it, the fluid velocity is higher, while at the lateral edges it is lower than that calculated for the intact model, with a maximum change of 29%. Our results suggest that the presence of a fatigue microcrack can alter the shear stress in regions near the crack. These alterations in shear stress have the potential to significantly alter mechanotransduction and may play a role in the initiation of the repair of fatigue microcracks.
Biomechanical Phenomena↗
Wavelet variance components in image space for spatiotemporal neuroimaging data.
Neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This allows inferences to be made about the signal estimates and resulting conclusions to be drawn about the underlying data. It can often be advantageous to interrogate temporal models after spatial transformation of the data into the wavelet domain. Wavelet bases provide a multiresolution decomposition of the spatial data dimension and an ensuing reduction in spatial correlation. However, widespread acceptance of these wavelet techniques has been hampered by the limited ability to reconstruct both parametric and error estimates into the image domain after analysis of temporal models in the wavelet domain. This paper introduces a derivation and a fast implementation of a method for the calculation of the variance of the parametric images obtained from wavelet filters. The technique is proposed for a class of estimators that have been shown to be useful in neuroimaging studies. The techniques are demonstrated for both functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) data sets.
Analysis of Variance↗
The neuroanatomy of general intelligence: sex matters.
We examined the relationship between structural brain variation and general intelligence using voxel-based morphometric analysis of MRI data in men and women with equivalent IQ scores. Compared to men, women show more white matter and fewer gray matter areas related to intelligence. In men IQ/gray matter correlations are strongest in frontal and parietal lobes (BA 8, 9, 39, 40), whereas the strongest correlations in women are in the frontal lobe (BA10) along with Broca's area. Men and women apparently achieve similar IQ results with different brain regions, suggesting that there is no singular underlying neuroanatomical structure to general intelligence and that different types of brain designs may manifest equivalent intellectual performance.
Adolescent↗