A new modulated Hebbian learning rule--biologically plausible method for local computation of a principal subspace

This paper presents one possible implementation of a transformation that performs linear mapping to a lower-dimensional subspace. Principal component subspace will be the one that will be analyzed. Idea implemented in this paper represents generalization of the recently proposed infinity OH neural method for principal component extraction. The calculations in the newly proposed method are performed locally--a feature which is usually considered as desirable from the biological point of view. Comparing to some other wellknown methods, proposed synaptic efficacy learning rule requires less information about the value of the other efficacies to make single efficacy modification. Synaptic efficacies are modified by implementation of Modulated Hebb-type (MH) learning rule. Slightly modified MH algorithm named Modulated Hebb Oja (MHO) algorithm, will be also introduced. Structural similarity of the proposed network with part of the retinal circuit will be presented, too.     

A robust subspace algorithm for principal component analysis

We present a noise robust PCA algorithm which is an extension of the Oja subspace algorithm and allows tuning the noise sensitivity. We derive a loss function which is minimized by this algorithm and interpret it in a noisy PCA setting. Results on the local stability analysis of this algorithm are given and it is shown that the locally stable equilibria are those which minimize the loss function.     

Exploring pleiotropy using principal components

A standard multivariate principal components (PCs) method was utilized to identify clusters of variables that may be controlled by a common gene or genes (pleiotropy). Heritability estimates were obtained and linkage analyses performed on six individual traits (total cholesterol (Chol), high and low density lipoproteins, triglycerides (TG), body mass index (BMI), and systolic blood pressure (SBP)) and on each PC to compare our ability to identify major gene effects. Using the simulated data from Genetic Analysis Workshop 13 (Cohort 1 and 2 data for year 11), the quantitative traits were first adjusted for age, sex, and smoking (cigarettes per day). Adjusted variables were standardized and PCs calculated followed by orthogonal transformation (varimax rotation). Rotated PCs were then subjected to heritability and quantitative multipoint linkage analysis. The first three PCs explained 73% of the total phenotypic variance. Heritability estimates were above 0.60 for all three PCs. We performed linkage analyses on the PCs as well as the individual traits. The majority of pleiotropic and trait-specific genes were not identified. Standard PCs analysis methods did not facilitate the identification of pleiotropic genes affecting the six traits examined in the simulated data set. In addition, genes contributing 20% of the variance in traits with over 0.60 heritability estimates could not be identified in this simulated data set using traditional quantitative trait linkage analyses. Lack of identification of pleiotropic and trait-specific genes in some cases may reflect their low contribution to the traits/PCs examined or more importantly, characteristics of the sample group analyzed, and not simply a failure of the PC approach itself.     

COPD phenotype description using principal components analysis

Background

Airway inflammation in COPD can be measured using biomarkers such as induced sputum and Fe_NO. This study set out to explore the heterogeneity of COPD using biomarkers of airway and systemic inflammation and pulmonary function by principal components analysis (PCA).

Subjects and Methods

In 127 COPD patients (mean FEV₁ 61%), pulmonary function, Fe_NO, plasma CRP and TNF-α, sputum differential cell counts and sputum IL8 (pg/ml) were measured. Principal components analysis as well as multivariate analysis was performed.

Results

PCA identified four main components (% variance): (1) sputum neutrophil cell count and supernatant IL8 and plasma TNF-α (20.2%), (2) Sputum eosinophils % and Fe_NO (18.2%), (3) Bronchodilator reversibility, FEV₁ and IC (15.1%) and (4) CRP (11.4%). These results were confirmed by linear regression multivariate analyses which showed strong associations between the variables within components 1 and 2.

Conclusion

COPD is a multi dimensional disease. Unrelated components of disease were identified, including neutrophilic airway inflammation which was associated with systemic inflammation, and sputum eosinophils which were related to increased Fe_NO. We confirm dissociation between airway inflammation and lung function in this cohort of patients.     

Parallel Analysis: a method for determining significant principal components

Abstract. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.     

A hierarchical method for finding optimal architecture and weights using evolutionary least square based learning

In this paper, we present a novel approach of implementing a combination methodology to find appropriate neural network architecture and weights using an evolutionary least square based algorithm (GALS).1 This paper focuses on aspects such as the heuristics of updating weights using an evolutionary least square based algorithm, finding the number of hidden neurons for a two layer feed forward neural network, the stopping criterion for the algorithm and finally some comparisons of the results with other existing methods for searching optimal or near optimal solution in the multidimensional complex search space comprising the architecture and the weight variables. We explain how the weight updating algorithm using evolutionary least square based approach can be combined with the growing architecture model to find the optimum number of hidden neurons. We also discuss the issues of finding a probabilistic solution space as a starting point for the least square method and address the problems involving fitness breaking. We apply the proposed approach to XOR problem, 10 bit odd parity problem and many real-world benchmark data sets such as handwriting data set from CEDAR, breast cancer and heart disease data sets from UCI ML repository. The comparative results based on classification accuracy and the time complexity are discussed.     

msBayes: Pipeline for testing comparative phylogeographic histories using hierarchical approximate Bayesian computation

Background  

Although testing for simultaneous divergence (vicariance) across different population-pairs that span the same barrier to gene flow is of central importance to evolutionary biology, researchers often equate the gene tree and population/species tree thereby ignoring stochastic coalescent variance in their conclusions of temporal incongruence. In contrast to other available phylogeographic software packages, msBayes is the only one that analyses data from multiple species/population pairs under a hierarchical model.     

A hybrid neural learning algorithm using evolutionary learning and derivative free local search method

In this paper we investigate a hybrid model based on the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. Also we discuss different variants for hybrid models using the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. The Discrete Gradient method has the advantage of being able to jump over many local minima and find very deep local minima. However, earlier research has shown that a good starting point for the discrete gradient method can improve the quality of the solution point. Evolutionary algorithms are best suited for global optimisation problems. Nevertheless they are cursed with longer training times and often unsuitable for real world application. For optimisation problems such as weight optimisation for ANNs in real world applications the dimensions are large and time complexity is critical. Hence the idea of a hybrid model can be a suitable option. In this paper we propose different fusion strategies for hybrid models combining the evolutionary strategy with the discrete gradient method to obtain an optimal solution much quicker. Three different fusion strategies are discussed: a linear hybrid model, an iterative hybrid model and a restricted local search hybrid model. Comparative results on a range of standard datasets are provided for different fusion hybrid models.     

Measuring surface potential components necessary for transmembrane current computation using microfabricated arrays

This study was designed to test the feasibility of using microfabricated electrodes to record surface potentials with sufficiently fine spatial resolution to measure the potential gradients necessary for improved computation of transmembrane current density. To assess that feasibility, we recorded unipolar electrograms from perfused rabbit right ventricular free wall epicardium (n = 6) using electrode arrays that included 25-microm sensors fabricated onto a flexible substrate with 75-microm interelectrode spacing. Electrode spacing was therefore on the size scale of an individual myocyte. Signal conditioning adjacent to the sensors to control lead noise was achieved by routing traces from the electrodes to the back side of the substrate where buffer amplifiers were located. For comparison, recordings were also made using arrays built from chloridized silver wire electrodes of either 50-microm (fine wire) or 250-microm (coarse wire) diameters. Electrode separations were necessarily wider than with microfabricated arrays. Comparable signal-to-noise ratios (SNRs) of 21.2 +/- 2.2, 32.5 +/- 4.1, and 22.9 +/- 0.7 for electrograms recorded using microfabricated sensors (n = 78), fine wires (n = 78), and coarse wires (n = 78), respectively, were found. High SNRs were maintained in bipolar electrograms assembled using spatial combinations of the unipolar electrograms necessary for the potential gradient measurements and in second-difference electrograms assembled using spatial combinations of the bipolar electrograms necessary for surface Laplacian (SL) measurements. Simulations incorporating a bidomain representation of tissue structure and a two-dimensional network of guinea pig myocytes prescribed following the Luo and Rudy dynamic membrane equations were completed using 12.5-microm spatial resolution to assess contributions of electrode spacing to the potential gradient and SL measurements. In those simulations, increases in electrode separation from 12.5 to 75.0, 237.5, and 875.0 microm, which were separations comparable to the finest available with our microfabricated, fine wire, and coarse wire arrays, led to 10%, 42%, and 81% reductions in maximum potential gradients and 33%, 76%, and 96% reductions in peak-to-peak SLs. Maintenance of comparable SNRs for source electrograms was therefore important because microfabrication provides a highly attractive methods to achieve spatial resolutions necessary for improved computation of transmembrane current density.     

Improve survival prediction using principal components of gene expression data

The purpose of many microarray studies is to find the association between gene expression and sample characteristics such as treatment type or sample phenotype. There has been a surge of efforts developing different methods for delineating the association. Aside from the high dimensionality of microarray data, one well recognized challenge is the fact that genes could be complicatedly inter-related, thus making many statistical methods inappropriate to use directly on the expression data. Multivariate methods such as principal component analysis （PCA） and clustering are often used as a part of the effort to capture the gene correlation, and the derived components or clusters are used to describe the association between gene expression and sample phenotype. We propose a method for patient population dichotomization using maximally selected test statistics in combination with the PCA method, which shows favorable results. The proposed method is compared with a currently well-recognized method.     

Joint modelling of paired sparse functional data using principal components

We propose a modelling framework to study the relationship betweentwo paired longitudinally observed variables. The data for eachvariable are viewed as smooth curves measured at discrete time-pointsplus random errors. While the curves for each variable are summarizedusing a few important principal components, the associationof the two longitudinal variables is modelled through the associationof the principal component scores. We use penalized splinesto model the mean curves and the principal component curves,and cast the proposed model into a mixed-effects model frameworkfor model fitting, prediction and inference. The proposed methodcan be applied in the difficult case in which the measurementtimes are irregular and sparse and may differ widely acrossindividuals. Use of functional principal components enhancesmodel interpretation and improves statistical and numericalstability of the parameter estimates.     

A hierarchical method for molecular docking using cloud computing

Discovering small molecules that interact with protein targets will be a key part of future drug discovery efforts. Molecular docking of drug-like molecules is likely to be valuable in this field; however, the great number of such molecules makes the potential size of this task enormous. In this paper, a method to screen small molecular databases using cloud computing is proposed. This method is called the hierarchical method for molecular docking and can be completed in a relatively short period of time. In this method, the optimization of molecular docking is divided into two subproblems based on the different effects on the protein–ligand interaction energy. An adaptive genetic algorithm is developed to solve the optimization problem and a new docking program (FlexGAsDock) based on the hierarchical docking method has been developed. The implementation of docking on a cloud computing platform is then discussed. The docking results show that this method can be conveniently used for the efficient molecular design of drugs.     

Discriminant analysis of event-related potential curves using smoothed principal components

Principal component analysis enhanced by the use of smoothing is used in conjunction with discriminant analysis techniques to devise a statistical classification method for the analysis of event-related potential data. A training set of premedication potentials collected from adolescents with attention-deficit hyperactive disorder (ADHD) is used to predict whether adolescents from an independent subject group will respond to long-term medication. Comparison of outcome prediction rates demonstrates that this method, which uses information from the whole ERP curve, is superior to the classification technique currently used by clinicians, which is based on a single ERP curve feature. The need to administer an initial dose of medication to classify patients is also eliminated.     

Robust functional estimation using the median and spherical principal components

We present robust estimators for the mean and the principalcomponents of a stochastic process in . Robustness and asymptotic properties of theestimators are studied theoretically, by simulation and by example.It is shown that the proposed estimators are generally morerobust to outliers than the commonly used sample mean and principalcomponents, although their properties depend on the spacingsof the eigenvalues of the covariance function.     

一种基于关键路径法的DNA计算用寡核苷酸序列设计算法

在原有的生物大分子序列比对算法的基础上,结合图论中的关健路径法,提出了一种新的计算两寡核苷酸序列间最大配对程度的算法。采用此算法结合生成并测试的方法,能够寻找给定长度的一组适用于DNA计算的寡核苷酸序列。同时采用DNA芯片杂交方法验证了用该算法设计的一组序列的杂交特异性。     

The use of the method of principal components for phenogenetic analysis of the integral domestication trait

In the course of long-term experiment on domestication of silver fox, it was necessary to determine the most important behavioral features, selection for which would give domestication effect. The mathematical method of principal components was used for the analysis of 20 fox behavior traits. The combination of the initial traits which reflected the structure of the integral trait, i.e. domesticated type of behavior, was determined. The practical use of this combination seems to more adequately estimate the level of domestication of a given animal, which is indispensable for subsequent effective selection.     

Investigation of inversion polymorphisms in the human genome using principal components analysis

Despite the significant advances made over the last few years in mapping inversions with the advent of paired-end sequencing approaches, our understanding of the prevalence and spectrum of inversions in the human genome has lagged behind other types of structural variants, mainly due to the lack of a cost-efficient method applicable to large-scale samples. We propose a novel method based on principal components analysis (PCA) to characterize inversion polymorphisms using high-density SNP genotype data. Our method applies to non-recurrent inversions for which recombination between the inverted and non-inverted segments in inversion heterozygotes is suppressed due to the loss of unbalanced gametes. Inside such an inversion region, an effect similar to population substructure is thus created: two distinct "populations" of inversion homozygotes of different orientations and their 1:1 admixture, namely the inversion heterozygotes. This kind of substructure can be readily detected by performing PCA locally in the inversion regions. Using simulations, we demonstrated that the proposed method can be used to detect and genotype inversion polymorphisms using unphased genotype data. We applied our method to the phase III HapMap data and inferred the inversion genotypes of known inversion polymorphisms at 8p23.1 and 17q21.31. These inversion genotypes were validated by comparing with literature results and by checking Mendelian consistency using the family data whenever available. Based on the PCA-approach, we also performed a preliminary genome-wide scan for inversions using the HapMap data, which resulted in 2040 candidate inversions, 169 of which overlapped with previously reported inversions. Our method can be readily applied to the abundant SNP data, and is expected to play an important role in developing human genome maps of inversions and exploring associations between inversions and susceptibility of diseases.     

Discriminant analysis of principal components: a new method for the analysis of genetically structured populations

Background

The etiology of complex diseases is due to the combination of genetic and environmental factors, usually many of them, and each with a small effect. The identification of these small-effect contributing factors is still a demanding task. Clearly, there is a need for more powerful tests of genetic association, and especially for the identification of rare effects

Results

We introduce a new genetic association test based on symbolic dynamics and symbolic entropy. Using a freely available software, we have applied this entropy test, and a conventional test, to simulated and real datasets, to illustrate the method and estimate type I error and power. We have also compared this new entropy test to the Fisher exact test for assessment of association with low-frequency SNPs. The entropy test is generally more powerful than the conventional test, and can be significantly more powerful when the genotypic test is applied to low allele-frequency markers. We have also shown that both the Fisher and Entropy methods are optimal to test for association with low-frequency SNPs (MAF around 1-5%), and both are conservative for very rare SNPs (MAF<1%)

Conclusions

We have developed a new, simple, consistent and powerful test to detect genetic association of biallelic/SNP markers in case-control data, by using symbolic dynamics and symbolic entropy as a measure of gene dependence. We also provide a standard asymptotic distribution of this test statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. The entropy test is generally as good or even more powerful than the conventional and Fisher tests. Furthermore, the entropy test is more computationally efficient than the Fisher's Exact test, especially for large number of markers. Therefore, this entropy-based test has the advantage of being optimal for most SNPs, regardless of their allele frequency (Minor Allele Frequency (MAF) between 1-50%). This property is quite beneficial, since many researchers tend to discard low allele-frequency SNPs from their analysis. Now they can apply the same statistical test of association to all SNPs in a single analysis., which can be especially helpful to detect rare effects.     

Neural mechanisms for learning hierarchical structures of information

Spatial and temporal information from the environment is often hierarchically organized, so is our knowledge formed about the environment. Identifying the meaningful segments embedded in hierarchically structured information is crucial for cognitive functions, including visual, auditory, motor, memory, and language processing. Segmentation enables the grasping of the links between isolated entities, offering the basis for reasoning and thinking. Importantly, the brain learns such segmentation without external instructions. Here, we review the underlying computational mechanisms implemented at the single-cell and network levels. The network-level mechanism has an interesting similarity to machine-learning methods for graph segmentation. The brain possibly implements methods for the analysis of the hierarchical structures of the environment at multiple levels of its processing hierarchy.     

Age-related changes in human body proportions studied by the method of principal components

The method for analysis of the ontogenetic changes of size and shape based on the decomposition of Kullback divergence into parts corresponding to the principal components, found for intragroup variability of signs is suggested. The application of this method is illustrated by the analysis of age changes of body proportions for boys 3-17 years old. Before the pubertal period the stable tendency to a relative lengthening of extremities which changes to a contrast one at age of 12-14 has been pointed out. The definitive differences of proportions to a considerable extent is determined by variability of biological age at the group of children.