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.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

An HPLC system for the automatic sampling and analysis of time-series kinetic studies

Robotics were used to automate a high performance liquid chromatography (HPLC) system which was designed for the unattended sampling and analysis of time-series kinetic studies. The system allowed for the direct injection of samples containing whole cells and particulates witout plugging the analytical column. Coarse debris was removed from the injected sample by a 0.5 μm inline filter. Finer particulates were removed by a guard column that was layered with three different size packing resins. To demonstrate the system's capabilities, data are presented from an 8 day progress curve showing the anaerobic biodegradation of p-cresol by a sulfate-reducing enrichment. On fitting the data to the Michaelis-Menten equation by nonlinear regression, the apparent kinetic constants K_m and V_max were calculated to be 126 μM and 4.0 μM/h, respectively, for p-cresol metabolism by the enrichment.     

A robust numerical algorithm for studying biomolecular transport processes

We present a numerical algorithm that is well suited for the study of biomolecular transport processes. In the algorithm a continuous Markov process is discretized as a jump process and the jump rates are derived from local solutions of the continuous system. Consequently, the algorithm has two advantages over standard numerical methods: (1) it preserves detailed balance for equilibrium processes, (2) it is able to handle discontinuous potentials. The formulation of the algorithm also allows us to calculate the effective diffusion coefficient or, equivalently, the randomness parameter. We provide several simple examples of how to implement the algorithm. All the MATLAB functions files needed to reproduce the results presented in the article are available from www.amath.unc.edu/Faculty/telston/matlab_functions.     

A robust and efficient automated docking algorithm for molecular recognition.

A completely automated method is described for determining the most likely mode of binding of two (macro)molecules from the knowledge of their three-dimensional structures alone. The method is based on well-known graph theoretical techniques and has been used successfully to determine and rationalize the binding of a number of known macromolecular complexes. In this article we present results for a special case of the general molecular recognition problem--given the information concerning the particular atoms involved in the binding for one of the molecules, the algorithm can correctly identify the corresponding (contacting) atoms of the other molecule. The approach used can be easily extended to the general molecular recognition problem and requires the extraction of maximal common subgraphs. In these studies the docking of the macromolecules was achieved without the aid of computer graphics or other visual aids. The algorithm has been used to determine the correct mode of binding of a protein antigen to an antibody in approximately 100 min on a DEC micro VAX 3600.     

A parallel algorithm for robust fault detection in semiconductor manufacturing processes

The semiconductor manufacturing consists of a number of processes, and even a small fault occurring at any point can damage the product quality. The fast and accurate detection of such faults is essential to maintain high manufacturing yields. In this paper, we propose a parallel algorithm for fault detection in semiconductor manufacturing processes. The algorithm is a modification of the discord detection algorithm called HOT SAX, which adopted the SAX representation of time-series for efficient storage and computation. We first propose a sequential algorithm and then extend it to a parallel version. We evaluate our algorithm through experiments using the data obtained from a real-world semiconductor plasma etching process. As a result, our fault detection algorithm achieved 100 % accuracy without any false positive or false negative.     

A robust statistical method for association-based eQTL analysis

Background

It has been well established that theoretical kernel for recently surging genome-wide association study (GWAS) is statistical inference of linkage disequilibrium (LD) between a tested genetic marker and a putative locus affecting a disease trait. However, LD analysis is vulnerable to several confounding factors of which population stratification is the most prominent. Whilst many methods have been proposed to correct for the influence either through predicting the structure parameters or correcting inflation in the test statistic due to the stratification, these may not be feasible or may impose further statistical problems in practical implementation.

Methodology

We propose here a novel statistical method to control spurious LD in GWAS from population structure by incorporating a control marker into testing for significance of genetic association of a polymorphic marker with phenotypic variation of a complex trait. The method avoids the need of structure prediction which may be infeasible or inadequate in practice and accounts properly for a varying effect of population stratification on different regions of the genome under study. Utility and statistical properties of the new method were tested through an intensive computer simulation study and an association-based genome-wide mapping of expression quantitative trait loci in genetically divergent human populations.

Results/Conclusions

The analyses show that the new method confers an improved statistical power for detecting genuine genetic association in subpopulations and an effective control of spurious associations stemmed from population structure when compared with other two popularly implemented methods in the literature of GWAS.     

A robust system for production of minicircle DNA vectors

Minicircle DNA vectors allow sustained transgene expression in quiescent cells and tissues. To improve minicircle production, we genetically modified Escherichia coli to construct a producer strain that stably expresses a set of inducible minicircle-assembly enzymes, ΦC31 integrase and I-SceI homing endonuclease. This bacterial strain produces purified minicircles in a time frame and quantity similar to those of routine plasmid DNA preparation, making it feasible to use minicircles in place of plasmids in mammalian transgene expression studies.     

A fast and robust hepatocyte quantification algorithm including vein processing

Background  

Quantification of different types of cells is often needed for analysis of histological images. In our project, we compute the relative number of proliferating hepatocytes for the evaluation of the regeneration process after partial hepatectomy in normal rat livers.     

A fast and robust method for automated analysis of axonal transport

Cargo movement along axons and dendrites is indispensable for the survival and maintenance of neuronal networks. Key parameters of this transport such as particle velocities and pausing times are often studied using kymograph construction, which converts the transport along a line of interest from a time-lapse movie into a position versus time image. Here we present a method for the automatic analysis of such kymographs based on the Hough transform, which is a robust and fast technique to extract lines from images. The applicability of the method was tested on simulated kymograph images and real data from axonal transport of synaptophysin and tetanus toxin as well as the velocity analysis of synaptic vesicle sharing between adjacent synapses in hippocampal neurons. Efficiency analysis revealed that the algorithm is able to detect a wide range of velocities and can be used at low signal-to-noise ratios. The present work enables the quantification of axonal transport parameters with high throughput with no a priori assumptions and minimal human intervention.     

An improved algorithm for the detection of dynamical interdependence in bivariate time-series

 We describe a new algorithm for the detection of dynamical interdependence in bivariate time-series data sets. By using geometrical and dynamical arguments, we produce a method that can detect dynamical interdependence in weakly coupled systems where previous techniques have failed. We illustrate this by comparison of our algorithm with another commonly used technique when applied to a system of coupled Hénon maps. In addition, an improvement of ∼20% in the detection rate is observed when the technique is applied to human scalp EEG data, as compared with existing techniques. Such an improvement may assist an understanding of the role of large-scale nonlinear processes in normal brain function. Received: 28 December 2001 / Accepted in revised form: 2 October 2002 Correspondence to: J.R. Terry (e-mail: J.R.Terry@lboro.ac.uk) Acknowledgements. JRT acknowledges the support of the Royal Society and the London Mathematical Society for jointly funding a trip to the School of Physics at the University of Sydney and The Brain Dynamics Centre at Westmead Hospital, Sydney. The authors thank Professor Peter Robinson for useful conversations and the provision of local facilities within the School of Physics during the visit of JRT. The support of the EPSRC via Grant GR/N00340 is also acknowledged. MJB is a recipient of a University Postgraduate Award from the University of Sydney.     

A Bregman-proximal point algorithm for robust non-negative matrix factorization with possible missing values and outliers - application to gene expression analysis

Background

Non-Negative Matrix factorization has become an essential tool for feature extraction in a wide spectrum of applications. In the present work, our objective is to extend the applicability of the method to the case of missing and/or corrupted data due to outliers.

Results

An essential property for missing data imputation and detection of outliers is that the uncorrupted data matrix is low rank, i.e. has only a small number of degrees of freedom. We devise a new version of the Bregman proximal idea which preserves nonnegativity and mix it with the Augmented Lagrangian approach for simultaneous reconstruction of the features of interest and detection of the outliers using a sparsity promoting ? ₁ penality.

Conclusions

An application to the analysis of gene expression data of patients with bladder cancer is finally proposed.

     

A sampling algorithm for segregation analysis

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated.     

A robust and tunable system for targeted cell ablation in developing embryos

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