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.     

Analysis of confocal images using variable-width line profiles

A line profile of fluorescent intensities in confocal images is frequently examined. We have developed the computer software tool to analyse the profiles of intensities of fluorescent probes in confocal images. The software averages neighbouring pixels, adjacent to the central line, without reducing the spatial resolution of the image. As an experimental model, we have used the skeletal muscle fibre isolated from the rat skeletal muscle extensor digitorum brevis. As a marker of myofibrils' structure, we have used phalloidin–rhodamine staining and the anti-TIM antibody to label mitochondria. We also tested the distribution of the protein kinase B/Akt. Since signalling is ordered in modules and large protein complexes appear to direct signalling to organelles and regulate specific physiological functions, a software tool to analyse such complexes in fluorescent confocal images is required. The software displays the image, and the user defines the line for analysis. The image is rotated by the angle of the line. The line profile is calculated by averaging one dimension of the cropped rotated image matrix. The spatial resolution in averaged line profile is not decreased compared with single-pixel line profile, which was confirmed by the discrete Fourier transform computed with a fast Fourier transform algorithm. We conclude that the custom software tool presented here is a useful tool to analyse line profiles of fluorescence intensities in confocal images.     

Stationarity stopping criterion for matching pursuit��framework and encephalographic illustration

We present a new stopping criterion for the matching pursuit (MP) algorithm, based on evaluating stationarity of the residua of the consecutive MP iterations. The new stopping criterion is based on a model of a nonstationary signal, which assumes that the part of the signal that is of interest is nonstationary and contaminated by a weakly stationary noise. Mean- and variance-stationarity of the residua obtained from each step of MP is evaluated by means of dedicated statistical tests-the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test and the White test, respectively. We illustrate the proposed concept by an example in which we analyse magnetoencephalographic (MEG) data.     

The ‘39 steps’: an algorithm for performing statistical analysis of data on energy intake and expenditure

The epidemics of obesity and diabetes have aroused great interest in the analysis of energy balance, with the use of organisms ranging from nematode worms to humans. Although generating energy-intake or -expenditure data is relatively straightforward, the most appropriate way to analyse the data has been an issue of contention for many decades. In the last few years, a consensus has been reached regarding the best methods for analysing such data. To facilitate using these best-practice methods, we present here an algorithm that provides a step-by-step guide for analysing energy-intake or -expenditure data. The algorithm can be used to analyse data from either humans or experimental animals, such as small mammals or invertebrates. It can be used in combination with any commercial statistics package; however, to assist with analysis, we have included detailed instructions for performing each step for three popular statistics packages (SPSS, MINITAB and R). We also provide interpretations of the results obtained at each step. We hope that this algorithm will assist in the statistically appropriate analysis of such data, a field in which there has been much confusion and some controversy.     

Parametric proportional hazards model for mapping genomic imprinting of survival traits

A number of imprinted genes have been observed in plants, animals and humans. They not only control growth and developmental traits, but may also be responsible for survival traits. Based on the Cox proportional hazards (PH) model, we constructed a general parametric model for dissecting genomic imprinting, in which a baseline hazard function is selectable for fitting the effects of imprinted quantitative trait loci (iQTL) genotypes on the survival curve. The expectation–maximisation (EM) algorithm is derived for solving the maximum likelihood estimates of iQTL parameters. The imprinting patterns of the detected iQTL are statistically tested under a series of null hypotheses. The Bayesian information criterion (BIC) model selection criterion is employed to choose an optimal baseline hazard function with maximum likelihood and parsimonious parameterisation. We applied the proposed approach to analyse the published data in an F₂ population of mice and concluded that, among five commonly used survival distributions, the log-logistic distribution is the optimal baseline hazard function for the survival time of hyperoxic acute lung injury (HALI). Under this optimal model, five QTL were detected, among which four are imprinted in different imprinting patterns.     

Exploring the solution space of sorting by reversals, with experiments and an application to evolution

In comparative genomics, algorithms that sort permutations by reversals are often used to propose evolutionary scenarios of rearrangements between species. One of the main problems of such methods is that they give one solution while the number of optimal solutions is huge, with no criteria to discriminate among them. Bergeron et al. started to give some structure to the set of optimal solutions, in order to be able to deliver more presentable results than only one solution or a complete list of all solutions. However, no algorithm exists so far to compute this structure except through the enumeration of all solutions, which takes too much time even for small permutations. Bergeron et al. state as an open problem the design of such an algorithm. We propose in this paper an answer to this problem, that is, an algorithm which gives all the classes of solutions and counts the number of solutions in each class, with a better theoretical and practical complexity than the complete enumeration method. We give an example of how to reduce the number of classes obtained, using further constraints. Finally, we apply our algorithm to analyse the possible scenarios of rearrangement between mammalian sex chromosomes.     

Multi-objective workflow scheduling in Amazon EC2

Nowadays, scientists and companies are confronted with multiple competing goals such as makespan in high-performance computing and economic cost in Clouds that have to be simultaneously optimised. Multi-objective scheduling of scientific applications in these systems is therefore receiving increasing research attention. Most existing approaches typically aggregate all objectives in a single function, defined a-priori without any knowledge about the problem being solved, which negatively impacts the quality of the solutions. In contrast, Pareto-based approaches having as outcome a set of (nearly) optimal solutions that represent a tradeoff among the different objectives, have been scarcely studied. In this paper, we analyse MOHEFT, a Pareto-based list scheduling heuristic that provides the user with a set of tradeoff optimal solutions from which the one that better suits the user requirements can be manually selected. We demonstrate the potential of our method for multi-objective workflow scheduling on the commercial Amazon EC2 Cloud. We compare the quality of the MOHEFT tradeoff solutions with two state-of-the-art approaches using different synthetic and real-world workflows: the classical HEFT algorithm for single-objective scheduling and the SPEA2* genetic algorithm used in multi-objective optimisation problems. The results demonstrate that our approach is able to compute solutions of higher quality than SPEA2*. In addition, we show that MOHEFT is more suitable than SPEA2* for workflow scheduling in the context of commercial Clouds, since the genetic-based approach is unable of dealing with some of the constraints imposed by these systems.     

Improving the damage accumulation in a biomechanical bone remodelling model

We extend, reformulate and analyse a phenomenological model for bone remodelling. The original macrobiomechanical model (MBM), proposed by Hazelwood et al. [J Biomech 2001; 34:299–308], couples a population equation for the cellular activities of the basic multicellular units (BMUs) in the bone and a rate equation to account for microdamage and repair. We propose to account for bone failure under severe overstressing by incorporating a Paris-like power-law damage accumulation term. The extended model agrees with the Hazelwood et al. predictions when the bone is under-stressed, and allows for suitably loaded bones to fail, in agreement with other MBM and experimental data regarding damage by fatigue. We numerically solve the extended model using a convergent algorithm and show that for unchanging loads, the stationary solution captures fully the model behaviour. We compute and analyse the stationary solutions. Our analysis helps guide additional extensions to this and other BMU activity based models.     

Modular self-assembling and self-reconfiguring e-pucks

In this paper, we present the design of a new structural extension for the e-puck mobile robot. The extension may be used to transform what is traditionally a swarm robotics platform into a self-reconfigurable modular robotic system. We introduce a modified version of a previously developed collective locomotion algorithm and present new experimental results across three different themes. We begin by investigating how the performance of the collective locomotion algorithm is affected by the size and shape of the robotic structures involved, examining structures containing up to nine modules. Without alteration to the underlying algorithm, we then analyse the implicit self-assembling and self-reconfiguring capabilities of the system and show that the novel use of ‘virtual sensors’ can significantly improve performance. Finally, by examining a form of environment driven self-reconfiguration, we observe the behaviour of the system in a more complex environment. We conclude that the modular e-puck extension represents a viable platform for investigating collective locomotion, self-assembly and self-reconfiguration.     

Bayesian analysis of case control polygenic etiology studies with missing data

Many genetic studies are based on analysing multiple DNA regions of cases and controls. Usually each is tested separately for association with disease. However, some diseases may require interacting polymorphisms at several regions, and most disease susceptibility is polygenic. In this paper, we develop new methods for determining combinations of polymorphisms that affect the risk of disease. For example, two different genes might produce normal proteins, but these proteins improperly function when they occur together. We consider a Bayesian approach to analyse studies where DNA data from cases and controls have been analysed for polymorphisms at multiple regions and a polygenic etiology is suspected. The method of Gibbs sampling is used to incorporate data from individuals who have not had every region analysed at the DNA sequence or amino acid level. The Gibbs sampling algorithm alternatively generates a sample from the posterior distribution of the sequence of combinations of polymorphisms in cases and controls and then uses this sample to impute the data that are missing. After convergence the algorithm is used to generate a sample from the posterior distribution for the probability of each combination in order to identify groups of polymorphisms that best discriminate cases from controls. We apply the methods to a genetic study of type I diabetes. The protein encoded by the TAP2 gene is important in T cell function, and thus may affect the development of autoimmune diseases such as insulin dependent diabetes mellitus (IDDM). We determine pairs of polymorphisms of genetic fragments in the coding regions of linked HLA genes that may impact the risk of IDDM.     

Analysis of progress curves for a highly concentrated Michaelian enzyme in the presence or absence of product inhibition.

Methods are given for analysing the time course of an enzyme-catalysed reaction when the concentration of the enzyme itself is high, a situation which is often found in vivo. (1) The integrated form of the kinetic equation for a concentrated Michaelian enzyme in absence of product inhibition is given. Parameters are shown to be calculated easily using non-linear fitting procedures. (2) A general algorithm to analyse progress-curve data in more complex cases (i.e. when the analytical form of the integrated rate equation is not known or is exceedingly complex) is proposed. This algorithm may be used for any enzyme mechanism for which the differential form of the kinetic equation may be written analytically. We show that the method allows differentiation between the main types of product inhibition which may occur in the case of a highly concentrated Michaelian enzyme.     

The function of Notch signalling in segment formation in the crustacean Daphnia magna (Branchiopoda)

Ten years ago we showed for the first time that Notch signalling is required in segmentation in spiders, indicating the existence of similar mechanisms in arthropod and vertebrate segmentation. However, conflicting results in various arthropod groups hampered our understanding of the ancestral function of Notch in arthropod segmentation. Here we fill a crucial data gap in arthropods and analyse segmentation in a crustacean embryo. We analyse the expression of homologues of the Drosophila and vertebrate segmentation genes and show that members of the Notch signalling pathway are expressed at the same time as the pair-rule genes. Furthermore, inactivation of Notch signalling results in irregular boundaries of the odd-skipped-like expression domains and affects the formation of segments. In severe cases embryos appear unsegmented. We suggest two scenarios for the function of Notch signalling in segmentation. The first scenario agrees with a segmentation clock involving Notch signalling, while the second scenario discusses an alternative mechanism of Notch function which is integrated into a hierarchical segmentation cascade.     

Development of computational tools for the inference of protein interaction specificity rules and functional annotation using structural information

Relatively few protein structures are known, compared to the enormous amount of sequence data produced in the sequencing of different genomes, and relatively few protein complexes are deposited in the PDB with respect to the great amount of interaction data coming from high-throughput experiments (two-hybrid or affinity purification of protein complexes and mass spectrometry). Nevertheless, we can rely on computational techniques for the extraction of high-quality and information-rich data from the known structures and for their spreading in the protein sequence space. We describe here the ongoing research projects in our group: we analyse the protein complexes stored in the PDB and, for each complex involving one domain belonging to a family of interaction domains for which some interaction data are available, we can calculate its probability of interaction with any protein sequence. We analyse the structures of proteins encoding a function specified in a PROSITE pattern, which exhibits relatively low selectivity and specificity, and build extended patterns. To this aim, we consider residues that are well-conserved in the structure, even if their conservation cannot easily be recognized in the sequence alignment of the proteins holding the function. We also analyse protein surface regions and, through the annotation of the solvent-exposed residues, we annotate protein surface patches via a structural comparison performed with stringent parameters and independently of the residue order in the sequence. Local surface comparison may also help in identifying new sequence patterns, which could not be highlighted with other sequence-based methods.     

SEGMENT: identifying compositional domains in DNA sequences

MOTIVATION: DNA sequences are formed by patches or domains of different nucleotide composition. In a few simple sequences, domains can simply be identified by eye; however, most DNA sequences show a complex compositional heterogeneity (fractal structure), which cannot be properly detected by current methods. Recently, a computationally efficient segmentation method to analyse such nonstationary sequence structures, based on the Jensen-Shannon entropic divergence, has been described. Specific algorithms implementing this method are now needed. RESULTS: Here we describe a heuristic segmentation algorithm for DNA sequences, which was implemented on a Windows program (SEGMENT). The program divides a DNA sequence into compositionally homogeneous domains by iterating a local optimization procedure at a given statistical significance. Once a sequence is partitioned into domains, a global measure of sequence compositional complexity (SCC), accounting for both the sizes and compositional biases of all the domains in the sequence, is derived. SEGMENT computes SCC as a function of the significance level, which provides a multiscale view of sequence complexity.     

Self-organizing maps: stationary states,metastability and convergence rate

We investigate the effect of various types of neighborhood function on the convergence rates and the presence or absence of metastable stationary states of Kohonen's self-organizing feature map algorithm in one dimension. We demonstrate that the time necessary to form a topographic representation of the unit interval [0, 1] may vary over several orders of magnitude depending on the range and also the shape of the neighborhood function, by which the weight changes of the neurons in the neighborhood of the winning neuron are scaled. We will prove that for neighborhood functions which are convex on an interval given by the length of the Kohonen chain there exist no metastable states. For all other neighborhood functions, metastable states are present and may trap the algorithm during the learning process. For the widely-used Gaussian function there exists a threshold for the width above which metastable states cannot exist. Due to the presence or absence of metastable states, convergence time is very sensitive to slight changes in the shape of the neighborhood function. Fastest convergence is achieved using neighborhood functions which are "convex" over a large range around the winner neuron and yet have large differences in value at neighboring neurons.     

A Multiparametric Computational Algorithm for Comprehensive Assessment of Genetic Mutations in Mucopolysaccharidosis Type IIIA (Sanfilippo Syndrome)

Mucopolysaccharidosis type IIIA (MPS-IIIA, Sanfilippo syndrome) is a Lysosomal Storage Disease caused by cellular deficiency of N-sulfoglucosamine sulfohydrolase (SGSH). Given the large heterogeneity of genetic mutations responsible for the disease, a comprehensive understanding of the mechanisms by which these mutations affect enzyme function is needed to guide effective therapies. We developed a multiparametric computational algorithm to assess how patient genetic mutations in SGSH affect overall enzyme biogenesis, stability, and function. 107 patient mutations for the SGSH gene were obtained from the Human Gene Mutation Database representing all of the clinical mutations documented for Sanfilippo syndrome. We assessed each mutation individually using ten distinct parameters to give a comprehensive predictive score of the stability and misfolding capacity of the SGSH enzyme resulting from each of these mutations. The predictive score generated by our multiparametric algorithm yielded a standardized quantitative assessment of the severity of a given SGSH genetic mutation toward overall enzyme activity. Application of our algorithm has identified SGSH mutations in which enzymatic malfunction of the gene product is specifically due to impairments in protein folding. These scores provide an assessment of the degree to which a particular mutation could be treated using approaches such as chaperone therapies. Our multiparametric protein biogenesis algorithm advances a key understanding in the overall biochemical mechanism underlying Sanfilippo syndrome. Importantly, the design of our multiparametric algorithm can be tailored to many other diseases of genetic heterogeneity for which protein misfolding phenotypes may constitute a major component of disease manifestation.     

Online clustering algorithms

We introduce a set of clustering algorithms whose performance function is such that the algorithms overcome one of the weaknesses of K-means, its sensitivity to initial conditions which leads it to converge to a local optimum rather than the global optimum. We derive online learning algorithms and illustrate their convergence to optimal solutions which K-means fails to find. We then extend the algorithm by underpinning it with a latent space which enables a topology preserving mapping to be found. We show visualisation results on some standard data sets.     

Knowledge-based voting algorithm for automated protein functional annotation

Automated annotation of high-throughput genome sequences is one of the earliest steps toward a comprehensive understanding of the dynamic behavior of living organisms. However, the step is often error-prone because of its underlying algorithms, which rely mainly on a simple similarity analysis, and lack of guidance from biological rules. We present herein a knowledge-based protein annotation algorithm. Our objectives are to reduce errors and to improve annotation confidences. This algorithm consists of two major components: a knowledge system, called "RuleMiner," and a voting procedure. The knowledge system, which includes biological rules and functional profiles for each function, provides a platform for seamless integration of multiple sequence analysis tools and guidance for function annotation. The voting procedure, which relies on the knowledge system, is designed to make (possibly) unbiased judgments in functional assignments among complicated, sometimes conflicting, information. We have applied this algorithm to 10 prokaryotic bacterial genomes and observed a significant improvement in annotation confidences. We also discuss the current limitations of the algorithm and the potential for future improvement.