Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0

Atlas of Cancer Signalling Network: a systems biology resource for integrative analysis of cancer data with Google Maps.

Cancerogenesis is driven by mutations leading to aberrant functioning of a complex network of molecular interactions and simultaneously affecting multiple cellular functions. Therefore, the successful application of bioinformatics and systems biology methods for analysis of high-throughput data in cancer research heavily depends on availability of global and detailed reconstructions of signalling networks amenable for computational analysis. We present here the Atlas of Cancer Signalling Network (ACSN), an interactive and comprehensive map of molecular mechanisms implicated in cancer. The resource includes tools for map navigation, visualization and analysis of molecular data in the context of signalling network maps. Constructing and updating ACSN involves careful manual curation of molecular biology literature and participation of experts in the corresponding fields. The cancer-oriented content of ACSN is completely original and covers major mechanisms involved in cancer progression, including DNA repair, cell survival, apoptosis, cell cycle, EMT and cell motility. Cell signalling mechanisms are depicted in detail, together creating a seamless 'geographic-like' map of molecular interactions frequently deregulated in cancer. The map is browsable using NaviCell web interface using the Google Maps engine and semantic zooming principle. The associated web-blog provides a forum for commenting and curating the ACSN content. ACSN allows uploading heterogeneous omics data from users on top of the maps for visualization and performing functional analyses. We suggest several scenarios for ACSN application in cancer research, particularly for visualizing high-throughput data, starting from small interfering RNA-based screening results or mutation frequencies to innovative ways of exploring transcriptomes and phosphoproteomes. Integration and analysis of these data in the context of ACSN may help interpret their biological significance and formulate mechanistic hypotheses. ACSN may also support patient stratification, prediction of treatment response and resistance to cancer drugs, as well as design of novel treatment strategies.

Reduction of dynamical biochemical reactions networks in computational biology.

Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state (QSS) and quasi-equilibrium approximations (QE), and provide practical recipes for model reduction of linear and non-linear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques.

The mystery of two straight lines in bacterial genome statistics.

In special coordinates (codon position-specific nucleotide frequencies), bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position-specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean-field approximation, which is also known as context-free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature, respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.

Codon bias signatures, organization of microorganisms in codon space, and lifestyle.

New and simple numerical criteria based on a codon adaptation index are applied to the complete genomic sequences of 80 Eubacteria and 16 Archaea, to infer weak and strong genome tendencies toward content bias, translational bias, and strand bias. These criteria can be applied to all microbial genomes, even those for which little biological information is known, and a codon bias signature, that is the collection of strong biases displayed by a genome, can be automatically derived. A codon bias space, where genomes are identified by their preferred codons, is proposed as a novel formal framework to interpret genomic relationships. Principal component analysis confirms that although GC content has a dominant effect on codon bias space, thermophilic and mesophilic species can be identified and separated by codon preferences. Two more examples concerning lifestyle are studied with linear discriminant analysis: suitable separating functions characterized by sets of preferred codons are provided to discriminate: translationally biased (hyper)thermophiles from mesophiles, and organisms with different respiratory characteristics, aerobic, anaerobic, facultative aerobic and facultative anaerobic. These results suggest that codon bias space might reflect the geometry of a prokaryotic "physiology space." Evolutionary perspectives are noted, numerical criteria and distances among organisms are validated on known cases, and various results and predictions are discussed both on methodological and biological grounds.

Codon adaptation index as a measure of dominating codon bias.

UNLABELLED: We propose a simple algorithm to detect dominating synonymous codon usage bias in genomes. The algorithm is based on a precise mathematical formulation of the problem that lead us to use the Codon Adaptation Index (CAI) as a 'universal' measure of codon bias. This measure has been previously employed in the specific context of translational bias. With the set of coding sequences as a sole source of biological information, the algorithm provides a reference set of genes which is highly representative of the bias. This set can be used to compute the CAI of genes of prokaryotic and eukaryotic organisms, including those whose functional annotation is not yet available. An important application concerns the detection of a reference set characterizing translational bias which is known to correlate to expression levels; in this case, the algorithm becomes a key tool to predict gene expression levels, to guide regulatory circuit reconstruction, and to compare species. The algorithm detects also leading-lagging strands bias, GC-content bias, GC3 bias, and horizontal gene transfer. The approach is validated on 12 slow-growing and fast-growing bacteria, Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster. AVAILABILITY: http://www.ihes.fr/~materials.