Search

A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation. [ABSTRACT FROM AUTHOR]

Abstract Background A key challenge in systems biology is the reconstruction of an organism's metabolic network from its genome sequence. One strategy for addressing this problem is to predict which metabolic pathways, from a reference database of known pathways, are present in the organism, based on the annotated genome of the organism. Results To quantitatively validate methods for pathway prediction, we developed a large "gold standard" dataset of 5,610 pathway instances known to be present or absent in curated metabolic pathway databases for six organisms. We defined a collection of 123 pathway features, whose information content we evaluated with respect to the gold standard. Feature data were used as input to an extensive collection of machine learning (ML) methods, including naïve Bayes, decision trees, and logistic regression, together with feature selection and ensemble methods. We compared the ML methods to the previous PathoLogic algorithm for pathway prediction using the gold standard dataset. We found that ML-based prediction methods can match the performance of the PathoLogic algorithm. PathoLogic achieved an accuracy of 91% and an F-measure of 0.786. The ML-based prediction methods achieved accuracy as high as 91.2% and F-measure as high as 0.787. The ML-based methods output a probability for each predicted pathway, whereas PathoLogic does not, which provides more information to the user and facilitates filtering of predicted pathways. Conclusions ML methods for pathway prediction perform as well as existing methods, and have qualitative advantages in terms of extensibility, tunability, and explainability. More advanced prediction methods and/or more sophisticated input features may improve the performance of ML methods. However, pathway prediction performance appears to be limited largely by the ability to correctly match enzymes to the reactions they catalyze based on genome annotations.

Abstract Background Accurate assignment of genes to pathways is essential in order to understand the functional role of genes and to map the existing pathways in a given genome. Existing algorithms predict pathways by extrapolating experimental data in one organism to other organisms for which this data is not available. However, current systems classify all genes that belong to a specific EC family to all the pathways that contain the corresponding enzymatic reaction, and thus introduce ambiguity. Results Here we describe an algorithm for assignment of genes to cellular pathways that addresses this problem by selectively assigning specific genes to pathways. Our algorithm uses the set of experimentally elucidated metabolic pathways from MetaCyc, together with statistical models of enzyme families and expression data to assign genes to enzyme families and pathways by optimizing correlated co-expression, while minimizing conflicts due to shared assignments among pathways. Our algorithm also identifies alternative ("backup") genes and addresses the multi-domain nature of proteins. We apply our model to assign genes to pathways in the Yeast genome and compare the results for genes that were assigned experimentally. Our assignments are consistent with the experimentally verified assignments and reflect characteristic properties of cellular pathways. Conclusion We present an algorithm for automatic assignment of genes to metabolic pathways. The algorithm utilizes expression data and reduces the ambiguity that characterizes assignments that are based only on EC numbers.

In this paper we continue the study of distributional systems (drift less control affine systems) with quadratic cost and no constant rank of distribution. We will use the Pontyagin Maximum Principle and the constants variation method for nonhomogeneous second order differential equations to find the general solution. [ABSTRACT FROM AUTHOR]

In this paper the problem of compatibility between a nonlinear connection and other geometric structures on Lie algebroids is studied. The notion of dynamical covariant derivative is introduced and a metric nonlinear connection is found in the more general case of Lie algebroids. We prove that the canonical nonlinear connection induced by a regular Lagrangian on a Lie algebroid is the unique connection which is metric and compatible with the symplectic structure. [ABSTRACT FROM AUTHOR]

In this paper we give a new technique to obtain the Hamiltonian function in order to solve the driftless control affine systems (distributional systems) with positive homogeneous costs. The method consists by using the Lagrange multipliers and Legendre transformation associated to a singular Lagrangian. This method could be an alternative to the classical Pontryagin Maximum Principle. [ABSTRACT FROM AUTHOR]

In this paper we generalize the linear contravariant connection on Poisson manifolds to Lie algebroids and study its tensors of torsion and curvature. A Poisson connection which depends only on the Poisson bivector and structural functions of the Lie algebroid is given. The notions of complete and horizontal lifts are introduced and their compatibility conditions are pointed out. [ABSTRACT FROM AUTHOR]

In this paper we present new forms of the classical separation axioms on topological spaces. Our constructions generate a method to refine separation properties when passing to the quotient space and our results may be useful in the study of algebraic topological structures, such as topological groups and topological vector spaces. [ABSTRACT FROM AUTHOR]