On the connection between discrete linear repetitive processes and 2-D discrete linear systems

A direct method is developed that reduces a polynomial system matrix describinga discrete linear repetitive process to a 2-D singular state-space form such that all the relevant properties, including the zero structure of the system matrix, are retained. It is shown that the transformation linking the original polynomial system matrix with its associated 2-D singular form is zero coprime system equivalence. The exact nature of the resulting system matrix in singular form and the transformation involved are established

Serre's reduction of linear functional systems

Serre's reduction aims at reducing the number of unknowns and equations of a linear functional system (e.g., system of partial differential equations, system of differential time-delay equations, system of difference equations). Finding an equivalent representation of a linear functional system containing fewer equations and fewer unknowns generally simplifies the study of its structural properties, its closed-form integration as well as of different numerical analysis issues. The purpose of this paper is to present a constructive approach to Serre's reduction for determined and underdetermined linear functional systems

The CAFA challenge reports improved protein function prediction and new functional annotations for hundreds of genes through experimental screens

Background: The Critical Assessment of Functional Annotation (CAFA) is an ongoing, global, community-driven effort to evaluate and improve the computational annotation of protein function. Results: Here, we report on the results of the third CAFA challenge, CAFA3, that featured an expanded analysis over the previous CAFA rounds, both in terms of volume of data analyzed and the types of analysis performed. In a novel and major new development, computational predictions and assessment goals drove some of the experimental assays, resulting in new functional annotations for more than 1000 genes. Specifically, we performed experimental whole genome mutation screening in Candida albicans and aeruginosa genomes, which provided us with genome-wide experimental data for genes associated with biofilm formation and motility. We further performed targeted assays on selected genes in Drosophila melanogaster, which we suspected of being involved in long-term memory. Conclusion: We conclude that while predictions of the molecular function and biological process annotations have slightly improved over time, those of the cellular component have not. Term-centric prediction of experimental annotations remains equally challenging; although the performance of the top methods is significantly better than the expectations set by baseline methods in C. albicans and D. melanogaster, it leaves considerable room and need for improvement. Finally, we report that the CAFA community now involves a broad range of participants with expertise in bioinformatics, biological experimentation, biocuration, and bio-ontologies, working together to improve functional annotation, computational function prediction, and our ability to manage big data in the era of large experimental screens

The CAFA challenge reports improved protein function prediction and new functional annotations for hundreds of genes through experimental screens

Background The Critical Assessment of Functional Annotation (CAFA) is an ongoing, global, community-driven effort to evaluate and improve the computational annotation of protein function. Results Here, we report on the results of the third CAFA challenge, CAFA3, that featured an expanded analysis over the previous CAFA rounds, both in terms of volume of data analyzed and the types of analysis performed. In a novel and major new development, computational predictions and assessment goals drove some of the experimental assays, resulting in new functional annotations for more than 1000 genes. Specifically, we performed experimental whole-genome mutation screening in Candida albicans and Pseudomonas aureginosa genomes, which provided us with genome-wide experimental data for genes associated with biofilm formation and motility. We further performed targeted assays on selected genes in Drosophila melanogaster, which we suspected of being involved in long-term memory. Conclusion We conclude that while predictions of the molecular function and biological process annotations have slightly improved over time, those of the cellular component have not. Term-centric prediction of experimental annotations remains equally challenging; although the performance of the top methods is significantly better than the expectations set by baseline methods in C. albicans and D. melanogaster, it leaves considerable room and need for improvement. Finally, we report that the CAFA community now involves a broad range of participants with expertise in bioinformatics, biological experimentation, biocuration, and bio-ontologies, working together to improve functional annotation, computational function prediction, and our ability to manage big data in the era of large experimental screens.Peer reviewe

The CAFA challenge reports improved protein function prediction and new functional annotations for hundreds of genes through experimental screens

BackgroundThe Critical Assessment of Functional Annotation (CAFA) is an ongoing, global, community-driven effort to evaluate and improve the computational annotation of protein function.ResultsHere, we report on the results of the third CAFA challenge, CAFA3, that featured an expanded analysis over the previous CAFA rounds, both in terms of volume of data analyzed and the types of analysis performed. In a novel and major new development, computational predictions and assessment goals drove some of the experimental assays, resulting in new functional annotations for more than 1000 genes. Specifically, we performed experimental whole-genome mutation screening in Candida albicans and Pseudomonas aureginosa genomes, which provided us with genome-wide experimental data for genes associated with biofilm formation and motility. We further performed targeted assays on selected genes in Drosophila melanogaster, which we suspected of being involved in long-term memory.ConclusionWe conclude that while predictions of the molecular function and biological process annotations have slightly improved over time, those of the cellular component have not. Term-centric prediction of experimental annotations remains equally challenging; although the performance of the top methods is significantly better than the expectations set by baseline methods in C. albicans and D. melanogaster, it leaves considerable room and need for improvement. Finally, we report that the CAFA community now involves a broad range of participants with expertise in bioinformatics, biological experimentation, biocuration, and bio-ontologies, working together to improve functional annotation, computational function prediction, and our ability to manage big data in the era of large experimental screens.</p

On the Decoupling of a Class of Linear Functional Systems

Abstract Multivariate polynomial matrices arise from the treatment of functional linear systems such as systems described by partial differential equations, delay-differential equations or linear multidimensional discrete equations. In this paper we present conditions under which a class of multivariate polynomial matrices is equivalent to a block diagonal form. The conditions correspond to the decomposition of the associated linear systems of functional equations. The constructive method which can be easily implemented on a computer algebra system is illustrated by an example. Mathematics Subject Classification: 93C05, 93B11, 34C20, 68W30, 13P0

An equivalent matrix pencil for bivariate polynomial matrices

In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini’s type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established

Equivalence and reduction of delay-differential systems

A new direct method is presented which reduces a given high-order representation of a control system with delays to a firstorder form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann’s strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant