Realization theory for rational systems

In this paper we solve the problem of realization of response maps for rational systems. Sufficient and necessary conditions for a response map to be realizable by a rational system are presented. The properties of rational realizations such as observability, controllability, and minimality are studied. Finally, we briefly discuss the procedures for checking observability and controllability of rational systems and minimality of rational realizations and the procedure for constructing a rational system realizing a response map

Bound states in point-interaction star-graphs

We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a fixed spacing between the interaction sites. We prove that the essential spectrum of this system is the same as that of the infinite straight "polymer", but in addition there are isolated eigenvalues unless N=2 and the graph is a straight line. We also show that the system has many strongly bound states if at least one of the angles between the star arms is small enough. Examples of eigenfunctions and eigenvalues are computed numerically.Comment: 17 pages, LaTeX 2e with 9 eps figure

Yeast biodiversity in vineyard environments is increased by human intervention

One hundred and five grape samples were collected during two consecutive years from 33 locations on seven oceanic islands of the Azores Archipelago. Grape samples were obtained from vineyards that were either abandoned or under regular cultivation involving common viticultural interventions, to evaluate the impact of regular human intervention on grape yeast biota diversity in vineyards. A total of 3150 yeast isolates were obtained and 23 yeast species were identified. The predominant species were Hanseniaspora uvarum, Pichia terricola, Starmerella bacillaris and Issatchenkia hanoiensis. The species Barnettozyma californica, Candida azymoides and Pichia cecembensis were reported in grapes or wine-associated environments for the first time. A higher biodiversity was found in active vineyards where regular human intervention takes place (Shannon index: 1.89 and 1.53 in the first and second years, respectively) when compared to the abandoned ones (Shannon index: 0.76 and 0.31). This finding goes against the assumptions that human intervention can destroy biodiversity and lead to homogeneity in the environment. Biodiversity indices were considerably lower in the year with the heaviest rainfall. This study is the first to report on the grape yeast communities from several abandoned vineyards that have undergone no human intervention.Joao Drumonde Neves is the recipient of a fellowship of the Azorean Government (M321/006/F/2008) and PROEMPREGO. This work was supported by the strategic programme UID/BIA/04050/2013 (POCI-01-0145-FEDER-007569) funded by national funds through the FCT I.P. and by the ERDF through the COMPETE2020 - Programa Operacional Competitividade e Internacionalizacao (POCI), and by national funds through FCT by the projects FCOMP-01-0124-008775, PTDC/AGR-ALI/103392/2008 and PTDC/AGR-ALI/121062/2010.info:eu-repo/semantics/publishedVersio

Biochemical reaction systems – system theory and decomposition

Biochemical reaction networks may be modeled as biochemical reaction systems consisting of differential equations with rational functions. Biochemical reaction systems are defined as rational positive dynamic systems with inputs and outputs, and illustrated by examples. This formulation makes available the results from algebraic system theory for rational systems and a relation with computer algebra. It is shown how to decompose networks into subsystems and how to relate them to graphs. The realization problem for this class of systems is briefly discussed. Finally, control problems for biochemical reaction networks are formulated