Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability

International audienceIn this work, we provide an overview of the classical symbolic techniques for solving algebraic systems of equations and show the interest of such techniques in the study of some problems in dynamical system theory, namely testing the structural stability of multidimensional systems

Ultra-diffuse hydrothermal venting supports Fe-oxidizing bacteria and massive umber deposition at 5000 m off Hawaii

© International Society for Microbial Ecology, 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in The ISME Journal 5 (2011): 1748–1758, doi:10.1038/ismej.2011.48.A novel hydrothermal field has been discovered at the base of Lōihi Seamount, Hawaii, at 5000 mbsl. Geochemical analyses demonstrate that ‘FeMO Deep’, while only 0.2 °C above ambient seawater temperature, derives from a distal, ultra-diffuse hydrothermal source. FeMO Deep is expressed as regional seafloor seepage of gelatinous iron- and silica-rich deposits, pooling between and over basalt pillows, in places over a meter thick. The system is capped by mm to cm thick hydrothermally derived iron-oxyhydroxide- and manganese-oxide-layered crusts. We use molecular analyses (16S rDNA-based) of extant communities combined with fluorescent in situ hybridizations to demonstrate that FeMO Deep deposits contain living iron-oxidizing Zetaproteobacteria related to the recently isolated strain Mariprofundus ferroxydans. Bioenergetic calculations, based on in-situ electrochemical measurements and cell counts, indicate that reactions between iron and oxygen are important in supporting chemosynthesis in the mats, which we infer forms a trophic base of the mat ecosystem. We suggest that the biogenic FeMO Deep hydrothermal deposit represents a modern analog for one class of geological iron deposits known as ‘umbers’ (for example, Troodos ophilolites, Cyprus) because of striking similarities in size, setting and internal structures.Funding has been provided by the NSF Microbial Observatories Program (KJE, DE, BT, HS and CM), by the Gordon and Betty Moore Foundation (KJE), the College of Letters, Arts, and Sciences at the University of Southern California (KJE) and by the NASA Astrobiology Institute (KJE, DE)

The Structured Distance to the Nearest System Without Property P

For a system matrix M, this paper explores the smallest (Frobenius) norm additive structured perturbation δM for which a system property P (e.g., controllability, observability, stability, etc.) fails to hold, i.e., δM is the structured perturbation with smallest Frobenius norm such that there exists a property matrix R ∈ P for which M-δM-R drops rank. The Frobenius norm is used because of its direct dependence on the magnitude of each entry in the perturbation matrix. Necessary conditions on a locally minimum norm structured rank-reducing perturbation δM and associated property matrix R are set forth and proven. An iterative algorithm is also set forth that computes a locally minimum norm structured perturbation and associated property matrix satisfying the necessary conditions. Algorithm convergence is proven using a discrete Lyapunov function

Sampled-data systems

For digital devices to interact with the physical world, an interface is needed that transforms the signals from analog to digital and vice versa. Ideal samplers and zero-order hold devices are incorporated to derive discrete-time models of continuous-time systems. State variable descriptions and transfer functions are used