A structure preserving shift-invert infinite Arnoldi algorithm for a class of delay eigenvalue problems with Hamiltonian symmetry

In this work we consider a class of delay eigenvalue problems that admit a spectrum similar to that of a Hamiltonian matrix, in the sense that the spectrum is symmetric with respect to both the real and imaginary axis. More precisely, we present a method to iteratively approximate the eigenvalues of such delay eigenvalue problems closest to a given purely real or imaginary shift, while preserving the symmetries of the spectrum. To this end the presented method exploits the equivalence between the considered delay eigenvalue problem and the eigenvalue problem associated with a linear but infinite-dimensional operator. To compute the eigenvalues closest to the given shift, we apply a specifically chosen shift-invert transformation to this linear operator and compute the eigenvalues with the largest modulus of the new shifted and inverted operator using an (infinite) Arnoldi procedure. The advantage of the chosen shift-invert transformation is that the spectrum of the transformed operator has a "real skew-Hamiltonian"-like structure. Furthermore, it is proven that the Krylov space constructed by applying this operator, satisfies an orthogonality property in terms of a specifically chosen bilinear form. By taking this property into account during the orthogonalization process, it is ensured that even in the presence of rounding errors, the obtained approximation for, e.g., a simple, purely imaginary eigenvalue is simple and purely imaginary. The presented work can thus be seen as an extension of [V. Mehrmann and D. Watkins, "Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils", SIAM J. Sci. Comput. (22.6), 2001], to the considered class of delay eigenvalue problems. Although the presented method is initially defined on function spaces, it can be implemented using finite dimensional linear algebra operations

Toward a new data standard for combined marine biological and environmental datasets - expanding OBIS beyond species occurrences

The Ocean Biogeographic Information System (OBIS) is the world's most comprehensive online, open-access database of marine species distributions. OBIS grows with millions of new species observations every year. Contributions come from a network of hundreds of institutions, projects and individuals with common goals: to build a scientific knowledge base that is open to the public for scientific discovery and exploration and to detect trends and changes that inform society as essential elements in conservation management and sustainable development. Until now, OBIS has focused solely on the collection of biogeographic data (the presence of marine species in space and time) and operated with optimized data flows, quality control procedures and data standards specifically targeted to these data. Based on requirements from the growing OBIS community to manage datasets that combine biological, physical and chemical measurements, the OBIS-ENV-DATA pilot project was launched to develop a proposed standard and guidelines to make sure these combined datasets can stay together and are not, as is often the case, split and sent to different repositories. The proposal in this paper allows for the management of sampling methodology, animal tracking and telemetry data, biological measurements (e.g., body length, percent live cover, ...) as well as environmental measurements such as nutrient concentrations, sediment characteristics or other abiotic parameters measured during sampling to characterize the environment from which biogeographic data was collected. The recommended practice builds on the Darwin Core Archive (DwC-A) standard and on practices adopted by the Global Biodiversity Information Facility (GBIF). It consists of a DwC Event Core in combination with a DwC Occurrence Extension and a proposed enhancement to the DwC MeasurementOrFact Extension. This new structure enables the linkage of measurements or facts - quantitative and qualitative properties - to both sampling events and species occurrences, and includes additional fields for property standardization. We also embrace the use of the new parentEventID DwC term, which enables the creation of a sampling event hierarchy. We believe that the adoption of this recommended practice as a new data standard for managing and sharing biological and associated environmental datasets by IODE and the wider international scientific community would be key to improving the effectiveness of the knowledge base, and will enhance integration and management of critical data needed to understand ecological and biological processes in the ocean, and on land.Fil: De Pooter, Daphnis. Flanders Marine Institute; BélgicaFil: Appeltans, Ward. UNESCO-IOC; BélgicaFil: Bailly, Nicolas. Hellenic Centre for Marine Research, MedOBIS; GreciaFil: Bristol, Sky. United States Geological Survey; Estados UnidosFil: Deneudt, Klaas. Flanders Marine Institute; BélgicaFil: Eliezer, Menashè. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Fujioka, Ei. University Of Duke. Nicholas School Of Environment. Duke Marine Lab; Estados UnidosFil: Giorgetti, Alessandra. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Goldstein, Philip. University of Colorado Museum of Natural History, OBIS; Estados UnidosFil: Lewis, Mirtha Noemi. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Centro para el Estudio de Sistemas Marinos; ArgentinaFil: Lipizer, Marina. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Mackay, Kevin. National Institute of Water and Atmospheric Research; Nueva ZelandaFil: Marin, Maria Rosa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico; ArgentinaFil: Moncoiffé, Gwenaëlle. British Oceanographic Data Center; Reino UnidoFil: Nikolopoulou, Stamatina. Hellenic Centre for Marine Research, MedOBIS; GreciaFil: Provoost, Pieter. UNESCO-IOC; BélgicaFil: Rauch, Shannon. Woods Hole Oceanographic Institution; Estados UnidosFil: Roubicek, Andres. CSIRO Oceans and Atmosphere; AustraliaFil: Torres, Carlos. Universidad Autonoma de Baja California Sur; MéxicoFil: van de Putte, Anton. Royal Belgian Institute for Natural Sciences; BélgicaFil: Vandepitte, Leen. Flanders Marine Institute; BélgicaFil: Vanhoorne, Bart. Flanders Marine Institute; BélgicaFil: Vinci, Mateo. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Wambiji, Nina. Kenya Marine and Fisheries Research Institute; KeniaFil: Watts, David. CSIRO Oceans and Atmosphere; AustraliaFil: Klein Salas, Eduardo. Universidad Simon Bolivar; VenezuelaFil: Hernandez, Francisco. Flanders Marine Institute; Bélgic

Aligning Standards Communities for Omics Biodiversity Data: Sustainable Darwin Core-MIxS Interoperability

The standardization of data, encompassing both primary and contextual information (metadata), plays a pivotal role in facilitating data (re-)use, integration, and knowledge generation. However, the biodiversity and omics communities, converging on omics biodiversity data, have historically developed and adopted their own distinct standards, hindering effective (meta)data integration and collaboration.In response to this challenge, the Task Group (TG) for Sustainable DwC-MIxS Interoperability was established. Convening experts from the Biodiversity Information Standards (TDWG) and the Genomic Standards Consortium (GSC) alongside external stakeholders, the TG aimed to promote sustainable interoperability between the Minimum Information about any (x) Sequence (MIxS) and Darwin Core (DwC) specifications.To achieve this goal, the TG utilized the Simple Standard for Sharing Ontology Mappings (SSSOM) to create a comprehensive mapping of DwC keys to MIxS keys. This mapping, combined with the development of the MIxS-DwC extension, enables the incorporation of MIxS core terms into DwC-compliant metadata records, facilitating seamless data exchange between MIxS and DwC user communities.Through the implementation of this translation layer, data produced in either MIxS- or DwC-compliant formats can now be efficiently brokered, breaking down silos and fostering closer collaboration between the biodiversity and omics communities. To ensure its sustainability and lasting impact, TDWG and GSC have both signed a Memorandum of Understanding (MoU) on creating a continuous model to synchronize their standards. These achievements mark a significant step forward in enhancing data sharing and utilization across domains, thereby unlocking new opportunities for scientific discovery and advancement

A pseudo-spectra based characterisation of the robust strong H-infinity norm of time-delay systems with real-valued and structured uncertainties

This paper examines the robust (strong) H-infinity norm of a linear time-invariant system with discrete delays. The considered system is subject to real-valued, structured, Frobenius norm bounded uncertainties on the coefficient matrices. The robust H-infinity norm is the worst case value of the H-infinity norm over the realisations of the system and hence an important measure of robust performance in control engineering. However this robust H-infinity norm is a fragile measure, as for a particular realization of the uncertainties the H-infinity norm might be sensitive to arbitrarily small perturbations on the delays. Therefore, we introduce the robust strong H-infinity norm, inspired by the notion of strong stability of delay differential equations of neutral type, which takes into account both the perturbations on the system matrices and infinitesimal small delay perturbations. This quantity is a continuous function of the nominal system parameters and delays. The main contribution of this work is the introduction of a relation between this robust strong H-infinity norm and the the pseudo-spectrum of an associated singular delay eigenvalue problem. This relation is subsequently employed in a novel algorithm for computing the robust strong H-infinity norm of uncertain time-delay systems. Both the theoretical results and the algorithm are also generalized to systems with uncertainties on the delays, and systems described by a class of delay differential algebraic equations.status: Published onlin

Computing the robust H-infinity norm of time-delay LTI systems with real-valued and structured uncertainties

In this paper a new method to calculate the robust (worst-case) H∞-norm of a linear time-invariant time-delay system with an arbitrary number of delays with uncertainties both in the system matrices and the delay parameters is presented. The proposed approach fully exploits the real-valued and structured nature of the uncertainties. As in real-life applications, uncertainties can influence more than one system matrix. The algorithm utilizes the relation between the robust H∞-norm and the pseudo-spectrum of an associated non-linear (delay) eigenvalue problem with both real and complex perturbations. More precisely it uses the Newton-bisection method to find the robust complex distance to instability of this eigenvalue problem which will be shown to be equal to the reciprocal of the robust H∞-norm.status: publishe

Computing and optimising the robust strong H-in nity norm of uncertain time-delay systems

status: publishe

A pseudo-spectrum based characterization of the robust strong H-infinity norm of time-delay systems with real-valued and structured uncertainties

status: accepte

iobis/obistools: version 0.0.6

version 0.0.