ORCID Profile
0000-0002-1374-0388
Current Organisation
RMIT University
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Publisher: Cambridge University Press (CUP)
Date: 21-12-2018
DOI: 10.1017/S1446788718000411
Abstract: We consider a linear operator pencil with complex parameter mapping one Hilbert space onto another. It is known that the resolvent is analytic in an open annular region of the complex plane centred at the origin if and only if the coefficients of the Laurent series satisfy a doubly-infinite set of left and right fundamental equations and are suitably bounded. If the resolvent has an isolated singularity at the origin we propose a recursive orthogonal decomposition of the domain and range spaces that enables us to construct the key nonorthogonal projections that separate the singular and regular components of the resolvent and subsequently allows us to find a formula for the basic solution to the fundamental equations. We show that each Laurent series coefficient in the singular part of the resolvent can be approximated by a weakly convergent sequence of finite-dimensional matrix operators and we show how our analysis can be extended to find a global expression for the resolvent of a linear pencil in the case where the resolvent has only a finite number of isolated singularities.
Publisher: Springer Science and Business Media LLC
Date: 2015
Publisher: World Scientific Pub Co Pte Lt
Date: 30-11-2020
DOI: 10.1142/S0219691320500691
Abstract: In this paper, we study multivariate Gabor frames in matrix-valued signal spaces over locally compact abelian (LCA) groups, where the lower frame condition depends on a bounded linear operator [Formula: see text] on the underlying matrix-valued signal space. This type of Gabor frame is also known as a multivariate [Formula: see text]-Gabor frame. By extending work of G[Formula: see text]vruta, we present necessary and sufficient conditions for the existence of [Formula: see text]-Gabor frames of multivariate matrix-valued Gabor systems. Some operators which can transform multivariate matrix-valued Gabor and [Formula: see text]-Gabor frames into [Formula: see text]-Gabor frames in terms of adjointable operators are discussed. Finally, we give a Paley–Wiener-type perturbation result for multivariate matrix-valued [Formula: see text]-Gabor frames.
Publisher: Elsevier BV
Date: 2019
Publisher: University of Zagreb, Faculty of Science, Department of Mathematics
Date: 19-06-2018
DOI: 10.3336/GM.53.1.11
Publisher: IEEE
Date: 07-2017
Publisher: Springer Science and Business Media LLC
Date: 03-06-2019
Publisher: Cambridge University Press (CUP)
Date: 04-2020
DOI: 10.1017/S1446181120000140
Abstract: The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 13-01-2021
DOI: 10.21914/ANZIAMJ.V62.14843
Abstract: The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation. doi: 10.1017/S1446181120000140
Publisher: Elsevier BV
Date: 08-2019
Publisher: Wiley
Date: 02-08-2018
DOI: 10.1111/BRV.12359
Abstract: Much bio ersity data is collected worldwide, but it remains challenging to assemble the scattered knowledge for assessing bio ersity status and trends. The concept of Essential Bio ersity Variables (EBVs) was introduced to structure bio ersity monitoring globally, and to harmonize and standardize bio ersity data from disparate sources to capture a minimum set of critical variables required to study, report and manage bio ersity change. Here, we assess the challenges of a 'Big Data' approach to building global EBV data products across taxa and spatiotemporal scales, focusing on species distribution and abundance. The majority of currently available data on species distributions derives from incidentally reported observations or from surveys where presence-only or presence-absence data are s led repeatedly with standardized protocols. Most abundance data come from opportunistic population counts or from population time series using standardized protocols (e.g. repeated surveys of the same population from single or multiple sites). Enormous complexity exists in integrating these heterogeneous, multi-source data sets across space, time, taxa and different s ling methods. Integration of such data into global EBV data products requires correcting biases introduced by imperfect detection and varying s ling effort, dealing with different spatial resolution and extents, harmonizing measurement units from different data sources or s ling methods, applying statistical tools and models for spatial inter- or extrapolation, and quantifying sources of uncertainty and errors in data and models. To support the development of EBVs by the Group on Earth Observations Bio ersity Observation Network (GEO BON), we identify 11 key workflow steps that will operationalize the process of building EBV data products within and across research infrastructures worldwide. These workflow steps take multiple sequential activities into account, including identification and aggregation of various raw data sources, data quality control, taxonomic name matching and statistical modelling of integrated data. We illustrate these steps with concrete ex les from existing citizen science and professional monitoring projects, including eBird, the Tropical Ecology Assessment and Monitoring network, the Living Planet Index and the Baltic Sea zooplankton monitoring. The identified workflow steps are applicable to both terrestrial and aquatic systems and a broad range of spatial, temporal and taxonomic scales. They depend on clear, findable and accessible metadata, and we provide an overview of current data and metadata standards. Several challenges remain to be solved for building global EBV data products: (i) developing tools and models for combining heterogeneous, multi-source data sets and filling data gaps in geographic, temporal and taxonomic coverage, (ii) integrating emerging methods and technologies for data collection such as citizen science, sensor networks, DNA-based techniques and satellite remote sensing, (iii) solving major technical issues related to data product structure, data storage, execution of workflows and the production process/cycle as well as approaching technical interoperability among research infrastructures, (iv) allowing semantic interoperability by developing and adopting standards and tools for capturing consistent data and metadata, and (v) ensuring legal interoperability by endorsing open data or data that are free from restrictions on use, modification and sharing. Addressing these challenges is critical for bio ersity research and for assessing progress towards conservation policy targets and sustainable development goals.
Publisher: Elsevier BV
Date: 06-2020
Publisher: Springer Science and Business Media LLC
Date: 21-06-2017
Publisher: ISTE Group
Date: 2014
Publisher: Scientific Research Publishing, Inc.
Date: 2013
No related grants have been discovered for Geetika Verma.