Output Feedback Invariants

The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree $n\geq mp$, the product of number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system.Comment: 15 page

Convolutional decoding through a tracking problem

Convolutional codes can be regarded as discrete time linear systems. This relationship has been studied along decades, and concepts from both theories have found their counterparts into the other one. In this context, decoding of a received word can be interpreted as a tracking problem. This should allow to give practical decoding algorithms for convolutional codes. However, coding theory is usually studied over finite fields while optimal control problems have been considered over the real or complex fields. The solutions to these problems are not applicable as they make use of an Euclidean metric in which finite fields lack. We state a tracking problem over finite fields using the Hamming metric instead of a bilinear quadratic form, and we propose a solution via block decoding. In particular, we focus on the tracking problem associated to a convolutional decoding problem, which leads to a method for decoding general convolutional codes. Under some conditions, a bigger number of errors than half the minimum distance can be corrected

Simultaneous versal deformations of endomorphisms and invariant subspaces

We study the set M of pairs (f; V ), defined by an endomorphism f of Fn and a d- dimensional f–invariant subspace V . It is shown that this set is a smooth manifold that defines a vector bundle on the Grassmann manifold. We apply this study to derive conditions for the Lipschitz stability of invariant subspaces and determine versal deformations of the elements of M with respect to a natural equivalence relation introduced on it

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

The iPlant Collaborative: Cyberinfrastructure for Plant Biology

The iPlant Collaborative (iPlant) is a United States National Science Foundation (NSF) funded project that aims to create an innovative, comprehensive, and foundational cyberinfrastructure in support of plant biology research (PSCIC, 2006). iPlant is developing cyberinfrastructure that uniquely enables scientists throughout the diverse fields that comprise plant biology to address Grand Challenges in new ways, to stimulate and facilitate cross-disciplinary research, to promote biology and computer science research interactions, and to train the next generation of scientists on the use of cyberinfrastructure in research and education. Meeting humanity's projected demands for agricultural and forest products and the expectation that natural ecosystems be managed sustainably will require synergies from the application of information technologies. The iPlant cyberinfrastructure design is based on an unprecedented period of research community input, and leverages developments in high-performance computing, data storage, and cyberinfrastructure for the physical sciences. iPlant is an open-source project with application programming interfaces that allow the community to extend the infrastructure to meet its needs. iPlant is sponsoring community-driven workshops addressing specific scientific questions via analysis tool integration and hypothesis testing. These workshops teach researchers how to add bioinformatics tools and/or datasets into the iPlant cyberinfrastructure enabling plant scientists to perform complex analyses on large datasets without the need to master the command-line or high-performance computational services