101 results for Report, 1997

  • Recent Developments in Organic Food Production in New Zealand: Part 2: Kiwifruit in the Bay of Plenty

    Campbell, Hugh; Fairweather, John; Steven, David (1997)

    Report
    University of Otago

    This report presents the findings of research into the development of organic kiwifruit production in the Bay of Plenty. These results form the second of four case studies which constitute the Public Good Science Fund programme ‘Optimum Development of Certified Organic Horticulture in New Zealand’. The other case study regions are Canterbury (Campbell 1996), Gisborne (to be completed during 1997) and Nelson (to be completed by 1998). The primary objective of this report is to document developments in the organic export industry in the Bay of Plenty. Comparisons between Canterbury and the Bay of Plenty have occasionally been included in this report in order to provide more clarity about the development of organic production in the Bay of Plenty itself. While there is some discussion of the differences between Canterbury and the Bay of Plenty in the Conclusion, these are only brief. Full comparison of the regional factors influencing the development of organic exporting will be set aside until all four case studies have been completed.

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  • Adjoints, Absolute Values and Polar Decompostions

    Bridges, D.S; Richman, F; Schuster, P (1997-11)

    Report
    The University of Auckland Library

    Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given for the existence of an adjoint, and a general notion of a polar decomposition is developed. The Riesz representation theorem is proved without countable choice.

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  • Small Trivalent Graphs of Large Girth

    Conder, M (1997-06)

    Report
    The University of Auckland Library

    Definitions are given for seven trivalent Cayley graphs, of girths 17; 18; 20; 21; 22; 23 and 24. At the time of writing (June 1997) each of these is the smallest known trivalent graph of the corresponding girth.

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  • Computational Complementarity and Sofic Shifts

    Calude, C.S; Lipponen, M (1997-08)

    Report
    The University of Auckland Library

    Finite automata (with outputs but no initial states) have been extensively used as models of computational complementarity, a property which mimics the physical complementarity. All this work was focussed on “frames", i.e., on fixed, static, local descriptions of the system behaviour. In this paper we are mainly interested in the asymptotical description of complementarity. To this aim we will study the asymptotical behaviour of two complementarity principles by associating to every incomplete deterministic automaton (with outputs, but no initial state) certain sofic shifts: automata having the same behaviour correspond to a unique sofic shift. In this way, a class of sofic shifts reflecting complementarity will be introduced and studied. We will prove that there is a strong relation between “local complementarity", as it is perceived at the level of “frames", and “asymptotical complementarity" as it is described by the sofic shift.

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  • Nonassociative Computable Rings and Their Isomorphisms. (1997)

    Khoussainov, B.; Slinko, A. (1997-08)

    Report
    The University of Auckland Library

    We investigate computable isomorphism types of (nonassociative) rings. We prove that for any n Є ω U {ω} there exists a ring with exactly n computable isomorphism types. We also investigate the relationship between the number of computable isomorphism types of a ring and the number of computable isomorphism types of its expansion by a finite number of constants.

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  • Practical Enumeration Methods for Graphs of Bounded Pathwidth and Treewidth

    Dinneen, Michael (1997-09)

    Report
    The University of Auckland Library

    Using an algebraic representation for graphs of bounded pathwidth or treewidth we provide simple methods for generating these families in increasing order of the number of vertices and edges. We also study canonic representions of fixed- and free- boundaried graphs of bounded width.

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  • Chaitin Omega Numbers and Strong Reducibilities

    Calude, C.S; Nies, A (1997-10)

    Report
    The University of Auckland Library

    We prove that any Chaitin Ω number (i.e., the halting probability of a universal self-delimiting Turing machine) is wtt-complete, but not tt-complete. In this way we obtain a whole class of natural examples of wtt-complete but not tt-complete r.e. sets. The proof is direct and elementary.

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  • Invariance Properties of Random Sequences

    Hertling, P; Wang, Y (1997-10)

    Report
    The University of Auckland Library

    We present invariance characterizations of different types of random sequences. We correct Schnorr's original, incorrect characterization of Martin-Löf random sequences, compare it with Schnorr's corresponding characterization of his own randomness concept, and give a similar, new chararacterization of Kurtz random sequences. That is, we show that an infinite sequence ξ is Kurtz random if and only if for every partial, computable, measure-invariant function φ: ∑ ω→∑ ω the sequence φ (ξ) is not recursive.

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  • Feedback for Relations

    Cazanescu, V.E (1997-11)

    Report
    The University of Auckland Library

    In our previous papers [3,2] we have proved that there are nine types of finite relations which are closed under a natural definition of feedback. In this note we prove that this natural definition is the unique feedback which satisfies the axioms of a biflow over there usual composition and sum.

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  • Embedding Quantum Universes into Classical Ones

    Calude, C.S; Hertling, P.H; Svozil, K (1997-05)

    Report
    The University of Auckland Library

    Do the partial order and lattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Re-phrased, how far might a classical understanding of quantum mechanics be, in principle, possible? A celebrated result by Kochen and Specker answers the above question in the negative. However, this answer is just one among different possible ones, not all negative. It is our aim to discuss the above question in terms of mappings of quantum worlds into classical ones, more specifically, in terms of embeddings of quantum logics into classical logics; depending upon the type of restrictions imposed on embeddings the question may get negative or positive answers.

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  • Constructive Mathematics, in Theory and Programming Practice

    Bridges, D.S; Reeves, S (1997-11)

    Report
    The University of Auckland Library

    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). It gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-Löf's theory of types as a formal system for BISH.

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  • Linear Independence and Choice

    Bridges, D.S; Richman, F; Schuster, P (1997-05)

    Report
    The University of Auckland Library

    The notions of linear and metric independence are investigated in relation to the property: if U is a set of m + 1 independent vectors, and X is a set of m independent vectors, then adjoining some vector in U to X results in a set of m + 1 independent vectors. A weak countable choice axiom is introduced, in the presence of which linear and metric independence are equivalent. Proofs are carried out in the context of intuitionistic logic.

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  • Surjective Functions on Computably Growing Cantor Sets

    Hertling, P (1997-10)

    Report
    The University of Auckland Library

    Every infinite binary sequence is Turing reducible to a random one. This is a corollary of a result of Peter Gacs stating that for every co-r.e. closed set with positive measure of infinite sequences there exists a computable mapping which maps a subset of the set onto the whole space of infinite sequences. Cristian Calude asked whether in this result one can replace the positive measure condition by a weaker condition not involving the measure. We show that this is indeed possible: it is sufficient to demand that the co-r.e. closed set contains a computably growing Cantor set. Furthermore, in the case of a set with positive measure we construct a surjective computable map which is more effective than the map constructed by Gacs.

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  • Disjunctive Sequences: An Overview

    Calude, C.S; Priese, L; Staiger, L (1997-10)

    Report
    The University of Auckland Library

    Following Jürgensen and Thierrin [21] we say that an infinite sequence is disjunctive if it contains any (finite) word, or, equivalently, if any word appears in the sequence infinitely many times. “Disjunctivity” is a natural qualitative property; it is weaker, than the property of “normality” (introduced by Borel [1]; see, for instance, Kuipers, Niederreiter [24]). The aim of this paper is to survey some basic results on disjunctive sequences and to explore their role in various areas of mathematics (e.g. in automata-theoretic studies of ω-languages or number theory). To achieve our goal we will use various instruments borrowed from topology, measure-theory, probability theory, number theory, automata and formal languages.

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  • Recursively Enumerable Reals and Chaitin Omega Numbers

    Calude, C.S; Hertling, P.H; Khoussainov, B; Wang, Y (1997-10)

    Report
    The University of Auckland Library

    A real α is called recursively enumerable if it can be approximated by an increasing, recursive sequence of rationals. The halting probability of a universal self- delimiting Turing machine (Chaitin's Ω number, [10]) is a random r.e. real. Solovay's [25] Ω-like reals are also random r.e. reals. Solovay showed that any Chaitin Ω number is Ω-like. In this paper we show that the converse implication is true as well: any Ω-like real in the unit interval is the halting probability of a universal self-delimiting Turing machine. Following Solovay [25] and Chaitin [11] we say that an r.e. real α dominates an r.e. real β if from a good approximation of α from below one can compute a good approximation of β from below. We shall study this relation and characterize it in terms of relations between r.e. sets. Ω-like numbers are the maximal r.e. real numbers with respect to this order, that is, from a good approximation to an Ω-like real one can compute a good approximation for every r.e. real. This property shows the strength of Ω for approximation purposes. However, the situation is radically different if one wishes to compute digits of the binary expansion of an r.e. real: one cannot compute with a total recursive function the first n digits of the r.e. real 0:¬xK (the characteristic sequence of the halting problem) from the first g(n) digits of Ω, for any total recursive function g.

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  • Digital Geometry: Introduction and Bibliography

    Rosenfeld, Azriel (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/1997/CITR-TR-1.pdf under terms that include this permission. All other rights are reserved by the author(s). Digital geometry deals with geometrical properties of "digital objects", which are usually taken to be sets of lattice points in the discrete space Zⁿ. Such objects are often the result of applying a "digitization" process to objects in the Euclidean space Rⁿ. A central theme in digital geometry is how to characterize digital objects that could be the digitizations of "real" objects that have given geometric properties. The literature on digital geometry dates back to the late 1960's. The report includes a bibliography of more then 900 papers on the subject, organized by topic. It outlines the main lines of development of the field, and indicates areas in which interesting problems remain open.

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  • A Modular 10-DOF Vision System for High-Resolution Active Stereo

    Schlüns, Karsten; Fellenz, Winfried; Koschan, Andreas; Teschner, Matthias (1997)

    Report
    The University of Auckland Library

    We present a low-cost active vision system with ten degrees of freedom which has been built from off-the-shelf parts. To obtain high resolution depth information of fixated objects in the scene a general purpose calibration procedure is proposed which estimates intrinsic and extrinsic camera parameters including the vergence axes of both cameras. To produce enhanced dense depth maps a hierarchical block matching procedure is presented which employs color information. To simplify the development of controlling strategies for the head a modular hierarchy is proposed that distributes various tasks among different levels employing basic capabilities of the components of the head.

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  • Evaluation of MPEG Motion Compensation Algorithms

    Stegner, Axel; Klette, Reinhard (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). This paper describes on-going research about the development of an evaluation scheme which allows an objective comparison of different motion detection algorithms used while compressing image sequences: "real world" sequences as well as generated sequences containing special textures or objects. Its focus is on block motion detection algorithms used by MPEG video encoding and the goal is to develop an objective motion compensation quality.

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  • Shading Based 3D Shape Recovery in the Presence of Shadows

    Schlüns, Karsten (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Shadows usually cause various problems in three-dimensional shape recovery and measurement methods. In particular shading based approaches such as shape-from-shading or the photometric stereo method produce no or wrong results if the shadows are not treated appropriately. We show how information extracted from shadows can be employed to reduce the problems caused by them. This is done for multiple light-source photometric stereo. Unlike other published work, we formulate sufficient conditions to recover locally unique surface normals from two image irradiances (intensities) and a zero-irradiance caused by a shadow. We also distinguish between self-shadows and cast-shadows. Moreover we show how much information is obtainable by using the shadow analysis.

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  • The Irradiance Error and its Effect in Photometric Stereo

    Schlüns, Karsten (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). This paper discusses some essential aspects on evaluating the three-source photometric stereo method (PSM). PSM is a shading based 3D shape recovery approach that calculates a dense set of surface orientations from three input images taken by changing the illumination direction without moving the optical sensor. A subsequent step can be used to convert the surface gradients into a dense height map by means of an integration method. In a previous paper [2] we carried out evaluations of integration approaches. Here we show how the resolution of surface orientations depends on perturbations in the image irradiances (intensities). Previous methods considered only single light source configurations or particular image irradiance triples, hence no general predictions could be made. We give a simple geometrical interpretation to estimate upper bounds of angular deviations with respect to expected errors in image irradiances. Such predictions are necessary for the practical application of the photometric stereo method.

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