2022-01-24T14:48:25Zhttps://researchspace.auckland.ac.nz/dspace-oai/requestoai:researchspace.auckland.ac.nz:2292/26812008-08-29T04:56:08Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
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Coeurjolly, David
author
Klette, Reinhard
author
2001
The paper compares previously published length estimators having digitized curves as input. The evaluation uses multigrid convergence (theoretical results and measured speed of convergence) and further measures as criteria. The paper also suggests a new gradient-based method for length estimation.
Communication and Information Technology Research Technical Report 105, (2001)
1178-3640
http://hdl.handle.net/2292/2681
A Comparative Evaluation of Length Estimators
oai:researchspace.auckland.ac.nz:2292/34732009-04-16T23:43:22Zcom_2292_122col_2292_3452
00925njm 22002777a 4500
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Hosking, J.G.
author
Grundy, J.C.
author
1995-02
We describe a technique for dealing with partial mappings between different representations,
both formal and informal, of an evolving software system. This technique uses discrete "change
descriptions" to propagate changes between related views. These change descriptions my be
used to autiomatically modify affected views, or to annotate the view to indicate manual
intervention is required to maintain consistency.
Computer Science Technical Reports 109 (1995)
1173-3500
http://hdl.handle.net/2292/3473
Using change descriptions to maintain consistency across multiple representations
oai:researchspace.auckland.ac.nz:2292/49732009-08-28T12:35:47Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
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Nicholls, Geoff
author
2000
The Arak process is a solvable stochastic process which generates coloured patterns in the plane. Patterns are made up of a variable number of random non-intersecting polygons. We show that the distribution of Arak process states is the Gibbs distribution of its states in thermodynamic equilibrium in the grand canonical ensemble. The sequence of Gibbs distributions form a new model parameterised by temperature. We prove that there is a phase transition in this model, for some non-zero temperature. We illustrate this conclusion with simulation results. We measure the critical exponents of this off-lattice model and find they are consistent with those of the Ising model in two dimensions.
Department of Mathematics - Research Reports-455 (2000)
1173-0889
http://hdl.handle.net/2292/4973
Spontaneous magnetisation in the plane
oai:researchspace.auckland.ac.nz:2292/34692009-04-17T01:11:31Zcom_2292_122col_2292_3452
00925njm 22002777a 4500
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Gibbons, J.
author
Cai, W.
author
Skillicorn, D.
author
1993-03
Accumulations are higher-order operations on structured objects: they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree algorithms. We present two Erew Pram algorithms for computing accumulations on trees taking O(log n ) time on O (n/log n) processors, which is optional.
Computer Science Technical Reports 070 (1993)
1173-3500
http://hdl.handle.net/2292/3469
Efficient Parallel Algorithm for Tree Accumulations
oai:researchspace.auckland.ac.nz:2292/50902009-08-28T12:40:29Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
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Oleinik, V.L.
author
Pavlov, B.
author
2004-12
In [1] a probabilistic solution to the Infinite Merchant's Problem, an undecidable problem equivalent to the Halting Problem, was proposed. The solution uses a real Hilbert space and is based on the estimation of the exponential growth of an unbounded semigroup. In [2] was offered an alternative solution in terms of scattering processes on quantum dots. The authors reduced the problem to a special scattering problem and testify the "halting phenomenon" based on the quantum measurement of results of scattering with random input data. The a-posteriori probability of halting, subject to the negative results of multiple independent tests, was estimated. The possibility of location the number of the bag with false coins in finite-dimensional case was noticed in [1] and proved in [2]. The aim of this paper is to offer a solution of the latter problem in the infinite case. [1] C.S. Calude, B.S. Pavlov. Coins, quantum measurements, and Turing's barrier, Quantum Information Processing, 1, 1--2 (2002), 107--127. [2] V.A. Adamyan, C.S. Calude, B.S. Pavlov, A quantum scattering approach to undecidable problem. In: Quantum information and complexity, Proceedings of the Meijo Winter School 2003, Meijo University, Nagoya, Japan, 6 - 10 January 2003, edited by T Hida, K Saitô (Meijo University, Japan) and Si Si (Aichi Prefectural University, Japan).
Department of Mathematics - Research Reports-533 (2004)
1173-0889
http://hdl.handle.net/2292/5090
Probabilistic Solutions to Merchant Problems: Locating of the False Stack
oai:researchspace.auckland.ac.nz:2292/36552012-02-02T23:23:15Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
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Antoniou, I
author
Calude, C.S
author
Dinneen, M.J
author
2000-11
These are additional papers of talks that were presented at the Second International
Conference on Unconventional Models of Computation (UMC’2K).
UMC’2K, organized by the Centre for Discrete Mathematics and Theoretical
Computer Science, the International Solvay Institutes for Physics and Chemistry
and the Vrije Universiteit Brussel Theoretical Physics Division was held
at Solvay Institutes during December 13–16, 2000.
The conference encompasses all areas of unconventional computation, especially
quantum computing, DNA-based computation, evolutionary algorithms
and other proposals for computation models that go beyond the Turing model.
Additional refereed and invited papers of UMC’2K appear in the following proceedings:
I. Antoniou, C. S. Calude, M. J. Dinneen, editors. Unconventional
Models of Computation, UMC’2K, Springer-Verlag, London, December
2000, XI + 301 pages.
CDMTCS Research Reports CDMTCS-147 (2000)
1178-3540
http://hdl.handle.net/2292/3655
Supplemental Papers for the 2nd Unconventional Models of Computation Conference
oai:researchspace.auckland.ac.nz:2292/27232008-08-29T04:58:04Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
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Klette, Reinhard
author
2000
The history of cell complexes is closely related to the birth and development of topology in general. Johann Benedict Listing (1802-1882) introduced the term "topology" into mathematics in a paper published in 1847, and he also defined cell complexes for the first time in a paper published in 1862. Carl Friedrich Gauss (1777-1855) is often cited as the one who initiated these ideas, but he did not publish either on topology or on cell complexes. The pioneering work of Leonhard Euler (1707-1783) on graphs is also often cited as the birth of topology, and Euler's work was cited by Listing in 1862 as a stimulus for his research on cell complexes. There are different branches in topology which have little in common: point set topology, algebraic topology, differential topology etc. Confusion may arise if just "topology" is specied, without clarifying the used concept. Topological subjects in mathematics are often related to continuous models, and therefore quite irrelevant to computer based solutions in image analysis. Compared to this, only a minority of topology publications in mathematics addresses discrete spaces which are appropriate for computer-based image analysis. In these cases, often the notion of a cell complex plays a crucial role. This paper briefly reports on a few of these publications, which might be helpful or at least of interest for recent studies in topological issues in image analysis. It is not a balanced review, due to a certain randomness in the selection process of cited work. This paper is also not intended to cover the very lively progress in cell complex studies within the context of image analysis during the last two decades. Basically it stops its historic review at the time when this subject in image analysis research gained speed in 1980-1990. As a general point of view, the paper indicates that image analysis contributes to a fusion of two topological concepts, the geometric or abstract cell complex approach and point set topology, which leads to an in-depth study of topologies defined on geometric or abstract cell complexes.
Communication and Information Technology Research Technical Report 60, (2000)
1178-3685
http://hdl.handle.net/2292/2723
Cell Complexes through Time
oai:researchspace.auckland.ac.nz:2292/38242012-02-02T23:23:18Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
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Calude, C.S
author
Zimand, M
author
2008-01
Two objects are independent if they do not a ect each other. Independence is wellunderstood
in classical information theory, but less in algorithmic information theory.
Working in the framework of algorithmic information theory, the paper proposes two
types of independence for arbitrary in nite binary sequences and studies their properties.
Our two proposed notions of independence have some of the intuitive properties
that one naturally expects. For example, for every sequence x, the set of sequences
that are independent with x has measure one. For both notions of independence we investigate
to what extent pairs of independent sequences, can be e ectively constructed
via Turing reductions (from one or more input sequences). In this respect, we prove
several impossibility results. For example, it is shown that there is no e ective way of
producing from an arbitrary sequence with positive constructive Hausdor dimension
two sequences that are independent (even in the weaker type of independence) and
have super-logarithmic complexity. Finally, a few conjectures and open questions are
discussed.
CDMTCS Research Reports CDMTCS-317 (2008)
1178-3540
http://hdl.handle.net/2292/3824
Algorithmically Independent Sequences
oai:researchspace.auckland.ac.nz:2292/27922008-08-29T05:01:38Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
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Klette, Gisela
author
2006
Branch indices of points on curves (introduced by Urysohn and Menger) are of basic importance in the mathematical theory of curves, defined in Euclidean space. This paper applies the concept of branch points in the 3D orthogonal grid, motivated by the need to analyze curve-like structures in digital images. These curve-like structures have been derived as 3D skeletons (by means of thinning). This paper discusses approaches of defining branch indices for voxels on 3D skeletons, where the notion of a junction will play a crucial role. We illustrate the potentials of using junctions in 3D image analysis based on a recent project of analyzing the distribution of astrocytes in human brain tissue.
Communication and Information Technology Research Technical Report 178, (2006)
1178-3567
http://hdl.handle.net/2292/2792
Branch Voxels and Junctions in 3D Skeletons
oai:researchspace.auckland.ac.nz:2292/251222016-04-22T12:46:26Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
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Smith, Jill
author
2003-7
ACE papers, Issue 13: Multiliteracies and Other Ideas for Education in The Arts, Paper 2.
http://hdl.handle.net/2292/25122
Biculturalism: The relationship between education policy and art education practice in secondary schools in Aotearoa New Zealand
oai:researchspace.auckland.ac.nz:2292/28382008-08-29T05:03:22Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
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Hermann, Simon
author
Klette, Reinhard
author
2003
This report explains a new method for the estimation of curvature of plane curves and compares it with a method which has been presented in [2]. Both methods are based on global approximations of tangents by digital straight line segments. Experimental studies show that a replacement of global by local approximation results in errors which, in contrast to the global approximation, converge to constants > 0. We also apply the new global method for curvature estimation of curves to surface curvature estimation, and discuss a method for estimating mean curvature of surfaces which is based on Meusnier's theorem.
Communication and Information Technology Research Technical Report 129, (2003)
1178-3616
http://hdl.handle.net/2292/2838
Multigrid Analysis of Curvature Estimators
oai:researchspace.auckland.ac.nz:2292/278532016-04-22T14:17:15Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Hoffmann, S
author
Staiger, L
author
2015
The space of one-sided infinite words plays a crucial rôle in several parts of Theoretical Computer Science. Usually, it is convenient to regard this space as a metric space, the Cantor-space. It turned out that for several
purposes topologies other than the one of the Cantor-space are useful, e.g. for studying fragments of first-order logic over infinite words or for a topological characterisation of random infinite words.
Continuing the work of [SS10], here we consider two different refinements of the Cantor-space, given by measuring common factors, and common factors occurring infinitely often. In particular we investigate the relation of these topologies to the sets of infinite words definable by finite automata, that is, to regular !-languages.
CDMTCS Research Reports CDMTCS-484 (2015)
1178-3540
http://hdl.handle.net/2292/27853
Subword Metrics for Infinite Words
oai:researchspace.auckland.ac.nz:2292/49682009-08-28T12:30:43Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
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Koray, Semih
author
Slinko, Arkadii
author
2001-04
In this paper we introduce the concept of F-consistency of a social choice function relative to the given class F of social choice functions. This refines the concept of consistency (self-selectivity), introduced by the first author, and allows to discover a number of classes F for which there exist F-consistent social choice functions which are neither dictatorial nor antidictatorial. Furthermore, under certain mild conditions on F all F-consistent social choice functions are described.
Department of Mathematics - Research Reports-461 (2001)
1173-0889
http://hdl.handle.net/2292/4968
On consistent social choice functions
oai:researchspace.auckland.ac.nz:2292/34652009-11-17T02:23:28Zcom_2292_122col_2292_3452
00925njm 22002777a 4500
dc
Gibbons, J.
author
1992-11
Computer Science Technical Reports 064 (1992)
1173-3500
http://hdl.handle.net/2292/3465
Computing Downwards Accumulations on Trees Quickly (1992)
oai:researchspace.auckland.ac.nz:2292/51102009-11-19T00:45:30Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
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Harmer, M.
author
2004-04
A solvable model corresponding to a given quantum network is described in cite{MPP} without an explicit description of how to fit the parameters of the solvable model. Here we give a procedure to fit these parameters so that the solvable model reproduces the important features, viz. the scattering matrix for the physically relevant energies, of the quantum network, subject to the non-vanishing of a determinant.
Department of Mathematics - Research Reports-514 (2004)
1173-0889
http://hdl.handle.net/2292/5110
Fitting Parameters for a Solvable Model of a Quantum Network (Maths)
oai:researchspace.auckland.ac.nz:2292/27422008-08-29T04:59:30Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
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Luo, Jin
author
Schlüns, Karsten
author
1998
This paper presents a new approach to integrate the gradient field to the relative depth or height map from multiple view directions in polar coordinates. Traditional integration techniques are based on cartesian coordinates. In this approach, the surface normals are calculated by photometric stereo method. The object is illuminated by three light sources and rotated on a controlled turntable. The experimantal results of the cross section of the synthetic and real objects are feasible and promising.
Communication and Information Technology Research Technical Report 33, (1998)
1178-3712
http://hdl.handle.net/2292/2742
Height from Gradients in Polar Coordinates
oai:researchspace.auckland.ac.nz:2292/35732012-02-02T23:23:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
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Hertling, P
author
1997-10
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.
CDMTCS Research Reports CDMTCS-064 (1997)
1178-3540
http://hdl.handle.net/2292/3573
Surjective Functions on Computably Growing Cantor Sets
oai:researchspace.auckland.ac.nz:2292/251532016-04-22T12:50:42Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
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Mawson, Brent
author
2005-9
ACE papers, Issue 16: Approaches to Domain Knowledge in Early Childhood Pedagogy, Paper 8.
http://hdl.handle.net/2292/25153
Where do I start? Technology in early childhood
oai:researchspace.auckland.ac.nz:2292/374962018-07-21T12:31:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
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Staiger, L
author
2017
A quasiperiod of a finite or infinite string is a word whose occurrences cover every part of the string. An infinite string is referred to as quasiperiodic if it has a quasiperiod.
CDMTCS Research Reports CDMTCS-509 (2017)
1178-3540
http://hdl.handle.net/2292/37496
Quasiperiods of Infinite Words
oai:researchspace.auckland.ac.nz:2292/37032012-02-02T23:23:15Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude, C.S
author
Dinneen, Michael
author
Peper, F
author
2002-10
These are additional abstracts of talks that were presented at the Third International Conference on Unconventional Models of Computation (UMC’02). Computer Science, and the Kansai Advanced Research Centre of the Communications Research Laboratory was held at the Orbis hall in the centre of Kobe’s Rokko island, during October 15-19, 2002. The conference encompasses all areas of unconventional computation, especially quantum computing, DNA-based computation, evolutionary algorithms and other proposals for computation models that go beyond the Turing model. Additional refereed and invited papers of UMC’02 appear in the following proceedings: C.S. Calude, M.J. Dinneen, and F. Peper editors. Unconventional Models of Computation, UMC’02, LNCS 2509, Springer-Verlag, October 2002, VIII+300 pages.
CDMTCS Research Reports CDMTCS-195 (2002)
1178-3540
http://hdl.handle.net/2292/3703
Supplemental Papers for the 3nd Unconventional Models of Computation Conference
oai:researchspace.auckland.ac.nz:2292/49902009-08-28T12:38:54Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
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Melnikov, Y.
author
Pavlov, B.
author
2000
In actual paper we develop the spectral analysis of Schr"odinger operators on lattice type graphs. For basic example of qubic periodic graph the problem is reduced to the spectral analysis of the regular differential operators on a fundamental star-like subgraph with a selfadjoint condition at the central node and quasiperiodic conditions at the boundary vertices. Using an explicite expression for resolvent of lattice-type operator we develop in the second sections the Lippmann- Schwinger techniques for the perturbed periodic operator and construct the corresponding scattering matrix. It serves as a base for the approximation of the multy-dimensional Schr"odinger operator by the onedimansional operator on graph : in the third section of the paper for given $N$-dimensional Schr"odinger operators with rapidly decreasing potential we construct a lattice-type operator on cubic graph embedded into ${bf R}^N$ and show that the original $N$-dimensional scattering problem can be approximated in proper sense by the corresponding scattering problem for the perturbed lattice operator.
Department of Mathematics - Research Reports-439 (2000)
1173-0889
http://hdl.handle.net/2292/4990
Scattering on graphs and one-dimensional approximation of $N-$dimensional Schr"odinger operators
oai:researchspace.auckland.ac.nz:2292/49852009-08-28T12:36:39Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
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Harmer, M.
author
2000
The theory of self-adjoint extensions is closely related to the theory of hermitian symplectic geometry cite{Pav,Kost:Sch,Nov3}. Here we develop this idea, showing that it may also be used to consider symmetric extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange Grassmannian in terms of the unitary matrices $U (n)$. This allows us to explicitly describe all self-adjoint boundary conditions for the Schr"{o}dinger operator on the graph in terms of a unitary matrix. We show that the asymptotics of the scattering matrix can be simply expressed in terms of this unitary matrix. \ Using the construction of the asymptotic hermitian symplectic space cite{Nov1,Nov3} we derive a formula for the scattering matrix of a graph in terms of the scattering matrices of its subgraphs. This also provides a characterisation of the discrete eigenvalues embedded in the continuous spectrum.
Department of Mathematics - Research Reports-444 (2000)
1173-0889
http://hdl.handle.net/2292/4985
Hermitian symplectic geometry and the Schr"{o}dinger operator on the graph
oai:researchspace.auckland.ac.nz:2292/494842020-01-11T11:36:32Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
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Staiger, L
author
2019
Using an iterative tree construction we show that for simple computable
subsets of the Cantor space Hausdorff, constructive and computable
dimensions might be incomputable.
CDMTCS Research Reports CDMTCS-535 (2019)
1178-3540
http://hdl.handle.net/2292/49484
On the incomputability of computable dimension
oai:researchspace.auckland.ac.nz:2292/251392016-04-22T12:48:03Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
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McDonald, Lyn
author
2005-3
This article is based on a research study (McDonald, 2001) which identified and described the beliefs, attitudes and practices of associate (mentor) teachers within a New Zealand context. The purpose of the research was to investigate associate teachers’ supervision styles and to identify what makes them successful. Data was collected from associates, visiting lecturers and student teachers. Analysis of the data indicated that an effective associate teacher needs to motivate student teachers, find out about their learning needs, discuss their perceptions about teaching, and model effective teaching practice. Associate teachers should also provide regular feedback, and ensure that their classroom climate supports the supervision of students. Student teachers should have the opportunity to engage in critical reflection. The study concluded that associate teachers’ own personal pedagogy should be effective, that they should have up-to-date curriculum and professional knowledge and should also be clear communicators with the ability to talk and listen to students. The findings of this research confirmed the importance of successful practicum experiences for student teachers in the development of becoming an effective practitioner.
ACE papers, Issue 15: Pedagogy and practice under the lens, Paper 4.
http://hdl.handle.net/2292/25139
Effective mentoring of student teachers: Beliefs, attitudes and practices of successful New Zealand associate teachers
oai:researchspace.auckland.ac.nz:2292/26802008-08-29T04:56:04Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Klette, Reinhard
author
2001
This paper discusses different topologies on the planar orthogonal grid and shows homeomorphy between cellular models. It also points out that graph-theoretical topologies exist defined by planar extensions of the 4-adjacency graph. All these topologies are potential models for image carriers.
Communication and Information Technology Research Technical Report 106, (2001)
1178-3639
http://hdl.handle.net/2292/2680
Topologies on the Planar Orthogonal Grid
oai:researchspace.auckland.ac.nz:2292/36322012-02-02T23:23:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Castellanos, J
author
Paun, G
author
Rodriguez-Paton, A
author
2000-02
We consider a combination of P systems with objects described
by symbols with P systems with objects described by strings. Namely, we
work with multisets of strings and consider as the result of a computation
the number of strings in a given output membrane. The strings (also called
worms) are processed by replication, splitting, mutation, and recombination;
no priority among rules and no other ingredient is used. In these circumstances,
it is proved that (1) P systems of this type can generate all recursively
enumerable sets of numbers, and, moreover, (2) the Hamiltonian Path
Problem in a directed graph can be solved in a quadratic time, while the SAT
problem can be solved in a linear time.
CDMTCS Research Reports CDMTCS-123 (2000)
1178-3540
http://hdl.handle.net/2292/3632
Computing with Membranes: P Systems with Worm-Objects
oai:researchspace.auckland.ac.nz:2292/27272021-07-29T03:58:04Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Bülow, Thomas
author
Klette, Reinhard
author
1999
We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional euclidian space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far no algorithm was known for the calculation of such a shortest polygonal curve. This paper provides an iterative algorithmic solution, including a presentation of its foundations and of experimental results.
Communication and Information Technology Research Technical Report 55, (1999)
1178-3690
http://hdl.handle.net/2292/2727
Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm
oai:researchspace.auckland.ac.nz:2292/51482009-08-28T12:38:33Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Golubyatnikov, Vladimir P.
author
Likhoshvai, Vitalii A.
author
2002-03
We consider an evolution model of population of frogs on the aqueous stage of their development. Here we study the problem of determination of the parameters of the proposed model from the observation data, in particular, from the average times of attainment of different biological ages and from the survivability function. Our model gives possibility to estimate the number of morphologically indistinguishable ages which is particularly interesting in the case of incomplete experimental data.
Department of Mathematics - Research Reports-480 (2002)
1173-0889
http://hdl.handle.net/2292/5148
On modeling of amphibious population evolution
oai:researchspace.auckland.ac.nz:2292/317542017-02-11T11:30:48Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude, CS
author
Thompson, D
author
2016
Incompleteness and undecidability have been used for many years as arguments against automatising the practice of mathematics.
The advent of powerful computers and proof-assistants – programs that assist the development of formal proofs by human-machine collaboration – has revived the interest in formal proofs and diminished considerably the value of these arguments.
In this paper we discuss some challenges proof-assistants face in handling undecidable problems – the very results cited above – using for illustrations the generic proof-assistant Isabelle.
CDMTCS Research Reports CDMTCS-497 (2016)
1178-3540
http://hdl.handle.net/2292/31754
Incompleteness, Undecidability and Automated Proofs
oai:researchspace.auckland.ac.nz:2292/27192008-08-29T04:57:16Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Klette, Reinhard
author
Zunic, Jovisa
author
2000
The conceptual design of many procedures used in image analysis starts with models which assume as an input sets in Euclidean space which we regard as real objects. However, the application finally requires that the Euclidean (real) objects have to be modelled by digital sets, i.e. they are approximated by their corresponding digitizations. Also "continuous" operations (for example integrations or differentiations) are replaced by "discrete" counterparts (for example summations or differences) by assuming that such an replacement has only a minor impact on the accuracy or efficiency of the implemented procedure. This paper discusses applications of results in number theory with respect to error estimations, accuracy evalua- tions, correctness proofs etc. for image analysis procedures. Knowledge about digitization errors or approximation errors may help to suggest ways how they can be kept under required limits. Until now have been only minor impacts of image analysis on developments in number theory, by defining new problems, or by specifying ways how existing results may be discussed in the context of image analysis. There might be a more fruitful exchange between both disciplines in the future.
Communication and Information Technology Research Technical Report 63, (2000)
1178-3682
http://hdl.handle.net/2292/2719
Interactions between Number Theory and Image
oai:researchspace.auckland.ac.nz:2292/251112016-04-22T12:45:44Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
dc
Carpenter, Vicki M
author
2003-5
ACE papers, Issue 12: Curriculum Theory, Issues and Practice: Student Voices, Editorial Comment.
http://hdl.handle.net/2292/25111
Issue 12: Curriculum: Theory, Issues and Practice: Student voices - Editorial Comment
oai:researchspace.auckland.ac.nz:2292/239072015-01-28T11:38:32Zcom_2292_122col_2292_3508
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Calude, CS
author
Longo, G
author
2014
In this paper we briefly discuss various forms of randomness that physics, mathematics and computing
have proposed. Classical and quantum physics view randomness, that we describe as unpredictability in
the intended theory, in different ways. Computing allows to discuss this issue in an abstract, yet very expressive
mean, which yields useful hierarchies of randomness and may help to relate its various forms. We introduce then
the open field of biological randomness—its peculiar nature and role in ontogenesis and in evolutionary dynamics
(phylogenesis). Randomness does not oppose, but contributes to the organisms’ and populations’ structural
stability, in contexts where the notion of probability, as measurement of randomness, is not well defined.
CDMTCS Research Reports CDMTCS-474 (2014)
1178-3540
http://hdl.handle.net/2292/23907
Classical, Quantum and Biological Randomness as Relative Incomputability
oai:researchspace.auckland.ac.nz:2292/35892012-02-02T23:23:16Zcom_2292_122col_2292_3508
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Dinneen, Michael
author
Pritchard, G
author
Wilson, Mark
author
1998-04
We consider the problem of constructing networks with as many nodes as possible,
subject to upper bounds on the degree and broadcast time. This paper includes the
results of an extensive empirical study of broadcasting in small regular graphs using a stochastic
search algorithm to approximate the broadcast time. Significant improvements on
known results are obtained for cubic broadcast networks.
CDMTCS Research Reports CDMTCS-080 (1998)
1178-3540
http://hdl.handle.net/2292/3589
Degree- and Time- Constrained Broadcast Networks
oai:researchspace.auckland.ac.nz:2292/27902008-08-29T05:01:33Zcom_2292_122col_2292_2623
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Brimkov, Valentin
author
2006
Given a set M subset Z3, an enclosing polyhedron for M is any polyhedron P such that the set of integer points contained in P is precisely M . Representing a discrete volume by enclosing polyhedron is a fundamental problem in visualization. In this paper we propose the first proof of the long-standing conjecture that the problem of finding an enclosing polyhedron with a minimal number of 2-facets is strongly NP-hard and provide a lower bound for that number.
Communication and Information Technology Research Technical Report 179, (2006)
1178-3566
http://hdl.handle.net/2292/2790
Discrete Volume Polyhedrization is Strongly NP-Hard
oai:researchspace.auckland.ac.nz:2292/27052008-08-29T04:56:57Zcom_2292_122col_2292_2623
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McIvor, Alan
author
Zang, Qi
author
2000
This paper reviews papers on tracking people in a video surveillance system, and it presents a new system designed for being able to cope with shadows in a real-time application for counting people which is one of the remaining main problems in adaptive background subtraction in such video surveillance systems.
Communication and Information Technology Research Technical Report 78, (2000)
1178-3667
http://hdl.handle.net/2292/2705
The Background Subtraction Problem for Video Surveillance Systems
oai:researchspace.auckland.ac.nz:2292/37682012-02-02T23:23:13Zcom_2292_122col_2292_3508
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Calude, C.S
author
Calude, E
author
Dinneen, Michael
author
2005-04
The famous story of the number 1729, the smallest integer which can be expressed
as the sum of two positive cubes in two different ways, motivated the
introduction of Taxicab Numbers. The smallest number expressible as the sum of
two cubes in n different ways is called Taxicab(n). So, Taxicab(2) = 1729. Further
on, Taxicab(5) = 48988659276962496. Computing Taxicab(n) is challenging and
interesting, both from mathematical and programming points of view.
The exact value of Taxicab(6) is not known; in view of the results obtained
by Bernstein [1] and Rathbun [14] it follows that Taxicab(6) is in the interval
[10¹⁸, 24153319581254312065344]. In [5] we proved that with probability greater
than 99%, Taxicab(6) = 24153319581254312065344.
In this note we improve the method used in [5] in two ways: we use (1) a larger,
and (2) a better quality random sampling, namely, a sample of 562,500 quantum
random integers drawn from the above mentioned interval using Quantis, [10]. As a
result, we prove that the above value for Taxicab(6) is true with probability greater
than 99.8%.
CDMTCS Research Reports CDMTCS-261 (2005)
1178-3540
http://hdl.handle.net/2292/3768
What is the Value of Taxicab(6)? An Update
oai:researchspace.auckland.ac.nz:2292/37522012-02-02T23:23:19Zcom_2292_122col_2292_3508
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Harmer, M.
author
2004-07
A solvable model corresponding to a given quantum network is
described in [22] without an explicit description of how to fit the parameters
of the solvable model. Here we give a procedure to fit these
parameters so that the solvable model reproduces the important features,
viz. the scattering matrix for the physically relevant energies, of
the quantum network, subject to the non-vanishing of a determinant.
CDMTCS Research Reports CDMTCS-245 (2004)
1178-3540
http://hdl.handle.net/2292/3752
Fitting Parameters for a Solvable Model of a Quantum Network (CDMTCS)
oai:researchspace.auckland.ac.nz:2292/28002008-08-29T05:01:53Zcom_2292_122col_2292_2623
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Zhang, Xin
author
Morris, John
author
2005
This article discusses ways of measuring accuracy of a laser range finder (LRF) using a specially designed calibration cube (with 3D calibration marks) in the context of a particular application (i.e., measuring volumes). We also compare (by means of experiments) two alternative volume estimation methods.
Communication and Information Technology Research Technical Report 170, (2005)
1178-3575
http://hdl.handle.net/2292/2800
Volume Measurement Using a Laser Scanner
oai:researchspace.auckland.ac.nz:2292/251512016-04-22T12:49:35Zcom_2292_122col_2292_25032
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Babbington, Shiree
author
2005-9
The notion of numeracy in early childhood education is undoubtedly seen as a valid and important aspect of all young children’s learning. This is supported by the Literacy and Numeracy Strategy which stresses the important nature of early experience as a catalyst for high levels of success in future numeracy. However, it seems that our youngest citizens are not being deliberately exposed to numeracy experiences in early childhood settings. Although there is evidence that children tested at school entry have skills and knowledge above the first stages of the numeracy framework, early childhood teachers could be making a greater difference to children’s future success in numeracy if these resources were made available, and their use encouraged, in early childhood education and care settings
ACE papers, Issue 16: Approaches to Domain Knowledge in Early Childhood Pedagogy, Paper 6.
http://hdl.handle.net/2292/25151
Numeracy and New Zealand early childhood education
oai:researchspace.auckland.ac.nz:2292/135862020-11-24T07:44:29Zcom_2292_2857com_2292_122col_2292_3404col_2292_3452
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Yu, Young
author
Carpenter, Brian
author
2012
This document reviews currently proposed IPv4-IPv6 translation techniques and describes a simple performance study of three open-source IPv4-IPv6 translators. The purpose of this document is to introduce the fundamental ideas behind NAT-PT, NAT64 and HTTP proxy and to measure the performance effect on round-trip time of using these translators in a simple network with up to 100 simultaneous connections.
Computer Science Technical Reports (2012-001). 2012. University of Auckland Computer Science Department, New Zealand. 1173-3500
1173-3500
http://hdl.handle.net/2292/13586
IPv6, NAT-PT, NAT64
Measuring IPv4-IPv6 translation techniques
oai:researchspace.auckland.ac.nz:2292/51352009-08-28T12:38:14Zcom_2292_122col_2292_4963
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Bonnington, C. Paul
author
Hartsfield, Nora
author
Siran, Jozef
author
2003-01
A 2-cell embedding of an Eulerian digraph in a closed surface is said to be directed if the boundary of each face is a directed closed walk in $G$. We prove Kuratowski-type theorems about obstructions to directed embeddings of Eulerian digraphs in the plane.
Department of Mathematics - Research Reports-492 (2003)
1173-0889
http://hdl.handle.net/2292/5135
Obstructions to directed embeddings of Eulerian digraphs in the plane
oai:researchspace.auckland.ac.nz:2292/105632012-02-09T11:41:41Zcom_2292_122col_2292_3508
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Calude, C.S.
author
Calude, E.
author
2011
This paper presents on overview of results obtained with an algorithmic
uniform method to measure the complexity of a large class of mathematical
problems and discusses a few open problems.
CDMTCS Research Reports CDMTCS-410 (2011)
1178-3540
http://hdl.handle.net/2292/10563
The Complexity of Mathematical Problems: An Overview of Results and Open Problems
oai:researchspace.auckland.ac.nz:2292/213502014-05-26T12:33:27Zcom_2292_122col_2292_3508
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Tran Le, VB
author
Link, S
author
Ferrarotti, F
author
2013
SQL designs result from methodologies such as UML or Entity-Relationship
models, description logics, or relational normalization. Independently of the methodology, sample data is promoted by academia and industry to visualize and consolidate the designs produced. SQL table definitions are a standard-compliant encoding of their designers' perception about the semantics of an application domain.
Armstrong sample data visualize these perceptions. We present a tool that computes Armstrong samples for different classes of SQL constraints. Exploiting our tool, we then investigate empirically how these Armstrong samples help design
teams recognize domain semantics. New measures empower us to compute the
distance between constraint sets in order to evaluate the usefulness of our tool.
Extensive experiments con rm that users of our tool are likely to recognize domain
semantics they would overlook otherwise. The tool thereby e ffectively complements existing design methodologies in finding quality schemata that process data efficiently.
CDMTCS Research Reports CDMTCS-451 (2013)
1178-3540
http://hdl.handle.net/2292/21350
Effective Recognition and Visualization of Semantic Requirements by Perfect SQL Samples
oai:researchspace.auckland.ac.nz:2292/36982012-02-02T23:23:13Zcom_2292_122col_2292_3508
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Goncharov, S.S
author
Khoussainov, B
author
2002-05
[no abstract available]
CDMTCS Research Reports CDMTCS-190 (2002)
1178-3540
http://hdl.handle.net/2292/3698
Complexity of Computable Models
oai:researchspace.auckland.ac.nz:2292/198112013-01-07T11:31:57Zcom_2292_122col_2292_3508
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Abbott, A.A
author
Calude, C.S.
author
Conder, J.
author
Svozil, K
author
2012
We present a stronger variant of the Kochen-Specker theorem in which some quantum observables are identiﬁed to be provably value indeﬁnite. This result is utilised for the construction and certiﬁcation of a dichotomic quantum random number generator operating in a three-dimensional Hilbert space.
CDMTCS Research Reports CDMTCS-422 (2012)
1178-3540
http://hdl.handle.net/2292/19811
Kochen-Specker Theorem Revisited and Strong Incomputability of Quantum Randomness
oai:researchspace.auckland.ac.nz:2292/28022012-02-02T23:13:51Zcom_2292_122col_2292_3205
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Shin, Bok-Suk
author
Cha, Eui-Young
author
Cho, Kyoung-Won
author
Klette, Reinhard
author
Woo, Young Woon
author
2008
The report discusses insect footprint recognition. Footprint segments are extracted from scanned footprints, and appropriate features are calculated for those segments (or cluster of segments) in order to discriminate species of insects. The selection or identification of such features is crucial for this classification process.
Multimedia Imaging Report 12 (2008)
1178-5789
http://hdl.handle.net/2292/2802
Effective Feature Extraction by Trace Transform for Insect Footprint Recognition
oai:researchspace.auckland.ac.nz:2292/23992014-05-26T00:13:58Zcom_2292_122col_2292_3435
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Fenaughty, John
author
Braun, Virginia
author
Gavey, Nicola
author
Aspin, Clive
author
Reynolds, Paul
author
Schmidt, Johanna
author
2006
Background
• The existence of sexual assault, sexual coercion and unwanted sex among gay, bisexual and other men who have sex with men is seldom acknowledged — within gay communities, society at large, or in policy.
• Although prevalence is difficult to determine, international research has established that sexual assault, sexual coercion and unwanted sex are experienced by a significant number of gay, bisexual, and other men who have sex with men.
Our project
• This project consisted of two separate, but related, studies: a broader project, and a Kaupapa Māori project.
• The broader project was designed to explore the phenomenon of sexual coercion among gay and bisexual men in Aotearoa/New Zealand.
• It did not set out to investigate the broader issue of sexual assault against gay and bisexual men by men who do not identify as gay or bisexual (i.e., sexual violence which could more easily be categorised as hate crime).
• Twenty-three key informants were interviewed about their observations and views on sexual coercion among gay, bisexual, and other men who have sex with men.
• Eighteen gay and bisexual men were interviewed about their experiences of sexual coercion.
• Six focus groups were held with gay and bisexual men in order to generate accounts about how sexuality is understood and negotiated in gay communities.
• Five takatāpui tāne were interviewed for the Kaupapa Māori project on Māori men’s experiences of sexual coercion.
Research Report. Department of Psychology, The University of Auckland. (2006)
ISBN-10: 0 908689 79 9
ISBN-13 978 0 908689 79 9
http://hdl.handle.net/2292/2399
sexual coercion
gay men
bisexual men
takatāpui tāne
unwanted sex
safer sex
Sexual Coercion among Gay Men, Bisexual Men and Takatāpui Tāne in Aotearoa/New Zealand.
oai:researchspace.auckland.ac.nz:2292/35692012-02-02T23:23:19Zcom_2292_122col_2292_3508
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Calude, E
author
Lipponen, M
author
1997-10
We construct a minimal automaton for an output-incomplete Moore automa-
ton. The approach is motivated by physical interpretation of seeing deterministic finite
automata as models for elementary particles. When compared to some classical methods
our minimal automaton is unique up to an isomorphism and preserves also the undefined
or unspecified behaviour of the original automaton.
CDMTCS Research Reports CDMTCS-060 (1997)
1178-3540
http://hdl.handle.net/2292/3569
Minimal Deterministic Incomplete Automata
oai:researchspace.auckland.ac.nz:2292/450752019-01-12T11:31:25Zcom_2292_122col_2292_3508
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2018
Proceedings of the Asian Branch of International Conference on Membrane Computing (ACMC2018)
CDMTCS Research Reports CDMTCS-504 (2018)
1178-3540
http://hdl.handle.net/2292/45075
Proceedings of ACMC 2018
oai:researchspace.auckland.ac.nz:2292/35862012-02-02T23:23:19Zcom_2292_122col_2292_3508
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Hertling, P
author
1998-01
Including the range of a rational function over an interval is an im-
portant problem in numerical computation. A direct interval arithmetic
evaluation of a formula for the function yields in general a superset with
an error linear in the width of the interval. Special formulas like the cen-
tered forms yield a better approximation with a quadratic error. Alefeld
posed the question whether in general there exists a formula whose inter-
val arithmetic evaluation gives an approximation of better than quadratic
order. In this paper we show that the answer to this question is negative
if in the interval arithmetic evaluation of a formula only the basic four
interval operations +,-,•,/= are used.
CDMTCS Research Reports CDMTCS-077 (1998)
1178-3540
http://hdl.handle.net/2292/3586
A Lower Bound for Range Enclosure in Interval Arithmetic
oai:researchspace.auckland.ac.nz:2292/50022009-08-28T12:39:03Zcom_2292_122col_2292_4963
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Gartside, P.M.
author
Mohamad, Abdul M.
author
1999-09
This paper investigates metrization theory of manifolds. We show that diagonal properties play a central role in developing metrizability of manifolds.
Department of Mathematics - Research Reports-428 (1999)
1173-0889
http://hdl.handle.net/2292/5002
Metrizability of Manifolds by Diagonal Properties
oai:researchspace.auckland.ac.nz:2292/27302008-08-29T04:58:39Zcom_2292_122col_2292_2623
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Klette, Reinhard
author
Zunic, Jovisa
author
1999
This paper informs about estimates of worst-case bounds for quantization errors in calculating features such as moments, moment based features, or perimeters in image analysis, and about probability-theoretical estimates of error bounds (eg. standard derivations) for such digital approximations. New estimates (with proofs) and a review of previously known results are provided.
Communication and Information Technology Research Technical Report 52, (1999)
1178-3693
http://hdl.handle.net/2292/2730
Convergence of Calculated Features in Image Analysis
oai:researchspace.auckland.ac.nz:2292/250682016-04-22T12:40:32Zcom_2292_122col_2292_25032
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Ranford, Jodie
author
2015-04-10
Families, like trees, grow and develop with their surroundings. Seeds are blown by the wind and new trees are born elsewhere. Roots sink into the ground from which the new tree draws life. Children, like branches, stretch out. Families and trees have similar destinies (Ricciardi, cited in King, 1985:8).
ACE papers, Issue 6: Graduate Student Work - Issues in Contemporary Education, Paper 8.
http://hdl.handle.net/2292/25068
'Pakeha', Its Origin and Meaning
oai:researchspace.auckland.ac.nz:2292/37752012-02-02T23:23:16Zcom_2292_122col_2292_3508
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Greenberger, D.M
author
Svozil, K
author
2005-06
We introduce a quantum mechanical model of time travel which includes two figurative beam splitters in
order to induce feedback to earlier times. This leads to a unique solution to the paradox where one could kill
one’s grandfather in that once the future has unfolded, it cannot change the past, and so the past becomes
deterministic. On the other hand, looking forwards towards the future is completely probabilistic. This
resolves the classical paradox in a philosophically satisfying manner.
CDMTCS Research Reports CDMTCS-268 (2005)
1178-3540
http://hdl.handle.net/2292/3775
Quantum Theory Looks at Time Travel
oai:researchspace.auckland.ac.nz:2292/34952009-04-09T02:20:54Zcom_2292_122col_2292_3452
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Collberg, Christian
author
1997-11
[no abstract available]
Computer Science Technical Reports 161 (1997)
1173-3500
http://hdl.handle.net/2292/3495
Departmental Songbook (v1.3 $\beta$)
oai:researchspace.auckland.ac.nz:2292/32692012-02-02T23:13:50Zcom_2292_122col_2292_3205
00925njm 22002777a 4500
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Liu, Zhifeng
author
Klette, Reinhard
author
2008
This paper proposes a way to approximate ground truth for
real-world stereo sequences, and applies this for evaluating the performance
of di erent variants of dynamic programming stereo analysis. This
illustrates a way of performance evaluation, also allowing to derive sequence
analysis diagrams. Obtained results di er from those obtained for
the discussed algorithms on smaller, or engineered test data. This also
shows the value of real-world testing.
Multimedia Imaging Report 28 (2008)
1178-5789
http://hdl.handle.net/2292/3269
Dynamic Programming Stereo on Real-World Sequences
oai:researchspace.auckland.ac.nz:2292/37302012-02-02T23:23:16Zcom_2292_122col_2292_3508
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Arulanandham, J.J
author
Calude, C.S
author
Dinneen, Michael
author
2003-10
We propose a natural computational model called a balance machine. The computational model consists of components that resemble ordinary physical balances, each with an intrinsic property to automatically balance the weights on their left, right pans. If we start with certain fixed weights (representing inputs) on some of the pans, then the balance-like components would vigorously try to balance themselves by filling the rest of the pans with suitable weights (representing the outputs). This balancing act can be viewed as a computation. We will show that the model allows us to construct those primitive (hardware) components that serve as the building blocks of a general purpose (universal) digital computer: logic gates, memory cells (flip-flops), and transmission lines. One of the key features of the balance machine is its “bidirectional” operation: both a function and its (partial) inverse can be computed spontaneously using the same machine. Some practical applications of the model are discussed.
CDMTCS Research Reports CDMTCS-223 (2003)
1178-3540
http://hdl.handle.net/2292/3730
Balance Machines: Computing = Balancing
oai:researchspace.auckland.ac.nz:2292/251052016-04-22T12:45:24Zcom_2292_122col_2292_25032
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Holt, Glenys
author
2001-11
There is increasing national concern regarding the educational achievement of Maori in New Zealand. Recent international studies have highlighted Maori mathematics under-achievement in particular. This paper discusses appropriate teaching and learning practices, ethno-mathematics, constructivist approaches, the development of classroom culture, increasing teacher and learner expectation, and assessment practices that will improve the mathematics achievement of these students.
ACE papers, Issue 11: Issues in Mathematics Education, Paper 2.
http://hdl.handle.net/2292/25105
Mathematics education for Maori students in mainstream classrooms
oai:researchspace.auckland.ac.nz:2292/251182016-04-22T12:46:32Zcom_2292_122col_2292_25032
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Gallia, Jean
author
2003-5
This paper first examines differing definitions of assessment and evaluation. It considers the position of Eisner, and others, in various contexts within the assessment theoretical field. Eisner proposes new criteria for future assessment and these are described and discussed. Of key interest is the relationship between Eisner’s model and the NZCF.
ACE papers, Issue 12: Curriculum theory, issues and practice: Student voices, Paper 7.
http://hdl.handle.net/2292/25118
Elliot W. Eisner's model of assessment, and the New Zealand Curriculum Framework
oai:researchspace.auckland.ac.nz:2292/35132012-02-02T23:23:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
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Hafner, P.R
author
1995-06
We review the status of the Degree/Diameter problem for both,
graphs and digraphs and present new Cayley digraphs which yield improvements over some of the previously known largest vertex transitive digraphs of
given degree and diameter.
CDMTCS Research Reports CDMTCS-004 (1995)
1178-3540
http://hdl.handle.net/2292/3513
Large Cayley Graphs and Digraphs with Small Degree and Diameter
oai:researchspace.auckland.ac.nz:2292/50942009-08-28T12:40:35Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Marshall, Simon
author
2004-10
We study the recently discovered phenomenon of existence of comparative probability orderings on finite sets that violate Fishburn hypothesis - we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on the set of n=7 elements and showed that no extremal cones exist on the set of n< 7 elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1,725 of the 1,842 primes between 132 and 16,000, hence for all these primes extremal cones exist.
Department of Mathematics - Research Reports-529 (2004)
1173-0889
http://hdl.handle.net/2292/5094
On the Existence of Extremal Cones and Comparative Probability Orderings
oai:researchspace.auckland.ac.nz:2292/28432008-08-29T05:03:02Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Klette, Reinhard
author
Gimel'farb, Georgy
author
Huang, Fay
author
Scheibe, Karsten
author
Scheele, Martin
author
Börner, Anko
author
2003
This paper reviews research related to the design, production and application of cylindrical panoramic cameras. Such a camera is characterized by rotating linear sensors capturing one image column at a time. This allows for accurate mappings onto a cylindrical image surface and very high image resolutions paid by motion distortions in dynamic scenes. These panoramic images can be used, for example, for stereo visualization and stereo reconstruction in applications where extremely high image resolution is of benefit (for static scenes). The paper deals especially with aspects of stereo visualization and reconstruction.
Communication and Information Technology Research Technical Report 123, (2003)
1178-3622
http://hdl.handle.net/2292/2843
A Review on Research and Applications of Cylindrical Panoramas
oai:researchspace.auckland.ac.nz:2292/49932009-08-28T12:38:56Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Chou, Lin-yi
author
Sharp, P.W.
author
1999-12
Order five symplectic ERKN methods of five stages are known to exist. However, these methods do not have free parameters with which to minimise the error coefficients. By adding one derivative evaluation per step, to give either a six-stage non-FSAL family or a seven-stage FSAL family of methods, two free parameters become available for the minimisation. This raises the possibility of improving the efficiency of order five methods despite the extra cost of taking a step. We perform the minimisation of the two families to obtain an optimal method and then compare its performance with some published methods on the two-body problem for a range of eccentricities. These comparisons along with those based on the error coefficients show the new method is significantly more efficient than the five-stage methods. The numerical comparisons also suggest the new methods can be more efficient than some existing methods of other orders.
Department of Mathematics - Research Reports-436 (1999)
1173-0889
http://hdl.handle.net/2292/4993
Order 5 symplectic explicit Runge-Kutta Nystrom methods
oai:researchspace.auckland.ac.nz:2292/28542008-08-29T05:16:34Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Kawamoto, Kazuhiko
author
Yamada, Daisuke
author
Klette, Reinhard
author
2002
Video sequences capturing real scenes may be interpreted with respect to a dominant plane which is a planar surface covering 'a majority' of pixels in an image of a video sequence, i.e. that planar surface which is represented in the image by a maximum number of pixels. In this paper, we propose an algorithm for the detection of dominant planes from optical flow fields caused by camera motion in a static scene. We, in particular, intend to adopt this algorithm as a module for obstacle detection in vision-based navigation of autonomous robots.
Communication and Information Technology Research Technical Report 111, (2002)
1178-3634
http://hdl.handle.net/2292/2854
Navigation Using Optical Flow Fields: An Application of Dominant Plane Detection
oai:researchspace.auckland.ac.nz:2292/32582012-02-02T23:13:51Zcom_2292_122col_2292_3205
00925njm 22002777a 4500
dc
Hermann, Simon
author
Klette, Reinhard
author
Destenfanis, Eduardo
author
2008
Today's stereo vision algorithms and computing technology
allow real-time 3D data analysis, for example for driver assistance
systems. A recently developed Semi-Global Matching (SGM) approach
by H. Hirschm uller became a popular choice due to performance and
robustness. This paper evaluates di erent parameter settings for SGM,
and its main contribution consists in suggesting to include a second order
prior into the smoothness term of the energy function. It also proposes
and tests a new cost function for SGM. Furthermore, some preprocessing
(edge images) proved to be of great value for improving SGM stereo
results on real-world sequences, as previously already shown by S. Guan
and R. Klette for belief propagation. There is also a performance gain for
engineered stereo data (e.g.) as currently used on the Middlebury stereo
website. However, the fact that results are not as impressive as on the
.enpeda.. sequences indicates that optimizing for engineered data does
not neccessarily improve real world stereo data analysis.
Multimedia Imaging Report 16 (2008)
1178-5789
http://hdl.handle.net/2292/3258
Inclusion of a Second-Order Prior into Semi-Global Matching (2008)
oai:researchspace.auckland.ac.nz:2292/49722009-08-28T12:35:45Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Mira, Antonietta
author
Nicholls, Geoff
author
2003-09
Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multi-block Metropolis-Hastings estimators of citeN{chib01} are bridge sampling estimators. This identification leads to estimators for the quantity of interest which may be substantially more efficient. This report was submitted in July 2000. A revised version of this report was submitted in September 2003. The version below is the revised version. Print and electronic copies of the original version are available on request.
Department of Mathematics - Research Reports-456 (2003)
1173-0889
http://hdl.handle.net/2292/4972
Bridge estimation of the probability density at a point
oai:researchspace.auckland.ac.nz:2292/38042012-02-02T23:23:18Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Hay, N.J
author
Shorin, A
author
Wang, J
author
2007-01
This booklet contains the proceedings of the First University of Auckland Computer
Science Graduate Workshop (UACSGSW’06) held on Friday, 8 September 2006.
TheWorkshop, the first of its kind in our department, offers graduate students a chance
to present their research to an audience including computer science and information technology
graduate students, academics and industry representatives. The participants are
MSc, Honours, PGDipSci, PhD, MEng and stage-4 BE project students in computer science
and related areas. All submissions have been refereed.
CDMTCS Research Reports CDMTCS-297 (2007)
1178-3540
http://hdl.handle.net/2292/3804
University of Auckland Computer Science Graduate Workshop 2006
oai:researchspace.auckland.ac.nz:2292/450692019-01-12T11:31:30Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Yao, P
author
Hua, R
author
2018
CDMTCS Research Reports CDMTCS-523 (2018)
1178-3540
http://hdl.handle.net/2292/45069
Finding Maximum-sized Native Clique Embeddings: Implementing and Extending the Block Clique Embedding Algorithm
oai:researchspace.auckland.ac.nz:2292/105542012-02-09T11:41:47Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Gimel'farb, G.
author
Nicolescu, R.
author
Ragavan, S.
author
2011
Designing parallel versions of sequential algorithms has attracted renewed attention, due to recent hardware advances, including various general-purpose multi-core and many-core processors, as well as special-purpose FPGA implementations. P systems consist of networks of autonomous cells, such that each cell transforms
its input signals in accord with its symbol-rewriting rules and feeds the output results into its immediate neighbours. Inherent massive intra- and inter-cell parallelisms make P systems a prospective theoretical testbed for designing efficient parallel and parallel-sequential algorithms. This paper discusses the ability of P
systems to implement the symmetric dynamic programming stereo (SDPS) matching algorithm, which explicitly accounts for binocular or monocular visibility of 3D surface points. Given enough cells, the P system implementation speeds up the inner algorithm loop from O(nd) to O(n + d), where n is the width of a stereo
image and d is the disparity range. The implementation also gives an insight into
to a more general SDPS algorithm that allows a possible multiplicity of solutions
to the ill-posed optimal stereo matching problem.
CDMTCS Research Reports CDMTCS-401 (2011)
1178-3540
http://hdl.handle.net/2292/10554
P Systems in Stereo Matching (extended version)
oai:researchspace.auckland.ac.nz:2292/250932016-04-22T12:42:37Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
dc
Keenan, Jan
author
2001-6
ACE papers, Issue 9: Issues in Language and Literacy, Paper 3.
http://hdl.handle.net/2292/25093
Emergent Reading: Issues from Research and Practice
oai:researchspace.auckland.ac.nz:2292/51392009-08-28T12:38:22Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Yashiro, Tsukasa
author
2002-08
In this paper we describe geometric properties of embedded liftabilities of immersed 3--manifolds in 4--space into 5--space. It is known that a regular homotopy class of an immersed orientable surface in 3--space is constructed by a pair of an embedded surface and an immersed circle on it. We found an isotopy between embedded lifts of these constructed immersions in 4--space, which covers a regular homotopy of their projections in 3--space. Also we construct non-liftable immersed 3--spheres without quadruple points.
Department of Mathematics - Research Reports-488 (2002)
1173-0889
http://hdl.handle.net/2292/5139
Deformations of Surfaces in 4-space
oai:researchspace.auckland.ac.nz:2292/37932012-02-02T23:23:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Speidel, U
author
2006-10
This paper describes the derivation of the T-complexity and T-in-
formation theory from the decomposition of finite strings, based on the
duality of strings and variable-length T-codes. It further outlines its similarity to the string parsing algorithm by Lempel and Ziv. In its first
version [15], it was intended as a summary of work published mainly by
Titchener and Nicolescu. Apart from minor corrections, the present extended version incorporates feedback from previous readers and presents
new results obtained since.
CDMTCS Research Reports CDMTCS-286 (2006)
1178-3540
http://hdl.handle.net/2292/3793
T-Complexity and T-Information Theory--an Executive Summary, 2nd revised version
oai:researchspace.auckland.ac.nz:2292/213442014-05-26T12:34:18Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Nies, A
author
2013
Cost functions were introduced as a framework for constructions
of c.e. incomputable sets that are close to computable. We
carry out a systematic study of cost functions. We relate their algebraic
properties to their expressive strength. We show that additive cost functions
correspond to the K-trivial sets. We prove a cost function basis
theorem, and give a general construction for building c.e. sets that are
close to being Turing complete.
CDMTCS Research Reports CDMTCS-445 (2013)
1178-3540
http://hdl.handle.net/2292/21344
Calculus of Cost Functions
oai:researchspace.auckland.ac.nz:2292/198072013-01-07T11:31:32Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Hertel, J
author
2012
We use the recently introduced [1,2] inductive complexity measure to
evaluate the inductive complexity of Goodstein's Theorem, a statement that is
independent from Peano Arithmetic.
CDMTCS Research Reports CDMTCS-418 (2012)
1178-3540
http://hdl.handle.net/2292/19807
Inductive Complexity of Goodstein's Theorem
oai:researchspace.auckland.ac.nz:2292/28012008-08-29T05:01:55Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Liu, Gang
author
Klette, Reinhard
author
2005
Structure from Motion (SfM) is one of the most attractive approaches within computer vision which aims on estimating 3D structure from 2D image sequences. This paper focuses on a stability analysis and studies the error propagation of image noise. To stabilize SfM, we further present two optimization schemes by using a priori knowledge of the scene.
Communication and Information Technology Research Technical Report 169, (2005)
1178-3576
http://hdl.handle.net/2292/2801
Structure from Motion in the Presence of Noise
oai:researchspace.auckland.ac.nz:2292/238882016-04-22T12:35:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Böttcher, S
author
Link, S
author
Zhang, L
author
2014
We present LECQTER, a system for learning how to write sound conjunctive SQL
queries by example. The key novelty of LECQTER is its ability to construct for every
given conjunctive query Q without self-joins over every given database schema,
a database dbQ such that for every query Q'
in a large fragment of conjunctive
queries, Q and Q' produce matching answers on every database if and only if Q
and Q′ produce matching answers on dbQ. Since it is known that such construction
is impossible to achieve under set semantics, the key novelty relies on the use
of SQL’s bag semantics. LECQTER shows the answer to both the user query Q'
and the target query Q, such that users receive immediate feedback that either
their query is correct - and not just their query answer - or where their query
answer deviates from that of the target query. LECQTER can therefore automate
feedback and assessment in its primary application area of Massive Open Online
Courses. Everyone who requires basic SQL skills to match the demands of our
data-centric society can use LECQTER to confidently learn how to write sound
conjunctive queries under the semantics of the industry standard.
CDMTCS Research Reports CDMTCS-453 (2014)
1178-3540
http://hdl.handle.net/2292/23888
LECQTER: Learning Conjunctive SQL Queries Through Exemplars
oai:researchspace.auckland.ac.nz:2292/250742016-04-22T12:41:25Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
dc
Bradstreet, Anne
author
2015-04-10
ACE papers, Issue 7: Politics of Curriculum, Paper 3.
http://hdl.handle.net/2292/25074
Gender Equity in the New Zealand Curriculum: A change in focus
oai:researchspace.auckland.ac.nz:2292/27862008-08-29T05:01:22Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Brimkov, Valentin
author
Klette, Reinhard
author
2006
In this paper we define and study digital manifolds of arbitrary dimension, and provide (in particular) a general theoretical basis for curve or surface tracing in picture analysis. The studies involve properties such as one-dimensionality of digital curves and $(n-1)$-dimensionality of digital hypersurfaces that makes them discrete analogs of corresponding notions in topology. The presented approach is fully based on good pairs of adjacency relations and complements the concept of dimension as common in combinatorial topology. This work appears to be the first one on digital manifolds based on a graph-theoretical definition of dimension. In particular, a digital hypersurface in $n$D is an $(n-1)$-dimensional object, as it is in the case of continuous hypersurfaces. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension.
Communication and Information Technology Research Technical Report 184, (2006)
1178-3561
http://hdl.handle.net/2292/2786
Curves, Hypersurfaces, and Good Pairs
oai:researchspace.auckland.ac.nz:2292/27402008-08-29T04:59:27Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Yang, Nan
author
Klette, Reinhard
author
1998
The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this report we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed one-dimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for finding the shortest polygonal Jordan curve is introduced, and its correctness and complexity is discussed.
Communication and Information Technology Research Technical Report 35, (1998)
1178-3710
http://hdl.handle.net/2292/2740
Linear Time Calculation of 2D Shortest Polygonal Jordan Curves
oai:researchspace.auckland.ac.nz:2292/250942016-04-22T12:45:08Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
dc
Villers, Helen
author
2001-6
ACE papers, Issue 9: Issues in Language and Literacy, Paper 4.
http://hdl.handle.net/2292/25094
Can shared understandings about the nature and purpose of second language acquisition and literacy learning enhance achievement outcomes for older NESB students?
oai:researchspace.auckland.ac.nz:2292/251442016-04-22T12:49:44Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
dc
Steel, Marion
author
2005-3
ACE papers, Issue 15: Pedagogy and practice under the lens, Paper 9.
http://hdl.handle.net/2292/25144
Ability Grouping and Mathematics Education
oai:researchspace.auckland.ac.nz:2292/35932012-02-02T23:23:18Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude, C.S
author
Dinneen, Michael
author
1998-05
Is there any limit to discrete computation, and more generally, to scientific knowledge? This is one of the problems studied by the Centre for Discrete Mathematics and
Theoretical Computer Science of the University of Auckland.
CDMTCS Research Reports CDMTCS-084 (1998)
1178-3540
http://hdl.handle.net/2292/3593
Breaking the Turing Barrier
oai:researchspace.auckland.ac.nz:2292/36592012-02-02T23:23:17Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Bodlaender, H.L
author
Dinneen, Michael
author
Khoussainov, B
author
2001-04
In this paper, we study the complexity of deciding which player has a
winning strategy in certain types of McNaughton games. These graph games can be
used as models for computational problems and processes of infinite duration. We
consider the cases (1) where the first player wins when vertices in a specified set are
visited infinitely often and vertices in another specified set are visited finitely often, (2)
where the first player wins when exactly those vertices in one of a number of specified
disjoint sets are visited infinitely often, and (3) a generalization of these first two cases.
We give polynomial time algorithms to determine which player has a winning strategy
in each of the games considered.
CDMTCS Research Reports CDMTCS-151 (2001)
1178-3540
http://hdl.handle.net/2292/3659
On Game-Theoretic Models of Networks
oai:researchspace.auckland.ac.nz:2292/32572012-02-02T23:13:50Zcom_2292_122col_2292_3205
00925njm 22002777a 4500
dc
Wedel, Andreas
author
Rabe, Clemens
author
Vaudrey, Tobi
author
Brox, Thomas
author
Cremers, Daniel
author
2008
This paper presents a technique for estimating the threedimensional
velocity vector field that describes the motion of each visible
scene point (scene flow). The technique presented uses two consecutive
image pairs from a stereo sequence. The main contribution is to decouple
the position and velocity estimation steps, and to estimate dense velocities
using a variational approach. We enforce the scene flow to yield
consistent displacement vectors in the left and right images. The decoupling
strategy has two main advantages: Firstly, we are independent in
choosing a disparity estimation technique, which can yield either sparse
or dense correspondences, and secondly, we can achieve frame rates of
5 fps on standard consumer hardware. The approach provides dense velocity
estimates with accurate results at distances up to 50 meters.
Multimedia Imaging Report 11 (2008)
1178-5789
http://hdl.handle.net/2292/3257
Efficient Dense Scene Flow from Sparse or Dense Stereo Data
oai:researchspace.auckland.ac.nz:2292/36752012-02-02T23:23:16Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude, C.S
author
Dinneen, Michael
author
Shu, C.-K
author
2001-12
A Chaitin Omega number is the halting probability of a universal Chaitin (selfdelimiting
Turing) machine. Every Omega number is both computably enumerable
(the limit of a computable, increasing, converging sequence of rationals) and random
(its binary expansion is an algorithmic random sequence). In particular, every
Omega number is strongly non-computable. The aim of this paper is to describe a
procedure, which combines Java programming and mathematical proofs, for computing
the exact values of the first 63 bits of a Chaitin Omega:
000000100000010000100000100001110111001100100111100010010011100.
Full description of programs and proofs will be given elsewhere.
CDMTCS Research Reports CDMTCS-167 (2001)
1178-3540
http://hdl.handle.net/2292/3675
Computing a Glimpse of Randomness
oai:researchspace.auckland.ac.nz:2292/213472014-05-26T12:33:53Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude,CS
author
Staiger, L
author
2013
We present a systematic comparison between Liouville, computable, Borel normal and Martin-Lof random numbers. The nine non-empty combinations, all small in measure
or category, are illustrated with concrete examples. The sets of Liouville numbers
and Martin-Lof random numbers are disjoint, thus showing that the irrationality exponent is not a measure of randomness. Finally, we construct the first computable set of correlations appearing in every Martin-Lof random number, but not in all numbers.
CDMTCS Research Reports CDMTCS-448 (2013)
1178-3540
http://hdl.handle.net/2292/21347
Liouville Numbers, Borel Normality and Algorithmic Randomness
oai:researchspace.auckland.ac.nz:2292/37852012-02-02T23:23:14Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Schwarz, S
author
2006-05
We connect Lukasiewicz logic, a well-established many-valued logic, with
weighted logics, recently introduced by Droste and Gastin. We use this connection
to show that for formal series with coefficients in semirings derived from MValgebras,
recognizability and definability in a fragment of second order Lukasiewicz
logic coincide.
CDMTCS Research Reports CDMTCS-278 (2006)
1178-3540
http://hdl.handle.net/2292/3785
Lukasiewicz Logics and Weighted Logics over MV-Semirings
oai:researchspace.auckland.ac.nz:2292/35662012-02-02T23:23:15Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Hertling, P
author
1997-09
On countable structures computability is usually introduced via numberings. For
uncountable structures whose cardinality does not exceed the cardinality of the continuum the same can be done via representations. Which representations are appropriate for doing real number computations? We show that with respect to computable
equivalence there is one and only one equivalence class of representations of the real
numbers which make the basic operations computable. This characterizes the real
numbers in terms of the theory of effective algebras or computable structures, and is
reflected by observations made in real number computer arithmetic. We also give further evidence for the well-known non-appropriateness of the representation to some
base b by proving that strictly less functions are computable with respect to these
representations than with respect to a standard representation of the real numbers.
Furthermore we consider basic constructions of representations and the countable
substructure consisting of the computable elements of a represented, possibly uncountable structure. For countable structures we compare effectivity with respect to
a numbering and effectivity with respect to a representation. Special attention is paid
to the countable structure of the computable real numbers.
CDMTCS Research Reports CDMTCS-057 (1997)
1178-3540
http://hdl.handle.net/2292/3566
The Real Number Structure is Effectively Categorical
oai:researchspace.auckland.ac.nz:2292/38262012-02-02T23:23:19Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Svozil, K
author
2008-04
Aesthetics, among other criteria, can be statistically examined in terms of the complexity
required for creating and decrypting a work of art. We propose three laws of aesthetic
complexity. According to the first law of aesthetic complexity, too condensed encoding
makes a decryption of a work of art impossible and is perceived as chaotic by the untrained
mind, whereas too regular structures are perceived as monotonous, too orderly and not very
stimulating. Thus a necessary condition for an artistic form or design to appear appealing
is its complexity to lie within a bracket between monotony and chaos. According to the
second law of aesthetic complexity, due to human predisposition, this bracket is invariably
based on natural forms; with rather limited plasticity. The third law of aesthetic complexity
states that aesthetic complexity trends are dominated by the available resources, and thus
also by cost and scarcity.
CDMTCS Research Reports CDMTCS-319 (2008)
1178-3540
http://hdl.handle.net/2292/3826
Aesthetic Complexity
oai:researchspace.auckland.ac.nz:2292/37742012-02-02T23:23:13Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Titchener, M.R
author
Speidel, U
author
Yang, J
author
2005-05
This report compares a variety of computable information measures for finite strings. These include
Shannon’s n-block entropy, the three best known versions of the Lempel-Ziv production complexity
(LZ-76, LZ-77, and LZ-78), and the lesser known T-entropy. We apply these measures to strings of
known entropy, each derived from the logistic map. Pesin’s identity allows us to deduce corresponding
Shannon entropies (Kolmogorov-Sinai entropies) for the sample strings, without resorting to probabilistic
methods.
CDMTCS Research Reports CDMTCS-267 (2005)
1178-3540
http://hdl.handle.net/2292/3774
A Comparison of Practical Information Measures
oai:researchspace.auckland.ac.nz:2292/51282009-08-28T12:38:07Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Harmer, Mark
author
2003-06
We describe a `natural' set of coordinates for fundamental domains in the hyperbolic plane in the case when the fundamental domain is triangular. The metric, the measure and the Laplace-Beltrami operator are calculated in this new coordinate system. As a byproduct we give a hyperbolic analogue of the Euclidean expression of the area of a triangle in terms of its base and height.
Department of Mathematics - Research Reports-498 (2003)
1173-0889
http://hdl.handle.net/2292/5128
Barycentric Coordinates on the Hyperbolic Plane
oai:researchspace.auckland.ac.nz:2292/450762020-11-24T07:44:23Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Anuradha Mahasinghe, MJD
author
Dinneen, Michael
author
Liu, K
author
2018-02
In this paper we demonstrate how to solve the chromatic sum problem using a D-Wave quantum computer. Starting from a BIP (binary integer programming) formulation, we develop a D-Wave feasible QUBO quadratic unconstrained binary optimisation) formulation of the chromatic sum problem. Our construction requires nk qubits for a graph of n vertices and upper bound of k colours. Further, we present the experimental results obtained by running several QUBOs on a D-Wave quantum computer.
CDMTCS Research Reports CDMTCS-519 (2018)
1178-3540
http://hdl.handle.net/2292/45076
Finding the Chromatic Sums of Graphs Using a D-Wave Quantum Computer
oai:researchspace.auckland.ac.nz:2292/37482012-02-02T23:23:17Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude, C.S
author
Juergensen, H
author
2004-06
In this paper we prove Chaitin’s “heuristic principle”, the theorems of a finitelyspecified
theory cannot be significantly more complex than the theory itself, for an appropriate
measure of complexity. We show that the measure is invariant under the change
of the G¨odel numbering. For this measure, the theorems of a finitely-specified, sound,
consistent theory strong enough to formalize arithmetic which is arithmetically sound
(like Zermelo-Fraenkel set theory with choice or Peano Arithmetic) have bounded complexity,
hence every sentence of the theory which is significantly more complex than the
theory is unprovable. Previous results showing that incompleteness is not accidental, but
ubiquitous are here reinforced in probabilistic terms: the probability that a true sentence
of length n is provable in the theory tends to zero when n tends to infinity, while the
probability that a sentence of length n is true is strictly positive.
CDMTCS Research Reports CDMTCS-241 (2004)
1178-3540
http://hdl.handle.net/2292/3748
Is Complexity a Source of Incompleteness?
oai:researchspace.auckland.ac.nz:2292/26862008-08-29T04:56:22Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Chen, Chia-Yen
author
Klette, Reinhard
author
2001
This paper describes a method for the calculation of surface reflectance values via photometric stereo. Experimental results show that surfaces rendered with reflectance values calculated by the proposed method have more realistic appearances than those with constant albedo.
Communication and Information Technology Research Technical Report 100, (2001)
1178-3645
http://hdl.handle.net/2292/2686
Albedo Recovery Using a Photometric Stereo Method
oai:researchspace.auckland.ac.nz:2292/450732019-01-12T11:31:32Zcom_2292_122col_2292_3508
00925njm 22002777a 4500
dc
Calude, CS
author
Svozil, K.
author
2018
We study some aspects of the emergence of l´ogos from x´aos on a simple model of the universe using methods and techniques from algorithmic information and Ramsey theories. Thereby an intrinsic and unusual mixture of meaningful and (spurious) emerging laws surfaces. The emergent laws outnumber the meaningful ones, a picture which is compatible with the lawfulness hypothesis. In accord with the ancient Greek theogony one could say that l´ogos, the Gods and the laws of the universe, originate from “the void,” or from x´aos.
CDMTCS Research Reports CDMTCS-528 (2018)
1178-3540
http://hdl.handle.net/2292/45073
Spurious, Emergent Laws in Number Worlds
oai:researchspace.auckland.ac.nz:2292/250502016-04-22T12:50:37Zcom_2292_122col_2292_25032
00925njm 22002777a 4500
dc
Lomas, Gregor
author
2015-04-10
ACE papers, Issue 4: Staff Research Areas, Paper 5.
http://hdl.handle.net/2292/25050
Supervision of classroom practice: Giving feedback; a tertiary study
oai:researchspace.auckland.ac.nz:2292/50122009-08-28T12:39:12Zcom_2292_122col_2292_4963
00925njm 22002777a 4500
dc
Kurasov, Pavel
author
Pavlov, B.
author
1999-06
Selfadjoint extensions of symmetric operators with infinite deficiency indices are discussed. In particular the operators describing the system of several quantum particles are investigated in detail and a few-body analog of Krein's formula for generalized resolvents is proven. The conditions for the semiboundedness of the simplest $M$-body quantum Hamiltonian with point interactionsin in the three-dimensional space are derived
Department of Mathematics - Research Reports-418 (1999)
1173-0889
http://hdl.handle.net/2292/5012
FEW-BODY KREIN'S FORMULA
oai:researchspace.auckland.ac.nz:2292/35032009-04-17T01:12:40Zcom_2292_122col_2292_3452
00925njm 22002777a 4500
dc
Creak, G.A.
author
1999-12
[no abstract available]
Computer Science Technical Reports 169 (1999)
1173-3500
http://hdl.handle.net/2292/3503
Artificial Intelligence -- or not ?
oai:researchspace.auckland.ac.nz:2292/27482008-08-29T05:00:04Zcom_2292_122col_2292_2623
00925njm 22002777a 4500
dc
Kozera, Ryszard
author
Klette, Reinhard
author
1998
Differential equations (ODEs or PDEs) appear in many computer vision fields. Shape-from-shading, optical flow, optics, and 3D motion are examples of such fields. This report discusses theoretical criteria for the corresponding continuous problem, theoretical criteria for discrete numerical schemes, and experimental measurements for the implemented numerical schemes. These criteria are illustrated by discussing a shape-from-shading problem in which the reflectance map is linear.
Communication and Information Technology Research Technical Report 27, (1998)
1178-3718
http://hdl.handle.net/2292/2748
Criteria for Differential Equations in Computer Vision
oai:researchspace.auckland.ac.nz:2292/32112012-02-02T23:13:51Zcom_2292_122col_2292_3205
00925njm 22002777a 4500
dc
Badino, Hernan
author
Vaudrey, Tobi
author
Franke, Uwe
author
Mester, Rudolf
author
2008
This paper presents a method for the computation of free
space in complex traffic scenarios. Dynamic depth information
is estimated by integrating stereo disparity images over
time. Disparity and disparity speed are computed pixelwise
with Kalman filters. The stereo information is used
to compute stochastic occupancy grids. Dynamic programming
on a polar-like occupancy grid yield the free space.
Analysis of the calculated free space allows the detection of
the available free corridor in front of the ego-vehicle. The
method runs at a frame rate of 20 Hz in our demonstrator
vehicle.
Multimedia Imaging Report 6 (2008)
1178-5789
http://hdl.handle.net/2292/3211
Stereo-based Free Space Computation in Complex Traffic Scenarios
marc///com_2292_122/100