WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

The Cube : a very large-scale interactive engagement space

“The Cube” is a unique facility that combines 48 large multi-touch screens and very large-scale projection surfaces to form one of the world’s largest interactive learning and engagement spaces. The Cube facility is part of the Queensland University of Technology’s (QUT) newly established Science and Engineering Centre, designed to showcase QUT’s teaching and research capabilities in the STEM (Science, Technology, Engineering, and Mathematics) disciplines. In this application paper we describe, the Cube, its technical capabilities, design rationale and practical day-to-day operations, supporting up to 70,000 visitors per week. Essential to the Cube’s operation are five interactive applications designed and developed in tandem with the Cube’s technical infrastructure. Each of the Cube’s launch applications was designed and delivered by an independent team, while the overall vision of the Cube was shepherded by a small executive team. The diversity of design, implementation and integration approaches pursued by these five teams provides some insight into the challenges, and opportunities, presented when working with large distributed interaction technologies. We describe each of these applications in order to discuss the different challenges and user needs they address, which types of interactions they support and how they utilise the capabilities of the Cube facility.

Count-min sketches for estimating password frequency within Hamming distance two

The count-min sketch is a useful data structure for recording and estimating the frequency of string occurrences, such as passwords, in sub-linear space with high accuracy. However, it cannot be used to draw conclusions on groups of strings that are similar, for example close in Hamming distance. This paper introduces a variant of the count-min sketch which allows for estimating counts within a specified Hamming distance of the queried string. This variant can be used to prevent users from choosing popular passwords, like the original sketch, but it also allows for a more efficient method of analysing password statistics.

Information and Learning Experiences in the Cube: Vision, Implementation and Interaction

Executive Summary This project has commenced an exploration of learning and information experiences in the QUT Cube. Understanding learning in this environment has the potential to inform current implementations and future project development. In this report, we present early findings from the first phase of an investigation into what makes learning possible in the context of a giant interactive multi-media display such as the QUT Cube, which is an award-winning configuration that hosts several projects.

Constructing a frame of cube : connecting 3D shapes with direction, location and movement

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about 3D shapes with direction, location and movement, and how young children can mentally and visually construct virtual 3D shapes using movements in both egocentric and fixed frames of reference (FOR). Findings suggest that year 4 (aged 9) children can develop the capacity to construct a cube using egocentric FOR only, fixed FOR only or a combination of both FOR. However, these young participants were unable to articulate the effect of individual or combined FOR movements. Directions for future research are proposed.

Extensions of the cube attack based on low degree annihilators

At Crypto 2008, Shamir introduced a new algebraic attack called the cube attack, which allows us to solve black-box polynomials if we are able to tweak the inputs by varying an initialization vector. In a stream cipher setting where the filter function is known, we can extend it to the cube attack with annihilators: By applying the cube attack to Boolean functions for which we can find low-degree multiples (equivalently annihilators), the attack complexity can be improved. When the size of the filter function is smaller than the LFSR, we can improve the attack complexity further by considering a sliding window version of the cube attack with annihilators. Finally, we extend the cube attack to vectorial Boolean functions by finding implicit relations with low-degree polynomials.

Wind pressure measurements on a cube subjected to pulsed impinging jet flow

A pulsed impinging jet is used to simulate the gust front of a thunderstorm downburst. This work concentrates on investigating the peak transient loading conditions on a 30 mm cubic model submerged in the simulated downburst flow. The outflow induced pressures are recorded and compared to those from boundary layer and steady wall jet flow. Given that peak winds associated with downburst events are often located in the transient frontal region, the importance of using a non-stationary modelling technique for assessing peak downburst wind loads is highlighted with comparisons.

The experience of learning in “The Cube” : Queensland University of Technology’s giant interactive multimedia environment

In this paper we report findings of the first phase of an investigation, which explored the experience of learning amongst high-level managers, project leaders and visitors in QUT’s “Cube”. “The Cube” is a giant, interactive, multi-media display; an award-winning configuration that hosts several interactive projects. The research team worked with three groups of participants to understand the relationship between a) the learning experiences that were intended in the establishment phase; b) the learning experiences that were enacted through the design and implementation of specific projects; and c) the lived experiences of learning of visitors interacting with the system. We adopted phenomenography as a research approach, to understand variation in people’s understandings and lived experiences of learning in this environment. The project was conducted within the first twelve months of The Cube being open to visitors.

Cube Jam (Engagement Innovation Project)

Cube Jam is a project developed in response to the new and rising marketing in large-scale interactive public screens - the Cube being a premier site. Cube Jam will be a crossbreeding ‘think-ubator’ that rides on the back of the already nationally recognised Game On program and its digital communities. Via a bottom-up, non-directive approach Cube Jam will facilitate a series of design provocations within co-located Jam Studios; studios that are focused on supporting adaptation and new ideation and concept design. These Studios will seek new combinations of skills and knowledges with the intention of discovering provotypes of possibilities in both working and production methodologies and product outcomes.

Learning experiences in a giant interactive environment: Insights from The Cube

In November 2012, Queensland University of Technology in Australia launched a giant interactive learning environment known as The Cube. This article reports a phenomenographic investigation into visitors’ different experiences of learning in The Cube. At present very little is known about people’s learning experience in spaces featuring large interactive screens. We observed many visitors to The Cube and interviewed 26 people. Our analysis identified critical variation across the visitors’ experience of learning in The Cube. The findings are discussed as the learning strategy (in terms of Absorption, Exploration, Isolation and Collaboration); and the content learned (in terms of Technology, Skills and Topics). Other findings presented here are dimensions of the learning strategy and the content learned, with differing perspectives on each dimension. These outcomes provide early insights into the potential of giant interactive environments to enhance learning approaches and guide the design of innovative learning spaces in higher education.

Local texture and microstructure in cube-oriented nickel single crystal deformed by equal channel angular extrusion

Local texture and microstructure was investigated to study the deformation mechanisms during equal channel angular extrusion of a high purity nickel single crystal of initial cube orientation. A detailed texture and microstructure analysis by various diffraction techniques revealed the complexity of the deformation patterns in different locations of the billet. A modeling approach, taking into account slip system activity, was used to interpret the development of this heterogeneous deformation.

A Triangulation of CP3 as Symmetric Cube of S-2

The symmetric group acts on the Cartesian product (S (2)) (d) by coordinate permutation, and the quotient space is homeomorphic to the complex projective space a'',P (d) . We used the case d=2 of this fact to construct a 10-vertex triangulation of a'',P (2) earlier. In this paper, we have constructed a 124-vertex simplicial subdivision of the 64-vertex standard cellulation of (S (2))(3), such that the -action on this cellulation naturally extends to an action on . Further, the -action on is ``good'', so that the quotient simplicial complex is a 30-vertex triangulation of a'',P (3). In other words, we have constructed a simplicial realization of the branched covering (S (2))(3)-> a'',P (3).

Mapping joint ROM on a cube using electromagnetic trackers

This paper presents a unified framework using the unit cube for measurement, representation and usage of the range of motion (ROM) of body joints with multiple degrees of freedom (d.o.f) to be used for digital human models (DHM). Traditional goniometry needs skill and kn owledge; it is intrusive and has limited applicability for multi-d.o.f. joints. Measurements using motion capture systems often involve complicated mathematics which itself need validation. In this paper we use change of orientation as the measure of rotation; this definition does not require the identification of any fixed axis of rotation. A two-d.o.f. joint ROM can be represented as a Gaussian map. Spherical polygon representation of ROM, though popular, remains inaccurate, vulnerable due to singularities on parametric sphere and difficult to use for point classification. The unit cube representation overcomes these difficulties. In the work presented here, electromagnetic trackers have been effectively used for measuring the relative orientation of a body segment of interest with respect to another body segment. The orientation is then mapped on a surface gridded cube. As the body segment is moved, the grid cells visited are identified and visualized. Using the visual display as a feedback, the subject is instructed to cover as many grid cells as he can. In this way we get a connected patch of contiguous grid cells. The boundary of this patch represents the active ROM of the concerned joint. The tracker data is converted into the motion of a direction aligned with the axis of the segment and a rotation about this axis later on. The direction identifies the grid cells on the cube and rotation about the axis is represented as a range and visualized using color codes. Thus the present methodology provides a simple, intuitive and accura te determination and representation of up to 3 d.o.f. joints. Basic results are presented for the shoulder. The measurement scheme to be used for wrist and neck, and approach for estimation of the statistical distribution of ROM for a given population are also discussed.