Using Excel to generate empirical sampling distributions

Teachers in many introductory statistics courses demonstrate the Central Limit Theorem by using a computer to draw a large number of random samples of size n from a population distribution and plot the resulting empirical sampling distribution of the sample mean. There are
many computer applications that can be used for this (see, for example, the Rice Virtual Lab in Statistics: http://www.ruf.rice.edu/~lane/rvls.html). The effectiveness of such demonstrations has been questioned (see delMas et al (1999))) but in the work presented in this paper we do not rely on sampling distributions to convey or teach statistical concepts; only that the sampling distribution is independent of the distribution of the population, provided the sample size is sufficiently large.

We describe a lesson that starts out with a demonstration of the CTL, but sample from a (finite) population where actual census data is provided; doing this may help students more easily relate to the concepts – they can see the original data as a column of numbers and if the samples are shown they can also see random samples being taken. We continue with this theme of sampling from census data to teach the basic ideas of inference. We end up with standard resampling/bootstrap procedures.

We also demonstrate how Excel can provide a tool for developing a learning objects to support the program; a workbook called Sampling.xls is available from www.deakin.edu.au/~rodneyc/PS > Sampling.xls.

Classification of face images using local iterated function systems

There has been an increasing interest in face recognition in recent years. Many recognition methods have been developed so far, some very encouraging. A key remaining issue is the existence of variations in the input face image. Today, methods exist that can handle specific image variations. But we are yet to see methods that can be used more effectively in unconstrained situations. This paper presents a method that can handle partial translation, rotation, or scale variations in the input face image. The principal is to automatically identify objects within images using their partial self-similarities. The paper presents two recognition methods which can be used to recognise objects within images. A face recognition system is then presented that is insensitive to limited translation, rotation, or scale variations in the input face image. The performance of the system is evaluated through four experiments. The results show that the system achieves higher recognition rates than those of a number of existing approaches.

Is proof dead in the age of computers?

Some knowledge of what it means to construct a proof is an extremely important part of mathematics. All mathematics teachers and students should have some exposure to the ideas of proof and proving. This paper deals with the issue of creating proofs in mathematics problems.

Finite-time consensus algorithm of multi-agent networks

This paper is concerned with leader-follower finite-time consensus control of multi-agent networks with input disturbances. Terminal sliding mode control scheme is used to design the distributed control law. A new terminal sliding mode surface is proposed to guarantee finite-time consensus under fixed topology, with the common assumption that the position and the velocity of the active leader is known to its neighbors only. By using the finite-time Lyapunov stability theorem, it is shown that if the directed graph of the network has a directed spanning tree, then the terminal sliding mode control law can guarantee finite-time consensus even under the assumption that the time-varying control input of the active leader is unknown to any follower.

Muslim - Christian relations and the third crusade : medievalist imaginings

This article takes as its starting-point the responsiveness of children's literature to socio-political events, considering how contemporary anxieties about relationships between Muslim and Christian individuals and cultures inform three historical novels set in the period of the Third Crusade (1189-92): Karleen Bradford's Lionheart's Scribe (1999), K. M. Grant's Blood Red Horse (2004), and Elizabeth Laird's Crusade (2008). In these novels, encounters between young Christian and Muslim protagonists are represented through language and representational modes which owe a good deal to the habits of thought and expression which typify orientalist discourses in Western fiction. In effect, the novels produce two versions of medievalism: a Muslim medieval world which is irretrievably pre-modern, locked into rigid pracices and beliefs against which individuals are powerless; and a Christian medieval world which offers individuals the possibility of progressing to an enhanced state of personal fulfilment. The article argues that the narratives of all three novels incorporate particularly telling moments when Christian protagonists return to England, regretfully leaving Muslim friends. The impossibility of  enduring friendships between Muslims and Christians is based on the novels' assumptions about the incommensurability of cultures and religions; specifically, that there exists
an unbridgeable gulf between Islam and Christianity.

Stability theory and numerical analysis of non-autonomous dynamical systems

The development and use of cocycles for analysis of non-autonomous behaviour is a technique that has been known for several years. Initially developed as an extension to semi-group theory for studying rion-autonornous behaviour, it was extensively used in analysing random dynamical systems [2, 9, 10, 12]. Many of the results regarding asymptotic behaviour developed for random dynamical systems, including the concept of cocycle attractors were successfully transferred and reinterpreted for deterministic non-autonomous systems primarily by P. Kloeden and B. Schmalfuss [20, 21, 28, 29]. The theory concerning cocycle attractors was later developed in various contexts specific to particular classes of dynamical systems [6, 7, 13], although a comprehensive understanding of cocycle attractors (redefined as pullback attractors within this thesis) and their role in the stability of non-autonomous dynamical systems was still at this stage incomplete. It was this purpose that motivated Chapters 1-3 to define and formalise the concept of stability within non-autonomous dynamical systems. The approach taken incorporates the elements of classical asymptotic theory, and refines the notion of pullback attraction with further development towards a study of pull-back stability arid pullback asymptotic stability. In a comprehensive manner, it clearly establishes both pullback and forward (classical) stability theory as fundamentally unique and essential components of non-autonomous stability. Many of the introductory theorems and examples highlight the key properties arid differences between pullback and forward stability. The theory also cohesively retains all the properties of classical asymptotic stability theory in an autonomous environment. These chapters are intended as a fundamental framework from which further research in the various fields of non-autonomous dynamical systems may be extended. A preliminary version of a Lyapunov-like theory that characterises pullback attraction is created as a tool for examining non-autonomous behaviour in Chapter 5. The nature of its usefulness however is at this stage restricted to the converse theorem of asymptotic stability. Chapter 7 introduces the theory of Loci Dynamics. A transformation is made to an alternative dynamical system where forward asymptotic (classical asymptotic) behaviour characterises pullback attraction to a particular point in the original dynamical system. This has the advantage in that certain conventional techniques for a forward analysis may be applied. The remainder of the thesis, Chapters 4, 6 and Section 7.3, investigates the effects of perturbations and discretisations on non-autonomous dynamical systems known to possess structures that exhibit some form of stability or attraction. Chapter 4 investigates autonomous systems with semi-group attractors, that have been non-autonomously perturbed, whilst Chapter 6 observes the effects of discretisation on non-autonomous dynamical systems that exhibit properties of forward asymptotic stability. Chapter 7 explores the same problem of discretisation, but for pullback asymptotically stable systems. The theory of Loci Dynamics is used to analyse the nature of the discretisation, but establishment of results directly analogous to those discovered in Chapter 6 is shown to be unachievable. Instead a case by case analysis is provided for specific classes of dynamical systems, for which the results generate a numerical approximation of the pullback attraction in the original continuous dynamical system. The nature of the results regarding discretisation provide a non-autonomous extension to the work initiated by A. Stuart and J. Humphries [34, 35] for the numerical approximation of semi-group attractors within autonomous systems. . Of particular importance is the effect on the system's asymptotic behaviour over non-finite intervals of discretisation.

Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

Functional observability

A simple theorem for Functional Observability is presented considering the observable and unobservable states of a system based on Kalman decomposition. The proposed theorem is also consistent with two other theorems on Functional Observability which was based on eigen decomposition [6]. The paper also reports a new definition for Functional Observability which is consistent with previously reported definitions and theorems [4], [5], [6].

Retrodicting patch use by foraging swans in a heterogeneous environment using a set of functional responses

Effective conservation of important bird areas requires insight in the number of birds an area can support, and how this carrying capacity changes with habitat modifications. When food depletion is the dominant mechanism of competition, it should in principle be possible to calculate the total time foragers can spend per patch from their functional response (intake rate as a function of food density). However, in the field there are likely to be factors modulating the functional response. In this study previously published results of experiments on captive Bewick's swans were used to obtain functional responses of swans digging for tubers of Fennel pondweed on different foraging substrates: sandy and clayey sediment, and in shallow and deep water. In a field study, four 250×250 m sections belonging to different types (sandy–shallow, clayey–shallow, sandy–deep and clayey–deep) were delineated. Here tubers were sampled with sediment corers in three years, both before and after swan exploitation in autumn, and swans were observed and mapped from a hide in two of these years. Giving-up tuber biomass densities varied among sections. Substitution of these giving-up densities in the derived patch-type-specific functional responses yielded the quitting net energy intake rates in the four sections. As expected from the marginal value theorem, the quitting net energy intake rates did not vary among sections. Moreover, the observed foraging pressure (total foraging time per area) per patch type was in quantitative agreement with the integrated functional responses. These results suggest that in spatially heterogeneous environments, patch exploitation by foragers can be predicted from their functional responses after accounting for foraging substrate.

An introduction to compressive sensing and its potential applications in structural engineering

The Shannon/Nyquist sampling theorem specifies that to avoid losing information when capturing a signal, one must sample at least two times faster than the signal bandwidth. In order to capture and represent compressible signals at a rate significantly below the Nyquist rate, a new method, called compressive sensing (CS), is therefore proposed. CS theory asserts that one can recover certain signals from far fewer samples or measurements than traditional methods use. It employs non-adaptive linear projections that preserve the structure of the sparse signal; the signal is then reconstructed from these projections using an optimization process. It is believed that CS has far reaching implications, while most publications concentrate on signal processing fields (especially for images). In this paper, we provide a concise introduction of CS and then discuss some of its potential applications in structural engineering. The recorded vibration time history of a steel beam and the wave propagation result on a steel rebar are studied in detail. CS is adopted to reconstruct the time histories by using only parts of the signals. The results under different conditions are compared, which confirm that CS will be a promising tool for structural engineering.

Optimization and matrix constructions for classification of data

Max-plus algebras and more general semirings have many useful applications and have been actively investigated. On the other hand, structural matrix rings are also well known and have been considered by many authors. The main theorem of this article completely describes all optimal ideals in the more general structural matrix semirings. Originally, our investigation of these ideals was motivated by applications in data mining for the design of centroid-based classification systems, as well as for the design of multiple classification systems combining several individual classifiers.

Existence conditions for functional observability from an eigenspace perspective

Two theorems on conditions for nonexistence and for existence, of built functional observers, from an eigenspace perspective are presented and proved. One more theorem on Functional Observability in terms of constructed products of matrices A,C and L0 is also presented. This theorem provides an easy way to check Functional Observability before proceeding with the design of functional observers. The existence and the nonexistence theorems are used to unify previously reported theorems on Functional Observability by showing their equivalence. The connection between the concept of Functional Observability and the well known concept of State Observability is also presented.

Vision, ambiguity and perceptual possibility : why pictures matter in the critique of stereo-immersive VR

The acquisition of three-dimensional immersive space through advanced digitial imaging technology, suggests a profound shift from the relatively impoverished representational stratgies of two-dimensional pictorial imagery.  This entails an epistemological shift from pictorial representation, to the presentation of actual three-dimensional space through stereoscopic (3D) imagery.  Moreover, it suggests that visuality rather than 'virtuality' is the core issue in understanding the nature of the epistemological shift associated with stereo-immersive VR.

A shift in visual epistemology from 'flat' pictorial representation to three-dimensional stereo-immersion suggests a gainful move toward a visuality imbued with spatial possibilities.  In quantitative terms, these visual-spatial gains may seem self-evident.  However, certain aspects peculiar to pictorial representation are missing from stereo-immersive imaging.  That is lost in stereo-immersive imaging, and how it can be measured?

This thesis proposes that the inherent ambiguity of two-dimensional representations of three-dimensional spatial structure in pictures, invokes a perceptual response in which pictorial spaces elicit 'perceptual possibility'.  The robust three-dimentional spatiality of stereo-immersvie VR foreclosures such possibility.  Through examining stereo-immersive VR in terms of its visuality, the thesis develops a new appraoch to understanding VR that solves some of the issues associated with the problematic concept of 'virtuality'.  In addition, the thesis finds that by placing stereo-immersive VR and pictures within the shared paradigm of 'the visual', an important dimension of pictures that has been overlooked in past analyses re-emerges : the thesis proposes the concept of 'artifactuality' to account for the way pictures are fundamentally, and in the first instance, aesthetic objects for visual perception.  It is in their manner of appearing as pictures, that they are perceived as pictures of something.  It is from this fundamental basis that their many levels of meaning and signification - their manifold 'realisms' - can arise.

This thesis therefore addresses two intersecting problems within the paradigm of the visual: it proposes 1) that analyses of 'the virtual' be grounded in the 'artifactuality' of pictorial perception, and 2) that the spatiality of stereo-immersive VR be reinvigorated by purposefully 'under-contraining' its key percept - the robust, 'solid' stereoscopic structuring of visual space.  This approach opens up the discourse of stereo-immersive VR to new visual paradigms.  The thesis proposes that these be modelled not on the impossibility of 'the virtual', but on the possibilities of visual ambiguity drawn from the analysis of pictorial perception.

The digital contamination of dramatic theatre : subject technology in exception

Drawing on Derrida’s analysis of the metaphysics of presence, this paper examines the centrality of presence in much theatre commentary, arguing that such a privileging demonises projected media as a form of contamination. Through a close look at a hybrid work that integrates live performers with avatars from Second Life, I seek a way to move forward between conditions of possibility and impossibility.

A GA-PSO layered encoding evolutionary approach to 0/1 knapsack optimization

This paper presents a layered encoding cascade evolutionary approach to solve a 0/1 knapsack optimization problem. A layered encoding structure is proposed and developed based on the schema theorem and the concepts of cascade correlation and multi-population evolutionary algorithms. Genetic algorithm (GA) and particle swarm optimization (PSO) are combined with the proposed layered encoding structure to form a generic optimization model denoted as LGAPSO. In order to enhance the finding of both local and global optimum in the evolutionary search, the model adopts hill climbing evaluation criteria, feature of strength Pareto evolutionary approach (SPEA) as well as nondominated spread lengthen criteria. Four different sizes benchmark knapsack problems are studied using the proposed LGAPSO model. The performance of LGAPSO is compared to that of the ordinary multi-objective optimizers such as VEGA, NSGA, NPGA and SPEA. The proposed LGAPSO model is shown to be efficient in improving the search of knapsack’s optimum, capable of gaining better Pareto trade-off front.