Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

On a Syntactic Characterization of Classification with a Mind Change Bound

Most learning paradigms impose a particular syntax on the class of concepts to be learned; the chosen syntax can dramatically affect whether the class is learnable or not. For classification paradigms, where the task is to determine whether the underlying world does or does not have a particular property, how that property is represented has no implication on the power of a classifier that just outputs 1’s or 0’s. But is it possible to give a canonical syntactic representation of the class of concepts that are classifiable according to the particular criteria of a given paradigm? We provide a positive answer to this question for classification in the limit paradigms in a logical setting, with ordinal mind change bounds as a measure of complexity. The syntactic characterization that emerges enables to derive that if a possibly noncomputable classifier can perform the task assigned to it by the paradigm, then a computable classifier can also perform the same task. The syntactic characterization is strongly related to the difference hierarchy over the class of open sets of some topological space; this space is naturally defined from the class of possible worlds and possible data of the learning paradigm.

Outdoor simultaneous localisation and mapping using RatSLAM

In this paper an existing method for indoor Simultaneous Localisation and Mapping (SLAM) is extended to operate in large outdoor environments using an omnidirectional camera as its principal external sensor. The method, RatSLAM, is based upon computational models of the area in the rat brain that maintains the rodent’s idea of its position in the world. The system uses the visual appearance of different locations to build hybrid spatial-topological maps of places it has experienced that facilitate relocalisation and path planning. A large dataset was acquired from a dynamic campus environment and used to verify the system’s ability to construct representations of the world and simultaneously use these representations to maintain localisation.

Multifractal characterisation and analysis of complex networks

Complex networks have been studied extensively due to their relevance to many real-world systems such as the world-wide web, the internet, biological and social systems. During the past two decades, studies of such networks in different fields have produced many significant results concerning their structures, topological properties, and dynamics. Three well-known properties of complex networks are scale-free degree distribution, small-world effect and self-similarity. The search for additional meaningful properties and the relationships among these properties is an active area of current research. This thesis investigates a newer aspect of complex networks, namely their multifractality, which is an extension of the concept of selfsimilarity. The first part of the thesis aims to confirm that the study of properties of complex networks can be expanded to a wider field including more complex weighted networks. Those real networks that have been shown to possess the self-similarity property in the existing literature are all unweighted networks. We use the proteinprotein interaction (PPI) networks as a key example to show that their weighted networks inherit the self-similarity from the original unweighted networks. Firstly, we confirm that the random sequential box-covering algorithm is an effective tool to compute the fractal dimension of complex networks. This is demonstrated on the Homo sapiens and E. coli PPI networks as well as their skeletons. Our results verify that the fractal dimension of the skeleton is smaller than that of the original network due to the shortest distance between nodes is larger in the skeleton, hence for a fixed box-size more boxes will be needed to cover the skeleton. Then we adopt the iterative scoring method to generate weighted PPI networks of five species, namely Homo sapiens, E. coli, yeast, C. elegans and Arabidopsis Thaliana. By using the random sequential box-covering algorithm, we calculate the fractal dimensions for both the original unweighted PPI networks and the generated weighted networks. The results show that self-similarity is still present in generated weighted PPI networks. This implication will be useful for our treatment of the networks in the third part of the thesis. The second part of the thesis aims to explore the multifractal behavior of different complex networks. Fractals such as the Cantor set, the Koch curve and the Sierspinski gasket are homogeneous since these fractals consist of a geometrical figure which repeats on an ever-reduced scale. Fractal analysis is a useful method for their study. However, real-world fractals are not homogeneous; there is rarely an identical motif repeated on all scales. Their singularity may vary on different subsets; implying that these objects are multifractal. Multifractal analysis is a useful way to systematically characterize the spatial heterogeneity of both theoretical and experimental fractal patterns. However, the tools for multifractal analysis of objects in Euclidean space are not suitable for complex networks. In this thesis, we propose a new box covering algorithm for multifractal analysis of complex networks. This algorithm is demonstrated in the computation of the generalized fractal dimensions of some theoretical networks, namely scale-free networks, small-world networks, random networks, and a kind of real networks, namely PPI networks of different species. Our main finding is the existence of multifractality in scale-free networks and PPI networks, while the multifractal behaviour is not confirmed for small-world networks and random networks. As another application, we generate gene interactions networks for patients and healthy people using the correlation coefficients between microarrays of different genes. Our results confirm the existence of multifractality in gene interactions networks. This multifractal analysis then provides a potentially useful tool for gene clustering and identification. The third part of the thesis aims to investigate the topological properties of networks constructed from time series. Characterizing complicated dynamics from time series is a fundamental problem of continuing interest in a wide variety of fields. Recent works indicate that complex network theory can be a powerful tool to analyse time series. Many existing methods for transforming time series into complex networks share a common feature: they define the connectivity of a complex network by the mutual proximity of different parts (e.g., individual states, state vectors, or cycles) of a single trajectory. In this thesis, we propose a new method to construct networks of time series: we define nodes by vectors of a certain length in the time series, and weight of edges between any two nodes by the Euclidean distance between the corresponding two vectors. We apply this method to build networks for fractional Brownian motions, whose long-range dependence is characterised by their Hurst exponent. We verify the validity of this method by showing that time series with stronger correlation, hence larger Hurst exponent, tend to have smaller fractal dimension, hence smoother sample paths. We then construct networks via the technique of horizontal visibility graph (HVG), which has been widely used recently. We confirm a known linear relationship between the Hurst exponent of fractional Brownian motion and the fractal dimension of the corresponding HVG network. In the first application, we apply our newly developed box-covering algorithm to calculate the generalized fractal dimensions of the HVG networks of fractional Brownian motions as well as those for binomial cascades and five bacterial genomes. The results confirm the monoscaling of fractional Brownian motion and the multifractality of the rest. As an additional application, we discuss the resilience of networks constructed from time series via two different approaches: visibility graph and horizontal visibility graph. Our finding is that the degree distribution of VG networks of fractional Brownian motions is scale-free (i.e., having a power law) meaning that one needs to destroy a large percentage of nodes before the network collapses into isolated parts; while for HVG networks of fractional Brownian motions, the degree distribution has exponential tails, implying that HVG networks would not survive the same kind of attack.

A hybrid shifting bottleneck procedure algorithm for the parallel-machine job-shop scheduling problem

In practice, parallel-machine job-shop scheduling (PMJSS) is very useful in the development of standard modelling approaches and generic solution techniques for many real-world scheduling problems. In this paper, based on the analysis of structural properties in an extended disjunctive graph model, a hybrid shifting bottleneck procedure (HSBP) algorithm combined with Tabu Search metaheuristic algorithm is developed to deal with the PMJSS problem. The original-version SBP algorithm for the job-shop scheduling (JSS) has been significantly improved to solve the PMJSS problem with four novelties: i) a topological-sequence algorithm is proposed to decompose the PMJSS problem into a set of single-machine scheduling (SMS) and/or parallel-machine scheduling (PMS) subproblems; ii) a modified Carlier algorithm based on the proposed lemmas and the proofs is developed to solve the SMS subproblem; iii) the Jackson rule is extended to solve the PMS subproblem; iv) a Tabu Search metaheuristic algorithm is embedded under the framework of SBP to optimise the JSS and PMJSS cases. The computational experiments show that the proposed HSBP is very efficient in solving the JSS and PMJSS problems.

Tinamous and moa flock together : mitochondrial genome sequence analysis reveals independent losses of flight among ratites

Ratites are large, flightless birds and include the ostrich, rheas, kiwi, emu, and cassowaries, along with extinct members, such as moa and elephant birds. Previous phylogenetic analyses of complete mitochondrial genome sequences have reinforced the traditional belief that ratites are monophyletic and tinamous are their sister group. However, in these studies ratite monophyly was enforced in the analyses that modeled rate heterogeneity among variable sites. Relaxing this topological constraint results in strong support for the tinamous (which fly) nesting within ratites. Furthermore, upon reducing base compositional bias and partitioning models of sequence evolution among protein codon positions and RNA structures, the tinamou–moa clade grouped with kiwi, emu, and cassowaries to the exclusion of the successively more divergent rheas and ostrich. These relationships are consistent with recent results from a large nuclear data set, whereas our strongly supported finding of a tinamou–moa grouping further resolves palaeognath phylogeny. We infer flight to have been lost among ratites multiple times in temporally close association with the Cretaceous–Tertiary extinction event. This circumvents requirements for transient microcontinents and island chains to explain discordance between ratite phylogeny and patterns of continental breakup. Ostriches may have dispersed to Africa from Eurasia, putting in question the status of ratites as an iconic Gondwanan relict taxon. [Base composition; flightless; Gondwana; mitochondrial genome; Palaeognathae; phylogeny; ratites.]

Towards persistent localization and mapping with a continuous appearance-based topology

Appearance-based localization can provide loop closure detection at vast scales regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale not only with the size of the environment but also with the operation time of the platform. Additionally, repeated visits to locations will develop multiple competing representations, which will reduce recall performance over time. These properties impose severe restrictions on long-term autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. In this paper we present a graphical extension to CAT-SLAM, a particle filter-based algorithm for appearance-based localization and mapping, to provide constant computation and memory requirements over time and minimal degradation of recall performance during repeated visits to locations. We demonstrate loop closure detection in a large urban environment with capped computation time and memory requirements and performance exceeding previous appearance-based methods by a factor of 2. We discuss the limitations of the algorithm with respect to environment size, appearance change over time and applications in topological planning and navigation for long-term robot operation.

Towards persistent indoor appearance-based localization, mapping and navigation using CAT-Graph

The challenge of persistent appearance-based navigation and mapping is to develop an autonomous robotic vision system that can simultaneously localize, map and navigate over the lifetime of the robot. However, the computation time and memory requirements of current appearance-based methods typically scale not only with the size of the environment but also with the operation time of the platform; also, repeated revisits to locations will develop multiple competing representations which reduce recall performance. In this paper we present a solution to the persistent localization, mapping and global path planning problem in the context of a delivery robot in an office environment over a one-week period. Using a graphical appearance-based SLAM algorithm, CAT-Graph, we demonstrate constant time and memory loop closure detection with minimal degradation during repeated revisits to locations, along with topological path planning that improves over time without using a global metric representation. We compare the localization performance of CAT-Graph to openFABMAP, an appearance-only SLAM algorithm, and the path planning performance to occupancy-grid based metric SLAM. We discuss the limitations of the algorithm with regard to environment change over time and illustrate how the topological graph representation can be coupled with local movement behaviors for persistent autonomous robot navigation.

Querying a building information model for construction-specific spatial information

The design and construction community has shown increasing interest in adopting building information models (BIMs). The richness of information provided by BIMs has the potential to streamline the design and construction processes by enabling enhanced communication, coordination, automation and analysis. However, there are many challenges in extracting construction-specific information out of BIMs. In most cases, construction practitioners have to manually identify the required information, which is inefficient and prone to error, particularly for complex, large-scale projects. This paper describes the process and methods we have formalized to partially automate the extraction and querying of construction-specific information from a BIM. We describe methods for analyzing a BIM to query for spatial information that is relevant for construction practitioners, and that is typically represented implicitly in a BIM. Our approach integrates ifcXML data and other spatial data to develop a richer model for construction users. We employ custom 2D topological XQuery predicates to answer a variety of spatial queries. The validation results demonstrate that this approach provides a richer representation of construction-specific information compared to existing BIM tools.

Reasoning about component similarity in building product models from the construction perspective

Identifying the design features that impact construction is essential to developing cost effective and constructible designs. The similarity of building components is a critical design feature that affects method selection, productivity, and ultimately construction cost and schedule performance. However, there is limited understanding of what constitutes similarity in the design of building components and limited computer-based support to identify this feature in a building product model. This paper contributes a feature-based framework for representing and reasoning about component similarity that builds on ontological modelling, model-based reasoning and cluster analysis techniques. It describes the ontology we developed to characterize component similarity in terms of the component attributes, the direction, and the degree of variation. It also describes the generic reasoning process we formalized to identify component similarity in a standard product model based on practitioners' varied preferences. The generic reasoning process evaluates the geometric, topological, and symbolic similarities between components, creates groupings of similar components, and quantifies the degree of similarity. We implemented this reasoning process in a prototype cost estimating application, which creates and maintains cost estimates based on a building product model. Validation studies of the prototype system provide evidence that the framework is general and enables a more accurate and efficient cost estimating process.

Deriving construction features from an IFC model

In recent years, there has been a growing interest from the design and construction community to adopt Building Information Models (BIM). BIM provides semantically-rich information models that explicitly represent both 3D geometric information (e.g., component dimensions), along with non-geometric properties (e.g., material properties). While the richness of design information offered by BIM is evident, there are still tremendous challenges in getting construction-specific information out of BIM, limiting the usability of these models for construction. In this paper, we describe our approach for extracting construction-specific design conditions from a BIM model based on user-defined queries. This approach leverages an ontology of features we are developing to formalize the design conditions that affect construction. Our current implementation analyzes the component geometry and topological relationships between components in a BIM model represented using the Industry Foundation Classes (IFC) to identify construction features. We describe the reasoning process implemented to extract these construction features, and provide a critique of the IFC’s to support the querying process. We use examples from two case studies to illustrate the construction features, the querying process, and the challenges involved in deriving construction features from an IFC model.

Mobius markets : professional families in rural educational markets

Australia has many isolated communities that require human services provided by qualified professionals. Maintaining a viable and equitable spread of such educational capital across space as a public good is a challenge. Reports investigating this problem repeatedly point to ‘family issues’ such as limited options for children’s education, and limited access to ongoing professional development, as deterrents for rural/remote employment despite lucrative incentive schemes. This paper draws on semi-structured interviews with 30 parents of school-aged children, who work as doctors, nurses, teachers and police in six rural/remote towns in Queensland. We asked them how their family units reconcile career opportunities with educational strategy for family members over time and space. This paper considers these issues as a sociology of education problem in a context of educational marketisation and spiralling credentialism. This paper offers the concept of ‘mobius markets’ to capture the cyclical and intergenerational process underway in middle class professional families of investing in educational capitals, maintaining or maximising their value and profiting from them. A mobius strip is the topological anomaly of a single loop with one twist in it, whereby the loop becomes one continuous surface, not the double-sided shape it appears to be. This project is interested in how the middle class professional family is similarly on a constant circuit, investing in educational capitals, upgrading their currency/value, and profiting from them. This elaborated sense of educational markets extends the more usual sociological focus on school choice.

Odometry-driven inference to link multiple exemplars of a location

A major challenge for robot localization and mapping systems is maintaining reliable operation in a changing environment. Vision-based systems in particular are susceptible to changes in illumination and weather, and the same location at another time of day may appear radically different to a system using a feature-based visual localization system. One approach for mapping changing environments is to create and maintain maps that contain multiple representations of each physical location in a topological framework or manifold. However, this requires the system to be able to correctly link two or more appearance representations to the same spatial location, even though the representations may appear quite dissimilar. This paper proposes a method of linking visual representations from the same location without requiring a visual match, thereby allowing vision-based localization systems to create multiple appearance representations of physical locations. The most likely position on the robot path is determined using particle filter methods based on dead reckoning data and recent visual loop closures. In order to avoid erroneous loop closures, the odometry-based inferences are only accepted when the inferred path's end point is confirmed as correct by the visual matching system. Algorithm performance is demonstrated using an indoor robot dataset and a large outdoor camera dataset.

Do the kinematics of a baulked take-off in springboard diving differ from those of a completed dive

Consistency and invariance in movements are traditionally viewed as essential features of skill acquisition and elite sports performance. This emphasis on the stabilization of action has resulted in important processes of adaptation in movement coordination during performance being overlooked in investigations of elite sport performance. Here we investigate whether differences exist between the movement kinematics displayed by five, elite springboard divers (age 17 ± 2.4 years) in the preparation phases of baulked and completed take-offs. The two-dimensional kinematic characteristics of the reverse somersault take-off phases (approach and hurdle) were recorded during normal training sessions and used for intra-individual analysis. All participants displayed observable differences in movement patterns at key events during the approach phase; however, the presence of similar global topological characteristics suggested that, overall, participants did not perform distinctly different movement patterns during completed and baulked dives. These findings provide a powerful rationale for coaches to consider assessing functional variability or adaptability of motor behaviour as a key criterion of successful performance in sports such as diving.

Undulating matter : a topology of the studio

With specific reference to the writing of Dan Graham and the experiences of creative practice, this paper will elaborate an account of studio practice as a topology - a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. This paper will trace a brief sequence of topological formulations to draw together the expression of topology as form and its structural dimension as a methodology in the specific context of the author’s studio practice. In so doing, this paper seeks to expand the notion of topology in art beyond its association with Conceptual Art of the 1960s and 70s to propose that topology provides a dynamic theoretical model for apprehending the generative ‘logic’ that gives direction and continuity to the art-making process.