On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

A family of asymptotically good lattices having a lattice in each dimension

A new constructive family of asymptotically good lattices with respect to sphere packing density is presented. The family has a lattice in every dimension n >= 1. Each lattice is obtained from a conveniently chosen integral ideal in a subfield of the cyclotomic field Q(zeta(q)) where q is the smallest prime congruent to 1 modulo n.

An algorithm for the strip packing problem using collision free region and exact fitting placement

The irregular shape packing problem is approached. The container has a fixed width and an open dimension to be minimized. The proposed algorithm constructively creates the solution using an ordered list of items and a placement heuristic. Simulated annealing is the adopted metaheuristic to solve the optimization problem. A two-level algorithm is used to minimize the open dimension of the container. To ensure feasible layouts, the concept of collision free region is used. A collision free region represents all possible translations for an item to be placed and may be degenerated. For a moving item, the proposed placement heuristic detects the presence of exact fits (when the item is fully constrained by its surroundings) and exact slides (when the item position is constrained in all but one direction). The relevance of these positions is analyzed and a new placement heuristic is proposed. Computational comparisons on benchmark problems show that the proposed algorithm generated highly competitive solutions. Moreover, our algorithm updated some best known results. (C) 2012 Elsevier Ltd. All rights reserved.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Motivation, development and validation of a new spectral greenness index : a spectral dimension related to foliage projective cover

A method is presented for the development of a regional Landsat-5 Thematic Mapper (TM) and Landsat-7 Enhanced Thematic Mapper plus (ETM+) spectral greenness index, coherent with a six-dimensional index set, based on a single ETM+ spectral image of a reference landscape. The first three indices of the set are determined by a polar transformation of the first three principal components of the reference image and relate to scene brightness, percent foliage projective cover (FPC) and water related features. The remaining three principal components, of diminishing significance with respect to the reference image, complete the set. The reference landscape, a 2200 km2 area containing a mix of cattle pasture, native woodland and forest, is located near Injune in South East Queensland, Australia. The indices developed from the reference image were tested using TM spectral images from 19 regionally dispersed areas in Queensland, representative of dissimilar landscapes containing woody vegetation ranging from tall closed forest to low open woodland. Examples of image transformations and two-dimensional feature space plots are used to demonstrate image interpretations related to the first three indices. Coherent, sensible, interpretations of landscape features in images composed of the first three indices can be made in terms of brightness (red), foliage cover (green) and water (blue). A limited comparison is made with similar existing indices. The proposed greenness index was found to be very strongly related to FPC and insensitive to smoke. A novel Bayesian, bounded space, modelling method, was used to validate the greenness index as a good predictor of FPC. Airborne LiDAR (Light Detection and Ranging) estimates of FPC along transects of the 19 sites provided the training and validation data. Other spectral indices from the set were found to be useful as model covariates that could improve FPC predictions. They act to adjust the greenness/FPC relationship to suit different spectral backgrounds. The inclusion of an external meteorological covariate showed that further improvements to regional-scale predictions of FPC could be gained over those based on spectral indices alone.

Commentary : Biomaterials offer cancer research the third dimension

In a mini review from 2002, Tyler Jacks and Robert Weinberg commented on the pioneering three-dimensional (3D) culture work from Bissell laboratories and concluded: “Suddenly the study of cancer cells in two dimensions seems quaint if not archaic.” The relevance of this statement for planning and executing mechanistic biological studies and advanced drug testing has been largely disregarded by both academic researchers and the pharmaceutical and biomedical industry in the twenty-first century.

Automatic grading and packing of prawns

Prawns are a substantial Australian resource but presently are processed in a very labour-intensive manner. A prototype system has been developed for automatically grading and packing prawns into single-layer 'consumer packs' in which each prawn is approximately straight and has the same orientation. The novel technology includes a machine vision system that has been specially programmed to calculate relevant parameters at high speed and a gripper mechanism that can acquire, straighten and place prawns of various sizes. The system can be implemented on board a trawler or in an onshore processing facility. © 1993.

David Hicks and Cathie Holden (eds.) (2007). Teaching The Global Dimension. London: Routledge, Taylor & Francis Group, 212 pages.

Teaching The Global Dimension (2007) is intended for primary and secondary teachers, pre-service teachers and educators interested in fostering global concerns in the education system. It aims at linking theory and practice and is structured as follows. Part 1, the global dimension, proposes an educational framework for understanding global concerns. Individual chapters in this section deal with some educational responses to global issues and the ways in which young people might become, in Hick’s terms, more “world-minded”. In the first two chapters, Hicks presents first, some educational responses to global issues that have emerged in recent decades, and second, an outline of the evolution of global education as a specific field. As with all the chapters in this book, most of the examples are drawn from the United Kingdom. Young people’s concerns, student teachers’ views and the teaching of controversial issues, comprise the other chapters in this section. Taken collectively, the chapters in Part 2 articulate the conceptual framework for developing, teaching and evaluating a global dimension across the curriculum. Individual chapters in this section, written by a range of authors, explore eight key concepts considered necessary to underpin appropriate learning experiences in the classroom. These are conflict, social justice, values and perceptions, sustainability, interdependence, human rights, diversity and citizenship. These chapters are engaging and well structured. Their common format consists of a succinct introduction, reference to positive action for change, and examples of recent effective classroom practice. Two chapters comprise the final section of this book and suggest different ways in which the global dimension can be achieved in the primary and the secondary classroom.

Butterpaper, sweat & tears : the affective dimension of engaging students during the architectural critique

Considering how dominant a feature of architectural education the critique has been, and continues to be, little has been written about the affective dimension of engaging students during this key final stage of the design or documentation process. For most students, the critique is unlike any previous educational or life experience that they have ever confronted, and the abrupt change in the instructor’s role, from tutor to judge, can be disconcerting at a time when the student is feeling their most vulnerable. The fact that the period immediately leading up to the critique habitually entails not only a focused and sustained effort, but also sleepless nights of intensive work, further exacerbates this. The purpose of this paper is to recognise the affective phenomena influencing student engagement, during the critique. The participants of this research were second to fourth year architecture students at a major Australian university. Following the implementation of trials in alternative modes of critique in architectural design and technology studios, qualitative data was obtained from students, through questionnaires and interviews. Six indicators of engagement were investigated through this research: motivation and agency, transactional engagement with staff, transactional engagement with students, institutional support, active citizenship, and non-institutional support. This research confirms that affective phenomena play a significant role in the events of the critique; the relationship between instructor and student influences student engagement, as does the choreography and spatial planning of the critique environment; and these factors ultimately have an impact on the depth of student learning.

The neglected dimension of community liveability : impact on social connectedness and active ageing in higher density accommodation

Purpose This thesis is about liveability, place and ageing in the high density urban landscape of Brisbane, Australia. As with other major developed cities around the globe, Brisbane has adopted policies to increase urban residential densities to meet the main liveability and sustainability aim of decreasing car dependence and therefore pollution, as well as to minimise the loss of greenfield areas and habitats to developers. This objective hinges on urban neighbourhoods/communities being liveable places, which residents do not have to leave for everyday living. Community/neighbourhood liveability is an essential ingredient in healthy ageing in place and has a substantial impact upon the safety, independence and well-being of older adults. It is generally accepted that ageing in place is optimal for both older people and the state. The optimality of ageing in place generally assumes that there is a particular quality to environments or standard of liveability in which people successfully age in place. The aim of this thesis was to examine if there are particular environmental qualities or aspects of liveability that test optimality and to better understand the key liveability factors that contribute to successful ageing in place. Method A strength of this thesis is that it draws on two separate studies to address the research question of what makes high density liveable for older people. In Chapter 3, the two methods are identified and differentiated as Method 1 (used in Paper 1) and Method 2 (used in Papers 2, 3, 4 and 5). Method 1 involved qualitative interviews with 24 inner city high density Brisbane residents. The major strength of this thesis is the innovative methodology outlined in the thesis as Method 2. Method 2 involved a case study approach employing qualitative and quantitative methods. Qualitative data was collected using semi-structured, in-depth interviews and time-use diaries completed by participants during the week of tracking. The quantitative data was gathered using Global Positioning Systems for tracking and Geographical Information Systems for mapping and analysis of participants’ activities. The combination of quantitative and qualitative analysis captured both participants’ subjective perceptions of their neighbourhoods and their patterns of movement. This enhanced understanding of how neighbourhoods and communities function and of the various liveability dimensions that contribute to active ageing and ageing in place for older people living in high density environments. Both studies’ participants were inner-city high density residents of Brisbane. The study based on Method 1 drew on a wider age demographic than the study based on Method 2. Findings The five papers presented in this thesis by publication indicate a complex inter-relationship of the factors that make a place liveable. The first three papers identify what is comparable and different between the physical and social factors of high density communities/neighbourhoods. The last two papers explore relationships between social engagement and broader community variables such as infrastructure and the physical built environments that are risk or protective factors relevant to community liveability, active ageing and ageing in place in high density. The research highlights the importance of creating and/or maintaining a barrier-free environment and liveable community for ageing adults. Together, the papers promote liveability, social engagement and active ageing in high density neighbourhoods by identifying factors that constitute liveability and strategies that foster active ageing and ageing in place, social connections and well-being. Recommendations There is a strong need to offer more support for active ageing and ageing in place. While the data analyses of this research provide insight into the lived experience of high density residents, further research is warranted. Further qualitative and quantitative research is needed to explore in more depth, the urban experience and opinions of older people living in urban environments. In particular, more empirical research and theory-building is needed in order to expand understanding of the particular environmental qualities that enable successful ageing in place in our cities and to guide efforts aimed at meeting this objective. The results suggest that encouraging the presence of more inner city retail outlets, particularly services that are utilised frequently in people’s daily lives such as supermarkets, medical services and pharmacies, would potentially help ensure residents fully engage in their local community. The connectivity of streets, footpaths and their role in facilitating the reaching of destinations are well understood as an important dimension of liveability. To encourage uptake of sustainable transport, the built environment must provide easy, accessible connections between buildings, walkways, cycle paths and public transport nodes. Wider streets, given that they take more time to cross than narrow streets, tend to .compromise safety - especially for older people. Similarly, the width of footpaths, the level of buffering, the presence of trees, lighting, seating and design of and distance between pedestrian crossings significantly affects the pedestrian experience for older people and impacts upon their choice of transportation. High density neighbourhoods also require greater levels of street fixtures and furniture for everyday life to make places more useable and comfortable for regular use. The importance of making the public realm useful and habitable for older people cannot be over-emphasised. Originality/value While older people are attracted to high density settings, there has been little empirical evidence linking liveability satisfaction with older people’s use of urban neighbourhoods. The current study examined the relationships between community/neighbourhood liveability, place and ageing to better understand the implications for those adults who age in place. The five papers presented in this thesis add to the understanding of what high density liveable age-friendly communities/ neighbourhoods are and what makes them so for older Australians. Neighbourhood liveability for older people is about being able to age in place and remain active. Issues of ageing in Australia and other areas of the developed world will become more critical in the coming decades. Creating livable communities for all ages calls for partnerships across all levels of government agencies and among different sectors within communities. The increasing percentage of older people in the community will have increasing political influence and it will be a foolish government who ignores the needs of an older society.

Empirical analysis of the effect of dimension reduction and word order on semantic vectors

The aim of this paper is to provide a comparison of various algorithms and parameters to build reduced semantic spaces. The effect of dimension reduction, the stability of the representation and the effect of word order are examined in the context of the five algorithms bearing on semantic vectors: Random projection (RP), singular value decom- position (SVD), non-negative matrix factorization (NMF), permutations and holographic reduced representations (HRR). The quality of semantic representation was tested by means of synonym finding task using the TOEFL test on the TASA corpus. Dimension reduction was found to improve the quality of semantic representation but it is hard to find the optimal parameter settings. Even though dimension reduction by RP was found to be more generally applicable than SVD, the semantic vectors produced by RP are somewhat unstable. The effect of encoding word order into the semantic vector representation via HRR did not lead to any increase in scores over vectors constructed from word co-occurrence in context information. In this regard, very small context windows resulted in better semantic vectors for the TOEFL test.