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The paper aims to research the applications of topological geometry to the architectural concept design process and their combination with the modern digital technology to find novel architectural spaces and forms which are dynamic, easily adaptable to the context and surroundings.

The article uses the method of studying the existing literature on topological geometry and architectural design theory including design thinking, architectural design methods and architectural compositions to analyze and compare them with architectural practices and suggest new topological design tools and methods. Moreover, the paper tests the proposals with a number of preliminary design research experiments. In addition, graphic design software, parametric design, building information modeling (BIM) and digital development trends in architecture were explored and experienced to reveal the application potential of topological design thinking and methods in the trend of architectural digitization.

The paper has analyzed, synthesized and systematized the basic theories of topological geometry in order to clarify their applications in the architectural concept design process. On that basis, the paper proposes a novel topological design thinking and method for finding rich diversified architectural ideas and forms based on original invariant design constraints. Finally, the paper clarifies the combination as well as the mutual, motivating relationship between topological geometry and modern digital technologies when applied to architectural design.

The research contributes a novel design thinking and method based on topological geometry combined with modern digital technology to the architectural design theory. It will be a valuable tool capable of suggesting architects how to think and innovate in architecture in the era of industrial revolution 4.0.

This chapter compares and contrasts the diverse theoretical foundations of two paradigms in strategic project management. The first, older paradigm, draws on foundational ideas about nature (i.e., it is predictable) and human rationality (strategy and implementation are distinct) to conceptualize project management in terms of controlling predictable project processes and their inherent risks, so that project managers can optimize the trade-offs between timing, cost and quality. The second practice-based alternative paradigm conceptualizes people as sources of deterministic behavior in an otherwise often unpredictable world. Projects are key tools that are used to strategically create this predictable behavior, with project plans being used as scaffolding to help co-ordinate the distributed behavior of systemically connected people in space and time as the project proceeds. The chapter highlights how this second paradigm has a more robust scientific basis, shows how it informed the development of the Heathrow T5 project, and draws implications of for future theory and practice.

Relational thinking and spatial analyses have become highly relevant for higher education research. However, choices of research methods and specifically of statistical procedures do not often correspond to the epistemological underpinnings implied by relational perspectives. Against this background, this chapter illustrates the uses and challenges of geometric data analysis (GDA) for studying the complexities and dynamics of current spaces of higher education. GDA can be described as a set of statistical techniques that allow the identification, assessment and visualisation of complex relations in social science data. Using an investigation into the social topologies of first-year students as an example, we discuss the mathematical foundations, the step-by-step procedures of data analysis, the interpretation of results and strategies for integrating GDA into multimethod research designs. In sum, we argue that GDA does not only entail a comprehensive set of statistical instruments that permit visual analysis of relational structures, but also enables the systematic integration of qualitative and quantitative methods, hence supporting the development of innovative and coherent research designs and analytical strategies.

A robotic wheelchair system was designed to assist disabled people with disabilities to walk.

An anticipated sharing control strategy based on topological map is proposed in this paper, which is used to assist robotic wheelchairs to realize interactive navigation. Then, a robotic wheelchair navigation control system based on the brain-computer interface and topological map was designed and implemented.

In the field of robotic wheelchairs, the problems of poor use, narrow application range and low humanization are still not improved.

In the system, the topological map construction is not restricted by the environment structure, which helps to expand the scope of application; the shared control system can predict the users’ intention and replace the users’ decision to realize human-machine interactive navigation, which has higher security, robustness and comfort.

This chapter focuses on a new school-level instrument for international benchmarking and policy learning – the OECD’s PISA-based Test for Schools (“PISA for Schools”) – and how it helps to constitute new global spaces and relations of education policymaking and governance. Unlike main PISA, PISA for Schools assesses school performance in reading, mathematics, and science against the schooling systems measured by the main PISA test. Schools are thus positioned within a globally commensurate space of measurement and comparison, and are encouraged to engage with, and learn from, the policy expertise proffered by “high-performing” international schooling systems and the OECD itself. Drawing suggestively across literature and theorizing around new spatialities associated with globalization, the “becoming topological” of culture and “power-topologies,” and informed by document analysis and interviews with 33 policy actors from across the PISA for Schools policy cycle, the chapter examines how PISA for Schools helps the OECD to directly “reach into” local schooling spaces. This respatialized PISA for Schools, or “PISA to Schools”, provides the OECD with the means to influence how schooling is practised and conceived at the level of local policy implementation, while limiting mediation by national and/or subnational politics. Moreover, the school-to-system performance comparisons enabled by PISA for Schools arguably provide one of the first – if not the only – international data-driven catalysts of school-level reform. This furthers the relevance and diffusion of “lessons” from main PISA and the OECD to schools themselves, and helps extend the epistemic communities through which the OECD practices its global epistemological governance of education.

Believes that in the view of philosophy, a concept is the highest form of activity of human brain. This paper demonstrates Abstract Neural Automata and a more perfect brain's models that have the ability of transition of concept‐ability of thought. The transition of the concept of Abstract Neural automata results from the non‐uniqueness of its limit Gibbs measure‐variability of the structure of Abstract Neural Automata.By means of topological conjugate transformation, the previous theory of Abstract Neural Automata on a d‐dimensional (d≥1) integer lattice is extended to the compact Riemannian manifold. We have pointed out emphatically that functions of cognition and thought of Abstract Neural Automata depend crucially on its topological and the Riemannian structure, particularly, on its Riemannian volume of some relative places which are relative learning, memory, cognition and thought. Furthermore, the larger the Riemannian volume, the stronger the intelligent function. In the study of the human brain, and in particular, Einstein's brain, one has discovered such information.

The physical universe is the embodiment of necessary mathematical forms by ever‐present flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order, group opposition, and topological transformation are generators necessary and sufficient to construct mathematics. Homologous cognitive structures generate human mental development. Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two‐valued information, and topological transformation as spatial organization.

The relationship between the child and his/her physical environment is an area of interaction that includes social, psychological and cultural factors along with the spatial experience, perception and behavior of the child. This study is based on the effects of spatial perception and behavior of the child within the physical environment of primary schools. In this direction, the purpose of this paper is to investigate how spatial and physical characteristics of primary school typologies affect the spatial perception and behavior of the child. Also, the parameters affecting spatial perception and behavior are examined.

The question to be investigated is how the spatial and physical characteristics of the school’s physical environment affect the child’s spatial perception and behavior in primary schools with different typologies. Within this scope, Istanbul’s Kagithane region is selected as a case study. Schools are chosen for their similar spatial and dimensional features and similar socio-economic environment. The methodology of the study consists of a literature review, an observational study carried out to discover the interaction between the child and his/her school building and the analysis of the student’s cognitive maps. These maps were evaluated according to topological, projective, metric and imaginative parameters.

The results show spatial organization and physical characteristics of primary school buildings with a structure that allows for change and transformation, and contributes to the physical and cognitive development of children.

This study will provide an opportunity to develop the design of future primary school buildings that can support the spatial perception and spatial experiences of the children.

The aim of this paper is to highlight the educational value of algebraic numerical methods with respect to traditional numerical techniques based on differential formulation.

Algebraic formulations of electromagnetic fields are gaining a new interest in the research community. One common characteristic of these methods is that they impose field equations, for instance charge or mass conservation, directly in algebraic form as a sum of partial contributes, without using differential operators like the divergence one. This feature leads directly to a system of linear equations without requiring any intermediate differential formulation as in finite element method. In addition, these systems of linear equations can be efficiently expressed as a product of matrices related to problem topology and material characteristics.

Owing to these features, a MATLAB implementation of these theoretical frameworks is particularly efficient and simple and can be used by electrical engineering students which, even if with a basic mathematical background, have a good practice with network theory and its computer implementation. Following this way of thinking, a MATLAB based environment has been created and here it is presented and discussed.

The implementation of the algebraic formulation can be done by using very basic mathematical tools, therefore the algebraic method becomes also a good way to introduce the numerical field analysis to undergraduate students.