Visual Analysis of High-Dimensional Point Clouds using Topological Abstraction

This thesis is about visualizing a kind of data that is trivial to process by computers but difficult to imagine by humans because nature does not allow for intuition with this type of information: high-dimensional data. Such data often result from representing observations of objects under various aspects or with different properties. In many applications, a typical, laborious task is to find related objects or to group those that are similar to each other. One classic solution for this task is to imagine the data as vectors in a Euclidean space with object variables as dimensions. Utilizing Euclidean distance as a measure of similarity, objects with similar properties and values accumulate to groups, so-called clusters, that are exposed by cluster analysis on the high-dimensional point cloud. Because similar vectors can be thought of as objects that are alike in terms of their attributes, the point cloud\''s structure and individual cluster properties, like their size or compactness, summarize data categories and their relative importance. The contribution of this thesis is a novel analysis approach for visual exploration of high-dimensional point clouds without suffering from structural occlusion. The work is based on implementing two key concepts: The first idea is to discard those geometric properties that cannot be preserved and, thus, lead to the typical artifacts. Topological concepts are used instead to shift away the focus from a point-centered view on the data to a more structure-centered perspective. The advantage is that topology-driven clustering information can be extracted in the data\''s original domain and be preserved without loss in low dimensions. The second idea is to split the analysis into a topology-based global overview and a subsequent geometric local refinement. The occlusion-free overview enables the analyst to identify features and to link them to other visualizations that permit analysis of those properties not captured by the topological abstraction, e.g. cluster shape or value distributions in particular dimensions or subspaces. The advantage of separating structure from data point analysis is that restricting local analysis only to data subsets significantly reduces artifacts and the visual complexity of standard techniques. That is, the additional topological layer enables the analyst to identify structure that was hidden before and to focus on particular features by suppressing irrelevant points during local feature analysis. This thesis addresses the topology-based visual analysis of high-dimensional point clouds for both the time-invariant and the time-varying case. Time-invariant means that the points do not change in their number or positions. That is, the analyst explores the clustering of a fixed and constant set of points. The extension to the time-varying case implies the analysis of a varying clustering, where clusters appear as new, merge or split, or vanish. Especially for high-dimensional data, both tracking---which means to relate features over time---but also visualizing changing structure are difficult problems to solve

Vectorial light-matter interaction -- exploring spatially structured complex light fields

Research on spatially-structured light has seen an explosion in activity over the past decades, powered by technological advances for generating such light, and driven by questions of fundamental science as well as engineering applications. In this review we highlight work on the interaction of vector light fields with atoms, and matter in general. This vibrant research area explores the full potential of light, with clear benefits for classical as well as quantum applications

Roadmap on multimode light shaping

Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community.acceptedVersionPeer reviewe

Migrant Families in Ireland: Understanding the Culture Landscapes of Transnational Family Life

Being ‗migrant‘ in Ireland is often presented in the popular media and academic studies as being somewhat problematic. While this study acknowledges some of the difficulties facing Ireland‘s migrant population, I attend in particular to some of the more everyday and ordinary things done as part of living here, some of which express a ‗migrant‘ identity, and some which do not. Through the lenses of ‗family‘ and ‗home‘, I explore the cultural geographies of migrant relationships by engaging with Lithuanian, Indian, and United States research participants in Ireland. The key question is: How does the migration process reconstitute how people who move understand and experience family and home? Theoretically, I disrupt ‗The Family‘ as a coherent ontological existence. In doing so, I blend a poststructuralist ontology and epistemology of kin and non-kin relationships with a phenomenological way of knowing how relationships are performed in place. Methodologically, I develop an approach which fuses participatory photography with family album exploration as a means of interrogating what family means to each participant, and where feels most like home. The reflective nature of these questions facilitates an abstract interrogation of the everyday lived experiences of family and home, while I draw from cultural and political geographies of migration and transnational studies, in particular, in order to understand the particularity of the migrant case. The stories gathered are understood as a series of family landscapes – the expression of the social and spatial practices that produce families in particular ways, at particular times, and in particular places. The thesis reads, therefore, as a conceptual development of a landscape imaginary of families. The ‗architecture‘ of that conceptual framework is presented through a set of ‗scapes‘ in a way that offers the possibility of theoretical abstraction from this particular research for application to other family contexts too

The Necessary Structure of the All-pervading Aether: Discrete or Continuous? Simple or Symmetric?

In this book I investigate the necessary structure of the aether – the stuff that fills the whole universe. Some of my conclusions are. 1. There is an enormous variety of structures that the aether might, for all we know, have. 2. Probably the aether is point-free. 3. In that case, it should be distinguished from Space-time, which is either a fiction or a construct. 4. Even if the aether has points, we should reject the orthodoxy that all regions are grounded in points by summation. 5. If the aether is point-free but not continuous, its most likely structure has extended atoms that are not simples. 6. Space-time is symmetric if and only if the aether is continuous. 7. If the aether is continuous, we should reject the standard interpretation of General Relativity, in which geometry determines gravity. 8. Contemporary physics undermines an objection to discrete aether based on scale invariance, but does not offer much positive support

Numerical modeling of non-stationary boundary-layer flow in urban areas

The atmospheric boundary layer (ABL) has been the subject of active research due to its relevance to human welfare. Among the various research approaches, large eddy simulation (LES) has become a prevalent tool for studying ABL flow phenomena because of its inherent ability to provide reasonably accurate and detailed spatially-distributed velocity information without the need for many ad-hoc tuning parameters. Motivated by the need to understand fundamental ABL processes in their simplest form, previous LES investigations have primarily focused on idealized flow regimes characterized by, e.g., statistically stationary or homogeneous flow conditions. However, these simplified scenarios fail to capture much of the complexity that characterizes the real-world ABL, including its impact on various applications. Thus, there is a pressing need to explore more realistic flow scenarios that can capture a broader range of processes that occur in the ABL. This dissertation focuses on two aspects of real-world ABL flow complexity: non-stationary effects and flow in complex terrain. The first part of this work examines how non-stationarity—a prevalent but long-overlooked characteristic of real-world ABL flows—impacts the transfer of momentum between the land surface and the atmosphere. Specifically, the focus is on flow driven by time-varying pressure gradients, which are a common source of flow unsteadiness. The analysis is based on LES of pulsatile flow over resolved urban-like surfaces. This study proposes a sensitivity analysis to explore how key parameters governing ABL non-stationarity affect flow dynamics. Results shed light on the mechanisms responsible for changes in momentum transport and turbulence generation under non-stationary conditions. Based on these findings, two phenomenological models are proposed to capture variations in aerodynamic parameters under such conditions. The same flow system is further characterized from a coherent structure perspective to identify fundamental mechanisms controlling the transport of momentum. Non-stationarity is found to yield a time- and space-varying shear rate, which directly affects the topology of dominant coherent structures. These structures, in turn, modulate the ejection-sweep pattern, which is the dominant mechanism for momentum transfer in the ABL. The second part of the dissertation is devoted to evaluating the predictive abilities of finite-volume (FV) solvers in LES of ABL flows. The motivation is that these solvers are naturally suited for studying turbulent flows in complex terrain geometry, but a full assessment of their performance is still lacking. A suite of LES of turbulent channel flow are conducted at a moderate Reynolds number (??? = 2000), using a general-purpose, second-order-accurate FV solver. Results are compared against those from a mixed pseudo-spectral and finite-differences solver and the direct numerical simulation (DNS) benchmark, with a lens on first- and second-order statistics, and their sensitivity to the choice of numerical and physical parameters. Based on the findings, the study recommends an optimal setup for ABL simulations based on FV solvers

Roadmap on structured light

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized

Topology of spatial texture in the acousmatic medium

This research explores the dynamic fabric of experienced space in acousmatic music. The topology of spatial texture is a network of concepts treating music as a flexible, textural space, which deforms, shapes, and transforms in time. A comprehensive terminology is introduced, along with five fixed-media electroacoustic compositions, which exemplify a manifestation of spatial texture in composition and musical thinking. The theory draws from research on the cross-modality of texture perception, philosophical discourse on embodied meaning, physics, psychology of visual art, and discourse on space in acousmatic music. Several different structural perspectives are discussed, which reveal how spatial texture incorporates lower sound-structural levels, materiality, states and processes, motion, global networks and terrains, and relationships between space and time. Emphasis is put on visual and physical connections with spatiality in the acousmatic experience: cogency in spatial structure and dynamics reinforces links among modalities. The concepts and terminology are intended as a contribution to theory in the acousmatic medium, relevant to composition, analysis, and listening. The music represents an aesthetic orientation which emphasises materiality and morphology in texture, transformative processes, spatial design, and spatiotemporal polyvalence