Instant topological relationships hidden in the reality

In most applications of general topology, topology usually is not the first, primary structure, but the information which finally leads to the construction of the certain, for some purpose required topology, is filtered by more or less thick filter of the other mathematical structures. This fact has two main consequences: (1) Most important applied constructions may be done in the primary structure, bypassing the topology. (2) Some topologically important information from the reality may be lost (filtered out by the other, front-end mathematical structures). Thus some natural and direct connection between topology and the reality could be useful. In this contribution we will discuss a pointless topological structure which directly reflects relationship between various locations which are glued together by possible presence of a physical object or a virtual ``observer"

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Mixed Reality Architecture: Concept, Construction, Use

Mixed Reality Architecture (MRA) dynamically links and overlays physical and virtual spaces. This paper investigates the topology of and the relationships between the components of MRA. As a phenomenon, MRA takes its place in a long history of technologies that have influenced conditions for social interaction as well as the environment we build around us. However, by providing a flexible spatial topology spanning physical and virtual environments it presents new opportunities for social interaction across electronic media. An experimental MRA is described that allowed us to study some of the emerging issues in this field. It provided material for the development of a framework describing virtual and physical spaces, the links between those and the types of mixed reality structure that we can envisage it being possible to design using these elements. We propose that by re-introducing a level of spatiality into communication across physical and virtual environments MRA will support everyday social interaction, and may convert digital communication media from being socially conservative to a more generative form familiar from physical space

A Data Model for Exploration of Temporal Virtual Reality Geographic Information Systems

Geographic information systems deal with the exploration, analysis, and presentation of geo-referenced data. Virtual reality is a type of human-computer interface that comes close to the way people perceive information in the real world. Thus, virtual reality environments become the natural paradigm for extending and enhancing the presentational and exploratory capability of GIs applications in both the spatial and temporal domains. The main motivation of this thesis is the lack of a framework that properly supports the exploration of geographic information in a multi-dimensional and multi-sensorial environment (i.e., temporal virtual reality geographic information systems). This thesis introduces a model for virtual exploration of animations. Virtual exploration of animations is a framework composed of abstract data types and a user interface that allow non-expert users to control, manipulate, analyze, and present objects\u27 behaviors in a virtual-reality environment. In the model for virtual exploration of animations, the manipulation of the dynamic environment is accomplished through a set of operations performed over abstractions that represent temporal characteristics of actions. An important feature of the model is that the temporal information is treated as first-class entities and not as a mere attribute of action\u27s representations. Therefore, entities of the temporal model have their own built-in functionality and are able to represent complex temporal structures. In an environment designed for the manipulation of the temporal characteristics of actions, the knowledge of relationships among objects\u27 behaviors plays a significant role in the model. This information comes from the knowledge base of the application domain and is represented in the model through constraints among entities of the temporal model. Such constraints vary from simply relating the end points of two intervals to a complex mechanism that takes into account all relations between sequences of intervals of cyclic behaviors. The fact that the exploration of the information takes place in a virtual reality environment imposes new requirements on the animation model. This thesis introduces a new classification of objects in a VR environment and describes the associated semantics of each element in the taxonomy. These semantics are used to direct the way an object interacts with an observer and with other objects in the environment

The Riddle of Gravitation

There is no doubt that both the special and general theories of relativity capture the imagination. The anti-intuitive properties of the special theory of relativity and its deep philosophical implications, the bizzare and dazzling predictions of the general theory of relativity: the curvature of spacetime, the exotic characteristics of black holes, the bewildering prospects of gravitational waves, the discovery of astronomical objects as quasers and pulsers, the expansion and the (possible) recontraction of the universe..., are all breathtaking phenomena. In this paper, we give a philosophical non-technical treatment of both the special and the general theory of relativity together with an exposition of some of the latest physical theories. We then give an outline of an axiomatic approach to relativity theories due to Andreka and Nemeti that throws light on the logical structure of both theories. This is followed by an exposition of some of the bewildering results established by Andreka and Nemeti concerning the foundations of mathematics using the notion of relativistic computers. We next give a survey on the meaning and philosophical implications of the the quantum theory and end the paper by an imaginary debate between Einstein and Neils Bohr reflecting both Einstein's and Bohr's philosophical views on the quantum world. The paper is written in a somewhat untraditional manner; there are too many footnotes. In order not to burden the reader with all the details, we have collected the more advanced material the footnotes. We think that this makes the paper easier to read and simpler to follow. The paper in full is adressed more to experts.Comment: 40 pages, LaTeX-fil

The Strange Nature of Quantum Perception: To See a Photon, One Must _Be_ a Photon

This paper takes as its point of departure recent research into the possibility that human beings can perceive single photons. In order to appreciate what quantum perception may entail, we first explore several of the leading interpretations of quantum mechanics, then consider an alternative view based on the ontological phenomenology of Maurice Merleau-Ponty and Martin Heidegger. Next, the philosophical analysis is brought into sharper focus by employing a perceptual model, the Necker cube, augmented by the topology of the Klein bottle. This paves the way for addressing in greater depth the paper’s central question: Just what would it take to observe the quantum reality of the photon? In formulating an answer, we examine the nature of scientific objectivity itself, along with the paradoxical properties of light. The conclusion reached is that quantum perception requires a new kind of observation, one in which the observer of the photon adopts a concretely self-reflexive observational posture that brings her into close ontological relationship with the observed

Phase Changes in the Evolution of the IPv4 and IPv6 AS-Level Internet Topologies

In this paper we investigate the evolution of the IPv4 and IPv6 Internet topologies at the autonomous system (AS) level over a long period of time.We provide abundant empirical evidence that there is a phase transition in the growth trend of the two networks. For the IPv4 network, the phase change occurred in 2001. Before then the network's size grew exponentially, and thereafter it followed a linear growth. Changes are also observed around the same time for the maximum node degree, the average node degree and the average shortest path length. For the IPv6 network, the phase change occurred in late 2006. It is notable that the observed phase transitions in the two networks are different, for example the size of IPv6 network initially grew linearly and then shifted to an exponential growth. Our results show that following decades of rapid expansion up to the beginning of this century, the IPv4 network has now evolved into a mature, steady stage characterised by a relatively slow growth with a stable network structure; whereas the IPv6 network, after a slow startup process, has just taken off to a full speed growth. We also provide insight into the possible impact of IPv6-over-IPv4 tunneling deployment scheme on the evolution of the IPv6 network. The Internet topology generators so far are based on an inexplicit assumption that the evolution of Internet follows non-changing dynamic mechanisms. This assumption, however, is invalidated by our results.Our work reveals insights into the Internet evolution and provides inputs to future AS-Level Internet models.Comment: 12 pages, 21 figures; G. Zhang et al.,Phase changes in the evolution of the IPv4 and IPv6 AS-Level Internet topologies, Comput. Commun. (2010