Entropy, Decoherence and Spacetime Splitting

Objects in classical world model are in an "either/or" kind of state. A compass needle cannot point both north and south at the same time. The quantum world, by contrast, is "both/and" and a magnetic atom model has no trouble at pointing both directions at once. When that is the case, physicists say that a quantum object is in a "superposition" of states. In previous paper, we already discussed the major intrinsic limitations of "Science 1.0" arbitrary multi-scale (AMS) modeling and strategies to get better simulation results by "Science 2.0" approach. In 2014, Computational information conservation theory (CICT) has shown that even the most sophisticated instrumentation system is completely unable to reliably discriminate so called "random noise" (RN) from any combinatorically optimized encoded message (OECS, optimized exponential cyclic sequence), called "deterministic noise" (DN) by CICT. Unfortunately, the "probabilistic veil" can be quite opaque computationally, and misplaced precision leads to confusion. The "Science 2.0" paradigm has not yet been completely grasped by many contemporary scientific disciplines and current researchers, so that not all the implications of this big change have been realized hitherto, even less their related, vital applications. Thus, one of the key questions in understanding the quantum-classical transition is what happens to the superposition as you go up that atoms-to-apple scale. Exactly when and how does "both/and" become "either/or"? As an example, we present and discuss the observer space-time splitting case. In other words, we show spacetime mapping to classical system additive representation with entropy generation. It is exactly at this point that "both/and" becomes "either/or" representation by usual Science 1.0 approach. CICT new awareness of a discrete HG (hyperbolic geometry) subspace (reciprocal space) of coded heterogeneous hyperbolic structures, underlying the familiar Q Euclidean (direct space) surface representation can open the way to holographic information geometry (HIG) to recover system lost coherence and to overall system minimum entropy representation

Target Enumeration via Euler Characteristic Integrals

We solve the problem of counting the total number of observable targets (e.g., persons, vehicles, landmarks) in a region using local counts performed by a network of sensors, each of which measures the number of targets nearby but neither their identities nor any positional information. We formulate and solve several such problems based on the types of sensors and mobility of the targets. The main contribution of this paper is the adaptation of a topological sheaf integration theory — integration with respect to Euler characteristic — to yield complete solutions to these problems

Investigation of electromagnetism in a real Dirac algebra

The primary aim of this thesis is to investigate the utility of a Clifford-Dirac algebra Cℓ1,3 in describing relativistic electromagnetism. The motivation for choosing this algebra over other potential choices lies in the success of this algebra in describing relativistic quantum mechanics. The unit imaginary in is excluded in this algebra because a purely real description is sought and the supposition that the element is not required in order to formulate a covariant electromagnetic theory is to be tested. Square roots of the basis elements of the algebra are also investigated. An exhaustive computer search algorithm is developed to search for roots. This analysis provides general conditions for the formation of square roots where the basis elements have coefficients of equal magnitude. It is shown that such roots with two terms exist only for those elements which square to -1. No square roots are found with more than six terms. A simple algorithm is developed which enables the computational manipulation of Dirac-Clifford basis elements. A modified bubble-sort is used to perform multiplication of basis elements. This new algorithm is a reliable mechanism for performing multiplication. Maxwell's equations are developed using the Clifford-Dirac algebra. The derivation of the complete set of field equations appear in a particularly compact and elegant form. A further motivation is to explore the potential for new kinds of wave functions within the algebra. The larger number of basis elements which square to -1 presents the opportunity to study wave equation using replacements for the complex imaginary. Finally, the aim of this thesis is to examine the behaviour of the electromagnetic field equations under relativistic transformations to determine whether or not the field equations and algebra form a relativistically covariant system

Indoor Semantic Modelling for Routing: The Two-Level Routing Approach for Indoor Navigation

Humans perform many activities indoors and they show a growing need for indoor navigation, especially in unfamiliar buildings such as airports, museums and hospitals. Complexity of such buildings poses many challenges for building managers and visitors. Indoor navigation services play an important role in supporting these indoor activities. Indoor navigation covers extensive topics such as: 1) indoor positioning and localization; 2) indoor space representation for navigation model generation; 3) indoor routing computation; 4) human wayfinding behaviours; and 5) indoor guidance (e.g., textual directories). So far, a large number of studies of pedestrian indoor navigation have presented diverse navigation models and routing algorithms/methods. However, the major challenge is rarely referred to: how to represent the complex indoor environment for pedestrians and conduct routing according to the different roles and sizes of users. Such complex buildings contain irregular shapes, large open spaces, complicated obstacles and different types of passages. A navigation model can be very complicated if the indoors are accurately represented. Although most research demonstrates feasible indoor navigation models and related routing methods in regular buildings, the focus is still on a general navigation model for pedestrians who are simplified as circles. In fact, pedestrians represent different sizes, motion abilities and preferences (e.g., described in user profiles), which should be reflected in navigation models and be considered for indoor routing (e.g., relevant Spaces of Interest and Points of Interest). In order to address this challenge, this thesis proposes an innovative indoor modelling and routing approach – two-level routing. It specially targets the case of routing in complex buildings for distinct users. The conceptual (first) level uses general free indoor spaces: this is represented by the logical network whose nodes represent the spaces and edges stand for their connectivity; the detailed (second) level focuses on transition spaces such as openings and Spaces of Interest (SOI), and geometric networks are generated regarding these spaces. Nodes of a geometric network refers to locations of doors, windows and subspaces (SOIs) inside of the larger spaces; and the edges represent detailed paths among these geometric nodes. A combination of the two levels can represent complex buildings in specified spaces, which avoids maintaining a largescale complete network. User preferences on ordered SOIs are considered in routing on the logical network, and preferences on ordered Points of Interest (POI) are adopted in routing on geometric networks. In a geometric network, accessible obstacle-avoiding paths can be computed for users with different sizes. To facilitate automatic generation of the two types of network in any building, a new data model named Indoor Navigation Space Model (INSM) is proposed to store connectivity, semantics and geometry of indoor spaces for buildings. Abundant semantics of building components are designed in INSM based on navigational functionalities, such as VerticalUnit(VU) and HorizontalConnector(HC) as vertical and horizontal passages for pedestrians. The INSM supports different subdivision ways of a building in which indoor spaces can be assigned proper semantics. A logical and geometric network can be automatically derived from INSM, and they can be used individually or together for indoor routing. Thus, different routing options are designed. Paths can be provided by using either the logical network when some users are satisfied with a rough description of the path (e.g., the name of spaces), or a geometric path is automatically computed for a user who needs only a detailed path which shows how obstacles can be avoided. The two-level routing approach integrates both logical and geometric networks to obtain paths, when a user provides her/his preferences on SOIs and POIs. For example, routing results for the logical network can exclude unrelated spaces and then derive geometric paths more efficiently. In this thesis, two options are proposed for routing just on the logical network, three options are proposed for routing just on the geometric networks, and seven options for two-level routing. On the logical network, six routing criteria are proposed and three human wayfinding strategies are adopted to simulate human indoor behaviours. According to a specific criterion, space semantics of logical nodes is utilized to assign different weights to logical nodes and edges. Therefore, routing on the logical network can be accomplished by applying the Dijkstra algorithm. If multiple criteria are adopted, an order of criteria is applied for routing according to a specific user. In this way, logical paths can be computed as a sequence of indoor spaces with clear semantics. On geometric networks, this thesis proposes a new routing method to provide detailed paths avoiding indoor obstacles with respect to pedestrian sizes. This method allows geometric networks to be derived for individual users with different sizes for any specified spaces. To demonstrate the use of the two types of network, this thesis tests routing on one level (the logical or the geometric network). Four case studies about the logical network are presented in both simple and complex buildings. In the simple building, no multiple paths lie between spaces A and B, but in the complex buildings, multiple logical paths exist and the candidate paths can be reduced by applying these routing criteria in an order for a user. The relationships of these criteria to user profiles are assumed in this thesis. The proposed geometric routing regarding user sizes is tested with three case studies: 1) routing for pedestrians with two distinct sizes in one space; 2) routing for pedestrians with changed sizes in one space; and 3) a larger geometric network formed by the ones in a given sequence of spaces. The first case shows that a small increase of user size can largely change the accessible path; the second case shows different path segments for distinct sizes can be combined into one geometric path; the third case demonstrates a geometric network can be created ’on the fly’ for any specified spaces of a building. Therefore, the generation and routing of geometric networks are very flexible and fit to given users. To demonstrate the proposed two-level routing approach, this thesis designs five cases. The five cases are distinguished according to the method of model creation (pre-computed or ’on-the-fly’) and model storage (on the client or server). Two of them are realized in this thesis: 1) Case 1 just in the client pre-computes the logical network and derives geometric networks ’on the fly’; 2) Case 2 just in the client pre-computes and stores the logical and geometric networks for certain user sizes. Case 1 is implemented in a desktop application for building managers, and Case 2 is realized as a mobile mock-up for mobile users without an internet connection. As this thesis shows, two-level routing is powerful enough to effectively provide indicative logical paths and/or comprehensive geometric paths, according to different user requirements on path details. In the desktop application, three of the proposed routing options for two-level routing are tested for the simple OTB building and the complex Schiphol Airport building. These use cases demonstrate that the two-level routing approach includes the following merits: It supports routing in different abstraction forms of a building. The INSM model can describe different subdivision results of a building, and it allows two types of routing network to be derived – pure logical and geometric ones. The logical network contains the topology and semantics of indoor spaces, and the geometric network provides accurate geometry for paths. A consistent navigation model is formed with the two networks, i.e., the conceptual and detailed levels. On the conceptual level, it supports routing on a logical network and assists the derivation of a conceptual path (i.e., logical path) for a user in terms of space sequence. Routing criteria are designed based on the INSM semantics of spaces, which can generate logical paths similar to human wayfinding results such as minimizing VerticalUnit or HorizontalConnector. On the detailed level, it considers the size of users and results in obstacle-avoiding paths. By using this approach, geometric networks can be generated to avoid obstacles for the given users and accessible paths are flexibly provided for user demands. This approach can process changes of user size more efficiently, in contrast to routing on a complete geometric network. It supports routing on both the logical and the geometric networks, which can generate geometric paths based on user-specific logical paths, or re-compute logical paths when geometric paths are inaccessible. This computation method is very useful for complex buildings. The two-level routing approach can flexibly provide logical and geometric paths according to user preferences and sizes, and can adjust the generated paths in limited time. Based on the two-level routing approach, this thesis also provides a vision on possible cooperation with other methods. A potential direction is to design more routing options according to other indoor scenarios and user preferences. Extensions of the two-level routing approach, such as other types of semantics, multi-level networks and dynamic obstacles, will make it possible to deal with other routing cases. Last but not least, it is also promising to explore its relationships with indoor guidance, different building subdivisions and outdoor navigation. &nbsp

Indoor Semantic Modelling for Routing:

Humans perform many activities indoors and they show a growing need for indoor navigation, especially in unfamiliar buildings such as airports, museums and hospitals. Complexity of such buildings poses many challenges for building managers and visitors. Indoor navigation services play an important role in supporting these indoor activities. Indoor navigation covers extensive topics such as: 1) indoor positioning and localization; 2) indoor space representation for navigation model generation; 3) indoor routing computation; 4) human wayfinding behaviours; and 5) indoor guidance (e.g., textual directories). So far, a large number of studies of pedestrian indoor navigation have presented diverse navigation models and routing algorithms/methods. However, the major challenge is rarely referred to: how to represent the complex indoor environment for pedestrians and conduct routing according to the different roles and sizes of users. Such complex buildings contain irregular shapes, large open spaces, complicated obstacles and different types of passages. A navigation model can be very complicated if the indoors are accurately represented. Although most research demonstrates feasible indoor navigation models and related routing methods in regular buildings, the focus is still on a general navigation model for pedestrians who are simplified as circles. In fact, pedestrians represent different sizes, motion abilities and preferences (e.g., described in user profiles), which should be reflected in navigation models and be considered for indoor routing (e.g., relevant Spaces of Interest and Points of Interest). In order to address this challenge, this thesis proposes an innovative indoor modelling and routing approach – two-level routing. It specially targets the case of routing in complex buildings for distinct users. The conceptual (first) level uses general free indoor spaces: this is represented by the logical network whose nodes represent the spaces and edges stand for their connectivity; the detailed (second) level focuses on transition spaces such as openings and Spaces of Interest (SOI), and geometric networks are generated regarding these spaces. Nodes of a geometric network refers to locations of doors, windows and subspaces (SOIs) inside of the larger spaces; and the edges represent detailed paths among these geometric nodes. A combination of the two levels can represent complex buildings in specified spaces, which avoids maintaining a largescale complete network. User preferences on ordered SOIs are considered in routing on the logical network, and preferences on ordered Points of Interest (POI) are adopted in routing on geometric networks. In a geometric network, accessible obstacle-avoiding paths can be computed for users with different sizes. To facilitate automatic generation of the two types of network in any building, a new data model named Indoor Navigation Space Model (INSM) is proposed to store connectivity, semantics and geometry of indoor spaces for buildings. Abundant semantics of building components are designed in INSM based on navigational functionalities, such as VerticalUnit(VU) and HorizontalConnector(HC) as vertical and horizontal passages for pedestrians. The INSM supports different subdivision ways of a building in which indoor spaces can be assigned proper semantics. A logical and geometric network can be automatically derived from INSM, and they can be used individually or together for indoor routing. Thus, different routing options are designed. Paths can be provided by using either the logical network when some users are satisfied with a rough description of the path (e.g., the name of spaces), or a geometric path is automatically computed for a user who needs only a detailed path which shows how obstacles can be avoided. The two-level routing approach integrates both logical and geometric networks to obtain paths, when a user provides her/his preferences on SOIs and POIs. For example, routing results for the logical network can exclude unrelated spaces and then derive geometric paths more efficiently. In this thesis, two options are proposed for routing just on the logical network, three options are proposed for routing just on the geometric networks, and seven options for two-level routing. On the logical network, six routing criteria are proposed and three human wayfinding strategies are adopted to simulate human indoor behaviours. According to a specific criterion, space semantics of logical nodes is utilized to assign different weights to logical nodes and edges. Therefore, routing on the logical network can be accomplished by applying the Dijkstra algorithm. If multiple criteria are adopted, an order of criteria is applied for routing according to a specific user. In this way, logical paths can be computed as a sequence of indoor spaces with clear semantics. On geometric networks, this thesis proposes a new routing method to provide detailed paths avoiding indoor obstacles with respect to pedestrian sizes. This method allows geometric networks to be derived for individual users with different sizes for any specified spaces. To demonstrate the use of the two types of network, this thesis tests routing on one level (the logical or the geometric network). Four case studies about the logical network are presented in both simple and complex buildings. In the simple building, no multiple paths lie between spaces A and B, but in the complex buildings, multiple logical paths exist and the candidate paths can be reduced by applying these routing criteria in an order for a user. The relationships of these criteria to user profiles are assumed in this thesis. The proposed geometric routing regarding user sizes is tested with three case studies: 1) routing for pedestrians with two distinct sizes in one space; 2) routing for pedestrians with changed sizes in one space; and 3) a larger geometric network formed by the ones in a given sequence of spaces. The first case shows that a small increase of user size can largely change the accessible path; the second case shows different path segments for distinct sizes can be combined into one geometric path; the third case demonstrates a geometric network can be created ’on the fly’ for any specified spaces of a building. Therefore, the generation and routing of geometric networks are very flexible and fit to given users. To demonstrate the proposed two-level routing approach, this thesis designs five cases. The five cases are distinguished according to the method of model creation (pre-computed or ’on-the-fly’) and model storage (on the client or server). Two of them are realized in this thesis: 1) Case 1 just in the client pre-computes the logical network and derives geometric networks ’on the fly’; 2) Case 2 just in the client pre-computes and stores the logical and geometric networks for certain user sizes. Case 1 is implemented in a desktop application for building managers, and Case 2 is realized as a mobile mock-up for mobile users without an internet connection. As this thesis shows, two-level routing is powerful enough to effectively provide indicative logical paths and/or comprehensive geometric paths, according to different user requirements on path details. In the desktop application, three of the proposed routing options for two-level routing are tested for the simple OTB building and the complex Schiphol Airport building. These use cases demonstrate that the two-level routing approach includes the following merits: It supports routing in different abstraction forms of a building. The INSM model can describe different subdivision results of a building, and it allows two types of routing network to be derived – pure logical and geometric ones. The logical network contains the topology and semantics of indoor spaces, and the geometric network provides accurate geometry for paths. A consistent navigation model is formed with the two networks, i.e., the conceptual and detailed levels. On the conceptual level, it supports routing on a logical network and assists the derivation of a conceptual path (i.e., logical path) for a user in terms of space sequence. Routing criteria are designed based on the INSM semantics of spaces, which can generate logical paths similar to human wayfinding results such as minimizing VerticalUnit or HorizontalConnector. On the detailed level, it considers the size of users and results in obstacle-avoiding paths. By using this approach, geometric networks can be generated to avoid obstacles for the given users and accessible paths are flexibly provided for user demands. This approach can process changes of user size more efficiently, in contrast to routing on a complete geometric network. It supports routing on both the logical and the geometric networks, which can generate geometric paths based on user-specific logical paths, or re-compute logical paths when geometric paths are inaccessible. This computation method is very useful for complex buildings. The two-level routing approach can flexibly provide logical and geometric paths according to user preferences and sizes, and can adjust the generated paths in limited time. Based on the two-level routing approach, this thesis also provides a vision on possible cooperation with other methods. A potential direction is to design more routing options according to other indoor scenarios and user preferences. Extensions of the two-level routing approach, such as other types of semantics, multi-level networks and dynamic obstacles, will make it possible to deal with other routing cases. Last but not least, it is also promising to explore its relationships with indoor guidance, different building subdivisions and outdoor navigation