THE LOGIC OF TIME AND THE CONTINUUM IN KANT’S CRITICAL PHILOSOPHY

We aim to show that Kant’s theory of time is consistent by providing axioms whose models validate all synthetic a priori principles for time proposed in the Critique of Pure Reason. In this paper we focus on the distinction between time as form of intuition and time as formal intuition, for which Kant’s own explanations are all too brief. We provide axioms that allow us to construct ‘time as formal intuition’ as a pair of continua, corresponding to time as ‘inner sense’ and the external representation of time as a line Both continua are replete with infinitesimals, which we use to elucidate an enigmatic discussion of ‘rest’ in the Metaphysical foundations of natural science. Our main formal tools are Alexandroff topologies, inverse systems and the ring of dual numbers

Concepts of Space, Refiguration of Spaces, and Comparative Research: Perspectives from Economic Geography and Regional Economics

Following the concept of refiguration of spaces proposed by KNOBLAUCH and LÖW (2017), in this article I emphasize interfaces for theory building, methods, and comparative research from an economic geography and regional economics perspective. Since the refiguration of spaces offers an abstract frame capable of grasping spatial relations of any order and across various scales, I will discuss the utilization of concepts of space in both subdisciplines by employing a textbook analysis. Moreover, I will include two examples of current economic phenomena where refiguration takes place. Namely, I will analyze the internationalization of companies and world trade interdependencies according to concepts of space, their implication on methods, and comparative research. In my findings, I show that the abstract frame of refiguration of spaces unlocks great potential if applied consistently. Economic geography has a great deal to offer for the micro-foundation in the refiguration of spaces, working with qualitative methods and forward-thinking concepts of space (e.g., relational or topical points of view for comparison). Regional economics allows for progress concerning the macro-foundation in the refiguration of spaces through the increased availability of regional or big data and advanced quantitative methods (e.g., manifold indexes capturing refiguration).In Anlehnung an das von KNOBLAUCH und LÖW (2017) vorgeschlagene theoretische Rahmenwerk der "Refiguration von Räumen" hebe ich in diesem Beitrag Schnittstellen und Transfermöglichkeiten für Theoriebildung, Methoden und vergleichende Forschung aus einer wirtschaftsgeografischen und regionalökonomischen Perspektive hervor. Da die "Refiguration von Räumen" einen abstrakten Rahmen bietet, um räumliche Beziehungen beliebiger Ordnung und über verschiedene Maßstäbe hinweg zu erfassen, erläutere ich zunächst anhand einer Lehrbuchanalyse, wie in beiden Teildisziplinen grundlegende Raumkonzepte verwendet werden. Anschließend greife ich mit der Internationalisierung von Unternehmen und globalen Handelsverflechtungen zwei maßgebliche ökonomische Entwicklungen heraus, die für eine Betrachtung der Refiguration von Räumen prädestiniert sind, und analysiere die methodischen Implikationen und Möglichkeiten verschiedener Raumkonzepte für eine vergleichende Forschung. Ich zeige, dass der abstrakte Rahmen des Konzepts der "Refiguration von Räumen" bei konsistenter Anwendung erhebliche Potenziale für beide Subdisziplinen eröffnen kann. Wirtschaftsgeograf*innen haben für die Mikrofundierung der Refiguration von Räumen einiges zu bieten, da sie mit qualitativen Methoden und mannigfaltigen Raumkonzepten arbeiten (z.B. relationale oder topische Ansätze für eine vergleichende Forschung). Die Verwendung von Konzepten aus der Regionalökonomie erlaubt umgekehrt eine bessere Makrofundierung der Refiguration von Räumen" durch die zunehmende Verfügbarkeit von Big Data, von regionalisierten Daten und fortgeschrittenen quantitativen Methoden (z.B. komplexe Indizes)

A Tutorial on Fisher Information

In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different statistical paradigms. First, in the frequentist paradigm, Fisher information is used to construct hypothesis tests and confidence intervals using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher information is used to define a default prior; lastly, in the minimum description length paradigm, Fisher information is used to measure model complexity

Semantic Similarity of Spatial Scenes

The formalization of similarity in spatial information systems can unleash their functionality and contribute technology not only useful, but also desirable by broad groups of users. As a paradigm for information retrieval, similarity supersedes tedious querying techniques and unveils novel ways for user-system interaction by naturally supporting modalities such as speech and sketching. As a tool within the scope of a broader objective, it can facilitate such diverse tasks as data integration, landmark determination, and prediction making. This potential motivated the development of several similarity models within the geospatial and computer science communities. Despite the merit of these studies, their cognitive plausibility can be limited due to neglect of well-established psychological principles about properties and behaviors of similarity. Moreover, such approaches are typically guided by experience, intuition, and observation, thereby often relying on more narrow perspectives or restrictive assumptions that produce inflexible and incompatible measures. This thesis consolidates such fragmentary efforts and integrates them along with novel formalisms into a scalable, comprehensive, and cognitively-sensitive framework for similarity queries in spatial information systems. Three conceptually different similarity queries at the levels of attributes, objects, and scenes are distinguished. An analysis of the relationship between similarity and change provides a unifying basis for the approach and a theoretical foundation for measures satisfying important similarity properties such as asymmetry and context dependence. The classification of attributes into categories with common structural and cognitive characteristics drives the implementation of a small core of generic functions, able to perform any type of attribute value assessment. Appropriate techniques combine such atomic assessments to compute similarities at the object level and to handle more complex inquiries with multiple constraints. These techniques, along with a solid graph-theoretical methodology adapted to the particularities of the geospatial domain, provide the foundation for reasoning about scene similarity queries. Provisions are made so that all methods comply with major psychological findings about people’s perceptions of similarity. An experimental evaluation supplies the main result of this thesis, which separates psychological findings with a major impact on the results from those that can be safely incorporated into the framework through computationally simpler alternatives

Colossal Trajectory Mining: A unifying approach to mine behavioral mobility patterns

Spatio-temporal mobility patterns are at the core of strategic applications such as urban planning and monitoring. Depending on the strength of spatio-temporal constraints, different mobility patterns can be defined. While existing approaches work well in the extraction of groups of objects sharing fine-grained paths, the huge volume of large-scale data asks for coarse-grained solutions. In this paper, we introduce Colossal Trajectory Mining (CTM) to efficiently extract heterogeneous mobility patterns out of a multidimensional space that, along with space and time dimensions, can consider additional trajectory features (e.g., means of transport or activity) to characterize behavioral mobility patterns. The algorithm is natively designed in a distributed fashion, and the experimental evaluation shows its scalability with respect to the involved features and the cardinality of the trajectory dataset

Towards an Information Theoretic Framework for Evolutionary Learning

The vital essence of evolutionary learning consists of information flows between the environment and the entities differentially surviving and reproducing therein. Gain or loss of information in individuals and populations due to evolutionary steps should be considered in evolutionary algorithm theory and practice. Information theory has rarely been applied to evolutionary computation - a lacuna that this dissertation addresses, with an emphasis on objectively and explicitly evaluating the ensemble models implicit in evolutionary learning. Information theoretic functionals can provide objective, justifiable, general, computable, commensurate measures of fitness and diversity. We identify information transmission channels implicit in evolutionary learning. We define information distance metrics and indices for ensembles. We extend Price\u27s Theorem to non-random mating, give it an effective fitness interpretation and decompose it to show the key factors influencing heritability and evolvability. We argue that heritability and evolvability of our information theoretic indicators are high. We illustrate use of our indices for reproductive and survival selection. We develop algorithms to estimate information theoretic quantities on mixed continuous and discrete data via the empirical copula and information dimension. We extend statistical resampling. We present experimental and real world application results: chaotic time series prediction; parity; complex continuous functions; industrial process control; and small sample social science data. We formalize conjectures regarding evolutionary learning and information geometry

Topological Mapping and Navigation in Real-World Environments

We introduce the Hierarchical Hybrid Spatial Semantic Hierarchy (H2SSH), a hybrid topological-metric map representation. The H2SSH provides a more scalable representation of both small and large structures in the world than existing topological map representations, providing natural descriptions of a hallway lined with offices as well as a cluster of buildings on a college campus. By considering the affordances in the environment, we identify a division of space into three distinct classes: path segments afford travel between places at their ends, decision points present a choice amongst incident path segments, and destinations typically exist at the start and end of routes. Constructing an H2SSH map of the environment requires understanding both its local and global structure. We present a place detection and classification algorithm to create a semantic map representation that parses the free space in the local environment into a set of discrete areas representing features like corridors, intersections, and offices. Using these areas, we introduce a new probabilistic topological simultaneous localization and mapping algorithm based on lazy evaluation to estimate a probability distribution over possible topological maps of the global environment. After construction, an H2SSH map provides the necessary representations for navigation through large-scale environments. The local semantic map provides a high-fidelity metric map suitable for motion planning in dynamic environments, while the global topological map is a graph-like map that allows for route planning using simple graph search algorithms. For navigation, we have integrated the H2SSH with Model Predictive Equilibrium Point Control (MPEPC) to provide safe and efficient motion planning for our robotic wheelchair, Vulcan. However, navigation in human environments entails more than safety and efficiency, as human behavior is further influenced by complex cultural and social norms. We show how social norms for moving along corridors and through intersections can be learned by observing how pedestrians around the robot behave. We then integrate these learned norms with MPEPC to create a socially-aware navigation algorithm, SA-MPEPC. Through real-world experiments, we show how SA-MPEPC improves not only Vulcan’s adherence to social norms, but the adherence of pedestrians interacting with Vulcan as well.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144014/1/collinej_1.pd

Model based test suite minimization using metaheuristics

Software testing is one of the most widely used methods for quality assurance and fault detection purposes. However, it is one of the most expensive, tedious and time consuming activities in software development life cycle. Code-based and specification-based testing has been going on for almost four decades. Model-based testing (MBT) is a relatively new approach to software testing where the software models as opposed to other artifacts (i.e. source code) are used as primary source of test cases. Models are simplified representation of a software system and are cheaper to execute than the original or deployed system. The main objective of the research presented in this thesis is the development of a framework for improving the efficiency and effectiveness of test suites generated from UML models. It focuses on three activities: transformation of Activity Diagram (AD) model into Colored Petri Net (CPN) model, generation and evaluation of AD based test suite and optimization of AD based test suite. Unified Modeling Language (UML) is a de facto standard for software system analysis and design. UML models can be categorized into structural and behavioral models. AD is a behavioral type of UML model and since major revision in UML version 2.x it has a new Petri Nets like semantics. It has wide application scope including embedded, workflow and web-service systems. For this reason this thesis concentrates on AD models. Informal semantics of UML generally and AD specially is a major challenge in the development of UML based verification and validation tools. One solution to this challenge is transforming a UML model into an executable formal model. In the thesis, a three step transformation methodology is proposed for resolving ambiguities in an AD model and then transforming it into a CPN representation which is a well known formal language with extensive tool support. Test case generation is one of the most critical and labor intensive activities in testing processes. The flow oriented semantic of AD suits modeling both sequential and concurrent systems. The thesis presented a novel technique to generate test cases from AD using a stochastic algorithm. In order to determine if the generated test suite is adequate, two test suite adequacy analysis techniques based on structural coverage and mutation have been proposed. In terms of structural coverage, two separate coverage criteria are also proposed to evaluate the adequacy of the test suite from both perspectives, sequential and concurrent. Mutation analysis is a fault-based technique to determine if the test suite is adequate for detecting particular types of faults. Four categories of mutation operators are defined to seed specific faults into the mutant model. Another focus of thesis is to improve the test suite efficiency without compromising its effectiveness. One way of achieving this is identifying and removing the redundant test cases. It has been shown that the test suite minimization by removing redundant test cases is a combinatorial optimization problem. An evolutionary computation based test suite minimization technique is developed to address the test suite minimization problem and its performance is empirically compared with other well known heuristic algorithms. Additionally, statistical analysis is performed to characterize the fitness landscape of test suite minimization problems. The proposed test suite minimization solution is extended to include multi-objective minimization. As the redundancy is contextual, different criteria and their combination can significantly change the solution test suite. Therefore, the last part of the thesis describes an investigation into multi-objective test suite minimization and optimization algorithms. The proposed framework is demonstrated and evaluated using prototype tools and case study models. Empirical results have shown that the techniques developed within the framework are effective in model based test suite generation and optimizatio