Investigating Abstract Algebra Students' Representational Fluency and Example-Based Intuitions

The quotient group concept is a difficult for many students getting started in abstract algebra (Dubinsky et al., 1994; Melhuish, Lew, Hicks, and Kandasamy, 2020). The first study in this thesis explores an undergraduate, a first-year graduate, and second-year graduate students' representational fluency as they work on a "collapsing structure", quotient, task across multiple registers: Cayley tables, group presentations, Cayley digraphs to Schreier coset digraphs, and formal-symbolic mappings. The second study characterizes the (partial) make-up of two graduate learners' example-based intuitions related to orbit-stabilizer relationships induced by group actions. The (partial) make-up of a learner's intuition as a quantifiable object was defined in this thesis as a point viewed in R17, 12 variable values collected with a new prototype instrument, The Non-Creative versus Creative Forms of Intuition Survey (NCCFIS), 2 values for confidence in truth value, and 3 additional variables: error to non-error type, unique versus common, and network thinking. The revised Fuzzy C-Means Clustering Algorithm (FCM) by Bezdek et al. (1981) was used to classify the (partial) make-up of learners' reported intuitions into fuzzy sets based on attribute similarity

Flight Mechanics/Estimation Theory Symposium, 1990

This conference publication includes 32 papers and abstracts presented at the Flight Mechanics/Estimation Theory Symposium on May 22-25, 1990. Sponsored by the Flight Dynamics Division of Goddard Space Flight Center, this symposium features technical papers on a wide range of issues related to orbit-attitude prediction, determination and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Simulation of nonverbal social interaction and small groups dynamics in virtual environments

How can the behaviour of humans who interact with other humans be simulated in virtual environments? This thesis investigates the issue by proposing a number of dedicated models, computer languages, software architectures, and specifications of computational components. It relies on a large knowledge base from the social sciences, which offers concepts, descriptions, and classifications that guided the research process. The simulation of nonverbal social interaction and group dynamics in virtual environments can be divided in two main research problems: (1) an action selection problem, where autonomous agents must be made capable of deciding when, with whom, and how they interact according to individual characteristics of themselves and others; and (2) a behavioural animation problem, where, on the basis of the selected interaction, 3D characters must realistically behave in their virtual environment and communicate nonverbally with others by automatically triggering appropriate actions such as facial expressions, gestures, and postural shifts. In order to introduce the problem of action selection in social environments, a high-level architecture for social agents, based on the sociological concepts of role, norm, and value, is first discussed. A model of action selection for members of small groups, based on proactive and reactive motivational components, is then presented. This model relies on a new tagbased language called Social Identity Markup Language (SIML), allowing the rich specification of agents' social identities and relationships. A complementary model controls the simulation of interpersonal relationship development within small groups. The interactions of these two models create a complex system exhibiting emergent properties for the generation of meaningful sequences of social interactions in the temporal dimension. To address the issues related to the visualization of nonverbal interactions, results are presented of an evaluation experiment aimed at identifying the application requirements through an analysis of how real people interact nonverbally in virtual environments. Based on these results, a number of components for MPEG-4 body animation, AML — a tag-based language for the seamless integration and synchronization of facial animation, body animation, and speech — and a high-level interaction visualization service for the VHD++ platform are described. This service simulates the proxemic and kinesic aspects of nonverbal social interactions, and comprises such functionalities as parametric postures, adapters and observation behaviours, the social avoidance of collisions, intelligent approach behaviours, and the calculation of suitable interaction distances and angles

Chiral Random Matrix Theory: Generalizations and Applications

Kieburg M. Chiral Random Matrix Theory: Generalizations and Applications. Bielefeld: Fakultät für Physik; 2015

The role of supersymmetry in the black hole/qubit correspondence

This thesis explores the numerous relationships between the entropy of black hole solutions in supergravity and the entanglement of multipartite systems in quantum information theory: the so-called black hole/qubit correspondence. We examine how, through the correspondence, the dyonic charges in the entropy of supersymmetric black hole solutions are directly matched to the state vector coefficients in the entanglement measures of their quantum information analogues. Moreover the Uduality invariance of the black hole entropy translates to the stochastic local operations and classical communication (SLOCC) invariance of the entanglement measures. Several examples are discussed, with the correspondence broadening when the supersymmetric classification of black holes is shown to match the entanglement classification of the qubit/qutrit analogues. On the microscopic front, we study the interpretation of D-brane wrapping configurations as real qubits/qutrits, including the matching of generating solutions on black hole and qubit sides. Tentative generalisations to other dimensions and qubit systems are considered. This is almost eclipsed by more recent developments linking the nilpotent U-duality orbit classi cation of black holes to the nilpotent classi cation of complex qubits. We provide preliminary results on the corresponding covariant classi cation. We explore the interesting parallel development of supersymmetric generalisations of qubits and entanglement, complete with two- and three-superqubit entanglement measures. Lastly, we briefly mention the supergravity technology of cubic Jordan algebras and Freudenthal triple systems (FTS), which are used to: 1) Relate FTS ranks to threequbit entanglement and compute SLOCC orbits. 2) Define new black hole dualities distinct from U-duality and related by a 4D/5D lift. 3) Clarify the state of knowledge of integral U-duality orbits in maximally extended supergravity in four, five, and six dimensions

Flight Mechanics/Estimation Theory Symposium, 1989

Numerous topics in flight mechanics and estimation were discussed. Satellite attitude control, quaternion estimation, orbit and attitude determination, spacecraft maneuvers, spacecraft navigation, gyroscope calibration, spacecraft rendevous, and atmospheric drag model calculations for spacecraft lifetime prediction are among the topics covered

Complexity Science in Human Change

This reprint encompasses fourteen contributions that offer avenues towards a better understanding of complex systems in human behavior. The phenomena studied here are generally pattern formation processes that originate in social interaction and psychotherapy. Several accounts are also given of the coordination in body movements and in physiological, neuronal and linguistic processes. A common denominator of such pattern formation is that complexity and entropy of the respective systems become reduced spontaneously, which is the hallmark of self-organization. The various methodological approaches of how to model such processes are presented in some detail. Results from the various methods are systematically compared and discussed. Among these approaches are algorithms for the quantification of synchrony by cross-correlational statistics, surrogate control procedures, recurrence mapping and network models.This volume offers an informative and sophisticated resource for scholars of human change, and as well for students at advanced levels, from graduate to post-doctoral. The reprint is multidisciplinary in nature, binding together the fields of medicine, psychology, physics, and neuroscience

Texture and Colour in Image Analysis

Research in colour and texture has experienced major changes in the last few years. This book presents some recent advances in the field, specifically in the theory and applications of colour texture analysis. This volume also features benchmarks, comparative evaluations and reviews