Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

EXAMINING THE IMPACT OF TEACHER PRACTICE ON STUDENT LEARNING IN INTERACTIVE RADIO INSTRUCTION (IRI) CLASSROOMS: LESSONS FROM NEW DELHI AND RAJASTHAN (INDIA)

This quantitative study examines the impact of teacher practices on student achievement in classrooms where the English is Fun Interactive Radio Instruction (IRI) programs were being used. A contemporary IRI design using a dual-audience approach, the English is Fun IRI programs delivered daily English language instruction to students in grades 1 and 2 in Delhi and Rajasthan through 120 30-minute programs via broadcast radio (the first audience) while modeling pedagogical techniques and behaviors for their teachers (the second audience). Few studies have examined how the dual-audience approach influences student learning. Using existing data from 32 teachers and 696 students, this study utilizes a multivariate multilevel model to examine the role of the primary expectations for teachers (e.g., setting up the IRI classroom, following instructions from the radio characters and ensuring students are participating) and the role of secondary expectations for teachers (e.g., modeling pedagogies and facilitating learning beyond the instructions) in promoting students’ learning in English listening skills, knowledge of vocabulary and use of sentences. The study finds that teacher practice on both sets of expectations mattered, but that practice in the secondary expectations mattered more. As expected, students made the smallest gains in the most difficult linguistic task (sentence use). The extent to which teachers satisfied the primary and secondary expectations was associated with gains in all three skills – confirming the relationship between students’ English proficiency and teacher practice in a dual-audience program. When it came to gains in students’ scores in sentence use, a teacher whose focus was greater on primary expectations had a negative effect on student performance in both states. In all, teacher practice clearly mattered but not in the same way for all three skills. An optimal scenario for teacher practice is presented in which gains in all three skills are maximized. These findings have important implications for the way the classroom teacher is cast in IRI programs that utilize a dual-audience approach and in the way IRI programs are contracted insofar as the role of the teacher in instruction is minimized and access is limited to instructional support from the IRI lessons alone.

The acquisition of adjunct control: grammar and processing

This dissertation uses children’s acquisition of adjunct control as a case study to investigate grammatical and performance accounts of language acquisition. In previous research, children have consistently exhibited non-adultlike behavior for sentences with adjunct control. To explain children’s behavior, several different grammatical accounts have been proposed, but evidence for these accounts has been inconclusive. In this dissertation, I take two approaches to account for children’s errors. First, I spell out the predictions of previous grammatical accounts, and test these predictions after accounting for some methodological concerns that might have influenced children’s behavior in previous studies. While I reproduce the non-adultlike behavior observed in previous studies, the predictions of previous grammatical accounts are not borne out, suggesting that extragrammatical factors are needed to explain children’s behavior. Next, I consider the role of two different types of extragrammatical factors in predicting children’s non-adultlike behavior. With a new task designed to address the task demands in previous studies, children exhibit significantly higher accuracy than with previous tasks. This suggests that children’s behavior has been influenced by task- specific processing factors. In addition to the task, I also test the predictions of a similarity-based interference account, which links children’s errors to the same memory mechanisms involved in sentence processing difficulties observed in adults. These predictions are borne out, supporting a more continuous developmental trajectory as children’s processing mechanisms become more resistant to interference. Finally, I consider how children’s errors might influence their acquisition of adjunct control, given the distribution in the linguistic input. I discuss the results of a corpus analysis, including the possibility that adjunct control could be learned from the input. The kinds of information that could be useful to a learner become much more limited, however, after considering the processing limitations that would interfere with the representations available to the learner.

THE ROLE OF RULES, EXAMPLES AND INDIVIDUAL DIFFERENCES IN THE ACQUISITION OF DECLARATIVE AND PROCEDURAL SECOND LANGUAGE KNOWLEDGE

The relevance of explicit instruction has been well documented in SLA research. Despite numerous positive findings, however, the issue continues to engage scholars worldwide. One issue that was largely neglected in previous empirical studies - and one that may be crucial for the effectiveness of explicit instruction - is the timing and integration of rules and practice. The present study investigated the extent to which grammar explanation (GE) before practice, grammar explanation during practice, and individual differences impact the acquisition of L2 declarative and procedural knowledge of two grammatical structures in Spanish. In this experiment, 128 English-speaking learners of Spanish were randomly assigned to four experimental treatments and completed comprehension-based task-essential practice for interpreting object-verb (OV) and ser/estar (SER) sentences in Spanish. Results confirmed the predicted importance of timing of GE: participants who received GE during practice were more likely to develop and retain their knowledge successfully. Results further revealed that the various combinations of rules and practice posed differential task demands on the learners and consequently drew on language aptitude and WM to a different extent. Since these correlations between individual differences and learning outcomes were the least observed in the conditions that received GE during practice, we argue that the suitable integration of rules and practice ameliorated task demands, reducing the burden on the learner, and accordingly mitigated the role of participants’ individual differences. Finally, some evidence also showed that the comprehension practice that participants received for the two structures was not sufficient for the formation of solid productive knowledge, but was more effective for the OV than for the SER construction.