A Vector-Integration-to-Endpoint Model for Performance of Viapoint Movements

Viapoint (VP) movements are movements to a desired point that are constrained to pass through an intermediate point. Studies have shown that VP movements possess properties, such as smooth curvature around the VP, that are not explicable by treating VP movements as strict concatenations of simpler point-to-point (PTP) movements. Such properties have led some theorists to propose whole-trajectory optimization models, which imply that the entire trajectory is pre-computed before movement initiation. This paper reports new experiments conducted to systematically compare VP with PTP trajectories. Analyses revealed a statistically significant early directional deviation in VP movements but no associated curvature change. An explanation of this effect is offered by extending the Vector-Integration-To-Endpoint (VITE) model (Bullock and Grossberg, 1988), which postulates that voluntary movement trajectories emerge as internal gating signals control the integration of continuously computed vector commands based on the evolving, perceptible difference between desired and actual position variables. The model explains the observed trajectories of VP and PTP movements as emergent properties of a dynamical system that does not precompute entire trajectories before movement initiation. The new model includes a working memory and a stage sensitive to time-to-contact information. These cooperate to control serial performance. The structural and functional relationships proposed in the model are consistent with available data on forebrain physiology and anatomy.Office of Naval Research (N00014-92-J-1309, N00014-93-1-1364, N0014-95-1-0409

An Explanatory Sequential Mixed Methods Study of the School Leaders\u27 Role in Students\u27 Mathematics Achievement Through the Lens of Complexity Theory

Student achievement in the K-12 mathematics classroom is of concern to parents, teachers, and community leaders as complex modern technological innovations call for higher proficiency in problem solving and mathematically creative minds are necessary to fill the vital, higher-paying jobs of today and the future. School leaders are expected to make decisions that will measurably, and in some cases, dramatically, improve student achievement in mathematics. However, school leaders do not make decisions in isolation; rather, they make decisions as part of a complex adaptive system (CAS). There is limited research concerning content-specific school leadership and its effects on student achievement, particularly through the lens of complexity theory. This study focuses on the relationships between students’ mathematics achievement and the characteristics of school leaders, looks at the influences affecting the decisions and actions being made by school leaders, and then seeks to understand how a school leaders’ decisions and actions are associated with students’ mathematics achievement. A significant predictive model was found including evidence of interaction effects and multiplicative looping effects aligned with complexity theory. Distinctive patterns emerged between school leaders’ decisions and actions from schools who were performing higher than expected, about where expected, and lower than expected. Furthermore, result indicate that school leaders do play an indirect role in student mathematics achievement specifically through the ability to foster a shared vision of mathematics education in their respective schools

An Explanatory Sequential Mixed Methods Study of the School Leaders’ Role in Students’ Mathematics Achievement Through the Lens of Complexity Theory

School leaders are expected to make decisions that improve student mathematics achievement. However, one difficulty for school leaders has been the limited amount of research concerning content-specific (e.g., mathematics) school leadership and its effects on student achievement. School leaders do not make decisions in isolation; rather, they make decisions as part of a complex adaptive system (CAS), as proposed by complexity theory. The purpose of this study was to explore the role the school leader plays in students’ mathematics achievement through the lens of complexity theory. The researcher collected survey data from K-12 school leaders and conducted focus group interviews to answer the research questions. The researcher found a significant regression equation predicting the school-wide average SAGE mathematics proficiency scores based on several characteristics of the school leader and student demographics. Distinctive patterns emerged in the decisions and actions made by school leaders based on school-wide SAGE mathematics proficiency. Results suggest that the school leaders’ first role in promoting higher student mathematics achievement is to directly and indirectly facilitate a shared vision of mathematics education between stakeholders in the CAS. The school leader’s second role is to actively work to recruit and retain the highest quality teachers possible

Parallelism for Quantum Computation with Qudits

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates.Comment: 9 pages, 3 figure