Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails

Reinventing College Physics for Biologists: Explicating an epistemological curriculum

The University of Maryland Physics Education Research Group (UMd-PERG) carried out a five-year research project to rethink, observe, and reform introductory algebra-based (college) physics. This class is one of the Maryland Physics Department's large service courses, serving primarily life-science majors. After consultation with biologists, we re-focused the class on helping the students learn to think scientifically -- to build coherence, think in terms of mechanism, and to follow the implications of assumptions. We designed the course to tap into students' productive conceptual and epistemological resources, based on a theoretical framework from research on learning. The reformed class retains its traditional structure in terms of time and instructional personnel, but we modified existing best-practices curricular materials, including Peer Instruction, Interactive Lecture Demonstrations, and Tutorials. We provided class-controlled spaces for student collaboration, which allowed us to observe and record students learning directly. We also scanned all written homework and examinations, and we administered pre-post conceptual and epistemological surveys. The reformed class enhanced the strong gains on pre-post conceptual tests produced by the best-practices materials while obtaining unprecedented pre-post gains on epistemological surveys instead of the traditional losses.Comment: 35 pages including a 15 page appendix of supplementary material

Addressing student models of energy loss in quantum tunnelling

We report on a multi-year, multi-institution study to investigate student reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews, and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling. When sketching wave functions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical, and graphical models of quantum tunnelling. As part of a curriculum in quantum physics, we have developed instructional materials to help students develop a more robust and less inconsistent picture of tunnelling, and present data suggesting that we have succeeded in doing so.Comment: Originally submitted to the European Journal of Physics on 2005 Feb 10. Pages: 14. References: 11. Figures: 9. Tables: 1. Resubmitted May 18 with revisions that include an appendix with the curriculum materials discussed in the paper (4 page small group UW-style tutorial

Understanding and Affecting Student Reasoning About Sound Waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

Hippocampal theta sequences reflect current goals

8 9 a r t I C l e S In humans, the hippocampus is critical for the simulation of potential or imagined future possibilities, flexibly using past experiences to make predictions about the future If the hippocampus mediates similar cognitive functions across species in the performance of goal-directed behavior, planningrelated signals in the rodent hippocampus might occur in the framework of spatial representations. Hippocampal theta sequences, time-compressed, ensemble representations of trajectories through the environment Although such modulation of theta sequence content suggests a means by which the hippocampus could use a spatial framework to support goal-directed decision-making, an alternative possibility is that forward-shifted theta representations reflect a sensory-cued recall process, where landmark-place associations drive predictive representations of upcoming locations on the maze 19 . If theta sequences contain computations of prospective plans, ensemble spiking should reflect currently active spatial goals. To test this idea, we examined theta sequences as rats performed a value-guided decision-making task. Because behavior on the task was guided by rats' preferences rather than their attempts to determine and match reward contingencies set by the experimenter, this task offered a unique opportunity for testing how the hippocampus contributes to volitional navigation decisions akin to those made in natural settings. RESULTS We trained rats to perform a foraging task in which they chose whether or not to wait for food delivered after varying amounts of delay. Rats ran unidirectional laps around a circular track with three food pellet dispensers spaced evenly around the perimeter, each associated with a fixed-length delay. If subjects remained at a feeder site until the delay period passed, food pellets (the same type and quantity at each feeder) were dispensed. However, the rat was also free to move on to the next site. In either case, the feeder site became inactive until the rat approached it on the subsequent lap. In a session, the delay at each site remained fixed; however, across sessions, different sets of three delays were counterbalanced across the sites. A full account of behavior on this task has been presented previously Rats ran different patterns of trajectories between sites, depending on the spatial arrangement of delays in the session and their willingness to wait for delayed reward Rats were implanted with tetrode arrays targeting dorsal CA1 hippocampus. Consistent with previous reports np

Learning physics in context: a study of student learning about electricity and magnetism

This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel university class in electricity and magnetism are analyzed to demonstrate the central and inextricable role of context in student learning. This work sits within a broader effort to create and analyze environments which support student learning in the sciencesComment: 36 pages, 4 Figure

Sustaining Educational Reforms in Introductory Physics

While it is well known which curricular practices can improve student performance on measures of conceptual understanding, the sustaining of these practices and the role of faculty members in implementing these practices are less well understood. We present a study of the hand-off of Tutorials in Introductory Physics from initial adopters to other instructors at the University of Colorado, including traditional faculty not involved in physics education research. The study examines the impact of implementation of Tutorials on student conceptual learning across eight first-semester, and seven second-semester courses, for fifteen faculty over twelve semesters, and includes roughly 4000 students. It is possible to demonstrate consistently high, and statistically indistinguishable, student learning gains for different faculty members; however, such results are not the norm, and appear to rely on a variety of factors. Student performance varies by faculty background - faculty involved in, or informed by physics education research, consistently post higher student learning gains than less-informed faculty. Student performance in these courses also varies by curricula used - all semesters in which the research-based Tutorials and Learning Assistants are used have higher student learning gains than those semesters that rely on non-research based materials and do not employ Learning Assistants.Comment: 21 pages, 4 figures, and other essential inf

Bandit Models of Human Behavior: Reward Processing in Mental Disorders

Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for multi-armed bandit problem, which extends the standard Thompson Sampling approach to incorporate reward processing biases associated with several neurological and psychiatric conditions, including Parkinson's and Alzheimer's diseases, attention-deficit/hyperactivity disorder (ADHD), addiction, and chronic pain. We demonstrate empirically that the proposed parametric approach can often outperform the baseline Thompson Sampling on a variety of datasets. Moreover, from the behavioral modeling perspective, our parametric framework can be viewed as a first step towards a unifying computational model capturing reward processing abnormalities across multiple mental conditions.Comment: Conference on Artificial General Intelligence, AGI-1

Dynamical model of sequential spatial memory: winnerless competition of patterns

We introduce a new biologically-motivated model of sequential spatial memory which is based on the principle of winnerless competition (WLC). We implement this mechanism in a two-layer neural network structure and present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable of associative retrieval of pre-recorded sequences of spatial patterns.Comment: 4 pages, submitted to PR