Feedback Controlled Software Systems

Software systems generally suffer from a certain fragility in the face of disturbances such as bugs, unforeseen user input, unmodeled interactions with other software components, and so on. A single such disturbance can make the machine on which the software is executing hang or crash. We postulate that what is required to address this fragility is a general means of using feedback to stabilize these systems. In this paper we develop a preliminary dynamical systems model of an arbitrary iterative software process along with the conceptual framework for stabilizing it in the presence of disturbances. To keep the computational requirements of the controllers low, randomization and approximation are used. We describe our initial attempts to apply the model to a faulty list sorter, using feedback to improve its performance. Methods by which software robustness can be enhanced by distributing a task between nodes each of which are capable of selecting the best input to process are also examined, and the particular case of a sorting system consisting of a network of partial sorters, some of which may be buggy or even malicious, is examined

Cognitive Structures of Good and Poor Novice Problem Solvers in Physics

The way knowledge is organized in memory is generally expected to relate to the degree of success in problem solving. In the present study, we investigated whether good novice problem solvers have their knowledge arranged around problem types to a greater extent than poor problem solvers have. In the subject of physics (electricity and magnetism), 12 problem types were distinguished according to their underlying physics principles. For each problem type, a set of elements of knowledge containing characteristics of the problem situation, declarative knowledge, and procedural knowledge was constructed. All of the resulting 65 elements were printed on cards, and first-year university students in physics ( N = 47) were asked to sort these cards into coherent piles shortly after they had taken an examination on electricity and magnetism. Essentially, good novice problem solvers sorted the cards according to problem types; the sorting by the poor problem solvers seemed to be determined to a greater extent by the surface characteristics of the elements. We concluded than an organization of knowledge around problem types might be highly conducive to good performance in problem solving by novice problem solvers

Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG modes depending upon whether they have an even or odd value of their orbital angular momentum. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m=1) spatial states, covering the entire Poincare sphere of first-order transverse modes.Comment: 11 pages, 12 figures, 2 appendice

Heterogeneous Class Size Effects: New Evidence from a Panel of University Students

Over the last decade, many countries have experienced dramatic increases in university enrolment, which, when not matched by compensating increases in other inputs, have resulted in larger class sizes. Using administrative records from a leading UK university, we present evidence on the effects of class size on students’ test scores. We observe the same student and faculty members being exposed to a wide range of class sizes from less than 10 to over 200. We therefore estimate non-linear class size effects controlling for unobserved heterogeneity of both individual students and faculty. We find that (i) at the average class size, the effect size is -0.108; (ii) the effect size is however negative and significant only for the smallest and largest ranges of class sizes and zero over a wide range of intermediate class sizes; (iii) students at the top of the test score distribution are more affected by changes in class size, especially when class sizes are very large. We present evidence to rule out class size effects being due solely to the non-random assignment of faculty to class size, sorting by students onto courses on the basis of class size, omitted inputs, the difficulty of courses, or grading policies. The evidence also shows the class size effects are not mitigated for students with greater knowledge of the UK university system, this university in particular, or with greater family wealth.class size, heterogeneity, university education

Teaching Students and Teaching Each Other: The Importance of Peer Learning for Teachers

Using longitudinal elementary school teacher and student data, we document that students have larger test score gains when their teachers experience improvements in the observable characteristics of their colleagues. Using within-school and within-teacher variation, we further show that a teacher’s students have larger achievement gains in math and reading when she has more effective colleagues (based on estimated value-added from an out-of-sample preperiod). Spillovers are strongest for less-experienced teachers and persist over time, teachers perform best when they are the weakest of their peer group, and historical peer quality explains away about twenty percent of the own-teacher effect. These results suggest peer learning

Teacher Quality and Student Inequality (Revised 2014)

This paper examines the extent to which the allocation of teachers within and across public high schools is contributing to inequality in student test score performance. Using ten years of administrative data from North Carolina public high schools, I estimate a flexible education production function in which student achievement reflects student inputs, teacher quality, school quality, and a school-specific scaling factor that allows the impact of teaching quality to vary across schools. The existence of nearly 3,000 teacher transfers, combined with a testable exogenous mobility assumption, allows separate identification of each teacher’s quality from both school quality and school sensitivity to teacher quality. I find that teaching quality is surprisingly equitably distributed both within and across high schools. Schools predominantly serving underprivileged students employ teachers who are only slightly below average, and most students receive a mix of their school’s good and bad teachers. Overall, I find that the allocation of teacher and school inputs at the high school level contributes only 4% to the achievement gap between the top and bottom deciles of an index of student background. Finally, I find that schools that disproportionately serve disadvantaged students tend to be more sensitive to teacher quality