Skill set profile clustering based on student capability vectors computed from online tutoring data

In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. To address this, we introduce a capability matrix showing for each skill the proportion correct on all items tried by each student involving that skill. We apply variations of common clustering methods to this matrix and discuss conditioning on sparse subspaces. We demonstrate the feasibility and scalability of our method on several simulated datasets and illustrate the difficulties inherent in real data using a subset of online mathematics tutor data. We also comment on the interpretability and application of the results for teachers

Skill set profile clustering: the empty K-means algorithm with automatic specification of starting cluster centers

While students’ skill set profiles can be estimated with formal cognitive diagnosis models [8], their computational complexity makes simpler proxy skill estimates attractive [1, 4, 6]. These estimates can be clustered to generate groups of similar students. Often hierarchical agglomerative clustering or k-means clustering is utilized, requiring, for K skills, the specification of 2^K clusters. The number of skill set profiles/clusters can quickly become computationally intractable. Moreover, not all profiles may be present in the population. We present a flexible version of k-means that allows for empty clusters. We also specify a method to determine efficient starting centers based on the Q-matrix. Combining the two substantially improves the clustering results and allows for analysis of data sets previously thought impossible

Against the Wind: Radio Light Curves of Type Ia Supernovae Interacting with Low-Density Circumstellar Shells

For decades, a wide variety of observations spanning the radio through optical and on to the x-ray have attempted to uncover signs of type Ia supernovae (SNe Ia) interacting with a circumstellar medium (CSM). The goal of these studies is to constrain the nature of the hypothesized SN Ia mass-donor companion. A continuous CSM is typically assumed when interpreting observations of interaction. However, while such models have been successfully applied to core-collapse SNe, the assumption of continuity may not be accurate for SNe Ia, as shells of CSM could be formed by pre-supernova eruptions (novae). In this work, we model the interaction of SNe with a spherical, low density, finite-extent CSM and create a suite of synthetic radio synchrotron light curves. We find that CSM shells produce sharply peaked light curves, and identify a fiducial set of models that all obey a common evolution and can be used to generate radio light curves for interaction with an arbitrary shell. The relations obeyed by the fiducial models can be used to deduce CSM properties from radio observations; we demonstrate this by applying them to the non-detections of SN 2011fe and SN 2014J. Finally, we explore a multiple shell CSM configuration and describe its more complicated dynamics and resultant radio light curves.Comment: 15 pages, 11 figures, ApJ accepte

Pressures measured in flight on the aft fuselage and external nozzle of a twin-jet fighter

Fuselage, boundary layer, and nozzle pressures were measured in flight for a twin jet fighter over a Mach number range from 0.60 to 2.00 at test altitudes of 6100, 10,700, and 13,700 meters for angles of attack ranging from 0 deg to 7 deg. Test data were analyzed to find the effects of the propulsion system geometry. The flight variables, and flow interference. The aft fuselage flow field was complex and showed the influence of the vertical tail, nacelle contour, and the wing. Changes in the boattail angle of either engine affected upper fuselage and lower fuselage pressure coefficients upstream of the nozzle. Boundary layer profiles at the forward and aft locations on the upper nacelles were relatively insensitive to Mach number and altitude. Boundary layer thickness decreased at both stations as angle of attack increased above 4 deg. Nozzle pressure coefficient was influenced by the vertical tail, horizontal tail boom, and nozzle interfairing; the last two tended to separate flow over the top of the nozzle from flow over the bottom of the nozzle. The left nozzle axial force coefficient was most affected by Mach number and left nozzle boattail angle. At Mach 0.90, the nozzle axial force coefficient was 0.0013

Bridging the gap between agent based models and continuous opinion dynamics

There is a rich literature on microscopic models for opinion dynamics; most of them fall into one of two categories - agent-based models or differential equation models - with a general understanding that the two are connected in certain scaling limits. In this paper we show rigorously this is indeed the case. In particular we show that DEMs can be obtained from ABMs by simultaneously rescaling time and the distance an agent updates their opinion after an interaction. This approach provides a pathway to analyse much more diverse modelling paradigms, for example: the motivation behind several possible multiplicative noise terms in stochastic differential equation models; the connection between selection noise and the mollification of the discontinuous bounded confidence interaction function; and how the method for selecting interacting pairs can determine the normalisation in the corresponding differential equation. Our computational experiments confirm our findings, showing excellent agreement of solutions to the two classes of models in a variety of settings

Coherence properties of light propagated through a scattering medium

Partially-coherent, quasi-monochromatic optical fields are fully described by their Mutual Optical Intensity (MOI) or the phase-space equivalent, the Generalised Radiance (GR). This paper reports on the application of a propagation-based phase-space tomographic technique for determining both the MOI and the GR of wavefields. This method is applied to the reconstruction of the MOI and the GR of an optical wavefield propagated through a suspension of \~10micrometre diameter polystyrene spheres.Comment: Photonics 2004, 7th International conference on optoelectronics, fibre optics and photonics, Kochi, Indi

Precise time delays from strongly gravitationally lensed type Ia supernovae with chromatically microlensed images

Time delays between the multiple images of strongly gravitationally lensed Type Ia supernovae (glSNe Ia) have the potential to deliver precise cosmological constraints, but the effects of microlensing on time delay extraction have not been studied in detail. Here we quantify the effect of microlensing on the glSN Ia yield of the Large Synoptic Survey Telescope (LSST) and the effect of microlensing on the precision and accuracy of time delays that can be extracted from LSST glSNe Ia. Microlensing has a negligible effect on the LSST glSN Ia yield, but it can be increased by a factor of ∼2 over previous predictions to 930 systems using a novel photometric identification technique based on spectral template fitting. Crucially, the microlensing of glSNe Ia is achromatic until three rest-frame weeks after the explosion, making the early-time color curves microlensing-insensitive time delay indicators. By fitting simulated flux and color observations of microlensed glSNe Ia with their underlying, unlensed spectral templates, we forecast the distribution of absolute time delay error due to microlensing for LSST, which is unbiased at the sub-percent level and peaked at 1% for color curve observations in the achromatic phase, while for light-curve observations it is comparable to state-of-the-art mass modeling uncertainties (4%). About 70% of LSST glSN Ia images should be discovered during the achromatic phase, indicating that microlensing time delay uncertainties can be minimized if prompt multicolor follow-up observations are obtained. Accounting for microlensing, the 1-2 day time delay on the recently discovered glSN Ia iPTF16geu can be measured to 40% precision, limiting its cosmological utility