Tracing your roots

An event to allow students to trace back their ancestry with the assistance of the New England Historic Genealogical Societ

FAST: Feature-Aware Student Knowledge Tracing

Various kinds of e-learning systems, such as Massively Open Online Courses and intelligent tutoring systems, are now producing amounts of feature-rich data from students solving items at different levels of proficiency over time. To analyze such data, researchers often use Knowledge Tracing [4], a 20-year old method that has become the de-facto standard for inferring student’s knowledge from performance data. Knowledge Tracing uses Hidden Markov Models (HMM) to estimate the latent cognitive state (student’s knowledge) from the student’s performance answering items. Since the original Knowledge Tracing formulation does not allow to model general features, a considerable amount of research has focused on ad-hoc modifications to the Knowledge Tracing algorithm to enable modeling a specific feature of interest. This has led to a plethora of different Knowledge Tracing reformulations for very specific purposes. For example, Pardos et al. [5] proposed a new model to measure the effect of students’ individual characteristics, Beck et al. [2] modified Knowledge Tracing to assess the effect of help in a tutor system, and Xu and Mostow [7] proposed a new model that allows measuring the effect of subskills. These ad hoc models are successful for their own specific purpose, but they do not generalize to arbitrary features. Other student modeling methods which allow more flexible features have been proposed. For example, Performance Factor Analysis [6] uses logistic regression to model arbitrary features, but unfortunately it does not make inferences of whether the student has learned a skill. We present FAST (Feature-Aware Student knowledge Tracing), a novel method that allows general features into Knowledge Tracing. FAST combines Performance Factor Analysis (logistic regression) with Knowledge Tracing, by leveraging on previous work on unsupervised learning with features [3]. Therefore, FAST is able to infer student’s knowledge, like Knowledge Tracing does, while also allowing for arbitrary features, like Performance Factor Analysis does. FAST allows general features into Knowledge Tracing by replacing the generative emission probabilities (often called guess and slip probabilities) with logistic regression [3], so that these probabilities can change with time to infer student’s knowledge. FAST allows arbitrary features to train the logistic regression model and the HMM jointly. Training the parameters simultaneously enables FAST to learn from the features. This differs from using regression to analyze the slip and guess probabilities [1]. To validate our approach, we use data collected from real students interacting with a tutor. We present experimental results comparing FAST with Knowledge Tracing and Performance Factor Analysis. We conduct experiments with our model using features like item difficulty, prior successes and failures of a student for the skill (or multiple skills) associated with the item, according to the formulation of Performance Factor Analysis

Ray tracing program with options for diffraction gratings

Diffraction theory, developed in vectorial form and coded into ray tracing routines, permits tracing rays of any wavelength through surfaces that are plane, spherical, conical, or aspheric polynomial. Ruled diffraction gratings may run in either X-direction or Y-direction, where Z is optical axis

Tracing scientific influence

Scientometrics is the field of quantitative studies of scholarly activity. It has been used for systematic studies of the fundamentals of scholarly practice as well as for evaluation purposes. Although advocated from the very beginning the use of scientometrics as an additional method for science history is still under explored. In this paper we show how a scientometric analysis can be used to shed light on the reception history of certain outstanding scholars. As a case, we look into citation patterns of a specific paper by the American sociologist Robert K. Merton.Comment: 25 pages LaTe

Tracing Through Scalar Entanglement

As a toy model of a gapped system, we investigate the entanglement entropy of a massive scalar field in 1+1 dimensions at nonzero temperature. In a small mass m and temperature T limit, we put upper and lower bounds on the two largest eigenvalues of the covariance matrix used to compute the entanglement entropy. We argue that the entanglement entropy has exp(-m/T) scaling in the limit m >> T. We comment on the relation between our work and the Ryu-Takayanagi proposal for computing the entanglement entropy holographically.Comment: 17 pages, 11 figures; v2 ref added, typos fixed; v3 refs added, minor clarifications, version to appear in PR

The impact of prior information on estimates of disease transmissibility using Bayesian tools

The basic reproductive number (R₀) and the distribution of the serial interval (SI) are often used to quantify transmission during an infectious disease outbreak. In this paper, we present estimates of R₀ and SI from the 2003 SARS outbreak in Hong Kong and Singapore, and the 2009 pandemic influenza A(H1N1) outbreak in South Africa using methods that expand upon an existing Bayesian framework. This expanded framework allows for the incorporation of additional information, such as contact tracing or household data, through prior distributions. The results for the R₀ and the SI from the influenza outbreak in South Africa were similar regardless of the prior information (R0 = 1.36-1.46, μ = 2.0-2.7, μ = mean of the SI). The estimates of R₀ and μ for the SARS outbreak ranged from 2.0-4.4 and 7.4-11.3, respectively, and were shown to vary depending on the use of contact tracing data. The impact of the contact tracing data was likely due to the small number of SARS cases relative to the size of the contact tracing sample

The Place of the Trace: Negligence and Responsibility

One popular theory of moral responsibility locates responsible agency in exercises of control. These control-based theories often appeal to tracing to explain responsibility in cases where some agent is intuitively responsible for bringing about some outcome despite lacking direct control over that outcome’s obtaining. Some question whether control-based theories are committed to utilizing tracing to explain responsibility in certain cases. I argue that reflecting on certain kinds of negligence shows that tracing plays an ineliminable role in any adequate control-based theory of responsibility