On Achievable Rates of the Two-user Symmetric Gaussian Interference Channel

We study the Han-Kobayashi (HK) achievable sum rate for the two-user symmetric Gaussian interference channel. We find the optimal power split ratio between the common and private messages (assuming no time-sharing), and derive a closed form expression for the corresponding sum rate. This provides a finer understanding of the achievable HK sum rate, and allows for precise comparisons between this sum rate and that of orthogonal signaling. One surprising finding is that despite the fact that the channel is symmetric, allowing for asymmetric power split ratio at both users (i.e., asymmetric rates) can improve the sum rate significantly. Considering the high SNR regime, we specify the interference channel value above which the sum rate achieved using asymmetric power splitting outperforms the symmetric case.Comment: 7 pages, to appear in Allerton 201

Methods for Analyzing Pathways through a Physics Major

Physics Education Research frequently investigates what students studying physics do on small time scales (e.g. single courses, observations within single courses), or post-education time scales (e.g., what jobs do physics majors get?) but there is little research into how students get from the beginning to the end of a physics degree. Our work attempts to visualize students paths through the physics major, and quantitatively describe the students who take physics courses, receive physics degrees, and change degree paths into and out of the physics program at Michigan State University.Comment: submitted to Physics Education Research Conference Proceedings 201

Modeling student pathways in a physics bachelor's degree program

Physics education research has used quantitative modeling techniques to explore learning, affect, and other aspects of physics education. However, these studies have rarely examined the predictive output of the models, instead focusing on the inferences or causal relationships observed in various data sets. This research introduces a modern predictive modeling approach to the PER community using transcript data for students declaring physics majors at Michigan State University (MSU). Using a machine learning model, this analysis demonstrates that students who switch from a physics degree program to an engineering degree program do not take the third semester course in thermodynamics and modern physics, and may take engineering courses while registered as a physics major. Performance in introductory physics and calculus courses, measured by grade as well as a students' declared gender and ethnicity play a much smaller role relative to the other features included the model. These results are used to compare traditional statistical analysis to a more modern modeling approach.Comment: submitted to Physical Review Physics Education Researc

Examining the relationship between student performance and video interactions

In this work, we attempted to predict student performance on a suite of laboratory assessments using students' interactions with associated instructional videos. The students' performance is measured by a graded presentation for each of four laboratory presentations in an introductory mechanics course. Each lab assessment was associated with between one and three videos of instructional content. Using video clickstream data, we define summary features (number of pauses, seeks) and contextual information (fraction of time played, in-semester order). These features serve as inputs to a logistic regression (LR) model that aims to predict student performance on the laboratory assessments. Our findings show that LR models are unable to predict student performance. Adding contextual information did not change the model performance. We compare our findings to findings from other studies and explore caveats to the null-result such as representation of the features, the possibility of underfitting, and the complexity of the assessment.Comment: 4 pages, 1 figure, submitted to the PERC 2018 proceeding

No-Scale Inflation

Supersymmetry is the most natural framework for physics above the TeV scale, and the corresponding framework for early-Universe cosmology, including inflation, is supergravity. No-scale supergravity emerges from generic string compactifications and yields a non-negative potential, and is therefore a plausible framework for constructing models of inflation. No-scale inflation yields naturally predictions similar to those of the Starobinsky model based on $R + R^2$ gravity, with a tilted spectrum of scalar perturbations: $n_s \sim 0.96$, and small values of the tensor-to-scalar perturbation ratio $r < 0.1$, as favoured by Planck and other data on the cosmic microwave background (CMB). Detailed measurements of the CMB may provide insights into the embedding of inflation within string theory as well as its links to collider physics.Comment: Invited contribution to the forthcoming Classical and Quantum Gravity focus issue on "Planck and the fundamentals of cosmology". 22 pages, 7 figures, uses psfra

A No-Scale Inflationary Model to Fit Them All

The magnitude of B-mode polarization in the cosmic microwave background as measured by BICEP2 favours models of chaotic inflation with a quadratic $m^2 \phi^2/2$ potential, whereas data from the Planck satellite favour a small value of the tensor-to-scalar perturbation ratio $r$ that is highly consistent with the Starobinsky $R + R^2$ model. Reality may lie somewhere between these two scenarios. In this paper we propose a minimal two-field no-scale supergravity model that interpolates between quadratic and Starobinsky-like inflation as limiting cases, while retaining the successful prediction $n_s \simeq 0.96$.Comment: 25 pages, 12 figure

Phenomenological Aspects of No-Scale Inflation Models

We discuss phenomenological aspects of no-scale supergravity inflationary models motivated by compactified string models, in which the inflaton may be identified either as a K\"ahler modulus or an untwisted matter field, focusing on models that make predictions for the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ that are similar to the Starobinsky model. We discuss possible patterns of soft supersymmetry breaking, exhibiting examples of the pure no-scale type $m_0 = B_0 = A_0 = 0$, of the CMSSM type with universal $A_0$ and $m_0 \ne 0$ at a high scale, and of the mSUGRA type with $A_0 = B_0 + m_0$ boundary conditions at the high input scale. These may be combined with a non-trivial gauge kinetic function that generates gaugino masses $m_{1/2} \ne 0$, or one may have a pure gravity mediation scenario where trilinear terms and gaugino masses are generated through anomalies. We also discuss inflaton decays and reheating, showing possible decay channels for the inflaton when it is either an untwisted matter field or a K\"ahler modulus. Reheating is very efficient if a matter field inflaton is directly coupled to MSSM fields, and both candidates lead to sufficient reheating in the presence of a non-trivial gauge kinetic function.Comment: 41 pages, 6 figure

Predicting time to graduation at a large enrollment American university

The time it takes a student to graduate with a university degree is mitigated by a variety of factors such as their background, the academic performance at university, and their integration into the social communities of the university they attend. Different universities have different populations, student services, instruction styles, and degree programs, however, they all collect institutional data. This study presents data for 160,933 students attending a large American research university. The data includes performance, enrollment, demographics, and preparation features. Discrete time hazard models for the time-to-graduation are presented in the context of Tinto's Theory of Drop Out. Additionally, a novel machine learning method: gradient boosted trees, is applied and compared to the typical maximum likelihood method. We demonstrate that enrollment factors (such as changing a major) lead to greater increases in model predictive performance of when a student graduates than performance factors (such as grades) or preparation (such as high school GPA).Comment: 28 pages, 11 figure