A Project Based Approach to Statistics and Data Science

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills

Discovery of a supernova associated with GRB 031203: SMARTS Optical-Infrared Lightcurves from 0.2 to 92 days

Optical and infrared monitoring of the afterglow site of gamma-ray burst (GRB) 031203 has revealed a brightening source embedded in the host galaxy, which we attribute to the presence of a supernova (SN) related to the GRB ("SN 031203"). We present details of the discovery and evolution of SN 031203 from 0.2 to 92 days after the GRB, derived from SMARTS consortium photometry in I and J bands. A template type Ic lightcurve, constructed from SN 1998bw photometry, is consistent with the peak brightness of SN 031203 although the lightcurves are not identical. Differential astrometry reveals that the SN, and hence the GRB, occurred less than 300 h_71^-1 pc (3-sigma) from the apparent galaxy center. The peak of the supernova is brighter than the optical afterglow suggesting that this source is intermediate between a strong GRB and a supernova.Comment: 11 pages, 3 figures, submitted to ApJ Letter

Simplex Solutions for Optimal Control Flight Paths in Urban Environments

This paper identifies feasible fight paths for Small Unmanned Aircraft Systems in a highly constrained environment. Optimal control software has long been used for vehicle path planning and has proven most successful when an adequate initial guess is presented flight to an optimal control solver. Leveraging fast geometric planning techniques, a large search space is discretized into a set of simplexes where a Dubins path solution is generated and contained in a polygonal search corridor free of path constraints. Direct optimal control methods are then used to determine the optimal flight path through the newly defined search corridor. Two scenarios are evaluated. The first is limited to heading rate control only, requiring the air vehicle to maintain constant speed. The second allows for velocity control which permits slower speeds, reducing the vehicles minimum turn radius and increasing the search domain. Results illustrate the benefits gained when including speed control to path planning algorithms by comparing trajectory and convergence times, resulting in a reliable, hybrid solution method to the SUAS constrained optimal control problem

Implementing Conditional Inequality Constraints for Optimal Collision Avoidance

Current Federal Aviation Administration regulations require that passing aircraft must either meet a specified horizontal or vertical separation distance. However, solving for optimal avoidance trajectories with conditional inequality path constraints is problematic for gradient-based numerical nonlinear programming solvers since conditional constraints typically possess non-differentiable points. Further, the literature is silent on robust treatment of approximation methods to implement conditional inequality path constraints for gradient-based numerical nonlinear programming solvers. This paper proposes two efficient methods to enforce conditional inequality path constraints in the optimal control problem formulation and compares and contrasts these approaches on representative airborne avoidance scenarios. The first approach is based on a minimum area enclosing superellipse function and the second is based on use of sigmoid functions. These proposed methods are not only robust, but also conservative, that is, their construction is such that the approximate feasible region is a subset of the true feasible region. Further, these methods admit analytically derived bounds for the over-estimation of the infeasible region with a demonstrated maximum error of no greater than 0.3% using the superellipse method, which is less than the resolution of typical sensors used to calculate aircraft position or altitude. However, the superellipse method is not practical in all cases to enforce conditional inequality path constraints that may arise in the nonlinear airborne collision avoidance problem. Therefore, this paper also highlights by example when the use of sigmoid functions are more appropriate

An in vitro model of impaction during hip arthroplasty

Impaction is required to properly seat press-fit implants and ensure initial implant stability and long term bone ingrowth, however excessive impaction or press-fit presents a high fracture risk in the acetabulum and femur. Current in-vitro impaction testing methods do not replicate the compliance of the soft tissues surrounding the hip, a factor that may be important in fracture and force prediction. This study presents the measurement of compliance of the soft tissues supporting the hip during impaction in operative conditions, and replicates these in vitro. Hip replacements were carried out on 4 full body cadavers while impact force traces and acetabular/femoral displacement were measured. Compliance was then simulated computationally using a Voigt model. These data were subsequently used to inform the design of a representative in-vitro drop rig. Effective masses of 19.7 kg and 12.7 kg, spring stiffnesses of 8.0 kN/m and 4.1 kN/m and dashpot coefficients of 595 N s/m and 322 N s/m were calculated for the acetabular and femoral soft tissues respectively. A good agreement between cadaveric and in-vitro peak displacement and rise time during impact is found. Such an in-vitro setup is of use during laboratory testing, simulation or even surgical training

Stable States of Biological Organisms

A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole. The organism is modeled by a five-dimensional dynamical system. The organism homeostasis is described by the evolution equations for five interacting components: healthy cells, ill cells, innate immune cells, specific immune cells, and pathogens. The stability analysis demonstrates that, in a wide domain of the parameter space, the system exhibits robust structural stability. There always exist four stable stationary solutions characterizing four qualitatively differing states of the organism: alive state, boundary state, critical state, and dead state.Comment: Latex file, 12 pages, 4 figure

Structured evaluation of virtual environments for special-needs education

This paper describes the development of a structured approach to evaluate experiential and communication virtual learning environments (VLEs) designed specifically for use in the education of children with severe learning difficulties at the Shepherd special needs school in Nottingham, UK. Constructivist learning theory was used as a basis for the production of an evaluation framework, used to evaluate the design of three VLEs and how they were used by students with respect to this learning theory. From an observational field study of student-teacher pairs using the VLEs, 18 behaviour categories were identified as relevant to five of the seven constructivist principles defined by Jonassen (1994). Analysis of student-teacher behaviour was used to provide support for, or against, the constructivist principles. The results show that the three VLEs meet the constructivist principles in very different ways and recommendations for design modifications are put forward

The EPICS Software Framework Moves from Controls to Physics

The Experimental Physics and Industrial Control System (EPICS), is an open-source software framework for high-performance distributed control, and is at the heart of many of the world’s large accelerators and telescopes. Recently, EPICS has undergone a major revision, with the aim of better computing supporting for the next generation of machines and analytical tools. Many new data types, such as matrices, tables, images, and statistical descriptions, plus users’ own data types, now supplement the simple scalar and waveform types of the former EPICS. New computational architectures for scientific computing have been added for high-performance data processing services and pipelining. Python and Java bindings have enabled powerful new user interfaces. The result has been that controls are now being integrated with modelling and simulation, machine learning, enterprise databases, and experiment DAQs. We introduce this new EPICS (version 7) from the perspective of accelerator physics and review early adoption cases in accelerators around the world