Improving QED-Tutrix by Automating the Generation of Proofs

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page

Extended I-Love relations for slowly rotating neutron stars

Observations of gravitational waves from inspiralling neutron star binaries---such as GW170817---can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called "Love numbers." The tidal Love numbers $k_2^\text{el}$ and $k_2^\text{mag}$ measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers $\mathfrak{f}^\text{o}$ and $\mathfrak{k}^\text{o}$ measure those raised by couplings between the applied field and the neutron star spin. In this work we compute these four Love numbers for perfect fluid neutron stars with realistic equations of state. We discover (nearly) equation-of-state independent relations between the rotational-tidal Love numbers and the moment of inertia, thereby extending the scope of I-Love-Q universality. We find that similar relations hold among the tidal and rotational-tidal Love numbers. These relations extend the applications of I-Love universality in gravitational-wave astronomy. As our findings differ from those reported in the literature, we derive general formulas for the rotational-tidal Love numbers in post-Newtonian theory and confirm numerically that they agree with our general-relativistic computations in the weak-field limit.Comment: 31 pages, 6 figures, 9 tables; v2: updated to match published versio

The direct evaluation of attosecond chirp from a streaking measurement

We derive an analytical expression, from classical electron trajectories in a laser field, that relates the breadth of a streaked photoelectron spectrum to the group-delay dispersion of an isolated attosecond pulse. Based on this analytical expression, we introduce a simple, efficient and robust procedure to instantly extract the attosecond pulse's chirp from the streaking measurement.Comment: 4 figure

ALTERNATE STRESS MANAGEMENT BEHAVIORAL TECHNIQUES DURING SUSTAINED STRESSFUL PERIODS

In this thesis, I use a meta narrative analysis approach to identity effective stress management techniques that fit the unique operational environment of the U.S. Navy from prior investigations. From the earlier literature, I identify effective behavioral techniques for stress management to include mindfulness, cognitive behavioral therapy, social resilience, physical activity, program interventions, meditation and mind-body medicine, emotion regulation, mental health awareness, self-care, and coping. I then map them to the domains of the Total Sailor Fitness used by the 21st Century Sailor initiative to provide stress management support to sailors. Furthermore, I analyze the responses to an exploratory questionnaire from two shore commands and find that sailors tend to use humor and engage in hobbies as social resilience techniques, although sailors perceive the most effective coping techniques to be video games and physical activity (aerobic exercise). These initial findings can inform a follow-on study that can augment the data collection within a pilot framework to support the assessment of the stress management programs currently offered by the Navy under the 21st Century Sailor initiative.NPS Naval Research ProgramThis project was funded in part by the NPS Naval Research Program.Lieutenant, United States NavyApproved for public release. Distribution is unlimited

Population biology and disturbance ecology of a native north American bamboo (Arundinaria gigantea)

This dissertation explores effects of windstorm and fire disturbances on the clonal and reproductive biology of cane (Arundinaria gigantea Muhl., Poaceae). In this collection of studies, multiple disturbances interact in complex ways, and some interactions appear only after a substantial lag. One implication of this research is that multiple, interacting disturbances might strongly influence the boundary between monodominant and species-rich plant communities. Cane is the only bamboo native to the United States, and once covered vast areas of bottomlands in the southeastern U.S. in monodominant stands called “canebrakes.” The study took place on the Buckhorn Wildlife Management Area in Tensas Parish of northeastern Louisiana, in the Mississippi alluvial valley. Here in 2000 a tornado blew down a large swath of bottomland hardwood forest. The four-year experimental study focused on the effects of windstorm and prescribed fire on cane ramet dynamics, reproduction and regeneration from seed. The effect on cane of a large windstorm-generated gap is accelerated new ramet production and increased ramet density. Cane spreads continually, albeit irregularly. This suggests that cane stands might shift location over time as small forest gaps open and close. The effects of fire on cane are complex, and some may be lasting. In the large wind-generated forest gap, populations of cane ramets grow faster for having been burned. Forest-grown ramet populations decline in the year of fires, but growth rates rebound the next year. Unburned populations decline during the study’s final year, but previously burned populations do not, suggesting that fire one year might impart resistance to shocks one or more years later. The dissertation proposes how a sequence of windstorm and fire disturbances might promote natural canebrake formation. The counterpoint is that without periodic disturbances, cane ramet populations decline. The dissertation explores cane reproductive ecology and regeneration, and discusses three critical stages: seed production, germination and seedling establishment. Cane seeds and seedlings appear to germinate and survive most frequently on sites receiving partial sunlight with a layer of leaf litter. The final chapter describes how these experimental results inform cane restoration, and suggests three pathways by which cane restoration might be achieved