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

Experimental compaction of anisotropic granular media

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic and weakly confined granular material, using high-resolution $\gamma$-ray adsorption. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical solicitations evolve to a dense state. We find that the packing fraction evolution is slowed by the grain anisotropy but, as for spherically shaped grains, can be well fitted by a stretched exponential. For a given type of grains, the characteristic times of relaxation and of convection are found to be of the same order of magnitude. On the contrary compaction mechanisms in the media strongly depend on the grain anisotropy.Comment: to appear in the european physical journal E (EPJE

Étude fonctionnelle-structurelle de deux extraits de manuels anciens de géométrie

Cet article vise à montrer l’utilité d’une approche fonctionnelle-structurelle pour l’étude des manuels scolaires en mathématiques. L’approche s’inspire de trois sources : la théorie des fonctions du langage de Duval, le modèle des fonctions du langage dans la communication de Jakobson et le modèle des structures sémiotiques développé par Richard. Après avoir présenté l’approche dans la première partie, nous l’appliquons ensuite à l’analyse de deux courts textes, tirés des manuels de géométrie qui ont été en usage au Québec, dans les écoles secondaires de langue française. L’intention adidactique qui se dégage des deux textes montre comment les moyens sémiotiques mobilisés sont mis au sevice de la qualité de la communication avec l’éventuel lecteur.The objective of this article is to show the pertinence of a functional-structural approach to the study of mathematics school texts. This approach is based on three sources : Duval’s theory of language functions, Jakobson’s model of language functions in communication, and the model of semiotic structures developed by Richard. Following the presentation of the approach in the first part, the authors apply this to an analysis of two short texts taken from a geometry text used in French secondary schools in Québec. The adidactic objective that can be derived from these two texts shows how the semiotic means used can serve to improve the quality of communication with the future reader.Este artículo tiene por obetivo demostrar la utilidad de un enfoque funcional-estructural para el estudio de los libros de texto en matemáticas. El enfoque origina de tres fuentes : la teoría de las funciones del lenguaje de Duval, el modelo de las funciones del lenguaje en la comunicación de Jakobson y el modelo de las estructuras semióticas desarrollado por Richard. Una vez presentado el enfoque en la primera parte, lo aplicaremos luego al análisis de dos breves textos que proceden de libros de geometría que han sido utilizados en Québec, en escuelas secundarias de lengua francesa. La intención adidáctica que resalta de los dos textos demuestra cómo los medios semióticos movilizados sirven la calidad de la comunicación con el eventual lector.Dieser Beitrag hat sich zum Ziel gesetzt, die Nützlichkeit einer funktionell-strukturellen Methode für die Untersuchung von Mathematiklehrbüchern zu beweisen. Die Grundlage dazu bilden drei Quellen : Die Theorie der Sprachfunktionen von Duval, das Sprachfunktionsmodell von Jakobson sowie das Modell der semiotischen Strukturen von Richard. Nach Erläuterung unserer Ausgangsquellen bringen wir diese bei der Analyse zweier kurzer Texte aus Geometrielehrbüchern, wie sie an französischen Sekundarschulen in Québec in Gebrauch sind, zur Anwendung. Trotz der in beiden Texten enthaltenen undidaktischen Intention wird deutlich, wie die eingesetzten semiotischen Mittel für die Kommunikationsqualität mit dem potentiellen Leser eingesetzt werden

On the existence of stationary states during granular compaction

When submitted to gentle mechanical taps a granular packing slowly compacts until it reaches a stationary state that depends on the tap characteristics. The properties of such stationary states are experimentally investigated. The influence of the initial state, taps properties and tapping protocol are studied. The compactivity of the packings is determinated. Our results strongly support the idea that the stationary states are genuine thermodynamic states.Comment: to be published in EPJE. The original publication will be available at www.europhysj.or

Feshbach resonances in ultracold ^{6,7}Li + ^{23}Na atomic mixtures

We report a theoretical study of Feshbach resonances in $^{6}$Li + $^{23}$Na and $^{7}$Li + $^{23}$Na mixtures at ultracold temperatures using new accurate interaction potentials in a full quantum coupled-channel calculation. Feshbach resonances for $l=0$ in the initial collisional open channel $^6$Li$(f=1/2, m_f=1/2) + ^{23}$Na$(f=1, m_f=1)$ are found to agree with previous measurements, leading to precise values of the singlet and triplet scattering lengths for the $^{6,7}$Li$+^{23}$Na pairs. We also predict additional Feshbach resonances within experimentally attainable magnetic fields for other collision channels.Comment: 4 pages, 3 figure

Automating the Generation of High School Geometry Proofs using Prolog in an Educational Context

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing, beforehand, the possible ways to solve a problem. Hence the need for an automated theorem prover that provide proofs as they would be written by a student. To achieve this objective, logic programming is a natural tool due to the similarity of its reasoning with a mathematical proof by inference. In this paper, we present the core ideas we used to implement such a prover, from its encoding in Prolog to the generation of the complete set of proofs. However, when dealing with educational aspects, there are many challenges to overcome. We also present the main issues we encountered, as well as the chosen solutions.Comment: In Proceedings ThEdu'19, arXiv:2002.1189

Overview of the Development and Applications of a Conceptual Framework for Analyzing Benefits and Costs of On-Farm Food Safety and Environmental Farm Plans

This series of six reports entitled: "On-Farm Food Safety and Environmental Farm Plans: Identifying and Classifying Benefits and Costs" was initiated soon after the launch of the Agricultural Policy Framework (APF) in 2002. The APF recognized the importance of food safety and environmental concerns for the future growth of the agriculture and Agri-food sector. For this reason, Agriculture and Agri-Food Canada (AAFC) commissioned this series of reports to develop a conceptual framework to strengthen our understanding of the potential benefit and cost implications of On-farm Food Safety (OFFS) and Environmental Farm Plans (EFP) that were key components of the APF. The reports were prepared by a group of academics with extensive knowledge of the agriculture and Agri-food sector and issues related to food safety, traceability and the environment. The first report presents a summary of the findings in the five main reports in the series. The second report presents the conceptual framework that was developed to help identify qualitatively the potential benefits and costs that the various players in the agriculture and agri-food supply chain would face in implementing OFFS and EFP programs. The third report applies this framework to pork, the fourth, to beef, the fifth, to grains and the sixth, to dairy. In general, benefits and costs are divided into both demand and supply side effects. In addition, both public and private costs and benefits are considered, especially since they help indicate where a role for government might be required and where markets are not working as well as they might. Based on these preliminary qualitative assessments, the beef and pork sector have more to gain from HACCP-based OFFS and EFP initiatives, due to their ability to gain market share from marketing their products internationally, while the grains sector already benefits internationally from its high quality reputation and the dairy sector is restricted to produce only for the domestic market. However, more work is required in these areas to validate and quantify costs and benefits.Agribusiness, Agricultural and Food Policy, Environmental Economics and Policy, Food Consumption/Nutrition/Food Safety, Production Economics, Resource /Energy Economics and Policy,

Identification of differentially expressed genes from multipotent epithelia at the onset of an asexual development

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Scientific Reports 6 (2016): 27357, doi:10.1038/srep27357.Organisms that have evolved alternative modes of reproduction, complementary to the sexual mode, are found across metazoans. The chordate Botryllus schlosseri is an emerging model for asexual development studies. Botryllus can rebuild its entire body from a portion of adult epithelia in a continuous and stereotyped process called blastogenesis. Anatomy and ontogenies of blastogenesis are well described, however molecular signatures triggering this developmental process are entirely unknown. We isolated tissues at the site of blastogenesis onset and from the same epithelia where this process is never triggered. We linearly amplified an ultra-low amount of mRNA (<10ng) and generated three transcriptome datasets. To provide a conservative landscape of transcripts differentially expressed between blastogenic vs. non-blastogenic epithelia we compared three different mapping and analysis strategies with a de novo assembled transcriptome and partially assembled genome as references, additionally a self-mapping strategy on the dataset. A subset of differentially expressed genes were analyzed and validated by in situ hybridization. The comparison of different analyses allowed us to isolate stringent sets of target genes, including transcripts with potential involvement in the onset of a non-embryonic developmental pathway. The results provide a good entry point to approach regenerative event in a basal chordate.This work was supported by AFM Telethon grant (#16611), IRG Marie Curie grant (#276974), ANR (ANR-14-CE02-0019-01) and IDEX Super (INDIBIO). L.R. was supported by an UPMC-EMREGENCE grant and by a FRM grant (#FDT20140931163). A.C. was supported by a FRM grant (ING 20140129231)

Snow Observations from Space: an Approach to Map Snow Cover from Three Decades of Landsat Imagery Across Switzerland

Snow accumulation is one of the most important forms of water storage. The natural cycle of water is being increasingly influenced by climate change and will continue to change in the future. To understand the evolution of snow cover and to perfect its accurate detection UN Environment/GRID-Geneva and the University of Geneva have developed a Snow Detection tool called Snow Observations from Space for the Swiss Data Cube. The Snow Detection tool uses the C Function of Mask to identify snow pixels and then subsequently produces a normalized detection raster. Through further development, this tool will reach its full potential as an accurate method of detecting snow cover change for Switzerland