A basic task in mathematics or mathematical modelling consists in solving equations. Since it is often times impossible to solve equations analytically, one is interested in understanding properties of the solution space of the equation, e.g. its cardinality. In this work we construct a method that allows to count the number of solutions of a real equation in one real variable without solving the equation. Based on geometric ideas, we construct an integral that counts the number of solutions to an equation under mild regularity assumptions.
In collaboration with a PhD student in micropaleontology and in order to understand the evolution of fossilized marine organisms, we conducted several statistical analyzes to determine whether the characteristic dimensions of these organisms allowed them to be grouped into different families. These analyzes were conducted for two distinct observation periods at different geographical locations.
This project was conducted during my PhD thesis: a joint collaboration between the University of Fribourg (Ecology and Informatics departments) and the HEIA-FR. Using a real dataset of niche-overlap graphs (graphs that depict the competition between species in the nature), we firstly developed a novel algorithm to detect efficiently chordless cycles and showed that these cycles are numerous in these graphs. Secondly, we investigated the structure of these networks using the theory of graphs. Finally, we simulated the abundance of species over time using systems of Lotka-Volterra differential equations and investigated the persistence of these species inside niche-overlap graphs networks using a generalized linear model.
We have developped a model that captures the trajectory of a gas balloon. With some sensors installed in the gondola we can anticipate potential instable atmospheric situations and predict the sand and gas consumption.
Moreover, we have developped tools to predict the trajectory of a balloon.
Under a collaboration between the ASAM Group and the Plastic Surgery Departments of Swiss University Hospitals, the ASAM group designed and implemented a databank intended to collect data related to bariatric surgery of a patient, as the pre and the post bariatric statuses, the prescribed treatments, the complications and others.
The ASAM Group has recently launched its Jupyter hub. The project intends to give students a set of interactive courses, as an introduction to the statistical software R. Thank Jupyter, one has the possibility to learn and test in a “live” environment line codes from different languages, as R, Python, Julia, etc. In the next years, the applied statistics master courses given by the ASAM Group will be each completed by Jupyter notebooks.
Absolute and relative change might be insufficient to meaningfully compare and interpret the sales volume of different sales channels. The goal of this project was to single out a meaningful indicator which is determined by some economically natural axioms and which allows to compare sales channels of different scales. The indicator proves to be interesting in its own right since it uncovers a relationship between marginal functions and economic elasticity and might be interpreted as a special kind of Cobb-Douglas-Function.
In order to study the air quality in houses, a large collection of data was carried out in new or renovated energy-efficient houses from Western Switzerland. The statistics consisted of analyzing questionnaires completed by the inhabitants as well as the measures of radon, volatile organic compounds and occurrence of molds. We had also to find which parameters (structure of the house, type of ventilation, maintenance,…) have an influence on a high level of radon, of volatile organic compound and mold.