Counting the Solutions of an Equation without Solving it


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.

N. Hungerbühler, M. Wasem, An integral that counts the zeros of a function, Open Math, 2018

Cluster analysis for multivariate data in micropaleontology

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.

Ref: Dr Monica Constandache,
Ref: Dr Monica Constandache, “Morphometric study of porosity and morphology of fossil Globigerinoides, during the Late Oligocene and Early Pliocene”

Psychosocial risks due to perceived work-life conflict: role of some organizational and psychographic variables – An empirical study within a Swiss police force

In this study, we seek to identify the means available to a public organization to prevent work-life conflict in an environment unlikely to reconcile these two spheres: the police profession. To do this, we will seek to understand the impacts of certain organizational variables (the perception of autonomy, the demands of the task, social and organizational support) and a psychographic variable (the sense of coherence) on the perception of this conflict.

Our mixed methodology mobilizes different approaches: a quantitative study that allows data exploration and individualinterviews.


Structure and Dynamics of Niche-Overlap Graphs

food web

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.

Gas balloon dynamics


The Gordon Bennett race ( is the oldest and the most popular gas balloon race.

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.


See Fribourg Freiburg Challenge for some nice pictures and videos.

Jupyter: a datascience interactive platform

Jupyter logo

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 vs Relative Key Performance Indicator

key performance indicator

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.

Mechanical modeling of plant growth

Air quality investigations in new and renovated energy-efficient houses


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.

Mathematics at your service