#### Overview

The main objective of the journal MathematicS in Action is to promote the interactions of Mathematics with other scientific fields (Biology, Medicine, Economics, Computer Science, Physics, Chemistry, Mechanics,  Environmental sciences, Engineering sciences, etc.) by publishing articles at their interfaces. These articles must be useful and globally accessible to both communities. Thus, the journal favours articles written by ay least two authors, one of them being a mathematician, the other one belonging to another scientific community.

The papers should address modelling issues (conception, analysis and validation of models),  numerical and/or  experimental methods.

They should preferably include both a mathematical part and, at choice, numerical or experimental results.
They should be very pedagogical on the motivations and the expected impact in both disciplines.

Each submitted paper will be evaluated equally for its mathematical quality and for its interest  to the concerned application field. To be accepted a paper needs to be of the highest scientific quality, original, and strongly interdisciplinary.

The Journal is an electronic publication and all articles are freely available. However, each year a printed version is sent to a selection of libraries.

News - The journal MathS in Action calls for papers in the field of « High Performance Computing and Mathematics with industrial applications »

This journal, previously hosted by Cedram, is now web-published by the Centre Mersenne.
In 2019, Cedram has become the
Centre Mersenne for open scientific publishing, a publishing platform for scientific journals developed by Mathdoc.

#### Fixed-Size Determinantal Point Processes Sampling For Species Phylogeny

Determinantal point processes (DPPs) are popular tools that supply useful information for repulsiveness. They provide coherent probabilistic models when negative correlations arise and also represent new algorithms for inference problems like sampling, marginalization and conditioning. Recently, DPPs have played an increasingly important role in machine learning and statistics, since they are used for diverse subset selection problems. In this paper we use $k$-DPP, a conditional DPP that models only sets of cardinality $k$, to sample a diverse subset of species from a large phylogenetic tree. The tree sampling task is important in many studies in modern bioinformatics. The results show a fast mixing sampler for $k$-DPP, for which a polynomial bound on the mixing time is given. This approach is applied to a real-world dataset of species, and we observe that leaves joined by a higher subtree are more likely to appear.

Available online:

#### Heuristic imaging from generic projections: backprojection outside the range of the Radon transform

Reflective tomography is an efficient method for optical imaging in the visible and near infrared ranges. It computes empirical reconstructions based on algorithms from X-ray tomography. This subject introduces mathematical gaps to be filled, about the meaning of the reconstructions, and about their artifacts. To tackle these questions, we study more generally the filtered backprojection on projections outside the range of the Radon transform. We consider generic projections that can involve any kind of physical and geometric parameters. We claim that the backprojection contains partially the geometry of the original scene. More precisely, we compare the singularities of the backprojection with the singularities of a representation of the scene. This comparison of wavefront sets, inspired by studies of the artifacts in X-ray tomography, is based on microlocal analysis. It gives a precise meaning to the well-reconstructed geometry, describes the invisible parts, and the artifacts. We illustrate the heuristic and the analysis principle on canonical cases that belong to various fields: shape from silhouettes, constructible tomography, cloaking, reconstruction from cartoon images, imaging of occluded lambertian objects. Numerical results show the relevance of the heuristic and its analysis. In a word, this study provides a mathematical framework that covers the solver of reflective tomography, and exhibits an imaging method whose range of application is wide.

Available online: