peer reviewed / In the context of fundamental flow studies, experimental databases are expected to provide uncertainty margins on the measured quantities. With the rapid increase in available computational power and the development of high-resolution fluid simulation techniques, Direct Numerical Simulation and Large Eddy Simulation are increasingly...
Automorphisms of the free group can be classified using their index. A maximal index indicates that the automorphism is rich as it would be geometric or parageometric. Geometric group automorphisms have been widely studied and are generated "easily". This cannot be said for parageometric automorphisms. Or could it be ?! The aim of the presentation ...
To manipulate numbers, we need to represent them. A numeration system is nothing but a set of rules that enables us to write each number as a sequence of symbols belonging to an alphabet of digits. In combinatorics on words, such a sequence is called a word. A result of Parry, dating back to 1960 and now classical, allows us to describe the numerat...
peer reviewed
peer reviewed / We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in a 2023 paper by Mohanty, Greenbury, Sarkany, Narayanan, Dingle, Ahnert, and Louis, whose primary scope is the maximum mutational robustness in genotype-p...
This thesis mainly addresses two topics: the first focuses on parameter estimation while the second explores applications relevant to safety pharmacology and disease studies. Solving parameter estimation problems poses significant challenges, especially in dynamical systems characterised by a large number of equations and parameters. The difficulti...
peer reviewed / Unconstrained Binary Polynomial Programs (UBPs) are a class of optimization problems relevant in a broad array of fields. In this paper, we examine an example from communication engineering, namely low autocorrelation binary sequences and propose a new dynamic programming approach that is particularly effective on UBP instances that...
peer reviewed / We study the pointwise regularity of the Multifractional Brownian Motion and in particular, we get the existence of slow points. It shows that a non self-similar process can still enjoy this property. We also consider various extensions of our results in the aim of requesting a weaker regularity assumption for the Hurst function wit...
