arXiv subjects

Geneviève Rollet

Publications and source records attributed to Geneviève Rollet.

5 recordsLinked to original sources

arXiv2021

An analytical reconstruction formula with efficient implementation for a modality of Compton Scattering Tomography with translational geometry

In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.

math.NA↗

arXiv2020

Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography

In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system is made of a single detector rotating around a fixed source. Unlike some previous CST, no collimator is used at the detector. Such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the associated Radon transform is a family of double circular arcs. As first main theoretical result, an analytic inversion formula is established for this new Radon transform. This is achieved through the formulation of the transform in terms of circular harmonic expansion satisfying the consistency conditions in Cormack's sense. Moreover, a fast and efficient numerical implementation via an alternative formulation based on Hilbert transform is carried out. Simulation results illustrate the theoretical feasibility of the new system. From a practical point of view, an uncollimated detector system considerably increases the amount of collected data, which is particularly significant in a scatter imaging system.

math.NA↗

arXiv2016

On discrete evolutionary dynamics driven by quadratic interactions

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of specific changes of basis, we study the evolution and possible stability of some examples. We also consider some examples that cannot be treated using the framework of genetic algebras. Among these are bistochastic matrices.

q-bio.PE↗

arXiv2012

Classification of Non-Affine Non-Hecke Dynamical R-Matrices

A complete classification of non-affine dynamical quantum $R$-matrices obeying the ${\mathcal G}l_n({\mathbb C})$-Gervais-Neveu-Felder equation is obtained without assuming either Hecke or weak Hecke conditions. More general dynamical dependences are observed. It is shown that any solution is built upon elementary blocks, which individually satisfy the weak Hecke condition. Each solution is in particular characterized by an arbitrary partition ${{\mathbb I}(i), i\in{1,...,n}}$ of the set of indices ${1,...,n}$ into classes, ${\mathbb I}(i)$ being the class of the index $i$, and an arbitrary family of signs $(ε_{\mathbb I})_{{\mathbb I}\in{{\mathbb I}(i), i\in{1,...,n}}}$ on this partition. The weak Hecke-type $R$-matrices exhibit the analytical behaviour $R_{ij,ji}=f(ε_{{\mathbb I}(i)}Λ_{{\mathbb I}(i)}-ε_{{\mathbb I}(j)}Λ_{{\mathbb I}(j)})$, where $f$ is a particular trigonometric or rational function, $Λ_{{\mathbb I}(i)}=\sum\limits_{j\in{\mathbb I}(i)}λ_j$, and $(λ_i)_{i\in{1,...,n}}$ denotes the family of dynamical coordinates.

math-ph↗

arXiv2007

Parametrization of semi-dynamical quantum reflection algebra

We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by dynamical conjugation matrices, Drinfel'd twist representations and quantum non-dynamical $R$-matrices. They yield factorized forms for the monodromy matrices.

math.QA↗