Abstract: Diffusely infiltrating gliomas in adults are currently classified into WHO grades I–IV, reflecting varying malignancy levels. Recent advances have led to a refined classification of diffusely infiltrating gliomas in adults into three groups: IDH-mutant, 1p/19q codeleted tumors (best prognosis), IDH-mutant, 1p/19q non-codeleted tumors (intermediate prognosis), and IDH wild-type tumors (poor prognosis). This study aims to use a deep learning (DL) image classification model on histopathology images from various cohorts to predict glioma grade, IDH status, and 1p/19q codeletion.

Abstract: In this study we introduce a novel deep learning model for denoising spatial transcriptomics RNA sequencing data, leveraging the power of optimal transport and graph attention mechanisms. We called our model Graph Attention with Optimal Transport, Transformers and Time diffusion (GO3T) which combines the mathematical accuracy of optimal transport to compute distance similarities with the dynamic learning capabilities of graph attention networks. This integration effectively mitigates noise and preserves spatial gene expression patterns. To validate our model's performance, we conducted a comprehensive benchmark against state-of-the-art methods such as GraphST, SpaGCN, and STAGATE as well as ScanPy. Our results demonstrate superior clustering metrics, highlighting the model's ability to maintain biological relevance.

Abstract: This document collects the work during the second year master internship at the Brain Institute of Paris (ICM) associated to the M2 master studied at Sorbonne University. The main objective has been the study and analysis of 2D and 3D brain cell images. More precisely, the segmentation and tracking of this cells as it can give essential information about the migration and behaviour of tumors. Several models for two-classes semantic segmentation have been compared in 2D datasets and instance segmentation has been performed using Mask-RCNN. Future work aims at expand it to 3D datasets working with different object representation like point clouds or meshes instead of stack images and perform tracking on both 2D and 3D datasets.

Abstract: The main objective of this work is the study of the fractional time diffusion equation. The Caputo fractional derivative will be used for this purpose. In the first part of the study a time scheme discretization will be applied to the fractional derivative, known as L1 scheme, and properties such as stability, consistency and convergence will be studied for classical solutions. The main result is the $O\left({\tau }^{2-\alpha }\right)$ error for solutions with adequate regularity, where alpha is the order of the fractional derivative. Later, in the next two sections the space discretization will be added, so we end up with two different schemes: implicit and explicit. The last one will be dismissed as the CFL consistency condition is too restrictive Closing the theoretical study, the next section is dedicated to weak solutions of the problem. Finally, last section is centered in the numerical study of the implicit scheme, using example solutions with and without sufficient regularity as to test if the errors are the ones derived from theory.