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Groups of participants will be supervised by lecturers or speakers for mini-projects in complement to the classes and theoretical or practical exercises will be discussed. Here is the list of mini-projects:
Mini Project 1: Exploration of squamous cell lung carcinoma dataset
The objective is to analyze and interpret various aspects of Squamous Cell Lung Carcinoma (SCC) using comprehensive multi-omics data to identify potential biomarkers, understand disease mechanisms, and explore therapeutic targets. We will obtain the dataset from The Cancer Genome Atlas (TCGA), which includes genomic, transcriptomic, proteomic, and clinical data. We will perform an Exploratory Data Analysis to identify patterns and correlations within the data, such as the distribution of mutations and differentially expressed genes, and try to correlate molecular findings with clinical parameters such as disease stage, patient demographics, and treatment outcomes.
Mini Project 2: Developing a mathematical model of Squamous Cell Lung Carcinoma
The objective is to create a mathematical model to simulate the TP53 pathway's role in Squamous Cell Lung Carcinoma to understand its impact on tumor suppression and therapeutic responses. The first aim is to identify key components of the TP53 pathway, including genes, proteins, and their interactions. Then, we will develop a differential equations model to describe the dynamics of TP53 activation, DNA damage response, and cellular outcomes, including feedback loops and regulatory mechanisms that influence TP53 activity.
Mini Project 3: A numerical simulation approach of osteoarthritis
The objective is to develop a numerical scheme in Freefem++ to simulate the spatial EPO/TNF-α interaction using medical images. We can first use ML to identify the osteoarthritis in the images, then mesh the images with Freefem++ and finally simulate the system of equations.
Mini Project 4: Predictive modeling of cholera outbreaks with spatial simulations
The objective is to create a mathematical model to simulate the spread of cholera bacteria in a geographic area, considering factors such as population density, water sources, and sanitation infrastructure to predict and mitigate outbreaks.
Mini Project 5: Using machine learning for infectious disease modeling
The objective is to use physics constrained machine learning to study infectious diseases that are modeled by systems of ordinary differential equations - so called "compartment models". The machine learning will be based on fully-connected neural networks with a loss function that combines data loss and a physics loss. The first loss term comes from observations and field measurements. The latter loss enforces respect of the ODE system. A wide variety of diseases can be studied, ranging from the simplest SIR model, to complicated models for Ebola, Dengue and Zika.
Mini Project 6: Automatic Differentiation with Julia
The objective is to start learning and using Julia, a programming language that leverages the best of C, Matlab, Fortran, Python and others. We will use it to investigate Automatic Differentiation (AD), an efficient technique to compute exact partial derivatives, up to machine precision. AD is currently used to solve many optimization problems and is based on Dual numbers, reals extended with an infinitesimal part. In this mini-project you are going to implement your own Julia library to do Automatic Differentiation and use it to address some optimization problems, including non-linear systems.
Mini Project 7: Parameters estimation and simulation of some PKPD models
The objective is to revisit the models studied in Annabelle’s lecture and develop your own programming code to simulate them. Using the resulting data, we will explore parameter estimation and delve into the simulation and analysis of the models.
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