 Mathematical Modelling of Biological Systems Mathematical Modelling of Biological Systems

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Deep Learning in Life Science: Generative Models
Summer Semester

•    Introduction to common neural network structures
•    Convolutional Neural Networks
•    ResNets
•    Introduction of generative models
•    Application of generative models

Lectures and Practical Work: We start with a brief introduction to common neural network structures, such as Convolutional Neural Networks in general and ResNets in particular and show how to implement and train them. We introduce different concepts of generative models and the training objectives behind them. We apply generative models to toy data sets and to the important problem of Protein/RNA folding.

Deep Learning in Life Science: Representation Learning
Winter Semester

•    Introduction to common neural network structures
•    Convolutional Neural Networks
•    ResNets
•    Construction of loss functions
•    Analytical expressions
•    Methods for Representation Learning
•    Methods for learning the data hyperplane
•    Representation Learning

Lectures and Practical Work: We start with a brief introduction to common neural network structures, such as Convolutional Neural Networks in general and ResNets in particular and show how to implement and train them. We show how to construct loss functions and how to find analytical expressions for the asymptotically optimal solutions, using Variational Calculus. We introduce Contrastive Learning --and Self-supervised Learning in general --as methods for Representation Learning. We introduce Autoencoders--and Generative Models in general --as methods for learning the data hyperplane. We discuss why including prior knowledge is the key for the success of Machine Learning Methods in diagnostic and therapeutic applications. In the practical work we apply Representation Learning to detect heart arrhythmias from realtime series data of patients andanomalies in (medical) image data.

QBio103: Mathematical Fundamentals
Winter Semester (ab 2021/2022)

•    Basic Calculus
•    Equation Solving
•    Vector Spaces
•    Linear System of Equations
•    Eigenvalue Problems
•    Functions and Differentiation
•    Integration
•    Vector Analysis
•    Fourier Series

Content: In this first semester module, the students repeat and deepen basic arithmetic operations, systems of inequalities, and equation solving. They get introduced into Linear Algebra with focus on solving systems of linear equations. In addition, exponential and logarithmic functions are introduced and the basics of differential and integral calculus are explained. This course serves as preparation for the mathematics-intensive courses in the following semesters and is intended to bring all students to the same level of knowledge in order to compensate for possible differences in previous knowledge of mathematics.

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