Moodle@Warwick

Topological Data Analysis (TDA) is an approach to data analysis based on techniques from algebraic topology. Topology is the study of properties of sets that are invariant under continuous deformations; it is concerned with concepts such as ``nearness'', ``neighbourhood'', and ``convergence''. Nowadays, topological ideas are an indispensable part of many fields of mathematics, ranging from number theory to partial differential equations. Algebraic topology, in particular, aims to understand topological properties of spaces through algebraic invariants. The premise of topological data analysis is that data there is an underlying topological structure to data. Familiar examples include clustering, where the aim is to subdivide data into different clusters, or ``connected components'', and connectivity in networks. In this module we introduce persistent homology, a powerful method for studying the topology of data. We discuss the theoretical foundations, as well as computational and algorithmic aspects and various applications. While the course is mainly theoretical in nature, you are encouraged to experiment using a range of available software and applications. The lecture material will be available as video recording and slides, and exercises will be published semi-regularly.

Intended Learning Outcomes

Upon completion of this module you should be able to:

• understand how topological information can be extracted from discrete data;
• use persistent homology to compute persistence diagrams and barcodes;
• explain the different parts of the persistent homology pipeline and the computational challenges involved;
• evaluate the stability and robustness of persistent homology computations;
• summarize different approaches to the topology of data and discuss applications

Literature

1. Steve Oudot. Persistence Theory: From Quiver Representations to Data Analysis. AMS 2015
2. Herbert Edelsbrunner and John Harer. Computational Topology, An Introduction. AMS 2010
3. Nina Otter, Mason A Porter, Ulrike Tillmann, Peter Grindrod & Heather A Harrington. A roadmap for the computation of persistent homology. 2017

More specialised sources and papers will be made available in time.

MD913 

This module will help you to gain a systematic understanding of the key issues in the design, statistical analysis and interpretation of the common types of epidemiological study.

• This module builds on the material covered by the module Epidemiology and Statistics (a prerequisite unless you can show evidence of equivalent knowledge/expertise), allowing you to further develop your research skills
• Learn about issues in the design, analysis and interpretation of: case-control studies; cohort studies; randomized controlled trials; and trial data meta-analyses
• Also, other practical issues in common epidemiological study designs (such as survey methods)
• This further module is of particular relevance to those studying a Masters in Public Health (MPH) and an MSc Research Methods in Health Sciences for whom Epidemiology and Statistics is a core module.

Welcome to the Research Methods in Clinical Education Module.

This module aims to ensure that you have a critical understanding of research methodology appropriate to clinical education, including qualitative, quantitative, multi-/mixed methods and ethical considerations.

You will need to draw on knowledge and skills from past modules, especially learning theories and your understanding of effective learning environments.

The Physical Biology of the Cell module is a core module of the MSc IBR, which underpins the MRC-funded IBR DTP.

The module aims to provide a physical sciences perspective to cellular biology and equip postgraduate students to begin a research career at the interface of biology and physics.

You will explore the basic physical concepts underlying the behaviour of biomolecules, dynamic cell processes, cellular structure and signalling events. You will learn how to estimate sizes, speed and energy requirements for a variety of biological processes and build simple explicit models to fit experimental data from cell biological experiments.

PBoC is about learning to ask and answer quantitative scientific questions in the realm of biophysical cell biology.

It is arguably possible to sask scientific questions that are not quantitative*, but in general, useful scientific ideas make quantitative predictions that can be tested by observation and experiment. And arguably again, the most powerful scientific ideas are those that make the firmest quantitative predictions, and can thereby be definitively disproved.

Our goal with this course is to equip you with a basic set of tools to think quantitatively about the biological world, design better (more incisive) experiments, and analyse and interpret your data in useful and formally correct ways.

On completing the module, you should be able to analyse and quantify physical biological properties and behaviours of living systems; formulate scientific questions by harnessing the core concepts of physical biology and design experiments that effectively address your scientific questions.

PBoC is designed to help you to think!  Your instructors will aim to make the material challenging, but accessible, and above all, interesting.