Discrete Applied Mathematics and Applications in Personalised Medicine and Data Science

This intensive short course explores the power of Discrete Applied Mathematics and Optimization and its profound impact on solving complex, real-world problems in Personalised Medicine and Data Science. Led by Professor Pablo Moscato, a pioneer in the field, this course delves into advanced optimisation techniques, Memetic Algorithms, and innovative data analysis methods. Through a series of engaging lectures and hands-on tutorials, participants will gain a deep understanding of how to model, solve, and interpret challenging problems, from combinatorial optimisation (like the Vertex Cover, the Hitting Set, the K-Feature set Problem and others) to the discovery of hidden patterns in large datasets for precision medicine and business intelligence.

By the end of the course, participants will:

• Master foundational concepts in discrete applied mathematics, including how to augment human intuition using computational tools for complex problems.
• Apply advanced optimisation techniques, such as Memetic Algorithms, safe reduction rules, and heuristics, to solve challenging problems in data science based on combinatorial optimisation.
• Formulate and solve novel problems in data mining and feature selection for the analysis of datasets, including the Alpha-beta-K-feature set problem and L-pattern identification.
• Utilise combinatorial optimisation and information theory (e.g., Jensen-Shannon Divergence) to effectively understand progression of diseases, cluster, and order large datasets, with a focus on applications in personalised medicine.
• Develop practical skills in Symbolic and Continued Fraction Regression for extracting meaningful mathematical relationships and insights from complex data.

Topics:

• Augmenting Human Intuition with Discrete Optimisation: Introduction to how discrete mathematics and computational methods enhance human problem-solving, illustrated through cases like the Vertex Cover problem and its progress diagrams.
• Memetic Algorithms: Theory, Landscapes, and Applications: Delving into the pioneering work in Memetic Algorithms, their theoretical underpinnings, landscape analysis, and diverse applications in data mining, information-based medicine, and data science.
• Combinatorial Optimisation for Data Insight: In-depth exploration of challenging problems like Vertex Cover and Set Cover, including safe data reduction rules and heuristic design. This section will also cover how these methods enable understanding, visualisation, and clustering of large datasets, with specific relevance to precision medicine.
• Advanced Data Mining and Feature Selection: Focused examination of the Alpha-beta-K-feature set problem and its variations, alongside the L-pattern identification problem, highlighting their role in optimisation and data mining applications.
• Information Theory and Symbolic Regression for Knowledge Discovery: Moving beyond “black box” approaches, this section explores how information theory (e.g., Jensen-Shannon Divergence) and Symbolic/Continued Fraction Regression can be used to understand diseases, discover underlying statistical relationships, and provide robust data analysis, even when data labels are imperfect.

Relevance:

This course is ideally suited for students, early-career researchers, and professionals in computer science, data science, mathematics, engineering, bioinformatics, and computational biology. It is particularly relevant for those passionate about applying sophisticated mathematical and computational methods to derive actionable insights from data, solve complex optimisation challenges, and contribute to advancements in personalised medicine and data-driven decision-making.

Pre-requisites:

This course is designed to be accessible to participants with a solid foundation in computational and mathematical thinking. While no advanced training in specific algorithms is required, participants are expected to have:

• A basic understanding of university-level mathematics, set theory notation and introductory mathematical modelling concepts.
• Familiarity with high school-level algebra and functions (e.g., constraints, optimisation objectives).
• Prior exposure to programming will be highly important for hands-on sessions.
• A strong interest in applying advanced mathematical and computational methods to solve real-world problems.

All theoretical concepts will be illustrated with practical examples, and participants will engage in hands-on modelling and implementation during tutorial sessions.

Pre-Reading:

• Introduction to Discrete Mathematics and Optimisation:
  • A chapter on fundamental discrete mathematical concepts (e.g., graph theory basics, combinatorics) from an introductory textbook.
  • An overview of basic optimisation concepts, including problem types and solution approaches.
• Fundamentals of Algorithms and Data Structures:
  • Review of essential algorithms, including search, sorting, and basic graph algorithms.
  • Familiarity with computational complexity (e.g. P vs. NP ).
• Basic Programming for Scientific Computing: