Ian Wood

This project merges data science with culinary insight, analysing Michelin-starred restaurants across France. Using data from the Michelin Guide and INSEE along with geoJSON shape files, we explore the relationship between elite restaurants and socio-economic factors such as demographics, income, and population density. The project includes extensive data processing, geospatial integration, and year-on-year tracking of changes in Michelin star ratings. By visualising these relationships, the analysis offers valuable insights into how economic and geographic conditions influence culinary excellence.

In addition to data analysis, we developed a web-based interactive application using Plotly Dash. The app allows users to view restaurant details, including star ratings, cuisine types, and pricing, and filter results based on location and star rating. The app is updated annually, aligning with new data from the Michelin Guide. The app has been refined for maintainability and scalability by modularising the codebase and improving user interface elements.

This work earned 1st Place in the Plotly Autumn App Challenge 2024, demonstrating excellence in interactive dashboard development and data visualisation. The codebase for this award-winning app can be accessed on GitHub.

Overview: The Double Pendulum Simulation models the physics of a double pendulum from first principles using Lagrangian and Hamiltonian mechanics. The equations of motion are derived symbolically and integrated numerically, allowing users to interact with and simulate both simple and compound pendulums. The web application, built using Plotly Dash, provides an engaging and visual exploration of this chaotic system.

Future Development: In the development of the chaos page, we are tackling the challenge of performing the millions of floating-point calculations required for accurate simulations of chaotic systems. The goal is to create a cloud-based database capable of handling the vast amounts of data produced by simulations, enabling complex visualisations like Poincaré sections and bifurcation diagrams to be rendered dynamically. Future work involves refining numerical integration methods to optimise both accuracy and performance.

This project processes biodiversity data from the U.S. National Parks Service into a structured format suitable for PostgreSQL analysis. A key component is the Extract and Transform Pipeline, which handles the extraction and transformation of raw species data.

The modular design supports easy scalability, while logs, backups, and review files guarantee robust data management. The final PostgreSQL schema supports efficient, complex analytical queries using OLAP and geospatial data, enabling deep exploration of biodiversity trends across U.S. National Parks.

The Himmelblau function (illustrated) is a widely used benchmark in optimisation, defined as: \[ f(x, y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2 \] It features four local minimisers, making it an excellent test case for evaluating the robustness and accuracy of optimisation algorithms. These minima occur at: \[ \mathbf{x} = (3, 2), (-2.805, 3.131), (-3.779, -3.283), (3.584, -1.848) \] We benchmarked the solvers by starting from various initial guesses to examine their ability to converge to the nearest minimum.

• Newton-Raphson: Demonstrated rapid convergence in well-behaved regions but occasionally diverged near saddle points due to poor initial guesses.
• Levenberg-Marquardt: Handled poorly conditioned regions effectively, dynamically balancing between steepest descent and Newton-like behaviour.

Challenging functions provided valuable insights into the trade-offs between computational cost and robustness, emphasising the practical importance of careful algorithm selection for nonlinear problems.