Category: Data Science

Human Blood Protein Atlas

A recent report in Science announced the publication of a new human blood protein atlas, describing the disease signatures of thousands of proteins circulating in the blood. Minimally invasive protein profiling marks a step forward in the personalisation of medicine. Some interesting statistical and machine learning techniques were employed.

Blood Protein Study

The researchers’ methods included a technique called proximity extension assay (PEA), which makes use of highly specific probes of DNA strands to detect minute concentrations of proteins in the blood plasma. Amplification with PCR (Polymerase Chain Reactions) allowed 5,416 proteins to be evaluated.

A longitudinal dataset showed dramatic changes as children passed through adolescence to adulthood. The central part of the study was a cross-sectional analysis, where age, sex and BMI were identified as important explanatory factors. The signatures of 59 clinically relevant diseases, in seven classes, can be viewed interactively in The Human Protein Atlas.

Into the secretome

Rather than the hideaway of a reclusive cockney, the secretome refers to the ensemble of secreted proteins. From a data science perspective, the challenge was how to find the signatures of a wide range of diseases, based on the differential abundance of over 5,400 proteins. This was complicated by the fact that many proteins elevated by a particular disease were also found to be elevated in other diseases.

“To investigate the distinct and shared proteomics signatures across diseases, we performed differential abundance analyses. Several groups were used as controls, including healthy samples, a disease background consisting of all other diseases, and samples from the same disease class.”

From The Human Protein Atlas

The differential abundance of proteins was evaluated using normalised protein expression units (NPX). The volcano chart above plots the p-values against the multiplicative (fold) change in NPX, both on log scales. The red values on the right were unusually high and the blue values on the left was exceptionally low.

The researchers used a logistic LASSO approach to identify the importance of proteins in providing a signature of each disease against its cohort. In the case of HIV above, CRTAM was the most significant explanatory factor, even though CD6 had the most extreme p-value.

How does logistic LASSO work?

A logistic model is trained on target values of one or zero, in this case representing the presence or absence of a disease. Least absolute shrinkage and selection operator (LASSO) is a version of linear regression that selects the most relevant explanatory variables using L1 regularisation. Adding the sum of the absolute values of the regression coefficients to the objective function forces the contribution of irrelevant variables towards zero as the hyper-parameter, λ, is increased. This property was particularly useful for the disease signature problem, where there were thousands of potential explanatory proteins.

The tricky aspect of LASSO is tuning the hyper-parameter, λ. You want it to be high enough to eliminate irrelevant variables, but not so high that it discounts the useful explanatory features. In the protein study, this was addressed using cross-validation: randomly splitting the data into 70:30 training and test sets, then rerunning the regression for a range of λ values. The quality of a model can be assessed in terms of both its accuracy and its required number of inputs, using criteria such as the Akaike information criterion or Bayesian information criterion, which favour parsimony. Repeating the randomisation 100 times, the researchers could home in on an optimal value of λ. The regression coefficients of the resulting model could then be used to rank the importance of the relevant proteins, as shown in the right hand side of the panel above.

Personalised health

The potential for a cheap, annual blood test to screen the whole population is immense. Proteomics adds to the arsenal of resources available to help people stay healthy. Early indications of diseases like cancer can be critical in initiating treatment. There is plenty of room to broaden the scope beyond the current 59 diseases, to include rarer conditions, such as Motor Neurone Disease, which has impacted some top sportsmen. It would be extremely helpful to find proteins related to the apparent epidemic of mental health issues, which are hard to define and lack objective, quantitative diagnostic criteria.

Round Britain By Bike

This morning I cheered on Bernard Bunting as he embarked on an epic tour Round Britain By Bike to raise money for the Rare Dementia Support Centre.

Bernard has set himself the impressive target of riding around the coastline of Britain. He will start and end at Putney Bridge in London, visiting 50 checkpoints along the way. This involves some serious route planning. The problem reminded me of the famous Travelling Salesmen Problem, where the challenge is to find the shortest route that visits each of a list of cities and returns to the starting point.

Bernard’s Checkpoints

Travelling Salesman Problem

Apart from cycling around Britain, the Travelling Salesman Problem is relevant in to circumstances, such as scheduling the order of supermarket deliveries or planning logistics for manufacturing processes. The problem is considered to be NP-hard, meaning that the number of combinations explodes exponentially as the number of cities increases. For example, considering only the order in which he passes the checkpoints, Bernard could set off for any of 49 destinations, then choose to go to any of 48 places, then one of the remaining 47 … before eventually returning to Putney Bridge, resulting in 49! (approximately 6.1 x 1062) possible routes. This makes it very hard to be absolutely sure that any particular route is the shortest. For most problems the best you can do is come up with a fairly good route.

Elastic band – a greedy approach

I have always imagined a quick way to find a reasonably good approach is to visualise the cities marked with pins on a map. You start by putting an elastic band around the outside (a convex hull). Then you consider all the points inside the band and pull the elastic in around the closest point. Repeat until you have all the points. This is approach is “greedy” in the sense that it only looks one step ahead when choosing the best option. It starts slowly, but gets faster as the number of remaining points is reduced.

Greedy elastic band algorithm for a route around Britain

Tweaking it

One problem with the simple greedy approach is that it sometime produces a path that crosses itself. This is inefficient because it is alway an uncrossed path as always shorter. Although it is very easy to spot a crossed path, writing an algorithm that makes sure no path crosses any other is quite time-consuming. A simpler approach is to step around the current route and reuse the original trick of finding the closest point to each edge. If it is better to divert to that point, update the route. Repeat until no improvements are found. Tweaking the route around Britain slightly reduced the overall length.

This is the tweaking process running on a more complicated problem involving 300 checkpoints. Once the initial route is built, the tweaking process reduces the path length from 15.01 to 14.44. Python code can be found on GitHub in my TSP repository.

Getting real

Although tweaking the result shortened the route around the 50 British checkpoints, it does not follow the coastline and it jumps directly from St Ives to Johnston in Wales. So this solution is not particularly useful for Bernard’s planning. Practical route finding must take account of roads and physical barriers.

Fortunately Bernard will be following his GPS route on his bike computer. He also has a printed card for each day. Let’s hope he doesn’t get lost.

You can follow Bernard on Strava and news will be posted on his website. Please consider supporting Bernard by making a donation.

Large Language Models for Cycling

Amid the fanfare about the extraordinary AI capabilities of large language models (LLMs), the race is on to produce LLM applications that actually do something useful. Several hurdles obstruct the way forward, including confabulation, privacy and limitations of training data. This article explains how Retrieval-Augmented Generation can address some of these issues and help find out some useful information about cycling.

Confabulation

Since they are trained only to predict the next word in a sentence, LLMs have no understanding of the text they generate. They can have a tendency to intersperse facts with inaccurate or untrue statements in a manner that seems entirely plausible and convincing. You should not rely on an LLM for advice on important decisions without validating its response. Note that if you ask an LLM for its sources, the citations may be imaginary or if they exist the references may not support the assertions.

One way to reduce the risk of confabulation is to ask the LLM to base its answer selected relevant documents.

Privacy

If you use an online ChatBot, everything you type or upload is stored on the provider’s server. This can be used as further training data or for snooping on users. There is a significant risk that a lot of personal and proprietary company information has already been hoovered up in this way. Companies need ways to sandbox internally developed LLM tools that contain sensitive data and prevent leakage of confidential information.

Privacy can be addressed by running LLMs on local networks. This is possible because inference is a simple task relative to training, which requires banks of data servers. Many free open-source models are available. Running an open-source model locally also avoids paying a subscription to an online provider.

Limitations of training data

LLMs are trained on vast generic data sets. This is a very expensive task, so they are typically frozen at some point in time. If you ask an LLM about current news events, it will typically tell you that it was trained on data up to a certain date in the past and has no knowledge of the event. The models may also lack specialised data in narrow domains.

RAG provides a way to supplement the original training set with selected additional information relevant to the field of interest.

RAG

Retrieval-Augmented Generation is an approach that provides an LLM with additional information to help it answer a query. For example, when asked about current affairs, it would be very helpful to retrieve a copy of today’s newspaper. Companies may wish to develop LLM-based applications with specialist knowledge of internal documentation. RAG makes this possible.

When you interact with an LLM, your conversation is presented to the model in the form of a huge string of numbers called an embedding. LLMs are trained so that sentences with similar words and meanings have similar embeddings. The idea of RAG is to take one or more relevant supplementary documents, split them up into chunks and store the embeddings of these chunks in a vector database. When a user presents a query, the database retrieves the embeddings of chunks that most closely match the query. In this way, the query can be augmented with relevant chunks of text from the source material. Note that this avoids the need to do additional expensive training or fine-tuning of the LLM on specialist topics.

One weakness of RAG is that most LLMs have not been trained specifically on the types of prompts used in RAG, though some companies, like Cohere, are working on this.

Cycling Through the Pandemic

I decided to try this out using a freely available book called Cycling Through the Pandemic, which has the slightly cryptic subtitle, Tactical Urbanism and the Implementation of Pop-Up Bike Lanes in the Time of COVID-19. This 250-page book was published in 2024, so it could not have been part of the training set for the LLM that I was using.

It is unbelievably easy to download and then run an open-source LLM on your local machine. All you need to do is download LM Studio. I decided to use an open-source LLM model called Meta-Llama-3.1-8B-Instruct-GGUF. I dragged and dropped the pdf of the book into the chat-box and started asking questions.

A transcript of my conversation is recorded below. At each step, LM Studio retrieved three chunks of text from the book it considered most relevant to the query, allowing me to check the reliability of the model’s interpretation.

The model answered in good English, basing its responses on the content of the book. It corrected itself when challenged on the claim that Bogotá is in France. It even responded in French to a question posed in French. In my view, RAG can be used to produce genuinely useful applications for LLMs.

RAG dialogue based on a book about the impact of COVID 19 on cycling

You
CyclingCOVID.pdf

What is tactical urbanism

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Intermediate steps hidden. Click to expand.

Based on the provided information, tactical urbanism refers to a type of urban planning that involves temporary and low-cost interventions aimed at introducing rapid changes to urban spaces with a broader purpose in mind (Lydon and Garcia 2015). It can be seen as a practical approach to urban change where many small actions implemented at the hyper-local level can achieve longer-term goals of creating a liveable, walkable, sustainable community.

Tactical urbanism often involves shortcuts or rapid and unbureaucratic actions taken by municipalities in response to crises (Citation 1). It can be associated with grassroots initiatives but can also be used by authorities. This approach has been implemented in various contexts, including during the COVID-19 pandemic.

Tactical urbanism is characterized by its focus on temporary and flexible material approaches to urban change, which can be both a practical tool for citizens and enterprising governments alike (Citation 3).

It’s worth noting that there are different perspectives on tactical urbanism, with some viewing it as a means of achieving substantive change without state action, while others see the increasing professionalization of these activities as borrowing their material design language (Citation 2).

You
Why was cycling boosted by COVID 19?

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Retrieved 3 relevant citations for user query
Done predicting
Cycling saw a boost during the COVID-19 pandemic for several reasons (Citation 2). Firstly, people had less need to travel due to home working and distance learning. Secondly, the fear of infection led to a strong decline in ridership on public transport, which benefited cycling. Additionally, active mobilities such as cycling were promoted as a means of staying fit and getting exercise when other recreational facilities were closed.

The pandemic also led to an increase in cycling for leisure activities (Buehler and Pucher 2021b), with the strongest increase seen on weekends and in the afternoon. This shift towards cycling as a leisure activity is likely due to the rise of “undirected travel,” or trips without a specific destination, which was encouraged by social distancing measures.

In France, for instance, the first COVID-19 related lockdown led to a rapid increase in cycling use (Buehler and Pucher 2022) and implemented temporary cycle paths. Governments saw cycling as a solution to develop health-friendly mobility while responding to the possible desertion of public transport due to fear of catching the virus (Citation 3).

You
Has the COVID related boost in cycling persisted

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Retrieved 3 relevant citations for user query
Done predicting
The survey conducted in Geneva and Lausanne (Rérat et al. 2022; Schmassman and Rérat 2022) found that the COVID-related boost in cycling has largely persisted. The majority of respondents reported cycling as much or more often than before the pandemic, with a significant number even starting to cycle for the first time.

In Geneva, 42% of respondents cycled as much as before, while 44% cycled more often. In Lausanne, 58% cycled as much as before, and 27% cycled more often. This suggests that many people have adopted cycling as a mode of transport during the pandemic and are likely to continue using it.

The fact that 81% of respondents in Geneva (73% in Lausanne) agree or strongly agree that COVID cycle lanes make them feel safer also suggests that these temporary infrastructure projects had a lasting impact on cyclist safety and behavior.

However, as mentioned by Citation 2, the long-term sustainability of this boost is still uncertain. The study notes that most cycling infrastructure implemented during the pandemic involved existing projects, and it remains to be seen whether this “leap forward” will make a lasting difference in the trajectory of local public action or simply represent a spike on an upward graph.

Overall, while there are indications that the COVID-related boost in cycling has largely persisted, further analysis is needed to determine its long-term impact.

You
What has been the impact specifically in London?

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Retrieved 3 relevant citations for user query
Done predicting
The impact of temporary cycling infrastructure and “Tactical Urbanist” approaches in London is a complex issue with both positive and negative effects.

Positive impacts include:

The introduction of School Streets, which have shown to promote mode shift towards active modes of travel (Hopkinson et al. 2021) and improve air quality at schools (Air Quality Consultants 2021).
The implementation of temporary cycle lanes and other small-scale projects aimed at improving the smaller residential or local streets in London.
These efforts are part of the Healthy Streets approach, which aims to promote a more sustainable transportation system in London.
However, there have also been negative impacts, including:

Variable outcomes between sites, with some schemes showing little effect (Citation 2).
Criticisms that some projects were implemented too quickly or without adequate consultation, leading to concerns about the speed and process of decision-making.
Vandalism of planters, bollards, and cameras used to prevent through-traffic in some areas (Citation 3).
Removal of Low Traffic Neighbourhoods, especially in Outer London, due to opposition from local residents.
The Temporary City report by Asa Thomas highlights the importance of balancing big change with small impact, emphasizing the need for careful planning and consultation when implementing new transportation projects.

You
What research was done in French cities?

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Retrieved 3 relevant citations for user query
Done predicting
The research on French cities during the COVID-19 pandemic focused on understanding how urban planners and policymakers implemented measures to promote cycling and improve public transportation.

A study examined five French cities: Grenoble, Lyon, Montpellier, Rennes, and Bogotá (Citation 1). The study found that these cities had varying levels of population size, density, and surface area. For example, Bogotá was the most populous city with over 7 million inhabitants, while Grenoble had a smaller population of around 160,000.

Another study looked at the implementation of measures in French cities during the pandemic (Citation 2). The research found that some cities focused on improving cycling infrastructure within the city center, such as Lyon and Rennes. In contrast, other cities prioritized links between periurban municipalities or outer suburbs.

A book titled “Changing Bikeability: Everyday Cycling in Developed Territories” explores changing bikeability in French cities during the pandemic (Citation 3). The book examines six French cities: Grenoble, Lyon, Montpellier, Paris, Rennes, and Saint-Étienne. The research found that each city had its unique characteristics and ways of implementing measures to promote cycling.

These studies provide insights into how different types of cities implemented measures to improve cycling infrastructure during the pandemic, and whether these measures were made permanent.

You
Is Bogotá in France?

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Retrieved 3 relevant citations for user query
Done predicting
No, Bogotá is not in France. According to Citation 1 and Citation 2, Bogotá is located in Colombia, and it has been compared with four French cities: Grenoble, Lyon, Montpellier, and Rennes.

In fact, the study mentioned in Citation 3 compares the cycling infrastructure in these four French cities (Grenoble, Lyon, Montpellier, and Rennes) with that of Bogotá, a city located in Colombia.

You
Quels ont été les résultats à Grenoble ?

Assistant
Meta-Llama-3.1-8B-Instruct-GGUF
Retrieved 1 relevant citations for user query
Done predicting
Les résultats obtenus à Grenoble sont mentionnés dans la citation :

“Nous avons contacté le Syndicat Mixte des Mobilités de l’Aire Grenobloise et réussi à obtenir la base de données du réseau cyclable. De plus, un stagiaire a effectué une interview avec un technicien de cette organisation, et sur plusieurs occasions, il est allé visiter le site pour voir si les voies temporaires (pop-up tracks) existaient toujours.”

Cela indique que les auteurs ont réussi à collecter des données sur le réseau cyclable de Grenoble en contactant la Syndicat Mixte des Mobilités de l’Aire Grenobloise et en effectuant une interview avec un technicien. Cependant, il n’y a pas d’information sur les résultats concrets de ces efforts.

Cependant, on peut trouver plus d’informations dans le graphique (Figure 8.2) qui montre différents types de voies temporaires installés dans les cinq villes étudiées, dont Grenoble.

39.77 tok/sec

•

234 tokens

•

3.34s to first token

•

Stop: eosFound

Cyclo-Social Networks

World Tour Rider Network

When Mexico’s Isaac del Toro and the Brit, Finlay Pickering, joined World Tour teams in 2024, they became part of an elite group. The structure of the professional cycling community differs from other types of social network, because the sport is organised around close-knit teams. You may have heard of the idea that everyone in the world is connected by six degrees of separation. Many social networks include key individuals who act as hubs linking disparate groups. How closely connected are professional cyclist? Which cyclists are the most connected?

Forming a link

An obvious way for cyclists to become acquainted is by being part of the same team. They spend long periods travelling, training, eating and relaxing together, often sharing rooms. Working as a team through the trials and tribulations of elite competition develops high degrees of camaraderie.

Each rider’s page on ProCyclingStats includes a team history. So I checked the past affiliations of all the current UCI world team riders. The idea was to build a graph where each node represented a rider, with edges connecting riders who had been in the same team. Each edge was weighted by the number of years a pair of riders had been in the same team, reflecting the strength of their relationship.

Cyclo-social network

The resulting graphical network, displayed at the top of this blog, has some interesting properties that reveal the dynamics of professional cycling. The 18 world tour teams are displayed in different colours. The size of each rider node is scaled by length of career. An experienced rider, like Geraint Thomas, has a larger node and more connections, which are shown as light grey lines, where the thickness represents years in the pair of riders were in the same team. Newer riders, with fewer connections tend to be on the periphery. For example, Isaac del Toro is the orange UAE Team Emirates rider at the top.

There are no fixed rules about how to represent the network, but the idea is that more closely related riders ought to congregate together. The network shows INEOS near UAE as shades of orange in the top right. Next we have Team Visma Lease a Bike in cyan, around two o’clock, close to Lidl – Trek in light green, Bahrain – Victorious in darker blue and Cofidis in lighter blue. Yellow Groupama – FDJ lies above the dark brown Jayco AlUla riders in the lower right. Red Movistar, light green Team dsm-firmenich PostNLand light blue BORA – Hansgrohe are near 6 o’clock, though Primož Roglič lies much closer to his old team. Decathlon AG2R La Mondiale is light blue in the lower left, near the darker blue of Alpecin – Deceuninck and pale green EF Education – EasyPost. Astana is orange, around nine o’clock. Dark blue Soudal Quick-Step, lighter blue Intermarché – Wanty and red Arkéa – B&B Hotels all hover around the top left. Teams that are more dispersed would be indicative of higher annual turnover.

3 degrees of separation

No rider is more than three steps from any other. In fact the average distance between riders is two steps, because the chances are that two riders have ridden with someone in common over their careers. Although the neo-pros are obviously more distantly connected, Isaac del Toro rides with Adam Yates, who spent six years alongside Jack Haig at Michelton Scott, but who now rides for Bahrain Victorious as a teammate of Finlay Pickering.

Bob Jungels is the most connected rider, having been a teammate of 100 riders in the current peloton. Since 2012, he has ridden for five different teams. He and Florian Senechal are only two steps from all riders. The Polish rider Łukasz Wiśniowski has been with six teams and has 94 links. Then we have Mark Cavendish with 91 and Rui Costa with 89.

In contrast, taking account of spending multiple years as teammates, Geraint Thomas tops the list with 218 teammate years. Interestingly, he is followed by Jonathan Castroviejo, Salvatore Puccio, Michal Kwiatkowski, Luke Rowe, Ben Swift, all long-time colleagues at INEOS Grenadiers. This suggests they are very happy (or well paid) staying where they are.

If we estimate “long-term team loyalty” by number of teammate years divided by number teammates, Geraint is top, followed by Salvatore Puccio, Michael Hepburn, Luke Durbridge, Luke Rowe, Simon Yates and Jasper Stuyven.

Best buddies

The riders who have been teammates for the longest are Luke Durbridge/ Michael Hepburn and Robert Gesink/Steven Kruijswijk both 15 years,
Geraint Thomas has ridden with Ben Swift and Salvatore Puccio for 14 years and Luke Rowe with Salvatore Puccio for 13.

Outliers

In a broader analysis that includes all the Pro Continental teams alongside the World Tour, the graph below shows a notable team of outliers. This is Team Novo Nordisk for athletes who compete with type 1 diabetes. Their Hungarian rider, Peter Kusztor, was the teammate of several current riders, such as Jan Tratnik, prior to joining Novo Nordisk, in a career that stretches back to 2006. The team is an inspiration to everyone affected by diabetes.

World Tour and Pro Continental Teams

Analysis

This analysis was performed in Python, using the NetworkX library.

Code can be found here.

Generating music videos using Stable Diffusion

Video generated using Stable Diffusion

In my last post I described how to generate a series of images by feeding back the output of a Stable Diffusion image-to-image model as the input for the next image. I have now developed this into a Generative AI pipeline that creates music videos from the lyrics of songs.

Learning to animate

In my earlier blog about dreaming of the Giro, I saved a series of key frames in a GIF, resulting in an attractive stream of images, but the result was rather clunky. The natural next step was to improve the output by inserting frames to smooth out the transitions between the key frames, saving the result as a video in MP4 format, at a rate of 20 frames per second.

I started experimenting with a series of prompts, combined with the styles of different artists. Salvador Dali worked particularly well for dreamy animations of story lines. In the Dali example below, I used “red, magenta, pink” as a negative prompt to stop these colours swamping the image. The Kandinsky and Miro animations became gradually more detailed. I think these effects were a consequence of the repetitive feedback involved in the pipeline. The Arcimboldo portraits go from fish to fruit to flowers.

Animations in the styles of Dali, Kandinsky, Miro and Arcimboldo

Demo app

A created a demo app on Hugging Face called AnimateYourDream. In order to get this to work, you need to duplicate it and then run it using a GPU on your Hugging Face account (costing $0.06 per hour). The idea was to try to recreate a dream I’d had the previous night. You can choose the artistic style, select an option to zoom in, enter three guiding prompts with the desired number of frames and choose a negative prompt. The animation process takes 3-5 minutes on a basic GPU.

For example, setting the style as “Dali surrealist”, zooming in, with 5 frames each of “landscape”, “weird animals” and “a castle with weird animals” produced the following animation.

Demo of my AnimateYourDream app on Hugging Face

Music videos

After spending some hours generating animations on a free Google Colab GPU and marvelling over the animations, I found that the images were brought to life by the music I was playing in the background. This triggered the brainwave of using the lyrics of songs as prompts for the Stable Diffusion model.

In order to produce an effective music video, I needed the images to change in time with the lyrics. Rather than messing around editing my Python code, I ended up using a Excel template spreadsheet as a convenient way to enter the lyrics alongside the time in the track. It was useful to enter “text” as a negative prompt and a sometimes helpful to mention a particular colour to stop it dominating the output. By default an overall style is added to each prompt, but it is convenient to change the style on certain prompts. By default the initial image is used as a “shadow”, which contributes 1% to every subsequent frame, in an attempt to retain an overall theme. This can also be overridden on each prompt.

Finally, it was very useful to be able to define target images. If defined for the initial prompt, this saves loading an additional Stable Diffusion text-to-image pipeline to create the first frame. Otherwise, defining a target image for a particular prompt drags the animation towards the target, by mixing increasing proportions of the target with the current image, progressively from the previous prompt. This is also useful for the final frame of the animation. One way to create target images is to run a few prompts through Stable Diffusion here.

Although some lyrics explicitly mention objects that Stable Diffusion can illustrate, I found it helps to focus on specific key words. This is my template for “No more heroes” by The Stranglers. It produced an awesome video that I put on GitHub.

Once an Excel template is complete, the following pipeline generates the key frames by looping through each prompt and calculating how many frames are required to fill the time until the next prompt for the desired seconds per frame. A basic GPU takes about 3 seconds per key frame, so a song takes about 10-20 minutes, including inserting a smoothing steps between the key frames.

Sample files and a Jupyter notebook are posted on my GitHub repository.

I’ve started a YouTube channel

Having previously published my music on SoundCloud, I am now able to generate my own videos. So I have set up a YouTube channel, where you can find a selection of my work. I never expected the fast.ai course to lead me here.

PyData London

I presented this concept at the PyData London – 76th meetup on 1 August 2023. These are my slides.

Percolating Python with ChatGPT

A YouTube video about “percolation” includes an interesting animation of shifting colours that exhibits a sudden phase transition. As a challenge, I set out to replicate the evolving pattern in Python. But then I remembered hearing that ChatGPT was good at writing code, so I asked it for help

Percolation

Percolation models can be used to simulate physical systems, such as liquids permeating through porous materials. The idea is to take a grid pattern of nodes with edges between them, and then remove edges at random. Each edge survives with a probability, p. If the edges were pipes, we could imagine that water could percolate through a well-connected grid (image on the left), but, as more edges are removed, the nodes form connected islands that prevent onward percolation (image on the right).

Connected grid
Sparsely connected

Asking ChatGPT

I started by asking ChatGPT to model a randomly connected lattice in Python. It suggested using a library called networkx that I have used in the past, so I pasted the code into a Jupyter notebook. The code worked, but the nodes were scattered at random, so I asked ChatGPT for code to produce a regular grid. This failed, so I passed the error message back to ChatGPT, which explained the problem and suggested revised code that worked perfectly, producing something like the left hand image above.

The next step was to apply the same colour to all connected nodes. Initially I called these clusters, but then I discovered that networkx has a method called connected_components, so I substituted this into ChatGPT’s code. After about half an hour, I had added more colours and some ipywidget sliders, to produce a fully working interactive model, where I could vary p and adjust the size of the grid.

The really interesting behaviour happens when p is around 0.5. Below this value the grid tends to form a disjoint set of unconnected islands, but above the critical value, the large areas quickly connect up. This image at the top of this blog occurs around the middle of the video below.

Percolation Model

Python code

This is the code if you want to try it yourself. You might need to pip install networkx and ipywidgets.

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
import random
from ipywidgets import interact

def randomLattice(p=0.5, n = 100):
    # Square grid m=n
    m=n
    # Create a 2D grid of nodes using NumPy
    nodes = np.array([(i, j) for i in range(m) for j in range(n)])

    # Convert the NumPy array to a list of tuples
    nodes = [tuple(node) for node in nodes]

    # Create an empty graph
    G = nx.Graph()

    # Add nodes to the graph
    G.add_nodes_from(nodes)

    # Connect adjacent nodes horizontally
    for i in range(m):
        for j in range(n-1):
            if random.random() < p:  # adjust the probability to control the connectivity
                G.add_edge((i, j), (i, j+1))

    # Connect adjacent nodes vertically
    for i in range(m-1):
        for j in range(n):
            if random.random() < p:  # adjust the probability to control the connectivity
                G.add_edge((i, j), (i+1, j))


    clusters = list(nx.connected_components(G))
    colours = ["b", "r", "g", "y", "m", "c", "k",'lime','cyan','violet','gold','indigo','navy','grey','peru']
    node_to_colour = {}
    for i, cluster in enumerate(clusters):
        for node in cluster:
            node_to_colour[node] = colours[i%len(colours)]
    #print(clusters)
    # Draw the graph as a regular grid
    pos = dict(zip(nodes, nodes))
    nx.draw(G, pos=pos, node_color=[node_to_colour[i] for i in nodes], 
            with_labels=False,node_size=20)
    #plt.savefig(f'Grid_{int(p*100):03d}.png')
    plt.show()
    return


interact(randomLattice,p=(0,1,0.01), n = (5,200,1));

Active Inference

Active Inference is a fascinating and ambitious book. It describes a very general normative approach to understanding the mind, brain and behaviour, hinting at potential applications in machine learning and the social sciences. The authors argue that the ways in which living beings interact with the environment can be modelled in terms of something called the free energy principle.

Active Inference builds on the concept of a Bayesian Brain. This is the idea that our brains continually refine an internal model of the external world, acting as probabilistic inference machines. The internal generative model continually predicts the state of the environment and compares its predictions with the inputs of sensory organs. When a discrepancy occurs, the brain updates its model. This is called perception.

But Active Inference goes further my recognising that living things can interact with their environments. Therefore an alternative way to deal with a discrepancy versus expectations is to do something that modifies the world. This is called action.

Variational Free Energy

Active Inference, Parr, Pezzulo, Friston

Either you change your beliefs to match the world or you change the world to match your beliefs. Active Inference makes this trade off by minimising variational free energy, which improves the match between an organism’s internal model and the external world.

The theory is expressed in elegant mathematical terms that lend themselves to systematic analysis. Minimising variational free energy can be considered in terms of finding a maximum entropy distribution, minimising complexity or reducing the divergence between the internal model and the actual posterior distribution.

Expected free energy

Longer term planning is handled in terms of expected free energy. This is where the consequences of future sequences of actions (policies) are evaluated by predicting the outcomes at each stage. The expected free energy of each policy is converted into a score, with the highest score determining the policy the organism expects to pursue. The process of selecting policies that improve the match with the priors pertaining to favoured states is called learning.

Planning is cast in terms of Bayesian inference. Once again the algebraic framework lends itself to a range of interpretations. For example, it automatically trades off information gain (exploration) against pragmatic value (exploitation). This contrasts with reinforcement learning, which handles the issue more heuristically, by trial and error, combined with the notion of a reward.

Applications

The book describes applications in neurobiology, learning and perception. Although readers are encouraged to apply the ideas to new areas, a full understanding of the subject demands the dedication to battle through some heavy duty mathematical appendices, covering Bayesian inference, partially observed Markov Decision Processes and variational calculus.

Nevertheless the book is filled with thought provoking ideas about how living things thrive in the face of the second law of thermodynamics.

Milan Sanremo in a Random Forest

  • Predicted top ten for Milan San Remo 2021

Last time I tried to predict a race, I trained up a neural network on past race results, ahead of the World Championships in Harrogate. The model backed Sam Bennett, but it did not take account of the weather conditions, which turned out to be terrible. Fortunately the forecast looks good for tomorrow’s Milan Sanremo.

This time I have tried using a Random Forest, based on the results of the UCI races that took place in 2020 and so far in 2021. The model took account of each rider’s past results, team, height and weight, together with key statistics about each race, including date, distance, average speed and type of parcours.

One of the nice things about this type of model is that it is possible to see how the factors contribute to the overall predictions. The following waterfall chart explains why the model uncontroversially has Wout van Aert as the favourite.

Breakdown of prediction for Wout van Aert

The largest positive contribution comes from being Wout van Aert. This is because he has a lot of good results. His height and weight favour Milan Sanremo. He also has a strong positive coming from his team. This distance and race type make further positive contributions.

We can contrast this with the model’s prediction for Mathieu van der Poel, who is ranked 9th.

Breakdown of prediction for Mathieu van der Poel

We see a positive personal contribution from being van der Poel, but having raced fewer UCI events, he has less of a strong set of results than van Aert. According to the model the Alpecin Fenix team contribution is not a strong as Jumbo Visma, but the long distance of the race works in favour of the Dutchman. The day of year gives a small negative contribution, suggesting that his road results have been stronger later in the year, but this could be due to last year’s unusual timing of races.

Each of the other riders in the model’s top 10 is in with a shout.

It’s taken me all afternoon to set up this model, so this is just a short post.

Post race comment

Where was Jasper Stuyven?

Like Mads Pedersen in Harrogate back in 2019, Jasper Stuyven was this year’s surprise winner in Sanremo. So what had the model expected for him? Scrolling down the list of predictions, Stuyven was ranked 39th.

Breakdown of prediction for Jasper Stuyven

His individual rider prediction was negative, perhaps because he has not had many good results so far this year, though he did win Omloop Het Nieuwsblad last year and had several top 10 finishes. The model assessed that his greatest advantage came from the length of the race, suggesting that he tends to do well over greater distances.

The nice thing about this approach is that that it identifies factors that are relevant to particular riders, in a quantitative fashion. This helps to overcome personal biases and the human tendency to overweight and project forward what has happened most recently.

Hexagons in the Arctic Circle

An attractive aspect of hexagonal patterns is that they can repeat in interesting ways across a cycling jersey. This is partly due to the fact that a hexagon can be divided up into three equal lozenge shapes, as seen near the neck of the top right jersey. These shapes can be combined in imaginative ways, as displayed in the lower two examples.

This three-way division of a hexagon can create a 3D optical illusion called a “Necker cube”, which can appear to flip from convex to concave and back again. The orange patch can appear to be the top of a cube viewed from above or the ceiling in a corner, viewed from below. See if this happens if you stare at the image below.

Looking down on a cube or up into the corner of a room?

Spoiler alert: from here things gets a bit mathematical

Tessellations

A tessellation, or tiling, is a way of covering a plane with polygons of various types. Tessellations have many interesting mathematical properties relating to their symmetries. It turns out that there are exactly 17 types of periodic patterns. Roger Penrose, who was awarded the 2020 Nobel Prize in Physics for his work on the formation of black holes, discovered many interesting aperiodic tilings, such as the Penrose tiling.

While some people were munching on mince pies before Christmas, I watched a thought-provoking video on a related topic, released by the Mathologer, Burkard Polster. He begins by discussing ways of tiling various shapes with dominoes and goes on describe something called the Arctic Circle Theorem. Around the middle of the video, he shifts to tiling hexagon shapes with lozenges, resulting in images with the weird 3D flipping effect described above. This prompted me to spend rather a lot of time writing Python code to explore this topic.

After much experimentation, I created some code that would generate random tilings by stochastically flipping hexagons. Colouring the lozenges according to their orientation resulted in some really interesting 3D effects.

Algorithm flips a random hexagon to create a new tiling.

Neckered

The video shows random tilings of a hexagonal area. These end up looking like a collection of 3D towers with orange tops. But if you focus on a particular cube and tilt your screen backwards, the whole image can flip, Necker-style into an inverted version where the floor becomes the ceiling and the orange segments push downwards.

I used my code to create random tilings of much bigger hexagons. It turned out that plotting the image on every iteration was taking a ridiculous amount of time. Suspending plotting until the end resulted in the code running 10,000 time faster! This allowed me to run 50 million iterations for a hexagon with 32 lozenges on each size, resulting in the fabled Arctic Circle promised by the eponymous theorem. The central area is chaotic, but the colours freeze into opposite solid patches of orange, blue and grey outside the circumference of a large inscribed circle.

Arctic Circle emerged on a hexagon of side 32 after 50 million iterations

Why does the Arctic Circle emerge?

There are two intuitive ways to understand why this happens. Firstly, if you consider the pattern as representing towers with orange tops, then every tower must be taller than the three towers in front of it. So if you try to add or remove a brick randomly, the towers at the back are more likely to become taller, while those near the front tend to become shorter.

Two examples of paths from left to right

The second way to think about it is that, if you look carefully, there is a unique path from each of the lozenges on the left hand vertical side to the corresponding lozenge on the right hand vertical side. At every step, each path either goes up (blue) or down (grey). The gaps between the various paths are orange. Each step of the algorithm flips between up-down and down-up steps on a particular path. On the large hexagon, the only way to prevent the topmost cell from being orange is for the highest path to go up (and remain blue) 32 times in a row. This is very unlikely when flips are random, though it can happen more often on a smaller size-6 hexagon like the one shown in the example.

Resources

A Jupyter notebook demonstrating the approach and Python code for running longer simulations are available on this GitHub page.

Back to cycling jerseys

The Dutch company DSM is proudly sponsoring a professional cycling team in 2021. And a hexagon lies at the heart of the DSM logo, that will appear on the team jerseys.

Pro cycling team networks

The COVID-19 pandemic has further exposed the weakness of the professional cycling business model. The competition between the teams for funding from a limited number of sponsors undermines the stability of the profession. With marketing budgets under strain, more teams are likely to face difficulties, in spite of the great advertising and publicity that the sport provides. Douglas Ryder is fighting an uphill struggle trying to keep his team alive after the withdrawal of NTT as a lead sponsor. One aspect of stability is financial, but another measure is the level of transfers between teams.

The composition of some teams is more stable than others. This is illustrated by analysing the history of riders’ careers, which is available on ProCyclingStats. The following chart is a network of the transfers between teams in the last year, where the yellow nodes are 2020 teams and the purple ones are 2019. The width of the edges indicates how many riders transferred between the teams, with the thick green lines representing the bulk of the riders who stuck with the same team. The blue labels give the initials of the official name of each team, such as M-S (Mitchelton-Scott), MT (Movistar Team), T-S (Trek-Segafredo) and TS (Team Sunweb). Riders who switched teams are labelled in red.

Although there is a Dutch/German grouping on the lower right, the main structure is from the outside towards the centre of the network.

The spikes around the end of the chart show riders like Geoffrey Soupe or Rubén Fernández, who stepped down to smaller non World Tour teams like Team Total Direct Energie (TTDE), Nippo Delko One Provence (NNDP), Euskaltel-Euskadi (E-E), Androni Giocattoli-Sidermec (AG-S ) or U-XPCT (Uno-X Pro Cycling Team).

The two World Tour outliers were Mitchelton-Scott (M-S) and Groupama FDJ (GF), who retained virtually all their riders from 2019. Moving closer in, a group of teams lies around the edge of the central mass, where a few transfers occurred. Moving anti-clockwise we see CCC Team (CT), Astana Pro Team (APT), Trek-Segafredo (T-S), AG2R Le Mondial (ALM), Circus-Wanty Gobert (C-WG), Team Jumbo Visma (TJV), Bora-Hansgrohe (B-H) and EF Pro Cycling (EPC).

Deeper in the mêlée, Ineos (TI_19/IG_20), Deceuninck – Quick Step (D-QS), UAE-Team Emirates (U-TE), Lotto Soudal (LS), Bahrain – McLaren (B-H) and Movistar Team(MT) exchanged a number of riders.

Right in the centre Israel Start-Up Nation (IS-UN) grabbed a whole lot of riders, including 7 from Team Arkéa Samsic (TAS). Meanwhile likes of Victor Campenaerts and Domenico Pozzovivo are probably regretting joining NTT Pro Cycling (TDD_19/NPC_20).

Looking forward

A few of the top riders have contracts for next year showing up on ProCyclingStats. So far 2020/2021 looks like the network below. Many riders are renewing with their existing teams, indicated by the broad green lines. But some big names are changing teams, including Chris Froome, Richie Porte, Laurens De Plus, Sam Oomen, Romain Bardet and Wilco Keldeman, Bob Jungels and Lilian Calmejane.

What about networks of riders?

My original thought when starting this analysis was that over their careers, certain riders must have been team mates with most of the riders in today’s peloton, so who is the most connected? Unfortunately this turned out to be ridiculously complicated, as shown in the image below, where nodes are riders with links if they were ever teammates and the colours represent the current teams. The highest ranked rider in each team is shown in red.

It is hard to make much sense of this, other than to note that those with shorter careers in the same team are near the edge and that Philippe Gilbert is close to the centre. Out of interest, the rider around 9 o’clock linking Bora and Jumbo Visma is Christoph Pfingsten, who moved this year. At least we can conclude that professional cyclists are well-connected.