Adtones intelligently tailors mobile ads to users in developing countries and shares the revenue with them to subsidize their phone bills.

Adtones

Boston Consulting Group is a management consulting firm that advises businesses and organizations on strategy, transformation and growth.

Boston  Consulting Group

The BCG Henderson Institute applies insights from academic disciplines to the strategic challenges facing business, government and society.

BCG Henderson Institute

Bit Bio is a human synthetic biology enterprise, which reprograms human cells for use in research, drug discovery and cell therapy.

BitBio

Cancer Research UK supports scientific and medical research to help beat cancer sooner. It is the world's largest cancer research charity.

Cancer Research UK

The Centre for Defence Enterprise funds research that could lead to a capability advantage for the armed forces and national security.

Centre for  Defence Enterprise

The U.S. Defence Advanced Research Projects Agency makes pivotal investments in breakthrough technologies that benefit national security.

Defence Advanced  Research Projects Agency

The U.S. Defence Threat Reduction Agency funds research to prepare for and combat weapons of mass destruction and improvised threats. 

Defence Threat  Reduction Agency

The European Innovation Council funds world-class scientists and innovators to develop and accelerate disruptive technology businesses.

European  Innovation Council

Framework Programme 7 was created by the European Commission to fund scientific research and innovation in Europe and associated countries.

Framework Programme 7

The Garfield Weston Foundation supports a range of charities across the UK and the restoration and redevelopment of their buildings.

Garfield Weston  Foundation

Horizon 2020 was created by the European Commission to fund scientific research and innovation across Europe and other member countries.

Horizon 2020

Invenia is a company of scientists and engineers that uses machine learning to optimize complex decision making and reduce inefficiencies.

Invenia Labs

LIMS Ventures is the start-up incubator of the London Institute which accelerates projects with potential for widespread commercialization.

LIMS Ventures

The Medical Research Council, one of the seven UK Research Councils, supports basic and applied medical research throughout the UK.

Medical Research Council

The U.S. Office of Naval Research supports basic research and technology for future naval power and the preservation of national security.

Office of  Naval Research

The Pilgrim Trust supports the preservation of architecturally important buildings and historically significant artifacts and documents.

Pilgrim Trust

The Porter Foundation supports projects in education, the environment, culture, health and welfare that encourage excellence and innovation.

Porter Foundation

The Rose Foundation provides financial assistance to charities undertaking building restoration and development in and around London.

Rose Foundation

The Edward Harvist Trust supports organisations that improve the quality of life for local people in Westminster and other London boroughs.

Edward Harvist Trust

The European Commission Migration and Home Affairs supports research to ensure the security of the EU and cooperation with non-EU countries.

European Commission  Migration and Home Affairs

The London Institute for Mathematical Sciences

The generation of large graphs with a controllable number of short loops paves the way for building more realistic random networks.

Loopy random graphs

Rapid temperature cycling from one extreme to another affects the rate at which the mean particle size in solid or liquid solutions changes.

Microstructural coarsening

The London Institute marks the year’s successes at its Yuletide Winterfest, from 4pm on Friday 11 December—if it can get the spirits out.

Yuletide Winterfest

We have had joint research grants with over 50 universities and institutes from around the world, showcased in our new partners page.

Global partners

The Times welcomes the collaboration between biologists at Bit.Bio and physicists at the London Institute to crack cell reprogramming.

Bit.Bio cracks code

Yang Hui talks about how string phenomenology has led from differential geometry to computational geometry and now to machine learning.

Superstrings and AI

Our new approach to showcasing papers captures the main idea of each paper with an image and sentence and uses icons to indicate authors.

A new look for papers

Welcome to our new office manager Victoria Harrison. She’ll help integrate our Fellows, developers, postdocs, writers, accountant and Board.

Welcome Victoria

The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.

Deep layered machines

Most simple rules give rise to simple behaviours. But occasionally they generate surprisingly rich and varied dynamics. Some simple rules, such as Conway’s game of life, are even equivalent to a universal Turing machine and can compute any computable function. While applying simple rules is easy, deducing the rules from observed behaviour is both important and usually hard, as evidenced by the deduction of the laws of physics through science.
In this project we investigate different families of simple rules for discrete dynamics. We help classify elementary cellular automata by deducing general characteristics of their behaviour. We study the self-assembly of polyominoes and the reverse engineering of structures made from them. In simple models of competition, mathematical models help us track the long-term behaviour of a population.
Reverse engineering simple rules that generate desired behaviour can help us design efficient algorithms and low-cost methods for manufacturing. Understanding which rules give rise to dynamics that are neither fully stable nor entirely chaotic may help design systems for artificial life and synthetic biology.

Understanding complex dynamical behaviours generated by simple rules, such as cellular automata, polyominoes and models of competition.

Surprising results of simple rules

Bootstrap percolation originated as a simple cellular automata model of the spread of infection. Given a set of initially infected sites, in consecutive rounds sites become infected if they satisfy a certain infection rule, for example, more than a given number of their neighbours are infected. Percolation occurs if every node is eventually infected.
In this project we investigate the typical and extremal properties of bootstrap percolation for various infection rules and underlying networks. For sites that are initially randomly infected, we study the critical density of infection that leads to percolation. Alternatively, if the initial infected sites are set by hand, we study how many infected nodes are necessary to infect the whole network.
Bootstrap percolation can be used to model many real-life phenomena, such as pandemics, computer network failure, ferromagnetic behaviour, the spread of voting preferences and information processing in neural networks. A better mathematical theory will help us understand these processes and draw reliable conclusions well beyond what can be achieved through computer simulations.

Advancing the mathematical theory of bootstrap percolation, where active cells on a lattice with few active neighbours cease to be active.

Leaps in long-range connectivity

Modern medicine can access vast amounts of patient-specific data, such as individual genomes, blood bio-markers and medical images. But it fails to use this information effectively. Analysing next-generation data with previous-generation tools causes avoidable patient harm, misses clues to new treatments and contributes to the high failure rate of clinical trials.
In this project we create more powerful mathematical methods for predicting disease outcomes. Most present-day mathematical and machine learning methods have a common Achilles heel. When the amount of information becomes too large, they confuse real patterns with noise and miss the wood for the trees—a breakdown known as overfitting. Our approach to bypassing this is founded on treating topological patterns in medical data as constraints on a random graph ensemble.
More accurate clinical prediction reduces the likelihood of harmful, ineffective treatments and saves lives. Each doomed trial that gets stopped early by better analysis of preliminary data saves over £100m for health services and the drug industry. And rescuing failing trials by identifying appropriate drug recipients broadens the range of available drugs.

Creating powerful mathematical methods for predicting the outcomes of diseases that pinpoint the right treatments and speed up drug trials.

Mathematics for personalized medicine

Is space a continuum or is it composed of a discrete set of points? Once a purely philosophical question, there is now a pressing need to describe space and space-time as discretized in order to resolve quantum gravity. Yet despite sophisticated attempts at discretizing space, researchers have failed to construct even the simplest geometries.
In this project we investigate models of discrete space in which continuum-like behavior is recovered at large lengths. We show that if space is discrete, it must be disordered, and develop explicit recipes for growing disordered discrete space by sampling distributions of graphs at low temperature. We also pursue graph formulations of non-Euclidean metrics, especially the Minkowski metric from special relativity.
Models of discrete space and space-time could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of the real numbers, which has no direct observational support. They also set the stage for digital physics, in which information takes centre stage in describing the universe.

Creating discrete models of space and spacetime that appear continuous over long lengths and set the stage for non-continuum physics. 

Is continuous space an illusion?

Densely packed objects of a similar shape, from rocks to foams to spheres, have intrigued mathematicians since the ancients. The mechanical properties of these materials are determined by how big the gaps are between them—in particular, how close they are to their maximum random-packed density. Predicting this maximum, and how the material properties vary around it, is a geometric and physics challenge.
In this project we investigate the packing of spheres of the same size and mixtures of spheres with a range of sizes. While simulating packing is easy to program, the running time scales poorly with system size. To overcome this obstacle, we develop new mathematical techniques for determining the properties of dense packings using a simplified 1d model. This powerful approach captures essential features of higher-dimensional systems.
Understanding how objects fit closely together under pressure or by design is at the heart of materials science and branches of fluid dynamics. Predicting the behaviour of dense packings also sets the stage for reverse-engineering new composite materials to have desired properties.

Predicting the geometry and behaviour of densely packed objects in the natural and man-made worlds, from rocks to foams to spheres.

A private institutefor curiosity-drivenresearch

Mathematics for personalized medicine

Papers

Loopy random graphs

Papers

Microstructural coarsening

Events

Yuletide Winterfest

News

Global partners

NEWS

Bit.Bio cracks code

Events

Superstrings and AI

PAPERS

A new look for papers

PEOPLE

Welcome Victoria

Where we publish

Who's funding us