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

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

Physicists and mathematicians discuss quantitative models of group dynamics and emergent behaviour on 30 Jan from 6:30 pm. All welcome.

Collective behaviour

Our new About section sets out the London Institute’s purpose and describes how it is curiosity-driven, collegiate and competitive.

New About section

The imaginary replica method provides a new approach for calculating the spectral properties of an ensemble of random regular loopy graphs.

Imaginary replica analysis

Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on. 

Recursively divisible nos.

We optimize Bayesian data clustering by mapping the problem to the statistical physics of a gas and calculating the lowest entropy state.

Replica clustering

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

Recursive innovation

In Open Access Government, the London Institute argues that Britain’s record of scientific leadership will continue regardless of Brexit.

Science and Brexit

A dinner and discussion about collective imagination, strategies for acting on multiple timescales and how to respond to distant threats.

Science of Business IV

On 2 Sep at 6pm, Marc Warner talks about how to manage the safety of embedded artificial intelligence in our Science and Society series.

How to keep AI safe

We’ve captured the inside and outside of our building in a series of photographs which shows off the extensive renovation of the Institute.

Building in pictures

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

Discrete geometry

An overview of our past and present seminars, symposia, business dinners and other events can be found in our new Events page.

Events

Our research projects range from AI to materials to finance to cosmology. An overview of all of them is shown in our new Projects page.

Projects

At our 3rd Science of Business dinner we discuss innovation, technological change and new ways to combat climate change.

Business dinner

By tracking the tags of our research papers in real time, we provide a comprehensive overview of what we are working on and what’s new.

Research interests

In the Times Higher Education magazine, the London Institute argues that “We need to challenge the university monopoly on research”.

LIMS in THE

Understanding collective creativity: anonymous collaboration under constrained freedom that transcends the creativity of the individual.

Collective creativity

The London Institute has been awarded Independent Research Organization status and can now compete for £7bn of annual government funding.

Becoming an IRO

The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than others.

Faster innovation

A simple solvable model of memristive networks suggests an analogy between the asymptotic states of memristors and the Ising model.

Memristive networks

Sir John Beddington joins the Institute’s board of trustees, bringing experience in sustainability, science policy and scientific ventures.

New Trustee

Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.

Network physics

Sir Roy Anderson joins the Institute’s board of trustees, bringing experience in defence, governance and mathematical bio-medicine.

You can help determine the most important research to advance. Any funds that you give for a project will be spent entirely on that project.

Kickscience

The mean dissipated work is proportional to a relative entropy between probability distributions over all possible values of work.

One-shot statistics

The distributions of size and shape of a material’s grains can be constructed from a 2D slice of the material and electron diffraction data.

Materials inference

A dinner and discussion about speeding up innovation, forecasting technological change and the collective action problem in climate change.

Science of Business III

The Institute’s Christmas Party continued into the small hours as members served their local delicacies and held a Meccano competition.

Christmas goes crackers

A dinner and discussion about commitment and flexibility, acting on multiple timescales and learning and forgetting in the age of AI.

Science of Business II

Thomas Fink barbeques a Texan lunch in the popular seminar room fireplace as the London Institute celebrates American Independence Day. 

Independence Day BBQ

Developing a mathematical theory of how trust trees grow and how we can traverse them to exploit trust corridors in society for searching.

Trust-based search

A dinner and discussion about applying principles from evolution and ecology to seemingly intractable problems in business and politics.

Science of Business I 

Scientists and businessmen discuss the use of blockchain technologies across cryptocurrencies, commerce and the analysis of private data.

Future of blockchain

Leaders in intelligence, defence, business and academia discuss the technology behind ransomware and the cryptocurrencies that fund it.

Ransomware

Physicists and neuroscientists and discuss how artificial neural networks can shed light on the working of their biological counterparts.

Neuroscience and AI

Reconstructing the 3D shape distribution of grains or other objects randomly packed together with access only to 2d slices  through them.

Dimension reconstruction

Creating a mathematical model of combinatorial innovation to understand how innovation rates can be influenced as components are acquired.

Structure of innovation

Designing optimal self-similar structures for compact counter-current heat exchangers to reduce heating costs and greenhouse emissions.

Fractal heat exchange

Charles Epstein talks about the longstanding fractious but fruitful relationship between pure mathematics and mathematical physics. 

Mathematics vs physics

Robin Ball talks about a theoretical model of fibers in which their elasticity and curliness produce the characteristic shape of a ponytail.

Ponytail physics

Understanding the physical nature of information and how it relates to energy transfer and new technologies that make use of these insights. 

Information physics

Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution.

Hypercube geometry

Doyne Farmer talks about what technology is and how it evolves and our improving ability to forecast technological change into the future. 

Evolution of technology

Tiziana Di Matteo talks about the interdependence of multifractal financial time series and a new way to understand and forecast them.

Multifractal finance

Mark Girolami talks about how information, inference and data analysis drives the digital revolution in part 7 of our Grand Tour of Science. 

Science of information

Neil Lambert talks about subatomic particles and the elusive search for a theory of everything in part 6 of our Grand Tour of Science.

High energy physics

Brian Sutton talks about the path to understanding life, molecular biology and synthetic biology in part 5 of our Grand Tour of Science.

DNA and the genome

Chris Pickard talks about how Nature’s mysterious non-determinism is captured by quantum mechanics in part 4 of our Grand Tour of Science. 

Quantum theory 

Vittorio Loreto talks about the dynamics of correlated novelties in the evolution of biological systems, human society and technology.

Correlated novelties

Andrew Green talks about the theory of relativity, cosmology and the structure of the universe in part 3 of our Grand Tour of Science.

Relativity and cosmology

Thomas Fink talks about radical new mathematical developments that set the stage for modern physics in part 2 of our Grand Tour of Science. 

Revolutions in maths 

Robert Farr talks about the emergence of science from astronomy and the rise of classical physics in part 1 of our Grand Tour of Science.

Classical science

John Biggins talks about how he solved the mystery of the chain fountain, in which a chain spontaneously leaps up as it flows out of a jar. 

The chain fountain

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

Bootstrap percolation

Forecasting the rate of technological progress by harnessing empirical regularities captured by Moore’s law and Wright’s law.

Technological progress

Thomas Fink talks about physicists’ inner drive to systematize the world around them and the role of imagination in building theories

Is physics creative? 

Using fractal, or self-similar, patterns to design the lightest possible load-bearing structures with new strength-to-mass scaling laws.

Fractal structures

Rob Farr talks about the physics of architecture and how self-similar mechanical structures can make seemingly impossible designs a reality.

Fractal architecture

A two-day workshop sponsored by the Air Force Office of Scientific Research on network security, game semantics and computational topology.

Cybersecurity

Developing a new approach to resilience in which mistakes and unexpected events are mitigated by easy repairs rather than redundancy.

Repairable not robust

Creating mathematical tools for characterizing the structure of ideal graphs and irregular networks, and the behaviour of processes on them.

Graph structure

The simplest model of dimension is the hypercube. When the coordinates are given by a binary string, the distance between two strings is the number of spelling mistakes between them. By considering strings made of up more than two symbols, and connecting strings that differ by just one spelling mistake, the hypercube can be generalized into Hamming graphs. In information theory, messages are sent as strings which are subject to errors in transmission. To correct these mistakes, variants of a string must code for the same message as the string itself. In this way error correction is deeply connected to partitioning the Hamming graph into compact clusters.
In this project, we investigate the spectral properties of subgraphs of the hypercube and Hamming graphs. By studying a diffusing population on these graphs, we develop an analogy between mutational robustness and the eigenvalues of subgraphs that code for the same phenotype.
The spectral theory of Hamming graphs has direct applications to the theory of neutral evolution, in which biological information is carried by strings of nucleotides or amino acids. It is also at the heart of Hamming and other error correcting codes, and Hamming graphs feature in association schemes in coding theory.

Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution. 

Point, line, square, cube, tesseract

Technological progress is widely acknowledged as the main driver of economic growth, so any method for forecasting technological change is potentially very useful. But given that technological progress depends on innovation—generally thought of as something new and unanticipated—forecasting it might seem to be an oxymoron. In fact there are several postulated laws for technological improvement, such as Moore’s law and Wright’s law, but these are technology-dependent and we do not know how confident to be in their predictions.
In this project we investigate how to combine the forecasts of many technologies to make reliable distributional forecasts for a given technology. We use network theory and time series analysis to analyse performance curves and the large historical records of patenting activity to map the progress of technological ecosystems into the future.
The ability to forecast technological change with specified uncertainties can provide a foundation for a theory of economic growth. It can also offer clear recommendations for sustainability investments, where long-term planning is key. From a policy perspective, our insights provide an objective point of comparison to expert forecasts, which can be biased by vested interests.

The future of technological progress

Developing radical new approaches to inference and automated decision making using advances in quantum information and statistical physics.

Point, line, square, cube, tesseract

The London Institute for Mathematical Sciences gives scientists freedom and support to make fundamental discoveries.

Collective behaviourEv

New About sectionNe

Imaginary replica analysisPa

Recursively divisible nos.Pa

Where we publish

Who's funding us