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

In The Spectator, the London Institute talks about the value of basic science and what the British government should do to promote it.

Back to basics

Developing a theory of high-dimensional statistical inference using analytic tools from the statistical physics of disordered systems.

High-dimensional inference

Scientists discuss the potential of mathematical modelling in biology across problems in cell programming, immunology and gene regulation.

Modelling biology

Predicting the behaviour of graphs and processes on them by treating topological patterns as constraints on a random graph ensemble.

Intelligence of graphs

The London Institute and many of its papers have featured in the popular and scientific press. Our new Press section tells the story.

Fit to print

100 days in, our Twitter feed keeps you up to date on our papers, projects, events, press coverage and the shape of basic science in the UK.

100 days of Twitter

In Science Business, the London Institute welcomes the prospect of a UK DARPA and calls for faster funding schemes to support bold ideas.

Science post-Brexit

As well as research, we create games, build startups, invent traditions and develop tools for research and design—described in Diversions.

Diversions

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

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

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

The chain fountain

Capturing in simulations and mathematical form the surface structure of crystals and how they coalesce when heated but not melted.

At the surface of crystals

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

Slurries are fluids full of solid particles, like lava and ice cream. Their solid forms are made up of randomly oriented crystalline grains. Determining such materials’ 3D structures is tricky, requiring costly and tedious imaging techniques. One approach is x-ray tomography, where the structure is deduced by merging multiple 2D x-ray images taken at different angles. Another is an iterative imaging process, where a thin layer at the surface of a sample is repeatedly sliced off, and an image is acquired after each cut. 
In this project we develop a mathematical formalism for capturing the 3D structure of a material’s grains in a single shot. It allows for the quick measurement of the size and shape distribution of grains using just one 2D image and electron diffraction data. We verify our method on simulated materials consisting of randomly oriented ellipsoids and blocks, and test it on minerals. 
Our approach is applicable to any isotropic polycrystalline material, and will help geologists and materials scientists determine 3D structures at a fraction of the cost of current methods. It could shed light on fundamental processes of rock formation, help optimize oil extraction, and better connect percolation theory with geological percolation.

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

Deducing three dimensions from two

The design of efficient exchange devices is an important problem in engineering and biology. In industrial settings a variety of heat exchangers are employed, such as plate, coil and counter-current devices. In nature, lungs, leaf venation and blood circulation networks have evolved to meet multiple physiological needs. A distinctive feature of the biological examples is their fractal structure, with branching and usually anastomosing geometries. The fractal design provides a large surface for exchange but within a compact volume.
In this project we design optimal heat exchangers for industrial and domestic use that incorporate the design efficiencies of their biological counterparts. We develop a theory that links efficiency to the geometry of the exchange surface and supply network. By crumpling the exchange area into a fractal surface, our designs can be optimized for volume as well as performance. They are especially suited to 3D printing because they are not load bearing.
Optimal heat exchangers increase the efficiency of industrial processes and reduce the cost and size of passive heat exchange in houses. The underlying theory also provides insights into respiration, which may help develop diagnostic tests for breathing disorders.

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

Moving mass while keeping heat stationary

In modern statistical inference the number of inferred parameters often grows with the size of the data set. Inference in this high-dimensional regime is a serious challenge for classical statistics, which was developed for when the number of parameters is fixed. As a result, high-dimensional inference is often employed without understanding how it works. In the words of da Vinci, ‘he who loves practice without theory is like a sailor who boards a ship without rudder or compass and knows not where he is cast’.
In this project we use analytic tools from the statistical physics of disordered systems to develop a theory of high-dimensional statistical inference. The parameters of the statistical model play the role of the degrees of freedom and the likelihood of their values plays the role of energy. The inferred parameters correspond to the lowest energy state. Among other techniques, we harness the replica trick to average over the disorder embodied by the data.
A current problem with high-dimensional inference is the propensity to generate unsubstantiated and often unfalsifiable conclusions. A foundational theory will help discriminate between reliable and unreliable inference, as well as inform the design of efficient inference algorithms.

Deducing three dimensions from two

The London Institute for Mathematical Sciences is a private academic institute for curiosity-driven research.

Press

Back to basics

Projects

High-dimensional inference

Events

Modelling biology

Projects

Intelligence of graphs

Where we publish

Who's funding us