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

Yang-Hui He 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

We’re bringing mathematicians and biologists together to discuss novel techniques for modelling cell biology on Wednesday, 16th September.

Modelling cell biology

Simulating the molecular structure of materials under pressures so extreme that we are not yet able to study them in the laboratory.

Extreme pressure surprises

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.

Packing things into a crowded place

Networks represent interactions between multiple elements. Widely accessible and large data sets makes it easy to build networks, but extracting meaning from them remains a challenge. Part of the problem is that mathematical methods for characterizing networks are primitive and sundry. While the theory of graphs—idealized networks containing internal symmetry—is more advanced, the mathematical foundations for both networks and graphs, and their relation, are underdeveloped.
In this project we investigate new mathematical methods to describe the topology and geometry of networks and graphs, without regard to the kinds of data from which they are derived. The broad range of techniques under development include applications and extensions of spectral graph theory, tailored graph ensembles, replica methods, community detection and enumerative combinatorics.
A deeper understanding of network and graph structure underpins many other research endeavours. Examples range from biomedical data for personalized medicine to predicting behaviour from social interaction networks to the stability of interconnected financial institutions.

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

The structure of how things relate

Most real-world networks are either a snapshot of a graph that evolves over time, or one instance of a collection of related graphs. Some aspects of the graph are random while others—such as the connectivity or density of cycles—are fixed. The trick is to figure out which is which. By treating a graph as a random variable, it is possible to deduce the constraints by comparing the behaviour they give rise to with real data. This is hard, and nearly all random graphs that can be solved analytically are locally tree-like. But empirically we know that realistic graphs have short loops.
In this project we develop sophisticated mathematical methods for deducing the behaviour of graphs and processes on them. By treating topological patterns as constraints on a random graph ensemble, we go beyond the replica trick and cavity method to handle graphs with a finite fraction of short loops. We start with triangles, the “harmonic oscillator” of loopy random graphs, and proceed to larger loops, along the way introducing the imaginary replica technique.
The theory of tailored graph ensembles offers a deeper understanding of graph structure. It enables us to predict the null behaviour of neural and genetic regulatory networks and to detect network communities. It also offers an indirect approach to longstanding problems on lattices, like the 3D Ising model.

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

Artificial intelligence of graphs

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. 

A private institutefor curiosity-drivenresearch

Packing things into a crowded place

Events

Superstrings and AI

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A new look for papers

PEOPLE

Welcome Victoria

Papers

Deep layered machines

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