The London Institute’s papers are the official record of our discoveries. They allow others to build on and apply our work. Each one is the result of many months of research, so we strive to make them clear, inspiring and beautiful, and publish them in leading journals.

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AI-assisted maths

Learning 3-manifolds

3-manifolds represented as isomorphism signatures of their triangulations and associated Pachner graphs are analysed with machine learning.

YHYang-Hui HeFCEHEH
Journal of Physics A
Landau meets Kaufman
Statistical physics

Landau meets Kauffman

Insights from number theory suggest a new way to solve the critical Kauffman model, giving new bounds on the number and length of attractors.

FSForrest SheldonTFThomas Fink
Journal of Physics A
Image for the paper "Flowers of immortality"
Evolvability

Flowers of immortality

The eigenvalues of the mortality equation fall into two classes—the flower and the stem—but only the stem eigenvalues control the dynamics.

TFThomas FinkYHYang-Hui He
ArXiv
Image for the paper "Replica analysis of overfitting in generalized linear models"
Statistical physics

Replica analysis of overfitting

Statistical methods that normally fail for very high-dimensional data can be rescued via mathematical tools from statistical physics.

AMAlexander MozeikaFAFabrizio AntenucciACMSFL
Journal of Physics A
Inference, Statistical physics

Replica clustering

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

AMAC
Journal of Physics A
Graph theory

Exactly solvable random graphs

An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.

PBFLMFAC
Journal of Physics A
Statistical physics

Spin systems on Bethe lattices

Exact equations for the thermodynamic quantities of lattices made of d-dimensional hypercubes are obtainable with the Bethe-Peierls approach.

AMAC
Journal of Physics A
Graph theory

Entropies of graph ensembles

Explicit formulae for the Shannon entropies of random graph ensembles provide measures to compare and reproduce their topological features.

ERAC
Journal of Physics A
Quantum thermodynamics

Entanglement typicality

A review of the achievements concerning typical bipartite entanglement for random quantum states involving a large number of particles.

ODCLSMAS
Journal of Physics A
Biological networks

Multitasking immune networks

The immune system must simultaneously recall multiple defense strategies because many antigens can attack the host at the same time.

EAAAABACDT
Journal of Physics A
Mathematical medicine

Multi-tasking in immune networks

Associative networks with different loads model the ability of the immune system to respond simultaneously to multiple distinct antigen invasions.

EAAAABACDT
Journal of Physics A
Graph theory

Tailored random graph ensembles

New mathematical tools quantify the topological structure of large directed networks which describe how genes interact within a cell.

ERTSAC
Journal of Physics A