Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.
Landau meets Kauffman
A new, simple approach to the critical Kauffman model with connectivity one sharpens the bounds on the number and length of attractors.
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.
Replica analysis of overfitting
Statistical methods that normally fail for very high-dimensional data can be rescued via mathematical tools from statistical physics.
We optimize Bayesian data clustering by mapping the problem to the statistical physics of a gas and calculating the lowest entropy state.
Exactly solvable random graphs
An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.
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.
Entropies of graph ensembles
Explicit formulae for the Shannon entropies of random graph ensembles provide measures to compare and reproduce their topological features.
A review of the achievements concerning typical bipartite entanglement for random quantum states involving a large number of particles.
Multitasking immune networks
The immune system must simultaneously recall multiple defense strategies because many antigens can attack the host at the same time.
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.
Tailored random graph ensembles
New mathematical tools quantify the topological structure of large directed networks which describe how genes interact within a cell.