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.

- Date
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- Journal
- Citations
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Graph theory

### Transitions in loopy graphs

The generation of large graphs with a controllable number of short loops paves the way for building more realistic random networks.

Inference

### Exact linear regression

Exact methods supersede approximations used in high-dimensional linear regression to find correlations in statistical physics problems.

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.

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.

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.

Biological networks

### Protein interaction experiments

Properties of protein interaction networks test the reliability of data and hint at the underlying mechanism with which proteins recruit each other.

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.

Graph theory

### Random graphs with short loops

The analysis of real networks which contain many short loops requires novel methods, because they break the assumptions of tree-like models.

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.

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.

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.

Graph theory

### Unbiased randomization

Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.

Biological networks

### What you see is not what you get

Methods from tailored random graph theory reveal the relation between true biological networks and the often-biased samples taken from them.

Statistical physics

### Dynamics of Ising chains

A transfer operator formalism solves the macroscopic dynamics of disordered Ising chain systems which are relevant for ageing phenomena.

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.