# Life, learning and emergence

Developing mathematical foundations for life and artificial life, machine intelligence, and other emergent phenomena that defy reductionism.

What is life? Darwin’s theory provides a qualitative understanding of evolution. But from a physics perspective, we don’t know how life got started in the first place. We investigate the thermodynamic basis for emergent self-replication and adaptation, of which biology is just one instance. Can this be used to engineer artificial digital life? Can evolution itself be made a predictive science?

How do we make intelligent machines? Far from approaching artificial general intelligence, AI is stuck in high-dimensional curve-fitting. We seek mathematical insights that could lead to more intelligent AI, such as causal reasoning, reusable functional modules, and a representation of the environment. We investigate ways to use computation and AI to automate the search for new mathematical insights. Are there fundamental limits to AI, and what might this tell us about human intelligence?

What are the emergent properties of digital and neural computation, and might this shed light on autonomy and free will? We study information processing at the genetic level and the functional architecture of gene regulatory networks. We seek a theoretical understanding of cell programming and how to infer programming sets. Is causality itself an emergent phenomenon, as we traverse across different organisational length scales?

## Related papers

### BERT enhanced with recurrence

The quadratic complexity of attention in transformers is tackled by combining token-based memory and segment-level recurrence, using RMT.

### Cell soup in screens

Bursting cells can introduce noise in transcription factor screens, but modelling this process allows us to discern true counts from false.

### Optimal electronic reservoirs

Balancing memory from linear components with nonlinearities from memristors optimises the computational capacity of electronic reservoirs.

### 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.

### Structure of genetic computation

The structural and functional building blocks of gene regulatory networks correspond, which tell us how genetic computation is organised.

### True scale-free networks

The underlying scale invariance properties of naturally occurring networks are often clouded by finite-size effects due to the sample data.

### Coexistence in diverse ecosystems

Scale-invariant plant clusters explain the ability for a diverse range of plant species to coexist in ecosystems such as Barra Colorado.

### Quick quantum neural nets

The notion of quantum superposition speeds up the training process for binary neural networks and ensures that their parameters are optimal.

### Tumour infiltration

A delicate balance between white blood cell protein expression and the molecules on the surface of tumour cells determines cancer prognoses.

### Breaking classical barriers

Circuits of memristors, resistors with memory, can exhibit instabilities which allow classical tunnelling through potential energy barriers.

### Channels of contagion

Fire sales of common asset holdings can whip through a channel of contagion between banks, insurance companies and investments funds.

### Cancer and coronavirus

Cancer patients who contract and recover from Coronavirus-2 exhibit long-term immune system weaknesses, depending on the type of cancer.

### I want to be forever young

The mortality equation governs the dynamics of an evolving population with a given maximum age, offering a theory for programmed ageing.

### Exact linear regression

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

### Biological logics are restricted

The fraction of logics that are biologically permitted can be bounded and shown to be tiny, which makes inferring them from experiments easier.

### In life, there are few rules

The bipartite nature of regulatory networks means gene-gene logics are composed, which severely restricts which ones can show up in life.

### Deep layered machines

The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.

### Replica analysis of overfitting

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

### Energy harvesting with AI

Machine learning techniques enhance the efficiency of energy harvesters by implementing reversible energy-conserving operations.

### Memristive networks

A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.

### Physics of networks

Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.

### One-shot statistic

One-shot analogs of fluctuation-theorem results help unify these two approaches for small-scale, nonequilibrium statistical physics.

### Information asymmetry

Network users who have access to the network’s most informative node, as quantified by a novel index, the InfoRank, have a competitive edge.

### Solvable memristive circuits

Exact solutions for the dynamics of interacting memristors predict whether they relax to higher or lower resistance states given random initialisations.

### Grain shape inference

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.

### Volunteer clouds

A novel approach to volunteer clouds outperforms traditional distributed task scheduling algorithms in the presence of intensive workloads.

### From ecology to finance

Bipartite networks model the structures of ecological and economic real-world systems, enabling hypothesis testing and crisis forecasting.

### Hierarchies in directed networks

An iterative version of a method to identify hierarchies and rankings of nodes in directed networks can partly overcome its resolution limit.

### Dirac cones in 2D borane

The structure of two-dimensional borane, a new semi-metallic single-layered material, has two Dirac cones that meet right at the Fermi energy.

### Quantum neural networks

We generalise neural networks into a quantum framework, demonstrating the possibility of quantum auto-encoders and teleportation.

### Debunking in a world of tribes

When people operate in echo chambers, they focus on information adhering to their system of beliefs. Debunking them is harder than it seems

### Memristive networks and learning

Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.

### Dynamics of memristors

Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.

### 3d grains from 2d slices

Moment-based methods provide a simple way to describe a population of spherical particles and extract 3d information from 2d measurements.

### Disentangling links in networks

Inference from single snapshots of temporal networks can misleadingly group communities if the links between snapshots are correlated.

### Quantum thermodynamics

Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.

### Worst-case work entropic equality

A new equality which depends on the maximum entropy describes the worst-case amount of work done by finite-dimensional quantum systems.

### Spectral partitioning

The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.

### Optimal growth rates

An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.

### Photonic Maxwell's demon

With inspiration from Maxwell’s classic thought experiment, it is possible to extract macroscopic work from microscopic measurements of photons.

### Eigenvalues of neutral networks

The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.

### Self-organising adaptive networks

An adaptive network of oscillators in fragmented and incoherent states can re-organise itself into connected and synchronized states.

### Optimal heat exchange networks

Compact heat exchangers can be designed to run at low power if the exchange is concentrated in a crumpled surface fed by a fractal network.

### Instability in complex ecosystems

The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.

### Form and function in gene networks

The structural properties of a network motif predict its functional versatility and relate to gene regulatory networks.

### Clusters of neurons

Percolation theory shows that the formation of giant clusters of neurons relies on a few parameters that could be measured experimentally.

### Bootstrap percolation models

A subset of bootstrap percolation models, which stabilise systems of cells on infinite lattices, exhibit non-trivial phase transitions.

### 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.

### A measure of majorization

Single-shot information theory inspires a new formulation of statistical mechanics which measures the optimal guaranteed work of a system.

### Structure and stability of salts

The stable structures of calcium and magnesium carbonate at high pressures are crucial for understanding the Earth's deep carbon cycle.

### From memory to scale-free

A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.

### Maximum percolation time

A simple formula gives the maximum time for an n x n grid to become entirely infected having undergone a bootstrap percolation process.

### Easily repairable networks

When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.

### Entanglement typicality

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

### Percolation on Galton-Watson trees

The critical probability for bootstrap percolation, a process which mimics the spread of an infection in a graph, is bounded for Galton-Watson trees.

### Random close packing fractions

Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.

### Multitasking immune networks

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

### Scales in weighted networks

Information theory fixes weighted networks’ degeneracy issues with a generalisation of binary graphs and an optimal scale of link intensities.

### 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.

### Bootstrapping topology and risk

Information about 10% of the links in a complex network is sufficient to reconstruct its main features and resilience with the fitness model.

### Weighted network evolution

A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.

### Hierarchical space frames

A systematic way to vary the power-law scaling relations between loading parameters and volume of material aids the hierarchical design process.

### Networks for medical data

Network analysis of diagnostic data identifies combinations of the key factors which cause Class III malocclusion and how they evolve over time.

### Robust and assortative

Spectral analysis shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize.

### Clustering inverted

Edge multiplicity—the number of triangles attached to edges—is a powerful analytic tool to understand and generalize network properties.

### 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.

### Shear elastic deformation in cells

Analysis of the linear elastic behaviour of plant cell dispersions improves our understanding of how to stabilise and texturise food products.

### Dynamics of Ising chains

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

### Diffusional liquid-phase sintering

A Monte Carlo model simulates the microstructural evolution of metallic and ceramic powders during the consolidation process liquid-phase sintering.

### Assessing self-assembly

The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.

### Random cellular automata

Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.