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

  • MBM. BurtsevMRM. ReevesAJ MIT Sloan Management Review

    The limits of LLMs

    Large language models like ChatGPT can generate human-like text but businesses that overestimate their abilities risk misusing the technology.

  • DZDKFIMTDE... Meeting for the Association of Computational Linguistics

    DeepPavlov dream

    A new open-source platform is specifically tailored for developing complex dialogue systems, like generative conversational AI assistants.

  • Arxiv

    Cross-lingual knowledge

    Models trained on a Russian topical dataset, of knowledge-grounded human-human conversation, are capable of real-world tasks across languages.

  • Arxiv

    Speaking DNA

    A family of transformer-based DNA language models can interpret genomic sequences, opening new possibilities for complex biological research.

  • Submitted

    BERT enhanced with recurrence

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

  • Submitted

    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.

  • Submitted

    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.

  • Physical Review E

    Optimal electronic reservoirs

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

  • Arxiv

    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.

  • Submitted

    Structure of genetic computation

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

  • Proceedings of the National Academy of Sciences of the USA

    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.

  • Physical Review E

    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.

  • New Journal of Physics

    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.

  • Journal of Mathematical Biology

    Tumour infiltration

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

  • Science Advances

    Breaking classical barriers

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

  • Journal of Financial Stability

    Channels of contagion

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

  • Cancer Cell

    Cancer and coronavirus

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

  • Submitted

    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.

  • Physical Review E

    Exact linear regression

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

  • Draft

    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.

  • Physical Review Letters

    Deep layered machines

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

  • Journal of Physics A

    Replica analysis of overfitting

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

  • Journal of Physics A

    Replica clustering

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

  • Scientific Reports

    Energy harvesting with AI

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

  • EPL

    Memristive networks

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

  • Nature Reviews Physics

    Physics of networks

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

  • Physical Review E

    One-shot statistic

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

  • Journal of 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.

  • European Physical Journal B

    Solvable memristive circuits

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

  • Physical Review Materials

    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.

  • ACM Transactions on Modeling and Computer Simulation

    Volunteer clouds

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

  • Journal of Statistical Physics

    From ecology to finance

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

  • PLoS ONE

    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.

  • Physical Review B

    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.

  • npj Quantum Information

    Quantum neural networks

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

  • PLoS ONE

    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.

  • International Journal of Parallel, Emergent and Distributed Systems

    Memristive networks and learning

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

  • Physical Review E

    Dynamics of memristors

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

  • Mineralogical Magazine

    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.

  • Journal of Statistical Mechanics

    Disentangling links in networks

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

  • Proceedings of the Royal Society A

    Quantum jumps in thermodynamics

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

  • New Journal of Physics

    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.

  • Physical Review E

    Spectral partitioning

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

  • Physical Review E

    Optimal growth rates

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

  • Physical Review Letters

    Photonic Maxwell's demon

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

  • Discrete Mathematics

    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.

  • Scientific Reports

    Self-organising adaptive networks

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

  • Physical Review E

    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.

  • PLoS ONE

    Instability in complex ecosystems

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

  • Interface Focus

    Form and function in gene networks

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

  • Journal of Statistical Mechanics

    Clusters of neurons

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

  • Transactions of the American Mathematical Society

    Bootstrap percolation models

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

  • Journal of the Royal Society Interface

    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.

  • New Journal of Physics

    A measure of majorization

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

  • Physical Review B

    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.

  • EPL

    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.

  • SIAM Journal on Discrete Mathematics

    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.

  • Physical Review Letters

    Easily repairable networks

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

  • Journal of Physics A

    Entanglement typicality

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

  • Electronic Journal of Probability

    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.

  • Powder Technology

    Random close packing fractions

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

  • Journal of Physics A

    Multitasking immune networks

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

  • Social Informatics

    Scales in weighted networks

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

  • Journal of Physics A

    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.

  • Journal of Statistical Physics

    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.

  • Physical Review E

    Weighted network evolution

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

  • Mechanics Research Communications

    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.

  • PLoS ONE

    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.

  • EPL

    Robust and assortative

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

  • EPL

    Clustering inverted

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

  • Interface Focus

    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.

  • Food Biophysics

    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.

  • Philosophical Magazine

    Dynamics of Ising chains

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

  • Mathematics and Computers in Simulation

    Diffusional liquid-phase sintering

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

  • Physical Review E

    Assessing self-assembly

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

  • EPL

    Random cellular automata

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