Our 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 make a special effort to make our papers clear, inspiring and beautiful, and publish them in leading journals.
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AS
MD In press Physical Review AVortex bound states
Modelling the behaviour of two interacting bosonic particles in a chiral, dimerized optical lattice shows the pair form a vortex bound state.
Statistics
TF
DraftPaying for science
An analysis of UKRI grant funding gives a strategy for maximising unrestricted funds, thereby helping research centres cover their costs.
ES
SubmittedContinuous quivers
Continuous quivers enable exact Wilson loop calculation, reveal an emergent dimension, and raise tantalising questions on dual strings.
Quantum field theory
OG
ALMS Physical Review DPeculiar betas tamed
Inconsistencies between two approaches to deriving beta functions in two-dimensional sigma models are resolved by adding heavy superpartners.
Algebraic geometry
Schön complete intersections
A uniform approach to a class of varieties is described that includes important types of objects from geometry, optimisation and physics.
Algebraic geometry
Slight degenerations
The tools used to study polynomial equations with indeterminate coefficients are extended to some important cases with interrelated ones.
Condensed matter theory
Non-reciprocal breather
Producing the first examples of breathing solitons in one-dimensional non-reciprocal media allows their propagation dynamics to be analysed.
AI-assisted maths
On AI-driven discovery
Reviewing progress in the field of AI-assisted discovery for maths and theoretical physics reveals a triumvirate of different approaches.
AI-assisted maths
Triangulating polytopes
Machine learning generates desirable triangulations of geometric objects that are required for Calabi-Yau compactification in string theory.
AI-assisted maths
Learning to be Simple
Neural networks classify simple finite groups by generators, unlike earlier methods using Cayley tables, leading to a proven explicit criterion.
Neurocomputing
Spiky backpropagation
The training algorithm for digital neural networks is adapted and implemented entirely on an experimental chip inspired by brain physiology.
Condensed matter theory
Counting free fermions
A link between the statistical properties of free fermions in one dimension when either half- or alternating- states are initially occupied.
Representation theory
Group representation irreducibility
A general approach to proving the irreducibility of representations of infinite-dimensional groups within the frame of Ismagilov's conjecture.
Condensed matter theory
A kicked polaron
Modelling the final state of a mobile impurity particle immersed in a one-dimensional quantum fluid after the abrupt application of a force.
Gravity
Brightening black holes
Classical Kerr amplitudes for a rotating black hole derived using insights from recent advances in massive higher-spin quantum field theory.
Gravity
Spinning Root-Kerr
Two approaches that provide local formulae for Compton amplitudes of higher-spin massive objects in the quantum regime and classical limit.
Quantum field theory
PCM in arbitrary fields
The first exact solution for the vacuum state of an asymptotically free QFT in a general external field found for the Principal Chiral Model.
Algebraic geometry
Sparse singularities
Geometric properties, including delta invariants, are computed for singular points defined by polynomials with indeterminate coefficients.
Algebraic geometry
Permuting the roots
The Galois group of a typical rational function is described and similar problems solved using the topology of braids and tropical geometry.
AI-assisted maths
Clifford invariants by ML
Coxeter transformations for root diagrams of simply-laced Lie groups are exhaustively computed then machine learned to very high accuracy.
Condensed matter theory
Strange kinks
A new non-linear mechanical metamaterial can sustain topological solitons, robust solitary waves that could have exciting applications.
Machine learning
The limits of LLMs
Large language models like ChatGPT can generate human-like text but businesses that overestimate their abilities risk misusing the technology.
Number theory
Multiplicativity of sets
Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.
Linear algebra
Infinite parallelotope
We study the geometry of finite dimensional space as the dimension grows to infinity with an accent on the height of the parallelotope.
Combinatorics
The popularity gap
A cyclic group with small difference set has a nonzero element for which the second largest number of representations is twice the average.
Condensed matter theory
Mobile impurity
Explicit computation of injection and ejection impurity’s Green’s function reveals a generalisation of the Kubo-Martin-Schwinger relation.
AI-assisted maths
AI for cluster algebras
Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.
Number theory
Counting recursive divisors
Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.
Algebraic geometry
Bundled Laplacians
By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.
Representation theory
Infinite dimensional irreducibility
The criteria of irreducibility of representations of the inductive limit of certain general linear groups acting on three infinite rows.
Number theory
Recursive divisor properties
The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.
General relativity
Absorption with amplitudes
How gravitational waves are absorbed by a black hole is understood, for the first time, through effective on-shell scattering amplitudes.
Quantum field theory
Peculiar betas
The beta function for a class of sigma models is not found to be geometric, but rather has an elegant form in the context of algebraic data.
Machine learning
DeepPavlov dream
A new open-source platform is specifically tailored for developing complex dialogue systems, like generative conversational AI assistants.
AI-assisted maths
Computing Sasakians
Topological quantities for the Calabi-Yau link construction of G2 manifolds are computed and machine learnt with high performance scores.
Computational linguistics
Cross-lingual knowledge
Models trained on a Russian topical dataset, of knowledge-grounded human-human conversation, are capable of real-world tasks across languages.
Combinatorics
Representation for sum-product
A new way to estimate indices via representation theory reveals links to the sum-product phenomena and Zaremba’s conjecture in number theory.
Machine learning
Speaking DNA
A family of transformer-based DNA language models can interpret genomic sequences, opening new possibilities for complex biological research.
Algebraic geometry
Genetic polytopes
Genetic algorithms, which solve optimisation problems in a natural selection-inspired way, reveal previously unconstructed Calabi-Yau manifolds.
Condensed matter theory
Spin diffusion
The spin-spin correlation function of the Hubbard model reveals that finite temperature spin transport in one spatial dimension is diffusive.
Condensed matter theory
Spin-charge separation
A transformation for spin and charge degrees of freedom in one-dimensional lattice systems allows direct access to the dynamical correlations.
Statistical physics
Kauffman cracked
Surprisingly, the number of attractors in the critical Kauffman model with connectivity one grows exponentially with the size of the network.
Algebraic geometry
Analysing amoebae
Genetic symbolic regression methods reveal the relationship between amoebae from tropical geometry and the Mahler measure from number theory.
Combinatorics
Ungrouped machines
A new connection between continued fractions and the Bourgain–Gamburd machine reveals a girth-free variant of this widely-celebrated theorem.
Complex systems
Complex digital cities
A complexity-science approach to digital twins of cities views them as self-organising phenomena, instead of machines or logistic systems.
Number theory
Sum-product with few primes
For a finite set of integers with few prime factors, improving the lower bound on its sum and product sets affirms the Erdös-Szemerédi conjecture.
Group theory
On John McKay
This obituary celebrates the life and work of John Keith Stuart McKay, highlighting the mathematical miracles for which he will be remembered.
Machine learning
BERT enhanced with recurrence
The quadratic complexity of attention in transformers is tackled by combining token-based memory and segment-level recurrence, using RMT.
Number theory
Higher energies
Generalising the recent Kelley–Meka result on sets avoiding arithmetic progressions of length three leads to developments in the theory of the higher energies.
Combinatorics
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.
Number theory
Random Chowla conjecture
The distribution of partial sums of a Steinhaus random multiplicative function, of polynomials in a given form, converges to the standard complex Gaussian.
Algebraic geometry
Symmetric spatial curves
We study the geometry of generic spatial curves with a symmetry in order to understand the Galois group of a family of sparse polynomials.
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.
AI-assisted maths
AI for arithmetic curves
AI can predict invariants of low genus arithmetic curves, including those key to the Birch-Swinnerton-Dyer conjecture—a millennium prize problem.
Statistical physics
Multiplicative loops
The dynamics of the Kauffman network can be expressed as a product of the dynamics of its disjoint loops, revealing a new algebraic structure.
Synthetic biology
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.
Gravity
Black hole symmetry
Effective field theories for Kerr black holes, showing the 3-point Kerr amplitudes are uniquely predicted using higher-spin gauge symmetry.
Statistical physics
Network renormalization
Applying diffusion-based graph operators to complex networks identifies the proper spatiotemporal scales by overcoming small-world effects.
AI-assisted maths
Clustered cluster algebras
Cluster variables in Grassmannian cluster algebras can be classified with HPC by applying the tableaux method up to a fixed number of columns.
Number theory
Elliptical murmurations
Certain properties of the bivariate cubic equations used to prove Fermat’s last theorem exhibit flocking patterns, machine learning reveals.
Number theory
Bounding Zaremba’s conjecture
Using methods related to the Bourgain–Gamburd machine refines the previous bound on Zaremba’s conjecture in the theory of continued fractions.
String theory
World in a grain of sand
An AI algorithm of few-shot learning finds that the vast string landscape could be reduced by only seeing a tiny fraction to predict the rest.
Neurocomputing
Optimal electronic reservoirs
Balancing memory from linear components with nonlinearities from memristors optimises the computational capacity of electronic reservoirs.
String theory
Gauge theory and integrability
The algebra of a toric quiver gauge theory recovers the Bethe ansatz, revealing the relation between gauge theories and integrable systems.
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.
Combinatorics
Structure of genetic computation
The structural and functional building blocks of gene regulatory networks correspond, which tell us how genetic computation is organised.
Gravity
AI classifies space-time
A neural network learns to classify different types of spacetime in general relativity according to their algebraic Petrov classification.
String theory
Algebra of melting crystals
Certain states in quantum field theories are described by the geometry and algebra of melting crystals via properties of partition functions.
Combinatorics
Set additivity and growth
The additive dimension of a set, which is the size of a maximal dissociated subset, is closely connected to the rapid growth of higher sumsets.
AI-assisted maths
Machine learning Hilbert series
Neural networks find efficient ways to compute the Hilbert series, an important counting function in algebraic geometry and gauge theory.
AI-assisted maths
Line bundle connections
Neural networks find numerical solutions to Hermitian Yang-Mills equations, a difficult system of PDEs crucial to mathematics and physics.
AI-assisted maths
Calabi-Yau anomalies
Unsupervised machine-learning of the Hodge numbers of Calabi-Yau hypersurfaces detects new patterns with an unexpected linear dependence.
String theory
Mahler measure for quivers
Mahler measure from number theory is used for the first time in physics, yielding “Mahler flow” which extrapolates different phases in QFT.
Number theory
Recursively divisible numbers
Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on, recursively.
AI-assisted maths
Learning the Sato–Tate conjecture
Machine-learning methods can distinguish between Sato-Tate groups, promoting a data-driven approach for problems involving Euler factors.
Machine learning
Universes as big data
Machine-learning is a powerful tool for sifting through the landscape of possible Universes that could derive from Calabi-Yau manifolds.
Network theory
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.
Number theory
Reflexions on Mahler
With physically-motivated Newton polynomials from reflexive polygons, we find the Mahler measure and dessin d’enfants are in 1-to-1 correspondence.
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.
Statistical physics
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.
Neural networks
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.
Quantum physics
Going, going, gone
A solution to the information paradox uses standard quantum field theory to show that black holes can evaporate in a predictable way.
Mathematical medicine
Tumour infiltration
A delicate balance between white blood cell protein expression and the molecules on the surface of tumour cells determines cancer prognoses.
Neurocomputing
Breaking classical barriers
Circuits of memristors, resistors with memory, can exhibit instabilities which allow classical tunnelling through potential energy barriers.
String theory
QFT and kids’ drawings
Groethendieck's “children’s drawings”, a type of bipartite graph, link number theory, geometry, and the physics of conformal field theory.
Machine learning
Neurons on amoebae
Machine-learning 2-dimensional amoeba in algebraic geometry and string theory is able to recover the complicated conditions from so-called lopsidedness.
Group theory
New approaches to the Monster
Editorial of the last set of lectures given by the founder, McKay, of Moonshine Conjectures, the proof of which got Borcherds the Fields Medal.
Network theory
Physics of financial networks
Statistical physics contributes to new models and metrics for the study of financial network structure, dynamics, stability and instability.
Economic complexity
Channels of contagion
Fire sales of common asset holdings can whip through a channel of contagion between banks, insurance companies and investments funds.
Financial risk
Risky bank interactions
Networks where risky banks are mostly exposed to other risky banks have higher levels of systemic risk than those with stable bank interactions.
Mathematical medicine
Cancer and coronavirus
Cancer patients who contract and recover from Coronavirus-2 exhibit long-term immune system weaknesses, depending on the type of cancer.
Particle physics
Scale of non-locality
The number of particles in a higher derivative theory of gravity relates to its effective mass scale, which signals the theory’s viability.
Evolvability
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.
Inference
Exact linear regression
Exact methods supersede approximations used in high-dimensional linear regression to find correlations in statistical physics problems.
Combinatorics
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.
Number theory
Energy bounds for roots
Bounds for additive energies of modular roots can be generalised and improved with tools from additive combinatorics and algebraic number theory.
Number theory
Ample and pristine numbers
Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.
Financial markets
Network valuation in finance
Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.
Neural networks
Deep layered machines
The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.
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.
Theory of innovation
Taming complexity
Insights from biology, physics and business shed light on the nature and costs of complexity and how to manage it in business organizations.
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.
Theory of innovation
Recursive structure of innovation
A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.
Network theory
Bursting dynamic networks
A mathematical model captures the temporal and steady state behaviour of networks whose two sets of nodes either generate or destroy links.
Economic complexity
Renewable resource management
Modern portfolio theory inspires a strategy for allocating renewable energy sources which minimises the impact of production fluctuations.
Thermodynamics
Energy harvesting with AI
Machine learning techniques enhance the efficiency of energy harvesters by implementing reversible energy-conserving operations.
Geometry
Geometry of discrete space
A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.
Neurocomputing
Memristive networks
A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.
Statistical physics
Physics of networks
Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.
Theory of innovation
The rate of innovation
The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than other sectors.
Thermodynamics
One-shot statistic
One-shot analogs of fluctuation-theorem results help unify these two approaches for small-scale, nonequilibrium statistical physics.
Complex networks
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.
Quantum physics
A Hamiltonian recipe
An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.
Neurocomputing
Solvable memristive circuits
Exact solutions for the dynamics of interacting memristors predict whether they relax to higher or lower resistance states given random initialisations.
Inference
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.
Ignoble research
Volunteer clouds
A novel approach to volunteer clouds outperforms traditional distributed task scheduling algorithms in the presence of intensive workloads.
Financial networks
From ecology to finance
Bipartite networks model the structures of ecological and economic real-world systems, enabling hypothesis testing and crisis forecasting.
Graph theory
Hypercube eigenvalues
Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.
Technological progress
Forecasting technology deployment
Forecast errors for simple experience curve models facilitate more reliable estimates for the costs of technology deployment.
Financial networks
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.
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.
Financial networks
The interbank network
The large-scale structure of the interbank network changes drastically in times of crisis due to the effect of measures from central banks.
Theory of innovation
The science of strategy
The usefulness of components and the complexity of products inform the best strategy for innovation at different stages of the process.
Theory of materials
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.
Financial risk
Modelling financial systemic risk
Complex networks model the links between financial institutions and how these channels can transition from diversifying to propagating risk.
Mathematical medicine
Bayesian analysis of medical data
Bayesian networks describe the evolution of orthodontic features on patients receiving treatment versus no treatment for malocclusion.
Theory of innovation
The secret structure of innovation
Firms can harness the shifting importance of component building blocks to build better products and services and hence increase their chances of sustained success.
Neural networks
Quantum neural networks
We generalise neural networks into a quantum framework, demonstrating the possibility of quantum auto-encoders and teleportation.
Network theory
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.
Neurocomputing
Memristive networks and learning
Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.
Neurocomputing
Dynamics of memristors
Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.
Financial networks
Bipartite trade network
A new algorithm unveils complicated structures in the bipartite mapping between countries and products of the international trade network.
Sphere packing
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.
Complex systems
Disentangling links in networks
Inference from single snapshots of temporal networks can misleadingly group communities if the links between snapshots are correlated.
Thermodynamics
Quantum jumps in thermodynamics
Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.
Financial markets
Financial network reconstruction
Statistical mechanics concepts reconstruct connections between financial institutions and the stock market, despite limited data disclosure.
Financial risk
Pathways towards instability
Processes believed to stabilize financial markets can drive them towards instability by creating cyclical structures that amplify distress.
Thermodynamics
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.
Theory of innovation
Serendipity and strategy
In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.
Graph theory
Spectral partitioning
The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.
Complex networks, Financial risk
Non-linear distress propagation
Non-linear models of distress propagation in financial networks characterise key regimes where shocks are either amplified or suppressed.
Financial risk
Immunisation of systemic risk
Targeted immunisation policies limit distress propagation and prevent system-wide crises in financial networks according to sandpile models.
Complex networks
Optimal growth rates
An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.
Quantum computing
Tunnelling interpreted
Quantum tunnelling only occurs if either the Wigner function is negative, or the tunnelling rate operator has a negative Wigner function.
Financial risk
The price of complexity
Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.
Thermodynamics
Photonic Maxwell's demon
With inspiration from Maxwell’s classic thought experiment, it is possible to extract macroscopic work from microscopic measurements of photons.
Graph theory
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.
Network theory
Cascades in flow networks
Coupled distribution grids are more vulnerable to a cascading systemic failure but they have larger safe regions within their networks.
Percolation theory
Self-organising adaptive networks
An adaptive network of oscillators in fragmented and incoherent states can re-organise itself into connected and synchronized states.
Thermodynamics
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.
Financial markets
Instability in complex ecosystems
The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.
Discrete dynamics
Form and function in gene networks
The structural properties of a network motif predict its functional versatility and relate to gene regulatory networks.
Percolation theory
Clusters of neurons
Percolation theory shows that the formation of giant clusters of neurons relies on a few parameters that could be measured experimentally.
Gravity
Cyclic isotropic cosmologies
In an infinitely bouncing Universe, the scalar field driving the cosmological expansion and contraction carries information between phases.
Technological progress
Predicting technological progress
A formulation of Moore’s law estimates the probability that a given technology will outperform another at a certain point in the future.
Percolation theory
Bootstrap percolation models
A subset of bootstrap percolation models, which stabilise systems of cells on infinite lattices, exhibit non-trivial phase transitions.
Financial markets
News sentiment and price dynamics
News sentiment analysis and web browsing data are unilluminating alone, but inspected together, predict fluctuations in stock prices.
Network theory
Communities in networks
A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.
Financial markets
Effect of Twitter on stock prices
When the number of tweets about an event peaks, the sentiment of those tweets correlates strongly with abnormal stock market returns.
Complex networks
Democracy in networks
Analysis of the hyperbolicity of real-world networks distinguishes between those which are aristocratic and those which are democratic.
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.
Graph theory
Erdős-Ko-Rado theorem analogue
A random analogue of the Erdős-Ko-Rado theorem sheds light on its stability in an area of parameter space which has not yet been explored.
Complex networks
Collective attention to politics
Tweet volume is a good indicator of political parties' success in elections when considered over an optimal time window so as to minimise noise.
Thermodynamics
A measure of majorization
Single-shot information theory inspires a new formulation of statistical mechanics which measures the optimal guaranteed work of a system.
Financial risk
DebtRank and shock propagation
A dynamical microscopic theory of instability for financial networks reformulates the DebtRank algorithm in terms of basic accounting principles.
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.
Financial risk, Network theory
Fragility of the interbank network
The speed of a financial crisis outbreak sets the maximum delay before intervention by central authorities is no longer effective.
Theory of materials
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.
Economic complexity
Dynamics of economic complexity
Dynamical systems theory predicts the growth potential of countries with heterogeneous patterns of evolution where regression methods fail.
Neurocomputing
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.
Percolation theory
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.
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.
Economic complexity
Taxonomy and economic growth
Less developed countries have to learn simple capabilities in order to start a stable industrialization and development process.
Sphere packing
Viscosity of polydisperse spheres
A fast and simple way to measure how polydisperse spheres crowd around each other, termed the packing fraction, agrees well with rheological data.
Financial risk
Networks of credit default swaps
Time series data from networks of credit default swaps display no early warnings of financial crises without additional macroeconomic indicators.
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.
Network theory
Easily repairable networks
When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.
Quantum thermodynamics
Entanglement typicality
A review of the achievements concerning typical bipartite entanglement for random quantum states involving a large number of particles.
Theory of materials
Predicting interface structures
Generating random structures in the vicinity of a material’s defect predicts the low and high energy atomic structure at the grain boundary.
Percolation theory
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.
Financial risk
Memory effects in stock dynamics
The likelihood of stock prices bouncing on specific values increases due to memory effects in the time series data of the price dynamics.
Network theory
Self-healing complex networks
The interplay between redundancies and smart reconfiguration protocols can improve the resilience of networked infrastructures to failures.
Fractals
Structural imperfections
Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.
Financial risk
Default cascades in networks
The optimal architecture of a financial system is only dependent on its topology when the market is illiquid, and no topology is always superior.
Sphere packing
Random close packing fractions
Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.
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.
Economic complexity
Metrics for global competitiveness
A new non-monetary metric captures diversification, a dominant effect on the globalised market, and the effective complexity of products.
Economic complexity
Measuring the intangibles
Coupled non-linear maps extract information about the competitiveness of countries to the complexity of their products from trade data.
Network theory
The temperature of networks
A new concept, graph temperature, enables the prediction of distinct topological properties of real-world networks simultaneously.
Network theory
Scales in weighted networks
Information theory fixes weighted networks’ degeneracy issues with a generalisation of binary graphs and an optimal scale of link intensities.
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.
Fractals
Gentle loads
The most efficient load-bearing fractals are designed as big structures under gentle loads, a common situation in aerospace applications.
Financial networks
Interbank controllability
Complex networks detect the driver institutions of an interbank market and ascertain that intervention policies should be time-scale dependent.
Financial networks
Reconstructing credit
New mathematical tools can help infer financial networks from partial data to understand the propagation of distress through the network.
Financial networks
Complex derivatives
Network-based metrics to assess systemic risk and the importance of financial institutions can help tame the financial derivatives market.
Technological progress
Organized knowledge economies
The Yule-Simon distribution describes the diffusion of knowledge and ideas in a social network which in turn influences economic growth.
Financial risk
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.
Network theory
Weighted network evolution
A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.
Fractals
Ultralight fractal structures
The transition from solid to hollow beams changes the scaling of stability versus loading analogously to increasing the hierarchical order by one.
Fractals
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.
Economic complexity
Network analysis of export flows
Network theory finds unexpected interactions between the number of products a country produces and the number of countries producing each product.
Economic complexity
Metric for fitness and complexity
A quantitative assessment of the non-monetary advantage of diversification represents a country’s hidden potential for development and growth.
Mathematical medicine
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.
Financial markets
Search queries predict stocks
Analysis of web search queries about a given stock, from the seemingly uncoordinated activity of many users, can anticipate the trading peak.
Graph theory
Unbiased randomization
Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.
Network theory
Robust and assortative
Spectral analysis shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize.
Network theory
Clustering inverted
Edge multiplicity—the number of triangles attached to edges—is a powerful analytic tool to understand and generalize network properties.
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.
Ignoble research
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.
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.
Theory of materials
Diffusional liquid-phase sintering
A Monte Carlo model simulates the microstructural evolution of metallic and ceramic powders during the consolidation process liquid-phase sintering.
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.
Information theory
Assessing self-assembly
The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.
Sphere packing
Ever-shrinking spheres
Techniques from random sphere packing predict the dimension of the Apollonian gasket, a fractal made up of non-overlapping hyperspheres.
Discrete dynamics
Random cellular automata
Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.
Statistical physics
Single elimination competition
In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.