T. Fink

F. Sheldon

Surprisingly, the number of attractors in the critical Kauffman model with connectivity one grows exponentially with the size of the network.

Number of attractors in the critical Kauffman model is exponential

Exponential Kauffman scaling

S. Chen

Y. He

E. Hirst

A. Nestor

A. Zahabi

Genetic symbolic regression methods reveal the relationship between amoebae from tropical geometry and the Mahler measure from number theory.

Mahler measuring the genetic code of amoebae

Mahler measuring amoebae

A. Ashmore

E. Heyes

B. A. Ovrut

By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.


Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces

Bundled Laplacians

I. Shkredov

A new connection between continued fractions and the Bourgain–Gamburd machine reveals a girth-free variant of this widely-celebrated theorem.

On a girth-free variant of the Bourgain–Gamburd machine

Ungrouped machines

G. Caldarelli

E. Arcaute

M. Barthelemy

M. Batty

C. Gershenson

D. Helbing

S. Mancuso

Y. Moreno

J. J. Ramasco

C. Rozenblat

A. Sánchez

J. L. Fernández-Villacañas

A complexity-science approach to digital twins of cities views them as interwoven self-organising phenomena, instead of machines or logistic systems.

The role of complexity for digital twins of cities

Complex digital cities

B. Hanson

M. Rudnev

D. Zhelezov

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.

The sum-product problem for integers with few prime factors

Sum-product with few primes

This obituary celebrates the life and work of John Keith Stuart McKay, highlighting the mathematical miracles for which he will be remembered.



John Keith Stuart McKay: 1939-2022

On John McKay

M. Burtsev

A. Bulatov

Y. Kuratov

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


Scaling transformer to 1m tokens and beyond with RMT

BERT enhanced with recurrence

O. Klurman

M. W. Xu

The distribution of partial sums of a Steinhaus random multiplicative function, of polynomials in a given form, converges to the standard complex Gaussian.

On the random Chowla conjecture

Random Chowla conjecture

A new, simple approach to the critical Kauffman model with connectivity one sharpens the bounds on the number and length of attractors.

A simple solution of the critical Kauffman model with connectivity one

Landau meets Kauffman

A new, simpler approach to the critical Kauffman model with connectivity one reveals that it has more attractors than previously believed.

Exact dynamics of the critical Kauffman model with connectivity one

Single-input Boolean networks

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

When was a factor transfected? Sifting cells from soup in transcription factor screens

Cell soup in screens

L. Cangemi

M. Chiodaroli

H. Johansson

A. Ochirov

P. Pichini

E. Skvortsov

Effective field theories for Kerr black holes, showing the 3-point Kerr amplitudes are uniquely 
predicted using higher-spin gauge symmetry.

Kerr black holes enjoy massive higher-spin gauge symmetry

Kerr black holes symmetry

Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.

On some multiplicative properties of large difference sets

Multiplicativity of sets

P. Villegas

T. Gili

A. Gabrielli

Applying diffusion-based graph operators to complex networks identifies the proper spatiotemporal scales by overcoming small-world effects.

Laplacian renormalization group for heterogeneous networks

Network renormalization

M. Cheung

P. Dechant

J. Li

Cluster variables in Grassmannian cluster algebras can be classified with HPC by applying the tableaux method up to a fixed number of columns.

Clustering cluster algebras with clusters

Clustered cluster algebras

N. Moshchevitin

B. Murphy

Using methods related to the Bourgain–Gamburd machine refines the previous bound on Zaremba’s conjecture in the theory of continued fractions.

On Korobov bound concerning  Zaremba's conjecture

Bounding Zaremba’s conjecture

A. Kolchinsky

F. Caravelli

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

Computational capacity of  LRC, memristive and hybrid reservoirs

Optimal electronic reservoirs

J. Bao

The algebra of a toric quiver gauge theory recovers the Bethe ansatz, revealing the relation between gauge theories and integrable systems.

A note on quiver Yangians and ℛ-matrices

Gauge theory and integrability

The eigenvalues of the mortality equation fall into two classes—the flower and the stem—but only the stem eigenvalues control the dynamics.

Flowers of immortality

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

Regulatory motifs: structural and functional building blocks of genetic computation

Structure of genetic computation

J. Ipiña

A neural network learns to classify different types of spacetime in general relativity according to their algebraic Petrov classification.

Machine-learning the classification of spacetimes

AI classifies space-time

Certain states in quantum field theories are described by the geometry and algebra of melting crystals via properties of partition functions.

Crystal melting, BPS quivers and plethystics

Algebra of melting crystals

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.

Additive dimension and the growth of sets

Set additivity and growth

J. Hofscheier

A .Kasprzyk

S. Majumder

Neural networks find efficient ways to compute the Hilbert series, an important counting function in algebraic geometry and gauge theory.

Hilbert series, machine learning, and applications to physics

Machine learning Hilbert series

Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.

Cluster algebras: network science and machine learning

AI for cluster algebras

R. Deen

Neural networks find numerical solutions to Hermitian Yang-Mills equations, a difficult system of PDEs crucial to mathematics and physics.

Machine learning line bundle connections

Line bundle connections

D. S. Berman

Unsupervised machine-learning of the Hodge numbers of Calabi-Yau hypersurfaces detects new patterns with an unexpected linear dependence.

Machine learning Calabi-Yau hypersurfaces

Calabi-Yau anomalies 

Mahler measure from number theory is used for the first time in physics, yielding “Mahler flow” which extrapolates different phases in QFT.

Mahler measure for a quiver symphony

Mahler measure for quivers

Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on, recursively.

Recursively divisible numbers

K. Lee

T. Oliver

Machine-learning methods can distinguish between Sato-Tate groups, promoting a data-driven approach for problems involving Euler factors.

Machine-learning the Sato–Tate conjecture

Learning the Sato–Tate conjecture

Machine-learning is a powerful tool for sifting through the landscape of possible Universes that could derive from Calabi-Yau manifolds.

Universes as big data

M.Serafinoa

G. Cimini

A. Maritan

A. Rinaldo

S.Suweis

J. R. Banavar

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

True scale-free networks hidden by finite size effects

True scale-free networks

Unifying Mahler measure, dessins and gauge theory, Newton polynomials reveal a 1-to-1 correspondence between Mahler measure and dessins.

Reflexions on Mahler: Dessins, modularity and Gauge theories

Reflexions on Mahler

F. Aguirre López

A. Coolen

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

Transitions in loopy random graphs with fixed degrees and arbitrary degree distributions

Transitions in loopy graphs

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

Emergent spatial patterns of coexistence in species-rich plant communities

Coexistence in diverse ecosystems

T. Marsden

N. McCartan

J. Hadley

S. Tuck

L. Brown

A. J. Haire

Ch. L. Moss

S. Green

M. Van Hemelrijck

A. Santaolalla

E. Isaac

G. Brembilla

D. Kopcke

F. Giganti

H. Sidhu

S. Punwani

M. Emberton

C. M. Moore

An ongoing study tests the feasibility of using MRI scans to screen men for prostate cancer in place of unreliable antigen blood tests.

Update from the ReIMAGINE prostate cancer screening study NCT04063566: inviting men for prostate cancer screening using magnetic resonance imaging

Cancer screening with MRI

Y. Liao

D. Ebler

F. Liu

O. Dahlsten

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

Quantum speed-up in global optimization of binary neural nets

Quick quantum neural nets

A. Akil

L. Modesto

A solution to the information paradox uses standard quantum field theory to show that black holes can evaporate in a predictable way.

Conditional entanglement transfer via black holes: restoring predictability

Going, going, gone

Pathways towards instability

Serendipity and strategy