M. Bardoscia

P. Barucca

S. Battiston

F. Caccioli

G. Cimini

D. Garlaschelli

F. Saracco

T. Squartini

G. Caldarelli

Complex network theory unlocks systematic understanding of financial stability and climate finance in pursuit of a more sustainable society.

The physics of financial networks

M.Serafinoa

A. Maritan

A. Rinaldo

S.Suweis

J. R. Banavar

Naturally occurring networks have an underlying scale-free structure that is often clouded by finite-size effects in the sample data.

True scale-free networks hidden by finite size effects

True scale-free networks

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 random graphs

A. Mozeika

F. Aguirre Lopez

 M. Sheikh

 F. Antenucci

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

Some exact results for the statistical physics problem of high-dimensional linear regression

Exact linear regression

R. Farr

Rapid temperature cycling from one extreme to another affects the rate at which the mean particle size in solid or liquid solutions changes.

Coarsening without interfacial energy

Microstructural coarsening

T. Fink

Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.

Recursively abundant and recursively perfect numbers

Ample & pristine numbers

M. D’Errico

G. Visentin

Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.

Network valuation in financial systems

B. Li

D. Saad

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

The space of functions computed by deep layered machines

Deep layered machines

M. Sheikh

F. Aguirre-Lopez

F. Antenucci

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

Replica analysis of overfitting in generalized linear models

Replica analysis of overfitting

S. E. Ahnert

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

Form and function in gene regulatory networks

Form and function in gene networks

M. Reeves

S. Levin

A. Levina

Insights from biology, physics and business shed light on the nature and costs of complexity and how to manage it in business organizations.

Taming complexity

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

Recursively divisible numbers

T. Coolen

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

Replica analysis of Bayesian data clustering

Replica clustering

I. Teimouri

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

The mathematical structure of innovation

Recursive structure of innovation

F. Vanni

A mathematical model captures the temporal and steady state behaviour of  networks whose two sets of nodes either generate or destroy links.

Degree-correlations in a bursting dynamic network model

Bursting dynamic networks

A. Scala

A. Facchini

U. Perna

R. Basosi

Modern portfolio theory inspires a strategy for allocating renewable energy sources which minimises the impact of production fluctuations.

Portfolio analysis and geographical allocation of renewable sources: A stochastic approach

Renewable resource management

F. Liu

Y. Zhang

O. Dahlsten

F. Wang

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

Intelligently chosen interventions have potential to outperform the diode bridge in power conditioning

Energy harvesting with AI

J. Balogh

B. Bollobas

B. Narayanan

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.

Transference for the Erdős-Ko-Rado theorem

Erdős-Ko-Rado theorem analogue

S. Talaganis

The number of particles in a higher derivative theory of gravity relates to its effective mass scale, which signals the theory’s viability.

Scale of non-locality for a system of n particles

Scale of non-locality

Y. Mao

The topological structure of tie knots categorises them by shape, size and aesthetic appeal and defines the sequence of knots to produce them.

Tie knots, random walks and topology

Tie knots and topology

A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.

Phase transition creates the geometry of the continuum from discrete space

Geometry of discrete space

A. Zegarac

F. Caravelli

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

Memristive networks: from graph theory to statistical physics

Memristive networks

A. Gabrielli

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

The statistical physics of real-world networks

Physics of networks

The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than others.

How much can we influence the rate of innovation?

The rate of innovation

N. Halpern

A. Garner

V. Vedral

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

Maximum one-shot dissipated work from Rényi divergences

One-shot statistic

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

Tackling information asymmetry in networks: a new entropy-based ranking index

Information asymmetry

D. Branford

An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.

On defining the Hamiltonian beyond quantum theory

A Hamiltonian recipe

Z. Vukmanovic

M. Holness

E. Griffiths

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.

Reconstructing grain-shape statistics from electron back-scatter diffraction microscopy

Grain shape inference

T. Kobayashi

Complex networks model the links between financial institutions and how these channels can transition from diversifying to propagating risk.

Network models of financial systemic risk: a review

Modelling financial systemic risk

S. Sebastio

M. Amoretti

A. Lafuente

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

A holistic approach for collaborative workload execution in volunteer clouds

Volunteer clouds

M. Straka

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

From ecology to finance (and back?): a review on entropy-based null models for the analysis of bipartite networks

From ecology to finance

B. Bollobás

J. Lee

S. Letzter

Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.

Eigenvalues of subgraphs of the cube

Hypercube eigenvalues

I. Bordino

M. Cristelli

A. Ukkonen

I. Weber

Analysis of web search queries about a given stock, from the seemingly uncoordinated activity of many users, can anticipate the trading peak.

Web search queries can predict stock market volumes

Search queries predict stocks

P. Auconi

M. Scazzocchio

J. McNamara

L. Franchi

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

Using networks to understand medical data: the case of class III malocclusions

Networks for medical data

V. Zlatić

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

Networks with arbitrary edge multiplicities

Clustering inverted

G. D'Agostino

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

Robustness and assortativity for diffusion-like processes in scale-free networks

Robust and assortative

S. Ahnert

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

Optimal scales in weighted networks

Scales in weighted networks

A. Chessa

F. Pammolli

M. Puliga

New mathematical tools can help infer financial networks from partial data to understand the propagation of distress through the network.

Reconstructing a credit network

Reconstructing credit

C. Georg

R. May

J. Stiglitz

Network-based metrics to assess systemic risk and the importance of financial institutions can help tame the financial derivatives market.

Complex derivatives

T. Roukny

H. Bersini

H. Pirotte

The optimal architecture of a financial system is only dependent on its topology when the market is illiquid, and no topology is always superior.

Default cascades in complex networks: topology and systemic risk

Default cascades in networks

Estimate for the fractal dimension of the Apollonian gasket in d dimensions

More in Puzzles in packing

Shear elastic deformation in cells

Viscosity of polydisperse spheres

Random close packing fractions