### Ample & pristine numbers

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

### Network valuation in financial systems

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

### A fix for overfitting

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

### Deep layered machines

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

### 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.

### Recursively divisible numbers

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

### Replica clustering

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

### The mathematical structure of innovation

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

### 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.

### 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.

### Energy harvesting with AI

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

### 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.

### The rate of innovation

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

### 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.

### A Hamiltonian recipe

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

### 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.

### Exactly solvable model of memristive circuits: Lyapunov functional and mean field theory

In this paper we sketch a general methodology for studying the phase diagram of memristive circuits.

### 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.

### One-shot statistic

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

### Hypercube eigenvalues

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

### 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.

### How well do experience curves predict technological progress? A method for making distributional forecasts

We presented a method to test the accuracy and validity of experience curve forecasts.

### Resolution of ranking hierarchies in directed networks

Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications

### 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.

### Exactly solvable random graph ensemble with extensively many short cycles

Controlling analytically second or higher-order properties of networks is a great mathematical challenge.

### 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.

### Serendipity and strategy

In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

### Network models of financial systemic risk: a review

Stylized balance sheet of a bank

### Bayesian orthodontics

Bayesian networks describe the evolution of orthodontic features on patients receiving treatment versus no treatment for malocclusion.

### Dirac cones in 2D borane

Theoretical searches propose 2D borane as a new graphene-like material which is stable and semi-metallic with Dirac cone structure.

### Quantum neural networks

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

### Enhanced capital-asset pricing model for bipartite financial networks reconstruction

The challenge of statistical reconstruction is using the limited available information to predict stock holdings.

### Bipartite trade network

A new algorithm unveils complicated structures in the bipartite mapping between countries and products of the international trade network.

### Quantum thermodynamics

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

### 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

### 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.

### Spectral partitioning

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

### Memristive networks

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

### Entropic equality for worst-case work at any protocol speed

A battery from which work is taken or given to a single heat bath.

### Harnessing the secret structure of innovation

Firms can harness the shifting importance of component building blocks to build better products and services.

### Dynamics of memristors

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

### Pathways towards instability

Processes believed to stabilize financial markets can drive them towards instability by creating cyclical structures that amplify distress.

### Disentangling group and link persistence in Dynamic Stochastic Block models

We present a new way of finding communities in networks that change over time.

### Optimal counter-current exchange networks

A general analysis of exchange devices links their efficiency to the geometry of the exchange surface and supply network.

### Distress propagation in complex networks: the case of non-linear DebtRank

Interbank network and balance sheet.

### Mitigating cascades in sandpile models: an immunization strategy for systemic risk?

Cascades on a random graph

### Optimal growth rates

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

### The price of complexity

Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.

### Tunnelling interpreted

In quantum tunnelling, a particle tunnels through a barrier that it classically could not surmount.

### Form and function in gene regulatory networks

The structure of network motifs determines fundamental properties of their dynamical state space.

### Bounds on transient instability for complex ecosystems

Pseudospectrum of a random community matrix with S = 50, C = 0.1, μ = 1 and σ = 0.3, which is asymptotically stable.

### Emergence of strongly connected components in continuum disk-spin percolation

Single realization of random positions and orientations of 100 disks with an external field pointing in the direction of the red arrow.

### How predictable is technological progress?

Predicting the evolution of technology allow us to make better investments and policies.

### Geometric phases and cyclic isotropic cosmologies

Does a scalar field maintain a quantum memory from previous bounces?

### Eigenvalues of neutral networks: Interpolating between hypercubes

The first 16 ‘‘bricklayer’s graphs’’ and the principal eigenvalue of their adjacency matrices.

### Photonic Maxwell’s demon

By analogy with Maxwell’s original thought experiment, the setup uses energy extracted from a thermal system.

### Coupling news sentiment with web browsing data improves prediction of intra-day price dynamics

Complementary of the cumulative distribution function of the number of clicks a news receives for the ten assets.

### Subcritical U-Bootstrap percolation models have non-trivial phase transitions

Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices.

### Communities in networks

A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.

### The effects of Twitter sentiment on stock price returns

Distribution of sentiment polarity for the 260 detected Twitter peaks

### Democracy in networks

Analysis of the hyperbolicity of real-world networks distinguishes between those which are aristocratic and those which are democratic.

### Quantifying noise in mass spectrometry and yeast two-hybrid protein interaction detection experiments

Protein detection experiments seek to measure for each pair of protein species whether they interact in any complex.

### Transference for the Erdős-Ko-Rado theorem

Two constructions for an intersecting family of r-sets.

### Twitter-based analysis of the dynamics of collective attention to political parties

Daily tweet volume for each party around elections

### A measure of majorization emerging from single-shot statistical mechanics

Abstract depiction of the set of states, including the initial state ρ and final state σ . Each state is associated wi

### Spin systems on hypercubic Bethe lattices: a Bethe–Peierls approach

Hypercubic Bethe lattices retain many of the loops of the topology of realistic spin systems.

### DebtRank: a microscopic foundation for shock propagation

The DebtRank algorithm was introduced to account for the build-up of distress in the markets, before the occurrence of defaults.

### Self-organization of knowledge economies

Simulations for 106 periods, using different social networks.

### Structures and stability of calcium and magnesium carbonates at mantle pressures

Predicting stable structures of calcium and magnesium carbonate is crucial for understanding the Earth's deep carbon cycle.

### How the interbank market becomes systemically dangerous: an agent-based network model of financial distress propagation

We assess the fragility of the interbank lending market from 2004 to 2013

### 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.

### The heterogeneous dynamics of economic complexity

The growth dynamics of countries in the fitness-income plane exhibits a high degree of heterogeneity.

### Maximum percolation time in two-dimensional bootstrap percolation

What is the maximum percolation time in a two-dimensional grid?

### How the taxonomy of products drives the economic development of countries

A less developed country has to learn simple capabilities in order to start a stable industrialization and development process.

### Random graph ensembles with many short loops

Short loops (cycles) in real networks are a theoretical challenge for modeling.

### Simple heuristic for the viscosity of polydisperse hard spheres

Spheres crowd around each other in a manner that depends on their size distribution. We give a simple way to estimate the packing fraction.

### Credit default swaps networks and systemic risk

CDS spreads over time for the selected institutions

### Entropies of tailored random graph ensembles: bipartite graphs, generalized degrees, and node neighbourhoods

Ensembles of tailored random graphs allow us to reason quantitatively about the complexity of system.

### 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

We provide a measure of purity of an entanglement state.

### Predicting interface structures: from SrTiO 3 to graphene

Graphene grain boundary structures between armchair and zigzag regions.

### Bootstrap percolation on Galton–Watson trees

In bootstrap percolation, a node is infected when a sufficient number of neighbours are infected.

### Memory effects in stock price dynamics: evidences of technical trading

Price dynamics incorporates the strategies of traders and investors in the market.

### Self-healing networks: redundancy and structure

Infrastructure networks are very well engineered systems characterized by fluxes of commodities, from electric power to drinking water.

### Structural imperfections

Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.

### Default cascades in complex networks: topology and systemic risk

Frontier of large cascades evolution of the e-MID market in the period between January 1999 and January 2011.

### Immune networks: multitasking capabilities near saturation

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

### Random close packing fractions of lognormal distributions of hard spheres

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

### Economic complexity: conceptual grounding of a new metrics for global competitiveness

We introduce a novel method to define a self-consistent and non-monetary metrics for the competitiveness of countries.

### Measuring the intangibles: a metric for the economic complexity of countries and products

We present a framework to define a data-driven metrics to assess the level of competitiveness of a country.

### Low-temperature behaviour of social and economic networks

We define a generalized ensemble of graphs by introducing the concept of graph temperature.

### Immune networks: multi-tasking capabilities at medium load

An intriguing analogy exists between neural networks and immune networks.

### Towers of strength

The Eiffel Tower was never intended to be a permanent feature of the Parisian landscape.

### Hierarchical structures

We show that self-similar fractal structures exhibit new strength-to-mass scaling relations, offering unprecedented mechanical efficiency.

### Evolution of controllability in interbank networks

External inputs allow us to control the state of the interbank lending network.

### Reconstructing a credit network

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

### Complex derivatives

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

### Bootstrapping topology and systemic risk of complex network using the fitness model

Vulnerability and systemicity do not depend only on GDP but also on the complex network of financial relations.

### Weighted network evolution

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

### Ultralight fractal structures from hollow tubes

A material’s architecture can be controlled over an ever increasing set of length scales.

### A network analysis of countries’ export flows: firm grounds for the building blocks of the economy

The network of countries and products and the two possible projections.

### A new metric for countries’ fitness and products’ complexity

A snapshot of the bipartite network for the most important countries; size of vertices is the fitness and the complexity

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

Cephalogram reference points.

### Web search queries can predict stock market volumes

Graphical illustration of the analysis presented in this paper.

### Unbiased randomization

Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.

### Clustering inverted

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

### Random cellular automata

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

### What you see is not what you get: how sampling affects macroscopic features of biological networks

It is vital that we understand in detail how the topological characteristics of a real network relate to those of a finite random network.

### Shear elastic deformation and particle packing in plant cell dispersions

Schematic of the disruption of close-packed polyhedral cells in tomato tissue into individual cells.

### Transfer operator analysis of the parallel dynamics of disordered Ising chains

The dynamics of one-dimensional Ising chains is of interest in the context of ageing phenomena.

### Diffusional Monte Carlo model of liquid-phase sintering

Our Monte Carlo model sheds light on the Ostwald ripening, namely the growth of big particles at the expense of the small ones.

### Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

Our approach gives a rigorous quantitative method for prioritising network properties.

### Assessing self-assembly

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

### Ever-shrinking spheres

Techniques from random sphere packing predict the dimension of the Apollonian gasket, a fractal made up of non-overlapping hyperspheres.

### Tie knots, random walks and topology

The thirteen canonical knot classes and the corresponding most aesthetic knots.

### Strategy for conkers

In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.

### Microstructural coarsening

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