Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.
Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.
Statistical methods that normally fail for very high-dimensional data can be rescued via mathematical tools from statistical physics.
The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.
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 are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on.
We optimize Bayesian data clustering by mapping the problem to the statistical physics of a gas and calculating the lowest entropy state.
A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.
A mathematical model captures the temporal and steady state behaviour of networks whose two sets of nodes either generate or destroy links.
A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.
Machine learning techniques enhance the efficiency of energy harvesters by implementing reversible energy-conserving operations.
The number of particles in a higher derivative theory of gravity relates to its effective mass scale, which signals the theory’s viability.
The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than others.
A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.
Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.
An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.
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.
In this paper we sketch a general methodology for studying the phase diagram of memristive circuits.
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 analogs of fluctuation-theorem results help unify these two approaches for small-scale, nonequilibrium statistical physics.
Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.
A novel approach to volunteer clouds outperforms traditional distributed task scheduling algorithms in the presence of intensive workloads.
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.
Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications
The large-scale structure of the interbank network changes drastically in times of crisis due to the effect of measures from central banks.
Controlling analytically second or higher-order properties of networks is a great mathematical challenge.
The usefulness of components and the complexity of products inform the best strategy for innovation at different stages of the process.
In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.
Bayesian networks describe the evolution of orthodontic features on patients receiving treatment versus no treatment for malocclusion.
Theoretical searches propose 2D borane as a new graphene-like material which is stable and semi-metallic with Dirac cone structure.
We generalise neural networks into a quantum framework, demonstrating the possibility of quantum auto-encoders and teleportation.
The challenge of statistical reconstruction is using the limited available information to predict stock holdings.
A new algorithm unveils complicated structures in the bipartite mapping between countries and products of the international trade network.
Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.
When people operate in echo chambers, they focus on information adhering to their system of beliefs. Debunking them is harder than it seems
Moment-based methods provide a simple way to describe a population of spherical particles and extract 3d information from 2d measurements.
The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.
Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.
A battery from which work is taken or given to a single heat bath.
Firms can harness the shifting importance of component building blocks to build better products and services.
Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.
Processes believed to stabilize financial markets can drive them towards instability by creating cyclical structures that amplify distress.
We present a new way of finding communities in networks that change over time.
A general analysis of exchange devices links their efficiency to the geometry of the exchange surface and supply network.
Interbank network and balance sheet.
Cascades on a random graph
An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.
Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.
In quantum tunnelling, a particle tunnels through a barrier that it classically could not surmount.
The structure of network motifs determines fundamental properties of their dynamical state space.
Pseudospectrum of a random community matrix with S = 50, C = 0.1, μ = 1 and σ = 0.3, which is asymptotically stable.
Single realization of random positions and orientations of 100 disks with an external field pointing in the direction of the red arrow.
Predicting the evolution of technology allow us to make better investments and policies.
Does a scalar field maintain a quantum memory from previous bounces?
The first 16 ‘‘bricklayer’s graphs’’ and the principal eigenvalue of their adjacency matrices.
By analogy with Maxwell’s original thought experiment, the setup uses energy extracted from a thermal system.
Complementary of the cumulative distribution function of the number of clicks a news receives for the ten assets.
Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices.
A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.
Distribution of sentiment polarity for the 260 detected Twitter peaks
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.
Daily tweet volume for each party around elections
Abstract depiction of the set of states, including the initial state ρ and final state σ . Each state is associated wi
Hypercubic Bethe lattices retain many of the loops of the topology of realistic spin systems.
The DebtRank algorithm was introduced to account for the build-up of distress in the markets, before the occurrence of defaults.
Simulations for 106 periods, using different social networks.
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
A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.
The growth dynamics of countries in the fitness-income plane exhibits a high degree of heterogeneity.
What is the maximum percolation time in a two-dimensional grid?
A less developed country has to learn simple capabilities in order to start a stable industrialization and development process.
Short loops (cycles) in real networks are a theoretical challenge for modeling.
Spheres crowd around each other in a manner that depends on their size distribution. We give a simple way to estimate the packing fraction.
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.
When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.
Graphene grain boundary structures between armchair and zigzag regions.
In bootstrap percolation, a node is infected when a sufficient number of neighbours are infected.
Price dynamics incorporates the strategies of traders and investors in the market.
Infrastructure networks are very well engineered systems characterized by fluxes of commodities, from electric power to drinking water.
Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.
Frontier of large cascades evolution of the e-MID market in the period between January 1999 and January 2011.
The immune system must simultaneously recall multiple defense strategies because many antigens can attack the host at the same time.
Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.
We introduce a novel method to define a self-consistent and non-monetary metrics for the competitiveness of countries.
We present a framework to define a data-driven metrics to assess the level of competitiveness of a country.
We define a generalized ensemble of graphs by introducing the concept of graph temperature.
An intriguing analogy exists between neural networks and immune networks.
The Eiffel Tower was never intended to be a permanent feature of the Parisian landscape.
We show that self-similar fractal structures exhibit new strength-to-mass scaling relations, offering unprecedented mechanical efficiency.
External inputs allow us to control the state of the interbank lending network.
New mathematical tools can help infer financial networks from partial data to understand the propagation of distress through the network.
Network-based metrics to assess systemic risk and the importance of financial institutions can help tame the financial derivatives market.
Vulnerability and systemicity do not depend only on GDP but also on the complex network of financial relations.
A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.
A material’s architecture can be controlled over an ever increasing set of length scales.
The network of countries and products and the two possible projections.
A snapshot of the bipartite network for the most important countries; size of vertices is the fitness and the complexity
Cephalogram reference points.
Graphical illustration of the analysis presented in this paper.
Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.
Edge multiplicity—the number of triangles attached to edges—is a powerful analytic tool to understand and generalize network properties.
Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.
It is vital that we understand in detail how the topological characteristics of a real network relate to those of a finite random network.
Schematic of the disruption of close-packed polyhedral cells in tomato tissue into individual cells.
The dynamics of one-dimensional Ising chains is of interest in the context of ageing phenomena.
Our Monte Carlo model sheds light on the Ostwald ripening, namely the growth of big particles at the expense of the small ones.
Our approach gives a rigorous quantitative method for prioritising network properties.
The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.
Techniques from random sphere packing predict the dimension of the Apollonian gasket, a fractal made up of non-overlapping hyperspheres.
The thirteen canonical knot classes and the corresponding most aesthetic knots.
In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.