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

P. Barucca

M. Bardoscia

F. Caccioli

M. D’Errico

G. Visentin

G. Caldarelli

S. Battiston

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

A. Mozeika

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

T. Coolen

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

A fix for overfitting

S. E. Ahnert

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

Form and function in gene regulatory 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

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

F. Vanni

Degree-correlations in a bursting dynamic network model

A. Scala

A. Facchini

U. Perna

R. Basosi

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

F. Liu

Y. Zhang

O. Dahlsten

F. Wang

Cost function landscape. X-axis is period and Y-axis is delay, Z-axis is the cost function value.

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

J. Balogh

B. Bollobas

B. Narayanan

Two constructions for an intersecting family of r-sets.

Transference for the Erdős-Ko-Rado theorem

S. Talaganis

Scale of non-locality for a system of n particles

Y. Mao

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

Tie knots, random walks and topology

R. Farr

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

G. Cimini

T. Squartini

F. Saracco

D. Garlaschelli

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

Toy network, whose nodes have been ranked according to InfoRank.

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

D. Branford

The Hamiltonianin quantum theory (green arrow) acts as the axis of rotation as states evolve in the Bloch sphere (Color figure online)

On defining the Hamiltonian beyond quantum theory

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

Network models of financial systemic risk: a review

S. Sebastio

M. Amoretti

A. Lafuente

A holistic approach for collaborative workload execution in volunteer clouds

M. Straka

Illustration of several undirected bipartite motifs.

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

B. Bollobás

J. Lee

S. Letzter

Eigenvalues of subgraphs of the cube

I. Bordino

M. Cristelli

A. Ukkonen

I. Weber

Graphical illustration of the analysis presented in this paper.

Web search queries can predict stock market volumes

P. Auconi

M. Scazzocchio

J. McNamara

L. Franchi

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

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

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

Robust and assortative

S. Ahnert

Optimal 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

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

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

Default cascades in complex networks: topology and systemic risk

G. Ranco

D. Aleksovski

M. Grčar

I. Mozetič

Distribution of sentiment polarity for the 260 detected Twitter peaks

The effects of Twitter sentiment on stock price returns

Y. Eom

J. Smailović

Daily tweet volume for each party around elections

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

CDS spreads over time for the selected institutions

Credit default swaps networks and systemic risk

M. Borassi

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

Hyperbolicity measures democracy in real-world networks

Democracy in networks

J. Perotti

C. Tessone

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

Hierarchical mutual information for the comparison of hierarchical community structures in complex networks.

Communities in networks

G. Bormetti

F. Lillo

M. Treccani

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

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

G. Vivaldo

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

P. Lucentini

G. D’Agostino

Cascades in interdependent flow networks

S. Boccaletti

Concurrent enhancement of percolation and synchronization in adaptive networks

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

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

Grand canonical validation of the bipartite international trade network

Bipartite trade network

M. Scutari

Bayesian networks analysis of malocclusion data

D. Rayneau-Kirkhope

J. Segal

Hierarchical space frames for high mechanical efficiency: Fabrication and mechanical testing

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

Towers of strength

A. Hamma

M. Ventra

A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.

Scale-free networks as an epiphenomenon of memory

From memory to scale-free

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

Emergence of strongly connected components in continuum disk-spin percolation

Eigenvalues of subgraphs of the cube

Spectral partitioning

Bounds on transient instability for complex ecosystems

Eigenvalues of neutral networks: Interpolating between hypercubes

Robust and assortative