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Open Access


Article
 Open AccessPathways towards instability in financial networks
The spread of instabilities in financial systems, similarly to ecosystems, is influenced by topological features of the underlying network structures. Here the authors show, independently of specific financial models, that market integration and diversification can drive the system towards instability.
 Marco Bardoscia
 , Stefano Battiston
 & Guido Caldarelli

Article
 Open AccessLocal selfuniformity in photonic networks
The interaction between photonic bandgap materials and light is largely determined by the wavelengthscale material structure. Here, Sellerset al. develop a new metric of network structural order and demonstrate its connection to the photonic bandgap of an amorphous gyroid network.
 Steven R. Sellers
 , Weining Man
 & Marian Florescu

Article
 Open AccessUnravelling raked linear dunes to explain the coexistence of bedforms in complex dunefields
Raked linear dunes are a rare dune type, but the mechanisms for growth have not been constrained. Here, the authors show that a tridirectional wind regime is required to enable this extremely rare dune type to develop, where the raked pattern may develop preferentially on the leeward side.
 Ping Lü
 , Clément Narteau
 & Sylvain Courrech du Pont

Article
 Open AccessLocal dimensionality determines imaging speed in localization microscopy
Localisation microscopy enables nanometrescale imaging of biological samples, but the method is too slow to use on dynamic systems. Here, the authors develop a mathematical model that optimises the number of frames required and estimates the maximum speed for superresolution imaging.
 Patrick FoxRoberts
 , Richard Marsh
 & Susan Cox

Article
 Open AccessQuantumchemical insights from deep tensor neural networks
Machine learning is an increasingly popular approach to analyse data and make predictions. Here the authors develop a ‘deep learning’ framework for quantitative predictions and qualitative understanding of quantummechanical observables of chemical systems, beyond properties trivially contained in the training data.
 Kristof T. Schütt
 , Farhad Arbabzadah
 & Alexandre Tkatchenko

Article
 Open AccessQuantification of network structural dissimilarities
Identifying and quantifying dissimilarities among graphs is a problem of practical importance, but current approaches are either limited or computationally demanding. Here, the authors propose an efficiently computable measure for network comparison that can identify structural topological differences.
 Tiago A. Schieber
 , Laura Carpi
 & Martín G. Ravetti

Article
 Open AccessRegulation of persistent sodium currents by glycogen synthase kinase 3 encodes daily rhythms of neuronal excitability
It is not clear how circadian biochemical cascades are encoded into neural electrical signals. Here, using a combination of electrophysiology and modelling approaches in mice, the authors show activation of glycogen synthase kinase 3 modulates neural activity in the suprachiasmatic nuclei via regulation of the persistent sodium current, INaP.
 Jodi R. Paul
 , Daniel DeWoskin
 & Karen L. Gamble

Article
 Open AccessCompetition among networks highlights the power of the weak
Network science and game theory have been traditionally combined to analyse interactions between nodes of a network. Here, the authors model competition for importance among networks themselves, and reveal dominance of the underdogs in the fate of networksofnetworks.
 Jaime Iranzo
 , Javier M. Buldú
 & Jacobo Aguirre

Article
 Open AccessUnsupervised vectorbased classification of singlemolecule charge transport data
The stochastic nature of singlemolecule charge transport measurements requires collection of large data sets to capture their full complexity. Here, the authors adopt strategies from machine learning for the unsupervised classification of singlemolecule charge transport data without a prioriassumptions.
 Mario Lemmer
 , Michael S. Inkpen
 & Tim Albrecht

Article
 Open AccessThe backtracking survey propagation algorithm for solving random KSAT problems
The Ksatisfability problem is a combinatorial discrete optimization problem, which for K=3 is NPcomplete, and whose random formulation is of interest for understanding computational complexity. Here, the authors introduce the backtracking survey propagation algorithm for studying it for K=3 and K=4.
 Raffaele Marino
 , Giorgio Parisi
 & Federico RicciTersenghi

Article
 Open AccessUnsupervised learning in probabilistic neural networks with multistate metaloxide memristive synapses
Artificial neural networks exhibit learning abilities and can perform tasks which are tricky for conventional computing systems, such as pattern recognition. Here, Serb et al. show experimentally that memristor arrays can learn reversibly from noisy data thanks to sophisticated learning rules.
 Alexander Serb
 , Johannes Bill
 & Themis Prodromakis

Article
 Open AccessTerahertz timegated spectral imaging for content extraction through layered structures
Terahertz radiation may be used to nondestructively detect and study defects and structures within materials. Here the authors use terahertz timegated spectral imaging to extract occluded text from paper pages with subwavelength spacing.
 Albert RedoSanchez
 , Barmak Heshmat
 & Ramesh Raskar

Article
 Open AccessCapacity estimates for optical transmission based on the nonlinear Fourier transform
Optical fibres enable highspeed communication over long distances, but traditional systems are limited by nonlinear optical effects. Here, the authors quantify the increase in capacity that is made possible by using an alternative approach that uses a nonlinear Fourier transform.
 Stanislav A. Derevyanko
 , Jaroslaw E. Prilepsky
 & Sergei K. Turitsyn

Article
 Open AccessPrediction of allosteric sites and mediating interactions through bondtobond propensities
Allostery is a key molecular mechanism underpinning control and modulation in a variety of cellular processes. Here, the authors present a method that can be used to predict allosteric sites and the mediating interactions that connect them to the active site of the protein.
 B. R. C. Amor
 , M. T. Schaub
 & M. Barahona

Article
 Open AccessThermodynamics of freezing and melting
Melting is a classic firstorder phase transition, but an accurate thermodynamic description is still lacking. Here, Pedersen et al. develop a theory, validated by simulations of the LennardJones system, for the melting thermodynamics applicable to all systems characterized by hidden scale invariance.
 Ulf R. Pedersen
 , Lorenzo Costigliola
 & Jeppe C. Dyre

Article
 Open AccessVortex knots in tangled quantum eigenfunctions
Strings or long chains are prone to knotting. Here, the authors demonstrate that the vortex structure of quantum wavefunctions, such as that in a simple harmonic oscillator, can also contain knots, whose topological complexity can be a descriptor of the spatial order of the system.
 Alexander J. Taylor
 & Mark R. Dennis

Article
 Open AccessFaulttolerant error correction with the gauge color code
Construction of a scalable quantum computer requires errorcorrecting codes to overcome the errors introduced by noise. Here, the authors develop a decoding algorithm for the gauge color code, and obtain its threshold values when physical errors and measurement faults are included.
 Benjamin J. Brown
 , Naomi H. Nickerson
 & Dan E. Browne

Article
 Open AccessToughness and strength of nanocrystalline graphene
Graphene is known to be a remarkably strong material, but it can often contain defects. Here, the authors use largescale simulations and continuum modelling to show that the statistical variation in toughness and strength of polycrystalline graphene can be understood with 'weakestlink' statistics.
 Ashivni Shekhawat
 & Robert O. Ritchie

Article
 Open AccessSpatiotemporal propagation of cascading overload failures in spatially embedded networks
Overload failures propagate through hidden functional dependencies across networked systems. Here, the authors study the spatiotemporal propagation behaviour of cascading overload failures, and find that they spread radially from their origin with an approximately constant velocity.
 Jichang Zhao
 , Daqing Li
 & Shlomo Havlin

Article
 Open AccessAn eventbased architecture for solving constraint satisfaction problems
Constraint satisfaction problems are typically solved using conventional von Neumann computing architectures, which are however illsuited to solving them. Here, the authors present a prototype for an eventbased architecture that yield state of the art performance on random SAT problems.
 Hesham Mostafa
 , Lorenz K. Müller
 & Giacomo Indiveri

Article
 Open AccessThe minimal work cost of information processing
Irreversible computation cannot be performed without a work cost, and energy dissipation imposes limitations on devices' performances. Here the authors show that the minimal work requirement of logical operations is given by the amount of discarded information, measured by entropy.
 Philippe Faist
 , Frédéric Dupuis
 & Renato Renner

Article
 Open AccessChemical reaction mechanisms in solution from brute force computational Arrhenius plots
Obtaining activation entropies and enthalpies of a reaction is important for distinguishing between alternative reaction mechanisms. Here the authors use computational methods to accurately obtain the enthalpic/entropic components of the activation free energy for hydrolytic deamination reactions.
 Masoud Kazemi
 & Johan Åqvist

Article 
Ranking in interconnected multilayer networks reveals versatile nodes
A challenging problem is to identify the most central agents in interconnected multilayer networks. Here, De Domenico et al. present a mathematical framework to calculate centrality in such networks—versatility—and rank nodes accordingly.
 Manlio De Domenico
 , Albert SoléRibalta
 & Alex Arenas

Article 
A Bayesian modelling framework for tornado occurrences in North America
Tornadoes are one of nature’s most hazardous phenomena, yet prognostic tools for tornado occurrence are lacking. Here, the authors use Bayesian inference techniques to evaluate the spatiotemporal relationship between atmospheric variables and tornado activity in North America.
 Vincent Y.S. Cheng
 , George B. Arhonditsis
 & Heather Auld

Article
 Open AccessTrainable hardware for dynamical computing using error backpropagation through physical media
Machine learning systems use algorithms that can interpret data to make improved decisions. Hermans et al. develop a physical scheme for a computing system based on recurrent neural networks that physically implements the error backpropagation algorithm, thus performing its own training process.
 Michiel Hermans
 , Michaël Burm
 & Peter Bienstman

Article 
A surface curvature oscillation model for vapour–liquid–solid growth of periodic onedimensional nanostructures
Vapourliquidsolid process is widely used to prepare a variety of onedimensional nanostructures, but a quantitative understanding of the growth mechanism is missing. Here, Wang et al. show that the surface curvature oscillation of the liquid tip determines the growing process and thus the morphology.
 Hui Wang
 , JianTao Wang
 & XiaoHong Zhang

Article 
The theory of pattern formation on directed networks
The study of pattern formation in reaction–diffusion systems has been mainly restricted to symmetric (undirected) networks. Here, Asllani et al.identify a different pattern formation mechanism in a larger class of networks incorporating the possibility of unequal weights for transport along edges.
 Malbor Asllani
 , Joseph D. Challenger
 & Duccio Fanelli

Article 
Cluster synchronization and isolated desynchronization in complex networks with symmetries
Many networks exhibit patterns of synchronized clusters, but the conditions under which this occurs are poorly understood. Pecora et al. develop an analytical approach based on computational group theory to predict the emergence and disappearance of synchrony among local clusters in complex networks.
 Louis M. Pecora
 , Francesco Sorrentino
 & Rajarshi Roy

Article 
Quantum state majorization at the output of bosonic Gaussian channels
In quantum information the majorization conjecture states that the minimum amount of disorder at the output of a quantum Guassian channel is produced by coherent input states, but its proof has remained elusive. Now, Mari et al.solve this longstanding problem and highlight some of its implications.
 A. Mari
 , V. Giovannetti
 & A. S. Holevo

Article
 Open AccessExperimental demonstration of reservoir computing on a silicon photonics chip
Reservoir computing uses computational techniques related to neural networks to perform certain computing tasks. Here, the authors implement a passive optical reservoir computing scheme integrated on a silicon chip, operating at speeds up to 12.5 Gbit s^{−1}.
 Kristof Vandoorne
 , Pauline Mechet
 & Peter Bienstman

Article 
An experimental implementation of oblivious transfer in the noisy storage model
The oblivious transfer protocol is a cryptographic primitive used to create many different secure twoparty schemes. Here, Erven et al. provide the first implementation of the oblivious transfer protocol using entangled photons, within the noisy storage model.
 C. Erven
 , N. Ng
 & G. Weihs

Article 
Quantum computing on encrypted data
Practical quantum computers will require protocols to carry out computation on encrypted data, just like their classical counterparts. Here, the authors present such a protocol that allows an untrusted server to implement universal quantum gates on encrypted qubits without learning about the inputs.
 K. A. G. Fisher
 , A. Broadbent
 & K. J. Resch

Article 
StratonovichtoItô transition in noisy systems with multiplicative feedback
The noise in a stochastic differential equation can be interpreted by Itô or by Stratonovich calculus, and which one to use has been a subject of discussion in statistical physics. Pesce et al.show that the underlying dynamics induce a shift from Stratonovic to Itô calculus in a noisy electrical circuit.
 Giuseppe Pesce
 , Austin McDaniel
 & Giovanni Volpe

Article
 Open AccessA chiralbased magnetic memory device without a permanent magnet
Most new device concepts for randomaccess memory are based on inorganic spin filters, which need a permanent magnet to operate. Here, the authors exploit the chiralinduced spin selectivity effect in an organic spin filter to construct a novel type of memory device, which works without a permanent magnet.
 Oren Ben Dor
 , Shira Yochelis
 & Yossi Paltiel

Article 
Urban characteristics attributable to densitydriven tie formation
An enduring paradox of urban economics is why cities support levels of enterprise, such as patents and inventions, higher than the countryside. Here Pentland et al. suggest that the density of social ties provides a greater flow of ideas, resulting in increased productivity and innovation.
 Wei Pan
 , Gourab Ghoshal
 & Alex Pentland

Article 
Robust classification of salient links in complex networks
Methods to study the structure of complex networks often rely on casesensitive parameters that have limited applications. In this study, a new method—link salience—is used to classify network elements based on a consensus estimate of all nodes, finding generic topological features in many empirical networks.
 Daniel Grady
 , Christian Thiemann
 & Dirk Brockmann

Article 
Sustaining the Internet with hyperbolic mapping
Routing packets on the growing and changing underlying structure of the Internet is challenging and currently based only on local connectivity. Here, a global Internet map is devised: with a greedy forwarding algorithm, it is robust with respect to network growth, and allows speeds close to the theoretical best.
 Marián Boguñá
 , Fragkiskos Papadopoulos
 & Dmitri Krioukov