Mathematics and computing

  • Article
    | Open Access

    Optical fibres enable high-speed 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 Access

    Melting is a classic first-order phase transition, but an accurate thermodynamic description is still lacking. Here, Pedersen et al. develop a theory, validated by simulations of the Lennard-Jones system, for the melting thermodynamics applicable to all systems characterized by hidden scale invariance.

    • Ulf R. Pedersen
    • , Lorenzo Costigliola
    •  & Jeppe C. Dyre
  • Article
    | Open Access

    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 Access

    Construction of a scalable quantum computer requires error-correcting 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 Access

    Graphene is known to be a remarkably strong material, but it can often contain defects. Here, the authors use large-scale simulations and continuum modelling to show that the statistical variation in toughness and strength of polycrystalline graphene can be understood with 'weakest-link' statistics.

    • Ashivni Shekhawat
    •  & Robert O. Ritchie
  • Article
    | Open Access

    Overload failures propagate through hidden functional dependencies across networked systems. Here, the authors study the spatio-temporal 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 Access

    Constraint satisfaction problems are typically solved using conventional von Neumann computing architectures, which are however ill-suited to solving them. Here, the authors present a prototype for an event-based architecture that yield state of the art performance on random SAT problems.

    • Hesham Mostafa
    • , Lorenz K. Müller
    •  & Giacomo Indiveri
  • Article
    | Open Access

    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 Access

    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 |

    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 Solé-Ribalta
    •  & Alex Arenas
  • Article |

    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 Access

    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 |

    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 |

    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 |

    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 Access

    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 |

    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 |

    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 Access

    Most new device concepts for random-access memory are based on inorganic spin filters, which need a permanent magnet to operate. Here, the authors exploit the chiral-induced 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 |

    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 |

    Methods to study the structure of complex networks often rely on case-sensitive 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 |

    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