Mathematics and computing

  • Article
    | Open Access

    The security of DIQKD is difficult to prove, as one needs to take into account every possible attack strategy. Here, the authors develop a method to determine the entropy of a system as the sum of the entropies of its parts. Applied to DIQKD, this implies that it suffices to consider i.i.d. attacks.

    • Rotem Arnon-Friedman
    • , Frédéric Dupuis
    •  & Thomas Vidick
  • Article
    | Open Access

    Meso-scale architecture of connectomes is usually modeled as segregated clusters and communities. Here the authors report that non-assortative communities are better able to capture the functional connectivity for some networks and offer measures of community diversity that predict cognitive performance.

    • Richard F. Betzel
    • , John D. Medaglia
    •  & Danielle S. Bassett
  • Article
    | Open Access

    Single-cell RNA sequencing (scRNA-seq) data provides information on transcriptomic heterogeneity within cell populations. Here, Risso et al develop ZINB-WaVE for low-dimensional representations of scRNA-seq data that account for zero inflation, over-dispersion, and the count nature of the data.

    • Davide Risso
    • , Fanny Perraudeau
    •  & Jean-Philippe Vert
  • Article
    | Open Access

    Artificial intelligence is now superior to humans in many fully competitive games, such as Chess, Go, and Poker. Here the authors develop a machine-learning algorithm that can cooperate effectively with humans when cooperation is beneficial but nontrivial, something humans are remarkably good at.

    • Jacob W. Crandall
    • , Mayada Oudah
    •  & Iyad Rahwan
  • Article
    | Open Access

    Most time series techniques tend to ignore data uncertainties, which results in inaccurate conclusions. Here, Goswami et al. represent time series as a sequence of probability density functions, and reliably detect abrupt transitions by identifying communities in probabilistic recurrence networks.

    • Bedartha Goswami
    • , Niklas Boers
    •  & Jürgen Kurths
  • Article
    | Open Access

    Certain physical problems such as the rupture of a thin sheet can be difficult to solve as computations breakdown at the point of rupture. Here the authors propose a regularization approach to overcome this breakdown which could help dealing with mathematical models that have finite time singularities.

    • Panayotis G. Kevrekidis
    • , Constantinos I. Siettos
    •  & Yannis G. Kevrekidis
  • Article
    | Open Access

    Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.

    • Kevin P. O’Keeffe
    • , Hyunsuk Hong
    •  & Steven H. Strogatz
  • Article
    | Open Access

    Cascade propagation models represent a range of processes on networks, such as power-grid blackouts and epidemic outbreaks. Here the authors investigate temporal profiles of avalanches and show how nonsymmetric average avalanche shapes can occur at criticality.

    • James P. Gleeson
    •  & Rick Durrett
  • Article
    | Open Access

    New computing paradigms, such as in-memory computing, are expected to overcome the limitations of conventional computing approaches. Sebastian et al. report a large-scale demonstration of computational phase change memory (PCM) by performing high-level computational primitives using one million PCM devices.

    • Abu Sebastian
    • , Tomas Tuma
    •  & Evangelos Eleftheriou
  • Article
    | Open Access

    Classifying groups is an important challenge in mathematics and has led to the identification of groups which do not belong to the main families. Here Duncan et al. introduce a type of moonshine which is a connection between these groups, number theory and potentially physics.

    • John F. R. Duncan
    • , Michael H. Mertens
    •  & Ken Ono
  • Article
    | Open Access

    The description of temporal networks is usually simplified in terms of their dynamic community structures, whose identification however relies on a priori assumptions. Here the authors present a data-driven method that determines relevant timescales for the dynamics and uses it to identify communities.

    • Tiago P. Peixoto
    •  & Martin Rosvall
  • Article
    | Open Access

    Robots that can self-assemble into different morphologies are desired to perform tasks that require different physical capabilities. Mathews et al. design robots whose bodies and control systems can merge and split to form new robots that retain full sensorimotor control and act as a single entity.

    • Nithin Mathews
    • , Anders Lyhne Christensen
    •  & Marco Dorigo
  • Article
    | Open Access

    Biomechanical understanding of animal gait and maneuverability has primarily been limited to species with more predictable, steady-state movement patterns. Here, the authors develop a method to quantify movement predictability, and apply the method to study escape-related movement in several species of desert rodents.

    • Talia Y. Moore
    • , Kimberly L. Cooper
    •  & Ramanarayan Vasudevan
  • Article
    | Open Access

    While automated reaction systems typically work for the synthesis of pre-defined molecules, automated systems to discover reactivity are more challenging. Here the authors report an autonomous organic reaction search engine that allows discovery of the most reactive pathways in a multi-reagent, multistep reaction system.

    • Vincenza Dragone
    • , Victor Sans
    •  & Leroy Cronin
  • Article
    | Open Access

    The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

    • Steven L. Brunton
    • , Bingni W. Brunton
    •  & J. Nathan Kutz
  • Article
    | Open Access

    Deforestation and edge effects around cleared areas impact forest stability. Here, the authors examine human impacts on Amazonian forest-savanna bistability and show that tree cover bimodality is enhanced in regions close to human activities and is nearly absent in regions unaffected by human activities.

    • Bert Wuyts
    • , Alan R. Champneys
    •  & Joanna I. House
  • Article
    | Open Access

    Pore structure plays an important role in dictating gas storage performance for nanoporous materials. Here, Smit and colleagues develop a topological approach to quantify pore structure similarity, and exploit the resulting descriptor to screen for materials that possess structural similarities with top-performers.

    • Yongjin Lee
    • , Senja D. Barthel
    •  & Berend Smit
  • Article
    | Open Access

    Origami is widely practiced in the design of foldable structures for smart applications and usually consists of stiff sheets that only deform along prescribed creases. Pinsonet al. take a statistical physics approach to design and characterize arbitrary patterns as a function of folding energy.

    • Matthew B. Pinson
    • , Menachem Stern
    •  & Arvind Murugan
  • Article
    | Open Access

    Solutions of computations can be encoded in the ground state of many-body spin models. Here the authors show that solutions to generic reversible classical computations can be encoded in the ground state of a vertex model, which can be reached without finite temperature phase transitions.

    • C. Chamon
    • , E. R. Mucciolo
    •  & Z.-C. Yang
  • Article
    | Open Access

    Super-resolution localization microscopy produces biophysical information in the form of estimated positions of single molecules. Here, Lindénet al. estimate the uncertainty of single localizations, and show that this additional information can improve data analysis and localization precision.

    • Martin Lindén
    • , Vladimir Ćurić
    •  & Johan Elf
  • Article
    | Open Access

    Active fluids consist of self-driven particles that can drive spontaneous flow without the intervention of external forces. Here Woodhouseet al. show how to design logic circuits using this phenomenon in active fluid networks, which could be further exploited for autonomous microfluidic computing.

    • Francis G. Woodhouse
    •  & Jörn Dunkel
  • Article
    | Open Access

    The authors record both local and long-range neural activity during human epileptic seizures to study the underlying multi-scale dynamics. They find that coupling of activity across spatial scales increases during seizures through propagating waves that are fit by a model that combines neural activity and potassium concentration dynamics.

    • L-E Martinet
    • , G. Fiddyment
    •  & M. A. Kramer
  • Article
    | Open Access

    Drop evaporation can be used as a fabrication technology for targeted particle deposition or microflow control, yet previous research is limited to spherical drops. Here, Sáenzet al. generalize the evaporation dynamics for arbitrary drop geometry and show its potential for more sophisticated control.

    • P. J. Sáenz
    • , A. W. Wray
    •  & K. Sefiane
  • Article
    | Open Access

    Once a purely mathematical discipline, topology has become an essential tool to investigate physical phenomena such as topological states in liquid crystals. Posnjaket al. observe the existence of 3D point defects of higher than unit topological charge in thermally quenched chiral nematic droplets.

    • Gregor Posnjak
    • , Simon Čopar
    •  & Igor Muševič
  • Article
    | Open Access

    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 Access

    The interaction between photonic bandgap materials and light is largely determined by the wavelength-scale 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 Access

    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 Access

    Localisation microscopy enables nanometre-scale 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 super-resolution imaging.

    • Patrick Fox-Roberts
    • , Richard Marsh
    •  & Susan Cox
  • Article
    | Open Access

    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 quantum-mechanical observables of chemical systems, beyond properties trivially contained in the training data.

    • Kristof T. Schütt
    • , Farhad Arbabzadah
    •  & Alexandre Tkatchenko
  • Article
    | Open Access

    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 Access

    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 Access

    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 networks-of-networks.

    • Jaime Iranzo
    • , Javier M. Buldú
    •  & Jacobo Aguirre
  • Article
    | Open Access

    The stochastic nature of single-molecule 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 single-molecule charge transport data without a prioriassumptions.

    • Mario Lemmer
    • , Michael S. Inkpen
    •  & Tim Albrecht
  • Article
    | Open Access

    The K-satisfability problem is a combinatorial discrete optimization problem, which for K=3 is NP-complete, 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 Ricci-Tersenghi
  • 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