Applied mathematics articles within Nature Communications

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  • Article
    | Open Access

    It is often advantageous to transform a strongly nonlinear system into a linear one in order to simplify its analysis for prediction and control. Here the authors combine dynamical systems with deep learning to identify these hard-to-find transformations.

    • Bethany Lusch
    • , J. Nathan Kutz
    •  & Steven L. Brunton

  • Article
    | Open Access

    HIV infected cells persist for decades in patients under ART, but the mechanisms responsible remain unclear. Here, Reeves et al. use modeling approaches adapted from ecology to show that cellular proliferation, rather than viral replication, generates a majority of infected cells during ART.

    • Daniel B. Reeves
    • , Elizabeth R. Duke
    •  & Joshua T. Schiffer

  • Article
    | Open Access

    Self-folding origami have applications for mechanical metamaterials but one of their pitfalls is that many undesirable folding modes exist. Here the authors propose an algorithm to determine which folding joints to make stiffer in order to ensure that the sheet is folded into the chosen state.

    • Menachem Stern
    • , Viraaj Jayaram
    •  & Arvind Murugan

  • Article
    | Open Access

    Causality inference in time series analysis based on temporal precedence principle between cause and effect fails to detect mutual causal interactions. Here, Yang et al. introduce a causal decomposition approach based on the covariation principle of cause and effect that overcomes this limitation.

    • Albert C. Yang
    • , Chung-Kang Peng
    •  & Norden E. Huang

  • Article
    | Open Access

    Anticrack propagation in snow results from the mixed-mode failure and collapse of a buried weak layer and can lead to slab avalanches. Here, authors reproduce the complex dynamics of anticrack propagation observed in field experiments using a Material Point Method with large strain elastoplasticity.

    • J. Gaume
    • , T. Gast
    •  & C. Jiang

  • Article
    | Open Access

    Classifying crystal structures using their space group is important to understand material properties, but the process currently requires user input. Here, the authors use machine learning to automatically classify more than 100,000 simulated perfect and defective crystal structures.

    • Angelo Ziletti
    • , Devinder Kumar
    •  & Luca M. Ghiringhelli

  • Article
    | Open Access

    Mitochondrial populations in cells may consist of heteroplasmic mixtures of mtDNA types, and their evolution through development, aging and generations is central to genetic diseases. Here the authors dissect these population dynamics using a large mouse-based data set to characterise the dynamics of heteroplasmy mean and variance throughout life and across generations.

    • Joerg P. Burgstaller
    • , Thomas Kolbe
    •  & Iain G. Johnston

  • Article
    | Open Access

    Wolbachia infection in mosquitoes reduces dengue virus spread under specific lab conditions, prompting its use in disease control. Here, King et al. show that Wolbachia increases mean and variance in mosquito susceptibility and explain how this affects Wolbachia invasion and dengue transmission.

    • Jessica G. King
    • , Caetano Souto-Maior
    •  & M. Gabriela M. Gomes

  • Article
    | Open Access

    Droplet evaporation control has applications in inkjet printing and surface patterning. Here, the authors show that on slippery curved substrates droplets evaporate by slowly retracting and then suddenly snapping, which can be exploited to design surfaces that control an evaporation sequence.

    • Gary G. Wells
    • , Élfego Ruiz-Gutiérrez
    •  & Rodrigo Ledesma-Aguilar

  • Article
    | Open Access

    Sokolov et al. have previously shown how bacteria are expelled in response to a rotating microparticle. Here the authors find that when the microparticle is spun at much higher rotation rates bacteria are trapped around it and then are expelled radially upon rotation cessation in an explosion-like manner.

    • Andrey Sokolov
    • , Leonardo Dominguez Rubio
    •  & Igor S. Aranson

  • Article
    | Open Access

    Algorithmic information theory measures the complexity of strings. Here the authors provide a practical bound on the probability that a randomly generated computer program produces a given output of a given complexity and apply this upper bound to RNA folding and financial trading algorithms.

    • Kamaludin Dingle
    • , Chico Q. Camargo
    •  & Ard A. Louis

  • Article
    | Open Access

    Wave propagation is often nonlinear in character, yet the interplay between disorder and nonlinearity remains elusive. Kim et al. use experiments and corroborating numerical simulations to investigate this phenomenon and demonstrate superdiffusive energy transport in disordered granular chains.

    • Eunho Kim
    • , Alejandro J. Martínez
    •  & Jinkyu Yang

  • Article
    | Open Access

    Plants use multiple cues to monitor seasonal temperatures. Here, the authors show that Arabidopsis requires not only prolonged cold, but the absence of temperature spikes above 15 °C to epigenetically silence FLC during winter.

    • Jo Hepworth
    • , Rea L. Antoniou-Kourounioti
    •  & Caroline Dean

  • Article
    | Open Access

    Our understanding of material instabilities in soft solids remains elusive mainly due to the mathematical challenges in capturing localised phenomena within nonlinear elastic materials. Ciarletta develops an analytical theory to describe the nucleation threshold of creases in agreement with experiments.

    • P. Ciarletta

  • 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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

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