Applied mathematics articles within Nature Communications

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  • Article
    | Open Access

    Aberrant synchronous oscillations have been associated with numerous brain disorders, including essential tremor. The authors show that synchronous cerebellar activity can casually affect essential tremor and that its underlying mechanism may be related to the temporal coherence of the tremulous movement.

    • Sebastian R. Schreglmann
    • , David Wang
    •  & Nir Grossman

  • Article
    | Open Access

    As spiteful behaviors harm both the actor and the target, it is challenging to understand how these behaviors could be adaptive. Here Fulker et al. show that spite can be favored by feedbacks with network structure that create correlated and anti-correlated behavioral interactions simultaneously.

    • Zachary Fulker
    • , Patrick Forber
    •  & Christoph Riedl

  • Article
    | Open Access

    Lack of a widespread surveillance network hampers accurate infectious disease forecasting. Here the authors provide a framework to optimize the selection of surveillance site locations and show that accurate forecasting of respiratory diseases for locations without surveillance is feasible.

    • Sen Pei
    • , Xian Teng
    •  & Jeffrey Shaman

  • Article
    | Open Access

    Digital trace data from search engines lacks information about the experiences of the individuals generating the data. Here the authors link search data and human computation to build a tracking model of influenza-like illness.

    • Stefan Wojcik
    • , Avleen S. Bijral
    •  & David Lazer

  • Article
    | Open Access

    Influencer networks include a small set of highly-connected nodes and can reach synchrony only via strong node interaction. Tönjes et al. show that introducing an optimal amount of noise enhances synchronization of such networks, which may be relevant for neuroscience or opinion dynamics applications.

    • Ralf Tönjes
    • , Carlos E. Fiore
    •  & Tiago Pereira

  • Article
    | Open Access

    Standard benchmarking of single-molecule localization microscopy cannot quantify nanoscale accuracy of arbitrary datasets. Here, the authors present Wasserstein-induced flux, a method using a chosen perturbation and knowledge of the imaging system to measure confidence of individual localizations.

    • Hesam Mazidi
    • , Tianben Ding
    •  & Matthew D. Lew

  • Article
    | Open Access

    Current inequality and market consumption modelling appears to be subjective. Here the authors combined all three axes of poverty modelling - Engel-Krishnakumar’s microeconomics, Aoki-Chattopadhyay’s mathematical precept and found that multivariate construction is a key component of economic data analysis, implying all modes of income and expenditure need to be considered to arrive at a proper weighted prediction of poverty.

    • Amit K. Chattopadhyay
    • , T. Krishna Kumar
    •  & Iain Rice

  • Article
    | Open Access

    Supply networks with optimal structure do not contain loops but these can arise as a result of damages or fluctuations. Here Kaiser et al. uncover the mechanisms of loop formation, predict their location and draw analogies with loop formation in biological networks such as plants and animal vasculature.

    • Franz Kaiser
    • , Henrik Ronellenfitsch
    •  & Dirk Witthaut

  • Article
    | Open Access

    Multiplayer games can be used as testbeds for the development of learning algorithms for artificial intelligence. Omidshafiei et al. show how to characterize and compare such games using a graph-based approach, generating new games that could potentially be interesting for training in a curriculum.

    • Shayegan Omidshafiei
    • , Karl Tuyls
    •  & Rémi Munos

  • Article
    | Open Access

    Nested and modular patterns are vastly observed in mutualistic networks across genres and geographic conditions. Here, the authors show a unified mechanism that underlies the assembly and evolution of such networks, based on adaptive niche interactions of the participants.

    • Weiran Cai
    • , Jordan Snyder
    •  & Raissa M. D’Souza

  • Article
    | Open Access

    Beam shaping methods can generate optical fields with nontrivial topologies, which are invariant against perturbations and thus interesting for information encoding. Here, the authors introduce the realization of framed optical knots to encode programs with the conjoined use of prime factorization.

    • Hugo Larocque
    • , Alessio D’Errico
    •  & Ebrahim Karimi

  • Article
    | Open Access

    An ongoing global debate concerns effective and sustainable lockdown release strategies in the current pandemic. Here, the authors implement a network model at healthcare-relevant spatial scale to show that coordinated local strategies can be effective in containing further resurgence of the disease.

    • Fabio Della Rossa
    • , Davide Salzano
    •  & Mario di Bernardo

  • Article
    | Open Access

    Both the mathematics and outcomes of the Method of Reflections (MR) and Fitness and Complexity algorithm (FC) approaches differ largely. Here the authors recast both methods in a mathematical and multidimensional framework to reconcile both and show that the conflicts between the two methodologies to measure economic complexity can be resolved by a neat mathematical method based on linear-algebra tools within a bipartite-networks framework.

    • Carla Sciarra
    • , Guido Chiarotti
    •  & Francesco Laio

  • Article
    | Open Access

    The choice of molecular representations can severely impact the performances of machine-learning methods. Here the authors demonstrate a persistence homology based molecular representation through an active-learning approach for predicting CO2/N2 interaction energies at the density functional theory (DFT) level.

    • Jacob Townsend
    • , Cassie Putman Micucci
    •  & Konstantinos D. Vogiatzis

  • Article
    | Open Access

    Every year, hundreds of people die at sea because of vessel accidents, and a key challenge in reducing these fatalities is to make Search and Rescue (SAR) planning more efficient. Here, the authors uncover hidden flow features that attract floating objects, providing specific information for optimal SAR planning.

    • Mattia Serra
    • , Pratik Sathe
    •  & George Haller

  • Article
    | Open Access

    It is crucial yet challenging to identify cause-consequence relation in complex dynamical systems where direct causal links can mix with indirect ones. Leng et al. propose a data-driven model-independent method to distinguish direct from indirect causality and test its applicability to real-world data.

    • Siyang Leng
    • , Huanfei Ma
    •  & Luonan Chen

  • Article
    | Open Access

    Population structure enables emergence of cooperation among individuals, but the impact of the dynamic nature of real interaction networks is not understood. Here, the authors study the evolution of cooperation on temporal networks and find that temporality enhances the evolution of cooperation.

    • Aming Li
    • , Lei Zhou
    •  & Simon A. Levin

  • Article
    | Open Access

    The demands on transportation systems continue to grow while the methods for analyzing and forecasting traffic conditions remain limited. Here the authors show a parameter-independent approach for an accurate description, identification and forecasting of spatio-temporal traffic patterns directly from data.

    • A. M. Avila
    •  & I. Mezić

  • Article
    | Open Access

    Natural hazards can have huge impacts on individuals and societies, however, monitoring the economic recovery in the aftermath of extreme events remains a challenge. Here, the authors find that Facebook posting activity of small businesses can be used to monitor post-disaster economic recovery, and can allow local governments to better target distribution of resources.

    • Robert Eyre
    • , Flavia De Luca
    •  & Filippo Simini

  • Article
    | Open Access

    Aggregation of matter, common in stratified fluid systems, is essential to the carbon cycle and ocean ecology. Although the current understanding of aggregation involves only collision and adhesion, here Camassa et al. reveal a self-assembly phenomenon arising solely from diffusion-induced flows.

    • Roberto Camassa
    • , Daniel M. Harris
    •  & Richard M. McLaughlin

  • Article
    | Open Access

    Reconstructing system dynamics on complex high-dimensional energy landscapes from static experimental snapshots remains challenging. Here, the authors introduce a framework to infer the essential dynamics of physical and biological systems without need for time-dependent measurements.

    • Philip Pearce
    • , Francis G. Woodhouse
    •  & Jörn Dunkel

  • Article
    | Open Access

    Network properties can be modified when they interact with other networks, yet most previous results have focused on equilibrium states exclusively. Here the authors introduce a framework to examine the out-of-equilibrium dynamics of evolutionary processes to mimic real-world interconnected networks.

    • Javier M. Buldú
    • , Federico Pablo-Martí
    •  & Jacobo Aguirre

  • Article
    | Open Access

    Methods for dilation are currently limited to specific shapes and curvatures, with the potential for some of the structure's shape to encroach onto the final dilated volume. Here, the authors develop a method for creating dilational structures from arbitrary surfaces that avoids volume encroachment.

    • Freek G. J. Broeren
    • , Werner W. P. J. van de Sande
    •  & Just L. Herder

  • Article
    | Open Access

    The spatial structure of a population is often critical for the evolution of cooperation. Here, Allen and colleagues show that when spatial structure is represented by an isothermal graph, the effective number of neighbors per individual determines whether or not cooperation can evolve.

    • Benjamin Allen
    • , Gabor Lippner
    •  & Martin A. Nowak

  • Article
    | Open Access

    Theories state that transitions between extreme waves are allowed but experimental confirmations are lacking because of lack of control strategies. Here, the authors propose and experimentally report, for the first time, the use of topological indices to control the generation of extreme waves.

    • Giulia Marcucci
    • , Davide Pierangeli
    •  & Claudio Conti

  • Article
    | Open Access

    The brain can often continue to function despite lesions in many areas, but damage to particular locations may have serious effects. Here, the authors use the concept of Ollivier-Ricci curvature to investigate the robustness of brain networks.

    • Hamza Farooq
    • , Yongxin Chen
    •  & Christophe Lenglet

  • Article
    | Open Access

    Viruses have evolved protein containers with a wide spectrum of icosahedral architectures but the geometric constraints defining these container designs remain to be understood. Here authors revisit the construction of icosahedral architectures using the Archimedean lattices that explain the outliers to the current classification scheme.

    • Reidun Twarock
    •  & Antoni Luque

  • Article
    | Open Access

    Neural signalling is directional, but non-invasive neuroimaging methods are unable to map directed connections between brain regions. Here, the authors show how network communication measures can be used to infer signalling directionality from the undirected topology of brain structural connectomes.

    • Caio Seguin
    • , Adeel Razi
    •  & Andrew Zalesky

  • Article
    | Open Access

    When a viscous fluid is displaced by a less viscous phase between two plates, a finger-like instability occurs. Here the authors demonstrate how applying an external electric field can suppress the fingering instability without the need to alter the fluid flow rate or the gap geometry.

    • Tao Gao
    • , Mohammad Mirzadeh
    •  & Martin Z. Bazant

  • Article
    | Open Access

    Systematic methods to characterize human mobility can lead to more accurate forecasting of epidemic spreading and better urban planning. Here the authors present a methodology to analyse daily commuting data by representing it with an irrotational vector field and a corresponding scalar potential.

    • Mattia Mazzoli
    • , Alex Molas
    •  & José J. Ramasco

  • Article
    | Open Access

    Plasmodesmata channels connect neighbouring plant cells and respond to external stimuli via changes in permeability. Here Park et al. propose that mechanical forces can displace the dumbbell-shaped ER-desmotubule complex that spans the central plasmodesmatal cylinder leading to closure of the pore.

    • Keunhwan Park
    • , Jan Knoblauch
    •  & Kaare H. Jensen

  • Article
    | Open Access

    Designing alternative paradigms for bio-inspired analog computing that harnesses collective dynamics remains a challenge. Here, the authors exploit the synchronization dynamics of coupled vanadium dioxide-based insulator-to-metal phase-transition nano-oscillators for adaptive locomotion control.

    • Sourav Dutta
    • , Abhinav Parihar
    •  & Suman Datta

  • Article
    | Open Access

    Most microbiome studies make conclusions based on changes in relative abundance of taxa, inferred from sequencing data. Here, the authors highlight common pitfalls in comparing relative abundance across samples, and identify solutions that reveal microbial changes without the need to estimate total microbial load.

    • James T. Morton
    • , Clarisse Marotz
    •  & Rob Knight

  • Article
    | Open Access

    Failure to account for heterogeneity in TB risk can mislead model-based evaluation of proposed interventions. Here, the authors introduce a metric to estimate the distribution of risk in populations from routinely collected data and find that variation in infection acquisition is the most impactful.

    • M. Gabriela M. Gomes
    • , Juliane F. Oliveira
    •  & Christian Lienhardt

  • Article
    | Open Access

    Evaporation plays a key role in applications such as cooling and desalination. Here, the authors experimentally demonstrated a unifying relationship between dimensionless flux and driving potential for evaporation kinetics under different working conditions.

    • Zhengmao Lu
    • , Ikuya Kinefuchi
    •  & Evelyn N. Wang

  • Article
    | Open Access

    Microfluidic multipoles use arrays of sources and sinks to confine fluids and reagents without the use of physical channels. Here the authors use conformal mappings to predict both convective and diffusive transport in these flows and 3D print multipoles to automate surface-based immunoassays.

    • Pierre-Alexandre Goyette
    • , Étienne Boulais
    •  & Thomas Gervais

  • Article
    | Open Access

    Nonlinear machine learning methods have good predictive ability but the lack of transparency of the algorithms can limit their use. Here the authors investigate how these methods approach learning in order to assess the dependability of their decision making.

    • Sebastian Lapuschkin
    • , Stephan Wäldchen
    •  & Klaus-Robert Müller

  • Article
    | Open Access

    Universal cluster states for quantum computing can be assembled without feed-forward by fusing n-photon clusters with linear optics if the fusion success probability is above a threshold p. The authors bound p in terms of n and provide protocols for n = 3 clusters requiring lower fusion probability than before.

    • Mihir Pant
    • , Don Towsley
    •  & Saikat Guha

  • Article
    | Open Access

    Percolation is a tool used to investigate a network’s response as random links are removed. Here the author presents a generic analytic theory to describe how percolation properties are affected in coloured networks, where the colour can represent a network feature such as multiplexity or the belonging to a community.

    • Ivan Kryven

  • Article
    | Open Access

    Similarly to entropy, majorization allows to quantify deviation from uniformity in a wide range of fields. In this paper, the authors use its generalization to the quantum realm to derive a complete set of necessary and sufficient conditions for thermal transformations of quantum states.

    • Gilad Gour
    • , David Jennings
    •  & Iman Marvian

  • Article
    | Open Access

    Modern microscopes can generate high volumes of 3D images, driving difficulties in data handling and processing. Here, the authors present a content-adaptive image representation as an alternative to standard pixels that goes beyond data compression to overcome storage, memory, and processing bottlenecks.

    • Bevan L. Cheeseman
    • , Ulrik Günther
    •  & Ivo F. Sbalzarini

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