Applied mathematics articles within Nature Communications

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  • Article
    | Open Access

    Here, the authors develop a hybrid agent-based model to quantify the contributions of intrinsic cellular mechanisms and bone ecosystem factors to therapy resistance in multiple myeloma. They show that intrinsic mechanisms are essential for resistance, and that the bone microenvironment provides a protective niche that increases the likelihood.

    • Ryan T. Bishop
    • , Anna K. Miller
    •  & David Basanta
  • Article
    | Open Access

    When stem cells develop into tissues intracellular signalling is rewired, errors in this process lead to cancer. Here, authors applied tools from differential geometry made by Albert Einstein’s General Relativity to understand and predict biological network rewiring in health and disease.

    • Anthony Baptista
    • , Ben D. MacArthur
    •  & Christopher R. S. Banerji
  • Article
    | Open Access

    Forecasting the future behaviors based on observed data remains a challenging task especially for large nonlinear systems. The authors propose a data-driven approach combining manifold learning and delay embeddings for prediction of dynamics for all components in high-dimensional systems.

    • Tao Wu
    • , Xiangyun Gao
    •  & Jürgen Kurths
  • Perspective
    | Open Access

    Reservoir Computing has shown advantageous performance in signal processing and learning tasks due to compact design and ability for fast training. Here, the authors discuss the parallel progress of mathematical theory, algorithm design and experimental realizations of Reservoir Computers, and identify emerging opportunities as well as existing challenges for their large-scale industrial adoption.

    • Min Yan
    • , Can Huang
    •  & Jie Sun
  • Article
    | Open Access

    Predicting the evolution of dynamical systems remains challenging, requiring high computational effort or effective reduction of the system into a low-dimensional space. Here, the authors present a data-driven approach for predicting the evolution of systems exhibiting spatiotemporal dynamics in response to external input signals.

    • Francesco Regazzoni
    • , Stefano Pagani
    •  & Alfio Quarteroni
  • Article
    | Open Access

    Link prediction in temporal networks is relevant for many real-world systems, however, current approaches are usually characterized by high computational costs. The authors propose a temporal link prediction framework based on the sequential stacking of static network features, for improved computational speed, appropriate for temporal networks with completely unobserved or partially observed target layers.

    • Xie He
    • , Amir Ghasemian
    •  & Peter J. Mucha
  • Article
    | Open Access

    Early warning signals for rapid regime shifts in complex networks are of importance for ecology, climate and epidemics, where heterogeneities in network nodes and connectivity make construction of early warning signals challenging. The authors propose a method for selecting an optimal set of nodes from which a reliable early warning signal can be obtained.

    • Naoki Masuda
    • , Kazuyuki Aihara
    •  & Neil G. MacLaren
  • Article
    | Open Access

    Network structures can be examined at different scales, and subnetworks in the form of motifs can provide insights into global network properties. The authors propose an approach to decompose a network into a set of latent motifs, which can be used for network comparison, network denoising, and edge inference.

    • Hanbaek Lyu
    • , Yacoub H. Kureh
    •  & Mason A. Porter
  • Article
    | Open Access

    Antibody Mediated Prevention (AMP) trials showed that the broadly neutralizing antibody VRC01 could prevent some HIV-1 acquisitions. Here the authors use VRC01 levels and the sensitivity of each acquired HIV virus to predict viral loads in the AMP studies and show that VRC01 influenced viral loads, though potency was lower in vivo than expected.

    • Daniel B. Reeves
    • , Bryan T. Mayer
    •  & Srilatha Edupuganti
  • Article
    | Open Access

    Abrupt regime shifts could in theory be predicted from early warning signals. Here, the authors show that true critical transitions are challenging to classify in lake planktonic systems, due to mismatches between trophic levels, and reveal uneven performance of early warning signal detection methods.

    • Duncan A. O’Brien
    • , Smita Deb
    •  & Christopher F. Clements
  • Article
    | Open Access

    The usual treatment of wave scattering theory relies on a formalism that does not easily allow for probing optimal spectral response. Here, the authors show how an alternative formalism, encoding fundamental principles of causality and passivity, can be used to make sense of complex scattered fields’ structures.

    • Lang Zhang
    • , Francesco Monticone
    •  & Owen D. Miller
  • Article
    | Open Access

    Embedding of complex networks in the latent geometry allows for a better understanding of their features. The authors propose a framework for mapping complex networks into high-dimensional hyperbolic space to capture their intrinsic dimensionality, navigability and community structure.

    • Robert Jankowski
    • , Antoine Allard
    •  & M. Ángeles Serrano
  • Article
    | Open Access

    Studies of the evolution of cooperation often assume information use that is inconsistent with empirical observations. Here, the authors’ research on general imitation dynamics reveals that cooperation is fostered by individuals using less personal information and more social information.

    • Xiaochen Wang
    • , Lei Zhou
    •  & Aming Li
  • Article
    | Open Access

    In this study, the authors develop a mathematical modelling framework to estimate the impacts of non-pharmaceutical interventions and vaccination on COVID-19 incidence. The model accounts for changes in SARS-CoV-2 variant and population immunity, and here they use it to investigate epidemic dynamics in French Polynesia.

    • Lloyd A. C. Chapman
    • , Maite Aubry
    •  & Adam J. Kucharski
  • Article
    | Open Access

    Many real-world systems are characterized by bursty dynamics with interchanging periods of intense activity and quiescence. The authors propose a method to construct temporal networks that match a given activity pattern, and apply it to empirical bursty patterns.

    • Anzhi Sheng
    • , Qi Su
    •  & Joshua B. Plotkin
  • Article
    | Open Access

    Ecosystems must be able to bounce back from perturbations to persist without species extinctions. This study uses theoretical modelling to show the importance of reactivity—how species respond in the short term to perturbations—for assessing the health of complex ecosystems, revealing that it can be a better predictor of extinction risk than stability.

    • Yuguang Yang
    • , Katharine Z. Coyte
    •  & Aming Li
  • Article
    | Open Access

    Studies on mutant invasion typically assume populations in isolation, rather than part of an ecological community. Here, the authors use computational models to investigate how enemy-victim interactions influence properties of mutant invasion, showing that selection is substantially weakened.

    • Dominik Wodarz
    •  & Natalia L. Komarova
  • Article
    | Open Access

    Critical transitions and qualitative changes of dynamics in cardiac, ecological, and economical systems, can be characterized by discrete-time bifurcations. The authors propose a deep learning framework that provides early warning signals for critical transitions in discrete-time experimental data.

    • Thomas M. Bury
    • , Daniel Dylewsky
    •  & Gil Bub
  • Article
    | Open Access

    In 1952, Turing unlocked the reaction-diffusion basis of natural patterns, such as zebra stripes. The authors propose a reaction-diffusion model that recreates characteristics of the flagellar waveform for bull sperm and Chlamydomonas flagella.

    • James F. Cass
    •  & Hermes Bloomfield-Gadêlha
  • Article
    | Open Access

    Capillary breakup in multimaterial fibers is explored for the self-assembly of optoelectronic systems. However, its insights primarily stem from numerical simulations, qualitative at best. The authors formulate an analytical model of such breakup, obtaining a window in the governing parameters where the generally chaotic breakup becomes predictable and thus engineerable.

    • Camila Faccini de Lima
    • , Fan Wang
    •  & Alexander Gumennik
  • Article
    | Open Access

    Personal communication networks through mobile phones and online platforms can be characterized by patterns of tie strengths. The authors propose a model to explain driving mechanisms of emerging tie strength heterogeneity in social networks, observing similarity of patterns across various datasets.

    • Gerardo Iñiguez
    • , Sara Heydari
    •  & Jari Saramäki
  • Article
    | Open Access

    In stochastic games, there is a feedback loop between a group’s social behaviors and its environment. Kleshnina et al. show that groups are often more cooperative when they know the exact state of their environment, although there are also intriguing cases when ignorance is beneficial.

    • Maria Kleshnina
    • , Christian Hilbe
    •  & Martin A. Nowak
  • Article
    | Open Access

    The authors show that the ramified ductal network of the mouse salivary gland develops from a set of simple probabilistic rules, where ductal elongation and branching are driven by the persistent expansion of the surrounding tissue.

    • Ignacio Bordeu
    • , Lemonia Chatzeli
    •  & Benjamin D. Simons
  • Article
    | Open Access

    The authors propose a confocal complemented signal-object collaborative regularization method for non-line-of-sight (NLOS) imaging without specific requirements on the spatial pattern of measurement points. The method extends the application range of NLOS imaging.

    • Xintong Liu
    • , Jianyu Wang
    •  & Lingyun Qiu
  • Article
    | Open Access

    Efficient spatial targeting of interventions could reduce the spread of infections in transportation hubs. Here, the authors assess the optimal locations to target in Heathrow airport using disease transmission models informed by a contact network based on anonymised location data from 200,000 individuals.

    • Mattia Mazzoli
    • , Riccardo Gallotti
    •  & José J. Ramasco
  • Article
    | Open Access

    Triadic interactions are higher-order interactions relevant to many real complex systems. The authors develop a percolation theory for networks with triadic interactions and identify basic mechanisms for observing dynamical changes of the giant component such as the ones occurring in neuronal and climate networks.

    • Hanlin Sun
    • , Filippo Radicchi
    •  & Ginestra Bianconi
  • Article
    | Open Access

    As lamellar materials, smectics exhibit both liquid and solid characteristics, making them difficult to model at the mesoscale. Paget et al. propose a complex tensor order parameter that reflects the smectic symmetries, capable of describing complex defects including dislocations and disclinations.

    • Jack Paget
    • , Marco G. Mazza
    •  & Tyler N. Shendruk
  • Article
    | Open Access

    Populations of swarming coupled oscillators with inhomogeneous natural frequencies and chirality are relevant for active matter systems and micro-robotics. The authors model and analyze a variety of their self-organized behaviors that mimic natural and artificial micro-scale collective systems.

    • Steven Ceron
    • , Kevin O’Keeffe
    •  & Kirstin Petersen
  • Article
    | Open Access

    Bubbles at an air-liquid interface will rupture when their spherical cap becomes sufficiently drained. It is now shown that the film thickness of large bare viscous bubbles is highly non-uniformly distributed, and that a bubble’s thickness profile relates to its drainage velocity.

    • Casey Bartlett
    • , Alexandros T. Oratis
    •  & James C. Bird
  • Article
    | Open Access

    Here the authors introduce dual communities, characterized by strong connections at their boundaries, and show that they are formed as a trade-off between efficiency and resilience in supply networks.

    • Franz Kaiser
    • , Philipp C. Böttcher
    •  & Dirk Witthaut
  • Article
    | Open Access

    Systemic risk and bank bailout approaches have been the source of discussions on scientific, financial and governmental forums. An artificial intelligence technique is proposed to inform equitable bailout decisions that minimise taxpayers’ losses.

    • Daniele Petrone
    • , Neofytos Rodosthenous
    •  & Vito Latora
  • Perspective
    | Open Access

    Theoretical models and structures recovered from measured data serve for analysis of complex networks. The authors discuss here existing gaps between theoretical methods and real-world applied networks, and potential ways to improve the interplay between theory and applications.

    • Leto Peel
    • , Tiago P. Peixoto
    •  & Manlio De Domenico
  • Article
    | Open Access

    Despite rapid and significant changes during the pandemic, prognostic models for COVID-19 patients do not currently account for data drifts. Here, the authors develop a framework for continuously monitoring and updating prognostic models and applied it to predict 28-day survival in COVID-19 patients.

    • Todd J. Levy
    • , Kevin Coppa
    •  & Theodoros P. Zanos
  • Article
    | Open Access

    Diffusive motions in complex environments such as living biological cells or soft matter systems can be analyzed with single-particle-tracking approaches, where accuracy of output may vary. The authors involve a machine-learning technique for decoding anomalous-diffusion data and provide an uncertainty estimate together with predicted output.

    • Henrik Seckler
    •  & Ralf Metzler
  • Article
    | Open Access

    Socioeconomic segregation is one of the main factors behind large-scale inequalities in urban areas and its characterisation remains challenging. The authors propose a family of non-parametric measures to quantify spatial heterogeneity through diffusion, and show how this relates to segregation and deprivation

    • Sandro Sousa
    •  & Vincenzo Nicosia
  • Article
    | Open Access

    The ’Roadmap’ for relaxation of COVID-19 restrictions in England in 2021 was informed by mathematical modelling. Here, the authors perform a retrospective assessment of the accuracy of modelling predictions and identify the main sources of uncertainty that led to observed values deviating from projections.

    • Matt J. Keeling
    • , Louise Dyson
    •  & Samuel Moore
  • Article
    | Open Access

    Accurate forecasts of lithium-ion battery performance will ease concerns about the reliability of electric vehicles. Here, the authors leverage electrochemical impedance spectroscopy and machine learning to show that future capacity can be predicted amid uneven use, with no historical data requirement.

    • Penelope K. Jones
    • , Ulrich Stimming
    •  & Alpha A. Lee
  • Article
    | Open Access

    In network systems governed by oscillatory activity, such as brain networks or power grids, configurations of synchrony may define network functions. The authors introduce a control approach for the formation of desired synchrony patterns through optimal interventions on the network parameters.

    • Tommaso Menara
    • , Giacomo Baggio
    •  & Fabio Pasqualetti
  • Article
    | Open Access

    Device-level complexity represents a big shortcoming for the hardware realization of analogue memory-based deep neural networks. Mackin et al. report a generalized computational framework, translating software-trained weights into analogue hardware weights, to minimise inference accuracy degradation.

    • Charles Mackin
    • , Malte J. Rasch
    •  & Geoffrey W. Burr
  • Article
    | Open Access

    Machine learning tools allow to extract dynamical systems from data, however this problem remains challenging for networks and systems of interacting agents. The authors introduce an approach to learn a predictive model for the dynamics of coupled agents in the form of partial differential equations using emergent spatial embeddings.

    • Felix P. Kemeth
    • , Tom Bertalan
    •  & Ioannis G. Kevrekidis