Applied mathematics articles within Nature Communications

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  • Article
    | Open Access

    Non-pharmaceutical interventions (NPIs) and COVID-19 vaccination have been implemented concurrently, making their relative effects difficult to measure. Here, the authors show that effects of NPIs reduced as vaccine coverage increased, but that NPIs could still be important in the context of more transmissible variants.

    • Yong Ge
    • , Wen-Bin Zhang
    •  & Shengjie Lai

  • Article
    | Open Access

    Defining the dimension in bounded, inhomogeneous or discrete physical systems may be challenging. The authors introduce here a dynamics-based notion of dimension by analysing diffusive processes in space, relevant for non-ideal physical systems and networks.

    • Robert Peach
    • , Alexis Arnaudon
    •  & Mauricio Barahona

  • Article
    | Open Access

    Data-driven recovery of topology is challenging for networks beyond pairwise interactions. The authors propose a framework to reconstruct complex networks with higher-order interactions from time series, focusing on networks with 2-simplexes where social contagion and Ising dynamics generate binary data.

    • Huan Wang
    • , Chuang Ma
    •  & Hai-Feng Zhang

  • Article
    | Open Access

    Turing structures emerge in reaction-diffusion processes far from thermodynamic equilibrium involving chemicals with different diffusion coefficients in classic Turing systems. Here, authors show that a Turing structure with near zero strain semi-coherence interfaces can be constructed in homogeneous solutions.

    • Yuanming Zhang
    • , Ningsi Zhang
    •  & Zhigang Zou

  • Article
    | Open Access

    Double-gyroid networks assemble in diverse soft materials, yet the molecular packing that underlies their complex structure remains obscure. Here, authors advance a theory that resolves a long-standing puzzle about their formation in block copolymers.

    • Abhiram Reddy
    • , Michael S. Dimitriyev
    •  & Gregory M. Grason

  • Article
    | Open Access

    Here, the authors simulate COVID-19 outbreaks on an empirical contact network derived from digital contact data collected on cruise ships. They model impacts of different control measures and find that combinations of measures, particularly vaccination and rapid antigen testing, are important for mitigating outbreaks.

    • Rachael Pung
    • , Josh A. Firth
    •  & Adam J. Kucharski

  • Article
    | Open Access

    This paper proposes HYPER, a method for screening more people using fewer tests by testing pools formed via hypergraph factorization. HYPER is not only efficient but is also simple to implement, flexible, and has maximally balanced pools.

    • David Hong
    • , Rounak Dey
    •  & Edgar Dobriban

  • Article
    | Open Access

    Integration of mathematical modeling, ecological analyses of patient biopsies, and neoantigen heterogeneity suggests recruitment of immunosuppressive cells is key to initializing transformation from adenoma to carcinoma in human colorectal cancer.

    • Chandler D. Gatenbee
    • , Ann-Marie Baker
    •  & Alexander R. A. Anderson

  • Article
    | Open Access

    The 2001–2019 web of international waste trade is investigated, allowing the identification of countries at threat of improper handling and disposal of waste. Chemical tracers are used to identify the environmental impact of waste in these countries.

    • Johann H. Martínez
    • , Sergi Romero
    •  & Ernesto Estrada

  • Article
    | Open Access

    Ranking lists are relevant to various areas of nature and society, however their evolution with the elements changing rank in time remained unexplored. The authors uncover a mechanism of ranking dynamics induced by the flux governing the arrival of new elements in the list, for improved predictability of ranking models.

    • Gerardo Iñiguez
    • , Carlos Pineda
    •  & Albert-László Barabási

  • Perspective
    | Open Access

    A grand challenge in robotics is realising intelligent agents capable of autonomous interaction with the environment. In this Perspective, the authors discuss the potential, challenges and future direction of research aimed at demonstrating embodied intelligent robotics via neuromorphic technology.

    • Chiara Bartolozzi
    • , Giacomo Indiveri
    •  & Elisa Donati

  • Article
    | Open Access

    The evolution of networks with structure changing in time is dependent on their past states and relevant to diffusion and spreading processes. The authors show that temporal network’s memory is described by multidimensional patterns at a microscopic scale, and cannot be reduced to a scalar quantity.

    • Oliver E. Williams
    • , Lucas Lacasa
    •  & Vito Latora

  • Article
    | Open Access

    The pedestrian-induced oscillation of the London Millennium Bridge is considered as an example of emerging synchronisation. Belykh et al. provide an alternative mechanism for emergence of coherent oscillatory bridge dynamics where synchrony is a consequence, not the cause, of the instability.

    • Igor Belykh
    • , Mateusz Bocian
    •  & Allan McRobie

  • Article
    | Open Access

    Twisted flux tubes are prominent candidates for the progenitors of solar active regions. Here, the authors show a clear signature of the emergence of pre-twisted magnetic flux tubes using magnetic winding, which detects the emerging magnetic topology despite the deformation experienced by the emerging magnetic field.

    • D. MacTaggart
    • , C. Prior
    •  & S. L. Guglielmino

  • Article
    | Open Access

    The movements of individuals within and among cities influence critical aspects of our society, such as well-being, the spreading of epidemics, and the quality of the environment. Here, the authors use deep neural networks to discover non-linear relationships between geographical variables and mobility flows.

    • Filippo Simini
    • , Gianni Barlacchi
    •  & Luca Pappalardo

  • Article
    | Open Access

    The Earth’s climate system is highly complex, however it exhibits certain persistent cyclic patterns like the El Niño Southern Oscillation. The authors apply the spectral theory of dynamical systems and data science techniques to extract such coherent modes of climate variability from high-dimensional observational data.

    • Gary Froyland
    • , Dimitrios Giannakis
    •  & Joanna Slawinska

  • Article
    | Open Access

    Gradient-based and non-gradient-based methods for training neural networks are usually considered to be fundamentally different. The authors derive, and illustrate numerically, an analytic equivalence between the dynamics of neural network training under conditioned stochastic mutations, and under gradient descent.

    • Stephen Whitelam
    • , Viktor Selin
    •  & Isaac Tamblyn

  • Article
    | Open Access

    Establishing the time since death (TSD) is vital in many forensic investigations. By combining thermometry, photogrammetry and numerical thermodynamic modelling, the TSD can be determined non-invasively for bodies of arbitrary shape and posture with an unprecedented accuracy of 0.26 h ± 1.38 h.

    • Leah S. Wilk
    • , Gerda J. Edelman
    •  & Maurice C. G. Aalders

  • Article
    | Open Access

    Rift Valley fever is a zoonotic haemorrhagic fever with complex transmission dynamics influenced by environmental variables and animal movements. Here, the authors develop a metapopulation model incorporating these factors and use it to identify the main drivers of transmission in the Comoros archipelago.

    • Warren S. D. Tennant
    • , Eric Cardinale
    •  & Raphaëlle Métras

  • Article
    | Open Access

    Finding a biologically-relevant inductive bias for training DNNs on large fitness landscapes is challenging. Here, the authors propose a method called Epistatic Net that improves DNN prediction accuracy and interpretation speed by integrating the knowledge that higher-order epistatic interactions are usually sparse.

    • Amirali Aghazadeh
    • , Hunter Nisonoff
    •  & Kannan Ramchandran

  • Article
    | Open Access

    Lineage tracing and snapshots of transcriptional state at the single-cell level are powerful, complementary tools for studying development. Here, the authors propose a mathematical method combining lineage tracing with trajectory inference to improve our understanding of development.

    • Aden Forrow
    •  & Geoffrey Schiebinger

  • Review Article
    | Open Access

    Seed banks are generated when individuals enter a dormant state, a phenomenon that has evolved among diverse taxa, but that is also found in stem cells, brains, and tumors. Here, Lennon et al. synthesize the fundamentals of seed-bank theory and the emergence of complex patterns and dynamics in mathematics and the life sciences.

    • Jay T. Lennon
    • , Frank den Hollander
    •  & Jochen Blath

  • Article
    | Open Access

    Prediction of contagion dynamics is of relevance for epidemic and social complex networks. Murphy et al. propose a data-driven approach based on deep learning which allows to learn mechanisms governing network dynamics and make predictions beyond the training data for arbitrary network structures.

    • Charles Murphy
    • , Edward Laurence
    •  & Antoine Allard

  • Article
    | Open Access

    The analysis of networks and network processes can require low-dimensional representations, possible for specific structures only. The authors propose a geometric formalism which allows to unfold the mechanisms of dynamical processes propagation in various networks, relevant for control and community detection.

    • Adam Gosztolai
    •  & Alexis Arnaudon

  • Article
    | Open Access

    In many machine learning applications, one uses pre-trained neural networks, having limited access to training and test data. Martin et al. show how to predict trends in the quality of such neural networks without access to this information, relevant for reproducibility, diagnostics, and validation.

    • Charles H. Martin
    • , Tongsu (Serena) Peng
    •  & Michael W. Mahoney

  • Article
    | Open Access

    Mechanisms of cluster formation in networks with directed links differ from those in undirected networks. Lodi et al. propose a method to compute interdependencies among clusters of nodes in directed networks. They show that clusters can be one-way dependent, as found in social and neural networks.

    • Matteo Lodi
    • , Francesco Sorrentino
    •  & Marco Storace

  • Article
    | Open Access

    Population structure can influence the probability of and time to fixation of new mutants. Here, Tkadlec et al. demonstrate mathematically that structures that increase fixation probability necessarily slow fixation, but also identify amplifying structures with minimal reductions in fixation time.

    • Josef Tkadlec
    • , Andreas Pavlogiannis
    •  & Martin A. Nowak

  • Article
    | Open Access

    The authors present a microwave imaging system that can operate in continuous transmit-receive mode. Using an array of transmitters, a single receiver and a reconstruction matrix that correlate random time patterns with the captured signal, they demonstrate real-time imaging and tracking through a wall.

    • Fabio C. S. da Silva
    • , Anthony B. Kos
    •  & Archita Hati

  • Article
    | Open Access

    Osimertinib and dacomitinib are approved as first-line treatment of EGFR-mutant NSCLC but resistance can arise. Here, the authors use a computational model to identify an optimal dosing schedule for osimertinib and dacomitinib combination therapy that was confirmed tolerable and effective in an ongoing phase I clinical trial.

    • Kamrine E. Poels
    • , Adam J. Schoenfeld
    •  & Franziska Michor

  • Article
    | Open Access

    Mobility restrictions implemented to reduce the spread of COVID-19 have significantly impacted walking behavior. In this study, the authors integrated mobility data from mobile devices and area-level data to study the walking patterns of 1.62 million anonymous users in 10 US metropolitan areas.

    • Ruth F. Hunter
    • , Leandro Garcia
    •  & Esteban Moro

  • Article
    | Open Access

    Despite the consensus that mass vaccination against SARS-CoV-2 will ultimately end the pandemic, it is not clear when and which control measures can be relaxed during the rollout of vaccination programmes. Here, the authors investigate relaxation scenarios using an age-structured transmission model that has been fitted to data for Portugal.

    • João Viana
    • , Christiaan H. van Dorp
    •  & Ganna Rozhnova

  • Article
    | Open Access

    Fluctuations in ecosystems and other large dynamical systems are driven by intrinsic and extrinsic noise and contain hidden information which is difficult to extract. Here, the authors derive analytical characterizations of fluctuations in random interacting systems, allowing inference of network properties from time series data.

    • Yvonne Krumbeck
    • , Qian Yang
    •  & Tim Rogers

  • Article
    | Open Access

    Social interaction outcomes can depend on the type of information individuals possess and how it is used in decision-making. Here, Zhou et al. find that self-evaluation based decision-making rules lead to evolutionary outcomes that are robust to different population structures and ways of self-evaluation.

    • Lei Zhou
    • , Bin Wu
    •  & Long Wang

  • Article
    | Open Access

    Reinbold et al. propose a physics-informed data-driven approach that successfully discovers a dynamical model using high-dimensional, noisy and incomplete experimental data describing a weakly turbulent fluid flow. This approach is relevant to other non-equilibrium spatially-extended systems.

    • Patrick A. K. Reinbold
    • , Logan M. Kageorge
    •  & Roman O. Grigoriev

  • Article
    | Open Access

    A single damage can lead to a complete collapse of supply networks due to a cascading failure mechanism. Kaiser et al. show that by adding new connections network isolators can be created, that can inhibit failure spreading relevant for power grids and water transmission systems.

    • Franz Kaiser
    • , Vito Latora
    •  & Dirk Witthaut

  • Article
    | Open Access

    Several prognostic indices are available to predict the long-term fate of emerging infectious diseases and the effect of their containment measures, including a variety of reproduction numbers. Here, the authors introduce the epidemicity index, a complementary index to evaluate the potential for transient increases of SARS-Cov-2 epidemics.

    • Lorenzo Mari
    • , Renato Casagrandi
    •  & Marino Gatto

  • Article
    | Open Access

    Massive unemployment during the COVID-19 pandemic could result in an eviction crisis in US cities. Here, the authors model the effect of evictions on SARS-CoV-2 epidemics, simulating viral transmission within and among households in a theoretical and applied urban settings.

    • Anjalika Nande
    • , Justin Sheen
    •  & Alison L. Hill

  • Article
    | Open Access

    Recent technological, social, and educational changes are profoundly impacting our work, but what makes labour markets resilient to those labour shocks? Here, the authors show that labour markets resemble ecological systems whose resilience depends critically on the network of skill similarities between different jobs.

    • Esteban Moro
    • , Morgan R. Frank
    •  & Iyad Rahwan

  • Article
    | Open Access

    The process of thin sheet crumpling is characterized by high complexity due to an infinite number of possible configurations. Andrejevic et al. show that ordered behavior can emerge in crumpled sheets, and uncover the correspondence between crumpling and fragmentation processes.

    • Jovana Andrejevic
    • , Lisa M. Lee
    •  & Chris H. Rycroft

  • Article
    | Open Access

    Controlling the behavior of a complex network usually requires a knowledge of the network dynamics. Baggio et al. propose a data-driven framework to control a complex dynamical network, effective for non-complete or random datasets, which is of relevance for power grids and neural networks.

    • Giacomo Baggio
    • , Danielle S. Bassett
    •  & Fabio Pasqualetti

  • Article
    | Open Access

    The dynamics of complex physical systems can be determined by the balance of a few dominant processes. Callaham et al. propose a machine learning approach for the identification of dominant regimes from experimental or numerical data with examples from turbulence, optics, neuroscience, and combustion.

    • Jared L. Callaham
    • , James V. Koch
    •  & Steven L. Brunton

  • Article
    | Open Access

    Phase diagrams describe how a system changes phenomenologically as an external parameter, such as a magnetic field strength, is varied. Here, the authors prove that in general such a phase diagram is uncomputable, by explicitly constructing a one-parameter Hamiltonian for which this is the case.

    • Johannes Bausch
    • , Toby S. Cubitt
    •  & James D. Watson

  • Article
    | Open Access

    Test, trace, and isolate programmes are central to COVID-19 control. Here, Viola Priesemann and colleagues evaluate how to allocate scarce resources to keep numbers low, and find that if case numbers exceed test, trace and isolate capacity, there will be a self-accelerating spread.

    • Sebastian Contreras
    • , Jonas Dehning
    •  & Viola Priesemann

  • 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

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