Applied mathematics

  • 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
  • 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