Higher-order correlations reveal complex memory in temporal hypergraphs.

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. The analysis of human interaction data reveals the existence of coherent and interdependent mesoscopic structures, thus capturing aggregation, fragmentation and nucleation processes in social systems. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the emerging pattern in the data.

Irreversibility of symbolic time series: A cautionary tale.

Many empirical time series are genuinely symbolic: Examples range from link activation patterns in network science, to DNA coding or firing patterns in neuroscience, to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility-the difference between forward and backward statistics in stationary time series-is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series-a classical way to encode chaotic trajectories via symbolic dynamics. In this paper we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis-and interpretation-of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of nonpalindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m<4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map.

Network bypasses sustain complexity.

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.

Lyapunov exponents for temporal networks.

By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network and construct a measure to estimate the network maximum Lyapunov exponent (nMLE) of a temporal network trajectory. Extending conventional algorithmic methods from nonlinear time-series analysis to networks, we show how to quantify sensitive dependence on initial conditions and estimate the nMLE directly from a single network trajectory. We validate our method for a range of synthetic generative network models displaying low- and high-dimensional chaos and finally discuss potential applications.

Chaotic renormalization group flow and entropy gradients over Haros graphs.

Haros graphs have been recently introduced as a set of graphs bijectively related to real numbers in the unit interval. Here we consider the iterated dynamics of a graph operator R over the set of Haros graphs. This operator was previously defined in the realm of graph-theoretical characterization of low-dimensional nonlinear dynamics and has a renormalization group (RG) structure. We find that the dynamics of R over Haros graphs is complex and includes unstable periodic orbits of arbitrary period and nonmixing aperiodic orbits, overall portraiting a chaotic RG flow. We identify a single RG stable fixed point whose basin of attraction is associated with the set of rational numbers, and find periodic RG orbits that relate to (pure) quadratic irrationals and aperiodic RG orbits, related with (nonmixing) families of nonquadratic algebraic irrationals and transcendental numbers. Finally, we show that the graph entropy of Haros graphs is globally decreasing as the RG flows towards its stable fixed point, albeit in a strictly nonmonotonic way, and that such graph entropy remains constant inside the periodic RG orbit associated to a subset of irrationals, the so-called metallic ratios. We discuss the possible physical interpretation of such chaotic RG flow and put results regarding entropy gradients along RG flow in the context of c-theorems.

Algorithmic hospital catchment area estimation using label propagation.

BACKGROUND: Hospital catchment areas define the primary population of a hospital and are central to assessing the potential demand on that hospital, for example, due to infectious disease outbreaks. METHODS: We present a novel algorithm, based on label propagation, for estimating hospital catchment areas, from the capacity of the hospital and demographics of the nearby population, and without requiring any data on hospital activity. RESULTS: The algorithm is demonstrated to produce a mapping from fine grained geographic regions to larger scale catchment areas, providing contiguous and realistic subdivisions of geographies relating to a single hospital or to a group of hospitals. In validation against an alternative approach predicated on activity data gathered during the COVID-19 outbreak in the UK, the label propagation algorithm is found to have a high level of agreement and perform at a similar level of accuracy. RESULTS: The algorithm can be used to make estimates of hospital catchment areas in new situations where activity data is not yet available, such as in the early stages of a infections disease outbreak.

The shape of memory in temporal networks.

How to best define, detect and characterize network memory, i.e. the dependence of a network's structure on its past, is currently a matter of debate. Here we show that the memory of a temporal network is inherently multidimensional, and we introduce a mathematical framework for defining and efficiently estimating the microscopic shape of memory, which characterises how the activity of each link intertwines with the activities of all other links. We validate our methodology on a range of synthetic models, and we then study the memory shape of real-world temporal networks spanning social, technological and biological systems, finding that these networks display heterogeneous memory shapes. In particular, online and offline social networks are markedly different, with the latter showing richer memory and memory scales. Our theory also elucidates the phenomenon of emergent virtual loops and provides a novel methodology for exploring the dynamically rich structure of complex systems.

Estimates of regional infectivity of COVID-19 in the United Kingdom following imposition of social distancing measures.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reproduction number has become an essential parameter for monitoring disease transmission across settings and guiding interventions. The UK published weekly estimates of the reproduction number in the UK starting in May 2020 which are formed from multiple independent estimates. In this paper, we describe methods used to estimate the time-varying SARS-CoV-2 reproduction number for the UK. We used multiple data sources and estimated a serial interval distribution from published studies. We describe regional variability and how estimates evolved during the early phases of the outbreak, until the relaxing of social distancing measures began to be introduced in early July. Our analysis is able to guide localized control and provides a longitudinal example of applying these methods over long timescales. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Household bubbles and COVID-19 transmission: insights from percolation theory.

In the era of social distancing to curb the spread of COVID-19, bubbling is the combining of two or more households to create an exclusive larger group. The impact of bubbling on COVID-19 transmission is challenging to quantify because of the complex social structures involved. We developed a network description of households in the UK, using the configuration model to link households. We explored the impact of bubbling scenarios by joining together households of various sizes. For each bubbling scenario, we calculated the percolation threshold, that is, the number of connections per individual required for a giant component to form, numerically and theoretically. We related the percolation threshold to the household reproduction number. We find that bubbling scenarios in which single-person households join with another household have a minimal impact on network connectivity and transmission potential. Ubiquitous scenarios where all households form a bubble are likely to lead to an extensive transmission that is hard to control. The impact of plausible scenarios, with variable uptake and heterogeneous bubble sizes, can be mitigated with reduced numbers of contacts outside the household. Bubbling of households comes at an increased risk of transmission; however, under certain circumstances risks can be modest and could be balanced by other changes in behaviours. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

COVID-19 and Its Global Economic Impact.

Pandemics are enormous threats to the world that impact all aspects of our lives, especially the global economy. The COVID-19 pandemic has emerged since December 2019 and has affected the global economy in many ways. As the world becomes more interconnected, the economic impacts of the pandemic become more serious. In addition to increased health expenditures and reduced labor force, the pandemic has hit the supply and demand chain massively and caused trouble for manufacturers who have to fire some of their employees or delay their economic activities to prevent more loss. With the closure of manufacturers and companies and reduced travel rates, usage of oil after the beginning of the pandemic has decreased significantly that was unprecedented in the last 30 years. The mining industry is a critical sector in several developing countries, and the COVID-19 pandemic has hit this industry too. Also, world stock markets declined as investors started to become concerned about the economic impacts of the COVID-19 pandemic. The tourism industry and airlines have also experienced an enormous loss too. The GDP has reduced, and this pandemic will cost the world more than 2 trillion at the end of 2020.

Correction: A flexible method for optimising sharing of healthcare resources and demand in the context of the COVID-19 pandemic.

[This corrects the article DOI: 10.1371/journal.pone.0241027.].

A population-based controlled experiment assessing the epidemiological impact of digital contact tracing.

While Digital contact tracing (DCT) has been argued to be a valuable complement to manual tracing in the containment of COVID-19, no empirical evidence of its effectiveness is available to date. Here, we report the results of a 4-week population-based controlled experiment that took place in La Gomera (Canary Islands, Spain) between June and July 2020, where we assessed the epidemiological impact of the Spanish DCT app Radar Covid. After a substantial communication campaign, we estimate that at least 33% of the population adopted the technology and further showed relatively high adherence and compliance as well as a quick turnaround time. The app detects about 6.3 close-contacts per primary simulated infection, a significant percentage being contacts with strangers, although the spontaneous follow-up rate of these notified cases is low. Overall, these results provide experimental evidence of the potential usefulness of DCT during an epidemic outbreak in a real population.

A flexible method for optimising sharing of healthcare resources and demand in the context of the COVID-19 pandemic.

As the number of cases of COVID-19 continues to grow, local health services are at risk of being overwhelmed with patients requiring intensive care. We develop and implement an algorithm to provide optimal re-routing strategies to either transfer patients requiring Intensive Care Units (ICU) or ventilators, constrained by feasibility of transfer. We validate our approach with realistic data from the United Kingdom and Spain. In the UK, we consider the National Health Service at the level of trusts and define a 4-regular geometric graph which indicates the four nearest neighbours of any given trust. In Spain we coarse-grain the healthcare system at the level of autonomous communities, and extract similar contact networks. Through random search optimisation we identify the best load sharing strategy, where the cost function to minimise is based on the total number of ICU units above capacity. Our framework is general and flexible allowing for additional criteria, alternative cost functions, and can be extended to other resources beyond ICU units or ventilators. Assuming a uniform ICU demand, we show that it is possible to enable access to ICU for up to 1000 additional cases in the UK in a single step of the algorithm. Under a more realistic and heterogeneous demand, our method is able to balance about 600 beds per step in the Spanish system only using local sharing, and over 1300 using countrywide sharing, potentially saving a large percentage of these lives that would otherwise not have access to ICU.

Shopper intent prediction from clickstream e-commerce data with minimal browsing information.

We address the problem of user intent prediction from clickstream data of an e-commerce website via two conceptually different approaches: a hand-crafted feature-based classification and a deep learning-based classification. In both approaches, we deliberately coarse-grain a new clickstream proprietary dataset to produce symbolic trajectories with minimal information. Then, we tackle the problem of trajectory classification of arbitrary length and ultimately, early prediction of limited-length trajectories, both for balanced and unbalanced datasets. Our analysis shows that k-gram statistics with visibility graph motifs produce fast and accurate classifications, highlighting that purchase prediction is reliable even for extremely short observation windows. In the deep learning case, we benchmarked previous state-of-the-art (SOTA) models on the new dataset, and improved classification accuracy over SOTA performances with our proposed LSTM architecture. We conclude with an in-depth error analysis and a careful evaluation of the pros and cons of the two approaches when applied to realistic industry use cases.

Predicting success in the worldwide start-up network.

By drawing on large-scale online data we are able to construct and analyze the time-varying worldwide network of professional relationships among start-ups. The nodes of this network represent companies, while the links model the flow of employees and the associated transfer of know-how across companies. We use network centrality measures to assess, at an early stage, the likelihood of the long-term positive economic performance of a start-up. We find that the start-up network has predictive power and that by using network centrality we can provide valuable recommendations, sometimes doubling the current state of the art performance of venture capital funds. Our network-based approach supports the theory that the position of a start-up within its ecosystem is relevant for its future success, while at the same time it offers an effective complement to the labour-intensive screening processes of venture capital firms. Our results can also enable policy-makers and entrepreneurs to conduct a more objective assessment of the long-term potentials of innovation ecosystems, and to target their interventions accordingly.

Visibility Graphs for Image Processing.

The family of image visibility graphs (IVG/IHVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such\an operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibility graphs encapsulates relevant information on the structure of the images and we explore their potential as image filters. We introduce several graph features, including the novel concept of Visibility Patches, and show through several examples that these features are highly informative, computationally efficient and universally applicable for general pattern recognition and image classification tasks.

On the physical origin of linguistic laws and lognormality in speech.

Physical manifestations of linguistic units include sources of variability due to factors of speech production which are by definition excluded from counts of linguistic symbols. In this work, we examine whether linguistic laws hold with respect to the physical manifestations of linguistic units in spoken English. The data we analyse come from a phonetically transcribed database of acoustic recordings of spontaneous speech known as the Buckeye Speech corpus. First, we verify with unprecedented accuracy that acoustically transcribed durations of linguistic units at several scales comply with a lognormal distribution, and we quantitatively justify this 'lognormality law' using a stochastic generative model. Second, we explore the four classical linguistic laws (Zipf's Law, Herdan's Law, Brevity Law and Menzerath-Altmann's Law (MAL)) in oral communication, both in physical units and in symbolic units measured in the speech transcriptions, and find that the validity of these laws is typically stronger when using physical units than in their symbolic counterpart. Additional results include (i) coining a Herdan's Law in physical units, (ii) a precise mathematical formulation of Brevity Law, which we show to be connected to optimal compression principles in information theory and allows to formulate and validate yet another law which we call the size-rank law or (iii) a mathematical derivation of MAL which also highlights an additional regime where the law is inverted. Altogether, these results support the hypothesis that statistical laws in language have a physical origin.

Quantifying and predicting success in show business.

In certain artistic endeavours-such as acting in films and TV, where unemployment rates hover at around 90%-sustained productivity (simply making a living) is probably a better proxy for quantifying success than high impact. Drawing on a worldwide database, here we study the temporal profiles of activity of actors and actresses. We show that the dynamics of job assignment is well described by a "rich-get-richer" mechanism and we find that, while the percentage of a career spent active is unpredictable, such activity is clustered. Moreover, productivity tends to be higher towards the beginning of a career and there are signals preceding the most productive year. Accordingly, we propose a machine learning method which predicts with 85% accuracy whether this "annus mirabilis" has passed, or if better days are still to come. We analyse actors and actresses separately, also providing compelling evidence of gender bias in show business.

Election Forensics: Quantitative methods for electoral fraud detection.

The last decade has witnessed an explosion on the computational power and a parallel increase of the access to large sets of data - the so called Big Data paradigm - which is enabling to develop brand new quantitative strategies underpinning description, understanding and control of complex scenarios. One interesting area of application concerns fraud detection from online data, and more particularly extracting meaningful information from massive digital fingerprints of electoral activity to detect, a posteriori, evidence of fraudulent behavior. In this short article we discuss a few quantitative methodologies that have emerged in recent years on this respect, which altogether form the nascent interdisciplinary field of election forensics. Aiming to foster discussion and raise awareness on this interdisciplinary area, we hereby enumerate a few of the most relevant approaches and methods.