The voter model has been studied extensively as a paradigmatic opinion dynamics model. However, its ability to model real opinion dynamics has not been addressed. We introduce a noisy voter …
The voter model has been studied extensively as a paradigmatic opinion dynamics model. However, its ability to model real opinion dynamics has not been addressed. We introduce a noisy voter model (accounting for social influence) with recurrent mobility of agents (as a proxy for social context), where the spatial and population diversity are taken as inputs to the model. We show that the dynamics can be described as a noisy diffusive process that contains the proper anisotropic coupling topology given by population and mobility heterogeneity. The model captures statistical features of U.S. presidential elections as the stationary vote-share fluctuations across counties and the long-range spatial correlations that decay logarithmically with the distance. Furthermore, it recovers the behavior of these properties when the geographical space is coarse grained at different scales---from the county level through congressional districts, and up to states. Finally, we analyze the role of the mobility range and the randomness in decision making, which are consistent with the empirical observations.
We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state …
We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully-connected, random and scale free networks with an update probability inversely proportional to the persistence, that is, the time since the last event. We find that in the thermodynamic limit, at variance with standard updates, the system orders slowly. The approach to the absorbing state is characterized by a power law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined.
Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements, as …
Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements, as disease spread is influenced by numerous factors, including the pathogen’s underlying transmission parameters and epidemiological dynamics, social networks and population connectivity, and environmental conditions. Here, using data from Sierra Leone, we analyze the spatiotemporal dynamics of recent cholera and Ebola outbreaks and compare and contrast the spread of these two pathogens in the same population. We develop a simulation model of the spatial spread of an epidemic in order to examine the impact of a pathogen’s incubation period on the dynamics of spread and the predictability of outbreaks. We find that differences in the incubation period alone can determine the limits of predictability for diseases with different natural history, both empirically and in our simulations. Our results show that diseases with longer incubation periods, such as Ebola, where infected individuals can travel farther before becoming infectious, result in more long-distance sparking events and less predictable disease trajectories, as compared to the more predictable wave-like spread of diseases with shorter incubation periods, such as cholera.
The growing number of large databases of animal tracking provides an opportunity for analyses of movement patterns at the scales of populations and even species. We used analytical approaches, developed …
The growing number of large databases of animal tracking provides an opportunity for analyses of movement patterns at the scales of populations and even species. We used analytical approaches, developed to cope with big data, that require no a priori assumptions about the behaviour of the target agents, to analyse a pooled tracking dataset of 272 elephant seals (Mirounga leonina) in the Southern Ocean, that was comprised of >500,000 location estimates collected over more than a decade. Our analyses showed that the displacements of these seals were described by a truncated power law distribution across several spatial and temporal scales, with a clear signature of directed movement. This pattern was evident when analysing the aggregated tracks despite a wide diversity of individual trajectories. We also identified marine provinces that described the migratory and foraging habitats of these seals. Our analysis provides evidence for the presence of intrinsic drivers of movement, such as memory, that cannot be detected using common models of movement behaviour. These results highlight the potential for big data techniques to provide new insights into movement behaviour when applied to large datasets of animal tracking.
Abstract The race between pathogens and their hosts is a major evolutionary driver, where both reshuffle their genomes to overcome and reorganize the defenses for infection, respectively. Evolutionary theory helps …
Abstract The race between pathogens and their hosts is a major evolutionary driver, where both reshuffle their genomes to overcome and reorganize the defenses for infection, respectively. Evolutionary theory helps formulate predictions on the future evolutionary dynamics of SARS-CoV-2, which can be monitored through unprecedented real-time tracking of SARS-CoV-2 population genomics at the global scale. Here we quantify the accelerating evolution of SARS-CoV-2 by tracking the SARS-CoV-2 mutation globally, with a focus on the Receptor Binding Domain (RBD) of the spike protein determining infection success. We estimate that the > 820 million people that had been infected by October 5, 2021, produced up to 10 21 copies of the virus, with 12 new effective RBD variants appearing, on average, daily. Doubling of the number of RBD variants every 89 days, followed by selection of the most infective variants challenges our defenses and calls for a shift to anticipatory, rather than reactive tactics involving collaborative global sequencing and vaccination.
The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for …
The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in complex networks. Additionally, multilayer networks produce profound changes in the dynamics of models. In this work, we investigate how a multilayer structure affects the dynamics of an ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While, below, a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking in which the majority opinion in the different layers takes opposite signs and that due to the ageing indefinitely delay the arrival at the absorbing state.
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, …
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds. In many situations, agents choose between discrete options. We analyze experimental data on binary opinion choices in humans. The data consists of two separate experiments in which humans answer questions with a binary response, where one is correct and the other is incorrect. The questions are answered without and with information on the answers of some previous participants. We find that a Bayesian approach captures the probability of choosing one of the answers. The influence of peers is uncorrelated with the difficulty of the question. The data is inconsistent with Weber's law, which states that the probability of choosing an option depends on the proportion of previous answers choosing that option and not on the total number of those answers. Last, the present Bayesian model fits reasonably well to the data as compared to some other previously proposed functions although the latter sometime perform slightly better than the Bayesian model. The asset of the present model is the simplicity and mechanistic explanation of the behavior.
Abstract The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications …
Abstract The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update their state decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in single-layer complex networks. In this work, we investigate how a multilayer structure affects the dynamics of the ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q *. Above it, the voter model always orders to an absorbing configuration. While below it a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking. In this latter case, the majority opinion in the different layers takes opposite signs and the arrival at the absorbing state is indefinitely delayed due to ageing.
Models of social diffusion reflect processes of how new products, ideas or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition …
Models of social diffusion reflect processes of how new products, ideas or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition of the number of adopters as a function of a control parameter. We explore a simple model of social adoption where the agents can be in two states, either adopters or non-adopters, and can switch between these two states interacting with other agents through a network. The probability of an agent to switch from non-adopter to adopter depends on the number of adopters in her network neighborhood, the adoption threshold $T$ and the adoption coefficient $a$, two parameters defining a Hill function. In contrast, the transition from adopter to non-adopter is spontaneous at a certain rate $\mu$. In a mean-field approach, we derive the governing ordinary differential equations and show that the nature of the transition between the global non-adoption and global adoption regimes depends mostly on the balance between the probability to adopt with one and two adopters. The transition changes from continuous, via a transcritical bifurcation, to discontinuous, via a combination of a saddle-node and a transcritical bifurcation, through a supercritical pitchfork bifurcation. We characterize the full parameter space. Finally, we compare our analytical results with Montecarlo simulations on annealed and quenched degree regular networks, showing a better agreement for the annealed case. Our results show how a simple model is able to capture two seemingly very different types of transitions, i.e., continuous and discontinuous and thus unifies underlying dynamics for different systems. Furthermore the form of the adoption probability used here is based on empirical measurements.
Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the …
Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model on fully connected networks, square lattices and Erd \"os-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link-dynamics have no counterpart under traditional node dynamics in the same topologies.
We present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. We initially …
We present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. We initially consider the phenomenon of bipartisanship breakdown by analyzing spatial distributions of several bipartisanship indices. We find that such breakdown is more prominently close to cosmopolite and largely populated areas and less important in rural areas where bipartisanship still prevails, and its evolution mildly consolidates in the 2016 round, with some evidence of bipartisanship reinforcement which we hypothesize to be due to psychological mechanisms of risk aversion. Subsequently, a functional network analysis detects an effective partition of municipalities which remarkably coincides with the first‐level political and administrative division of autonomous communities. Finally, we explore to which extent vote data are faithful by applying forensic techniques to vote statistics. Results based on deviation from Benford’s law are mixed and vary across different levels of aggregation. As a complementary metric, we further explore the cooccurring statistics of vote share and turnout, finding a mild tendency in the clusters of the conservative party to smear out towards the area of high turnout and vote share, what has been previously interpreted as a possible sign of incremental fraud.
The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence, the Balearic Islands remained almost fully isolated due to the closing …
The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence, the Balearic Islands remained almost fully isolated due to the closing of airports and ports, these isolation measures and the home-based confinement have led to a low prevalence of COVID-19 in this region. We propose a compartmental model for the spread of COVID-19 including five compartments (Susceptible, Exposed, Presymptomatic Infective, Diseased, and Recovered), and the mobility between municipalities. The model parameters are calibrated with the temporal series of confirmed cases provided by the Spanish Ministry of Health. After calibration, the proposed model captures the trend of the official confirmed cases before and after the lockdown. We show that the estimated number of cases depends strongly on the initial dates of the local outbreak onset and the number of imported cases before the lockdown. Our estimations indicate that the population has not reached the level of herd immunization necessary to prevent future outbreaks. While the low prevalence, in comparison to mainland Spain, has prevented the saturation of the health system, this low prevalence translates into low immunization rates, therefore facilitating the propagation of new outbreaks that could lead to secondary waves of COVID-19 in the region. These findings warn about scenarios regarding after-lockdown-policies and the risk of second outbreaks, emphasize the need for widespread testing, and could potentially be extrapolated to other insular and continental regions.
This research studies the evolution of COVID-19 crude incident rates, effective reproduction number R(t) and their relationship with incidence spatial autocorrelation patterns in the 19 months following the disease outbreak …
This research studies the evolution of COVID-19 crude incident rates, effective reproduction number R(t) and their relationship with incidence spatial autocorrelation patterns in the 19 months following the disease outbreak in Catalonia (Spain). A cross-sectional ecological panel design based on n = 371 health-care geographical units is used. Five general outbreaks are described, systematically preceded by generalized values of R(t) > 1 in the two previous weeks. No clear regularities concerning possible initial focus appear when comparing waves. As for autocorrelation, we identify a wave's baseline pattern in which global Moran's I increases rapidly in the first weeks of the outbreak to descend later. However, some waves significantly depart from the baseline. In the simulations, both baseline pattern and departures can be reproduced when measures aimed at reducing mobility and virus transmissibility are introduced. Spatial autocorrelation is inherently contingent on the outbreak phase and is also substantially modified by external interventions affecting human behavior.
We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. …
We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. We model extinctions as node or interaction removals. For node removal, we consider random, directed and sequential extinctions; for interaction removal, we consider random extinctions. The bipartite network reorganizes showing an increase of the effective modularity and a fast decrease of the persistence of the species in the original communities with increasing number of extinction events. Second, we compare extinctions in a real mutualistic network with the growth of a bipartite network model. The modularity reaches a stationary value and nodes remain in the same community after joining the network. Our results show that perturbations and disruptive events affect the connectivity pattern of mutualistic networks at the mesoscale level. The increase of the effective modularity observed in some scenarios could provide some protection to the remaining ecosystem.
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern …
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution of these systems. However, conventional network representations primarily emphasize pairwise interactions, represented as edges in the network. In reality, many social interactions occur within groups rather than individual pairs. To capture this crucial aspect, higher-order network representations come into play, especially to describe those complex systems that are inherently composed of agents interacting with group dynamics. Despite recent research advancements in exploring temporal higher-order networks in various systems, our understanding of collaboration networks remains limited. Specifically, there is a lack of knowledge regarding the patterns of group interactions within scientific collaborations. How do groups form and evolve in this context? In this study, we aim to delve into the temporal properties of groups within collaboration networks. Our investigation focuses on uncovering the mechanisms that govern the global, group, and individual-level dynamics, shedding light on how individuals collaborate and how groups form and disband over time. By studying these temporal patterns, we take a significant stride forward in comprehending the intricate dynamics of higher-order interactions within human collaboration systems.
Abstract There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce …
Abstract There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce an analytically tractable model that enables one to connect two layers in a multilayer network by controlling the locality of coupling. In particular we introduce a tractable model for embedding one network (A) into another (B), focusing on the case where network A has many more nodes than network B. In our model, nodes in network A are assigned, or embedded, to the nodes in network B using an assignment rule where the extent of node localization is controlled by a single parameter. We start by mapping an unassigned “source” node in network A to a randomly chosen “target” node in network B. We then assign the neighbors of the source node to the neighborhood of the target node using a random walk starting at the target node and with a per-step stopping probability q . By varying the parameter q , we are able to produce a range of embeddings from local ( q = 1) to global ( q → 0). The simplicity of the model allows us to calculate key quantities, making it a useful starting point for more realistic models.
Abstract The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence the Balearic Islands remained almost fully isolated due to the …
Abstract The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence the Balearic Islands remained almost fully isolated due to the closing of airports and ports, These isolation measures and the home-based confinement have led to a low prevalence of COVID-19 in this region. We propose a compartmental model for the spread of COVID-19 including five compartments (Susceptible, Latent, Infected, Diseased, and Recovered), and the mobility between municipalities. The model parameters are calibrated with the temporal series of confirmed cases provided by the Spanish Ministry of Health. After calibration, the proposed model captures the trend of the official confirmed cases before and after the lockdown. We show that the estimated number of cases depends strongly on the initial dates of the local outbreak onset and the number of imported cases before the lockdown. Our estimations indicate that the population has not reached the level of herd immunization necessary to prevent future outbreaks. While the low prevalence, in comparison to mainland Spain, has prevented the saturation of the health system, this low prevalence translates into low immunization rates, therefore facilitating the propagation of new outbreaks that could lead to secondary waves of COVID-19 in the region. These findings warn about scenarios regarding after-lockdown-policies and the risk of second outbreaks, emphasize the need for widespread testing, and could potentially be extrapolated to other insular and continental regions.
Abstract Evolutionary ecology theory provides an avenue to anticipate the future behavior of SARS-CoV-2. Here we quantify the accelerating evolution of SARS-CoV-2 by tracking the SARS-CoV-2 mutation globally, with a …
Abstract Evolutionary ecology theory provides an avenue to anticipate the future behavior of SARS-CoV-2. Here we quantify the accelerating evolution of SARS-CoV-2 by tracking the SARS-CoV-2 mutation globally, with a focus on the Receptor Binding Domain (RBD) of the spike protein believed to determine infectivity. We estimate that 384 million people were infected by March 1st, 2021, producing up to 10 21 copies of the virus, with one new RBD variant appearing for every 600,000 human infections, resulting in approximately three new effective RBD variants produced daily. Doubling the number of RBD variants every 71.67 days followed by selection of the most infective variants challenges our defenses and calls for a shift to anticipatory, rather than reactive tactics. One-Sentence Summary Accelerating evolution of SARS-CoV-2 demands formulating universal vaccines and treatments based on big-data simulations of possible new variants.
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June …
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. Vote counts are extracted at the level of municipalities, yielding an unusually high resolution dataset with over 8000 samples. We initially consider the phenomenon of Bipartisanship breakdown by analysing spatial distributions of several Bipartisanship indices. We find that such breakdown is more prominent close to cosmopolite and largely populated areas and less important in rural areas where Bipartisanship still prevails, and its evolution mildly consolidates in the 2016 round, with some evidence of Bipartisanship reinforcement which we hypothesize to be due to psychological mechanisms of risk aversion. On a third step we explore to which extent vote data are faithful by applying forensic techniques to vote statistics. We first explore the conformance of first digit distributions to Benford's law for each of the main political parties. The results and interpretations are mixed and vary across different levels of aggregation, finding a general good quantitative agreement at the national scale for both municipalities and precincts but finding systematic nonconformance at the level of individual precincts. As a complementary metric, we further explore the co-occurring statistics of voteshare and turnout, finding a mild tendency in the clusters of the conservative party to smear out towards the area of high turnout and voteshare, what has been previously interpreted as a possible sign of incremental fraud. In every case results are qualitatively similar between 2015 and 2016 elections.
There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce an …
There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce an analytically tractable model that enables one to connect two layers in a multilayer network by controlling the locality of coupling. In particular we introduce a tractable model for embedding one network (A) into another (B), focusing on the case where network A has many more nodes than network B. In our model, nodes in network A are assigned, or embedded, to the nodes in network B using an assignment rule where the extent of node localization is controlled by a single parameter. We start by mapping an unassigned `source' node in network A to a randomly chosen `target' node in network B. We then assign the neighbors of the source node to the neighborhood of the target node using a random walk starting at the target node and with a per-step stopping probability $q$. By varying the parameter $q$, we are able to produce a range of embeddings from local ($q = 1$) to global ($q \to 0$). The simplicity of the model allows us to calculate key quantities, making it a useful starting point for more realistic models.
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June …
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. Vote counts are extracted at the level of municipalities, yielding an unusually high resolution dataset with over 8000 samples. We initially consider the phenomenon of Bipartisanship breakdown by analysing spatial distributions of several Bipartisanship indices. We find that such breakdown is more prominent close to cosmopolite and largely populated areas and less important in rural areas where Bipartisanship still prevails, and its evolution mildly consolidates in the 2016 round, with some evidence of Bipartisanship reinforcement which we hypothesize to be due to psychological mechanisms of risk aversion. On a third step we explore to which extent vote data are faithful by applying forensic techniques to vote statistics. We first explore the conformance of first digit distributions to Benford's law for each of the main political parties. The results and interpretations are mixed and vary across different levels of aggregation, finding a general good quantitative agreement at the national scale for both municipalities and precincts but finding systematic nonconformance at the level of individual precincts. As a complementary metric, we further explore the co-occurring statistics of voteshare and turnout, finding a mild tendency in the clusters of the conservative party to smear out towards the area of high turnout and voteshare, what has been previously interpreted as a possible sign of incremental fraud. In every case results are qualitatively similar between 2015 and 2016 elections.
Abstract Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements …
Abstract Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements as disease spread is influenced by numerous factors, including the pathogen’s underlying transmission parameters and epidemiological dynamics, social networks and population connectivity, and environmental conditions. Here, using data from Sierra Leone we analyze the spatiotemporal dynamics of recent cholera and Ebola outbreaks and compare and contrast the spread of these two pathogens in the same population. We develop a simulation model of the spatial spread of an epidemic in order to examine the impact of a pathogen’s incubation period on the dynamics of spread and the predictability of outbreaks. We find that differences in the incubation period alone can determine the limits of predictability for diseases with different natural history, both empirically and in our simulations. Our results show that diseases with longer incubation periods, such as Ebola, where infected individuals can travel further before becoming infectious, result in more long-distance sparking events and less predictable disease trajectories, as compared to the more predictable wave-like spread of diseases with shorter incubation periods, such as cholera. Significance statement Understanding how infectious diseases spread is critical for preventing and containing outbreaks. While advances have been made in forecasting epidemics, much is still unknown. Here we show that the incubation period – the time between exposure to a pathogen and onset of symptoms – is an important factor in predicting spatiotemporal spread of disease and provides one explanation for the different trajectories of the recent Ebola and cholera outbreaks in Sierra Leone. We find that outbreaks of pathogens with longer incubation periods, such as Ebola, tend to have less predictable spread, whereas pathogens with shorter incubation periods, such as cholera, spread in a more predictable, wavelike pattern. These findings have implications for the scale and timing of reactive interventions, such as vaccination campaigns.
Social interactions are fundamental in animal groups, including humans, and can take various forms, such as competition, cooperation, or kinship. Understanding these interactions in marine environments has been historically challenging …
Social interactions are fundamental in animal groups, including humans, and can take various forms, such as competition, cooperation, or kinship. Understanding these interactions in marine environments has been historically challenging due to data collection difficulties. However, advancements in acoustic telemetry now enable remote analysis of such behaviors. This study proposes a method to derive leader-follower networks from presence data collected by a single acoustic receiver at a specific location. Using the Kolmogorov-Smirnov distance, the method analyzes lag times between consecutive presences of individuals to infer directed relationships. Tested on simulated data, it was then applied to detection data from acoustically tagged reef manta rays (\textit{Mobula~alfredi}) frequenting a known site. Results revealed temporal patterns, including circadian rhythms and burst-like behavior with power-law distributed time gaps between presences. The inferred leader-follower network highlighted key behavioral patterns: females followed males more often than expected, males showed stronger but fewer associations with specific females, and smaller individuals followed others less consistently than larger ones. These findings align with ecological insights, revealing structured social interactions and providing a novel framework for studying marine animal behavior through network theory.
This paper presents a methodological approach based on the use of complex networks to analyze the structure and content of curricula. We analyze the concept network built from the final …
This paper presents a methodological approach based on the use of complex networks to analyze the structure and content of curricula. We analyze the concept network built from the final year of a particular high school Physics curriculum, as well as that of Mathematics. We examine the most central nodes in each case, the community structures (coherent units or groupings), and the changes that occurred when the network was considered in isolation or integrated with Mathematics. The results show that the integrated Physics and Mathematics network has a higher average degree compared to the individual networks, driven by numerous interdisciplinary connections. The modularity analysis indicates similarities with the original curriculum layout, but also interesting differences that may suggest alternative ways of organizing the content. The differences between separated and integrated networks also highlights the prominence of certain key concepts.
This paper presents a methodological approach based on the use of complex networks to analyze the structure and content of curricula. We analyze the concept network built from the final …
This paper presents a methodological approach based on the use of complex networks to analyze the structure and content of curricula. We analyze the concept network built from the final year of a particular high school Physics curriculum, as well as that of Mathematics. We examine the most central nodes in each case, the community structures (coherent units or groupings), and the changes that occurred when the network was considered in isolation or integrated with Mathematics. The results show that the integrated Physics and Mathematics network has a higher average degree compared to the individual networks, driven by numerous interdisciplinary connections. The modularity analysis indicates similarities with the original curriculum layout, but also interesting differences that may suggest alternative ways of organizing the content. The differences between separated and integrated networks also highlights the prominence of certain key concepts.
Social interactions are fundamental in animal groups, including humans, and can take various forms, such as competition, cooperation, or kinship. Understanding these interactions in marine environments has been historically challenging …
Social interactions are fundamental in animal groups, including humans, and can take various forms, such as competition, cooperation, or kinship. Understanding these interactions in marine environments has been historically challenging due to data collection difficulties. However, advancements in acoustic telemetry now enable remote analysis of such behaviors. This study proposes a method to derive leader-follower networks from presence data collected by a single acoustic receiver at a specific location. Using the Kolmogorov-Smirnov distance, the method analyzes lag times between consecutive presences of individuals to infer directed relationships. Tested on simulated data, it was then applied to detection data from acoustically tagged reef manta rays (\textit{Mobula~alfredi}) frequenting a known site. Results revealed temporal patterns, including circadian rhythms and burst-like behavior with power-law distributed time gaps between presences. The inferred leader-follower network highlighted key behavioral patterns: females followed males more often than expected, males showed stronger but fewer associations with specific females, and smaller individuals followed others less consistently than larger ones. These findings align with ecological insights, revealing structured social interactions and providing a novel framework for studying marine animal behavior through network theory.
This research studies the evolution of COVID-19 crude incident rates, effective reproduction number R(t) and their relationship with incidence spatial autocorrelation patterns in the 19 months following the disease outbreak …
This research studies the evolution of COVID-19 crude incident rates, effective reproduction number R(t) and their relationship with incidence spatial autocorrelation patterns in the 19 months following the disease outbreak in Catalonia (Spain). A cross-sectional ecological panel design based on n = 371 health-care geographical units is used. Five general outbreaks are described, systematically preceded by generalized values of R(t) > 1 in the two previous weeks. No clear regularities concerning possible initial focus appear when comparing waves. As for autocorrelation, we identify a wave's baseline pattern in which global Moran's I increases rapidly in the first weeks of the outbreak to descend later. However, some waves significantly depart from the baseline. In the simulations, both baseline pattern and departures can be reproduced when measures aimed at reducing mobility and virus transmissibility are introduced. Spatial autocorrelation is inherently contingent on the outbreak phase and is also substantially modified by external interventions affecting human behavior.
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern …
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution of these systems. However, conventional network representations primarily emphasize pairwise interactions, represented as edges in the network. In reality, many social interactions occur within groups rather than individual pairs. To capture this crucial aspect, higher-order network representations come into play, especially to describe those complex systems that are inherently composed of agents interacting with group dynamics. Despite recent research advancements in exploring temporal higher-order networks in various systems, our understanding of collaboration networks remains limited. Specifically, there is a lack of knowledge regarding the patterns of group interactions within scientific collaborations. How do groups form and evolve in this context? In this study, we aim to delve into the temporal properties of groups within collaboration networks. Our investigation focuses on uncovering the mechanisms that govern the global, group, and individual-level dynamics, shedding light on how individuals collaborate and how groups form and disband over time. By studying these temporal patterns, we take a significant stride forward in comprehending the intricate dynamics of higher-order interactions within human collaboration systems.
Abstract The race between pathogens and their hosts is a major evolutionary driver, where both reshuffle their genomes to overcome and reorganize the defenses for infection, respectively. Evolutionary theory helps …
Abstract The race between pathogens and their hosts is a major evolutionary driver, where both reshuffle their genomes to overcome and reorganize the defenses for infection, respectively. Evolutionary theory helps formulate predictions on the future evolutionary dynamics of SARS-CoV-2, which can be monitored through unprecedented real-time tracking of SARS-CoV-2 population genomics at the global scale. Here we quantify the accelerating evolution of SARS-CoV-2 by tracking the SARS-CoV-2 mutation globally, with a focus on the Receptor Binding Domain (RBD) of the spike protein determining infection success. We estimate that the > 820 million people that had been infected by October 5, 2021, produced up to 10 21 copies of the virus, with 12 new effective RBD variants appearing, on average, daily. Doubling of the number of RBD variants every 89 days, followed by selection of the most infective variants challenges our defenses and calls for a shift to anticipatory, rather than reactive tactics involving collaborative global sequencing and vaccination.
Abstract Evolutionary ecology theory provides an avenue to anticipate the future behavior of SARS-CoV-2. Here we quantify the accelerating evolution of SARS-CoV-2 by tracking the SARS-CoV-2 mutation globally, with a …
Abstract Evolutionary ecology theory provides an avenue to anticipate the future behavior of SARS-CoV-2. Here we quantify the accelerating evolution of SARS-CoV-2 by tracking the SARS-CoV-2 mutation globally, with a focus on the Receptor Binding Domain (RBD) of the spike protein believed to determine infectivity. We estimate that 384 million people were infected by March 1st, 2021, producing up to 10 21 copies of the virus, with one new RBD variant appearing for every 600,000 human infections, resulting in approximately three new effective RBD variants produced daily. Doubling the number of RBD variants every 71.67 days followed by selection of the most infective variants challenges our defenses and calls for a shift to anticipatory, rather than reactive tactics. One-Sentence Summary Accelerating evolution of SARS-CoV-2 demands formulating universal vaccines and treatments based on big-data simulations of possible new variants.
The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence, the Balearic Islands remained almost fully isolated due to the closing …
The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence, the Balearic Islands remained almost fully isolated due to the closing of airports and ports, these isolation measures and the home-based confinement have led to a low prevalence of COVID-19 in this region. We propose a compartmental model for the spread of COVID-19 including five compartments (Susceptible, Exposed, Presymptomatic Infective, Diseased, and Recovered), and the mobility between municipalities. The model parameters are calibrated with the temporal series of confirmed cases provided by the Spanish Ministry of Health. After calibration, the proposed model captures the trend of the official confirmed cases before and after the lockdown. We show that the estimated number of cases depends strongly on the initial dates of the local outbreak onset and the number of imported cases before the lockdown. Our estimations indicate that the population has not reached the level of herd immunization necessary to prevent future outbreaks. While the low prevalence, in comparison to mainland Spain, has prevented the saturation of the health system, this low prevalence translates into low immunization rates, therefore facilitating the propagation of new outbreaks that could lead to secondary waves of COVID-19 in the region. These findings warn about scenarios regarding after-lockdown-policies and the risk of second outbreaks, emphasize the need for widespread testing, and could potentially be extrapolated to other insular and continental regions.
Abstract The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence the Balearic Islands remained almost fully isolated due to the …
Abstract The Spanish government declared the lockdown on March 14th, 2020 to tackle the fast-spreading of COVID-19. As a consequence the Balearic Islands remained almost fully isolated due to the closing of airports and ports, These isolation measures and the home-based confinement have led to a low prevalence of COVID-19 in this region. We propose a compartmental model for the spread of COVID-19 including five compartments (Susceptible, Latent, Infected, Diseased, and Recovered), and the mobility between municipalities. The model parameters are calibrated with the temporal series of confirmed cases provided by the Spanish Ministry of Health. After calibration, the proposed model captures the trend of the official confirmed cases before and after the lockdown. We show that the estimated number of cases depends strongly on the initial dates of the local outbreak onset and the number of imported cases before the lockdown. Our estimations indicate that the population has not reached the level of herd immunization necessary to prevent future outbreaks. While the low prevalence, in comparison to mainland Spain, has prevented the saturation of the health system, this low prevalence translates into low immunization rates, therefore facilitating the propagation of new outbreaks that could lead to secondary waves of COVID-19 in the region. These findings warn about scenarios regarding after-lockdown-policies and the risk of second outbreaks, emphasize the need for widespread testing, and could potentially be extrapolated to other insular and continental regions.
Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements, as …
Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements, as disease spread is influenced by numerous factors, including the pathogen’s underlying transmission parameters and epidemiological dynamics, social networks and population connectivity, and environmental conditions. Here, using data from Sierra Leone, we analyze the spatiotemporal dynamics of recent cholera and Ebola outbreaks and compare and contrast the spread of these two pathogens in the same population. We develop a simulation model of the spatial spread of an epidemic in order to examine the impact of a pathogen’s incubation period on the dynamics of spread and the predictability of outbreaks. We find that differences in the incubation period alone can determine the limits of predictability for diseases with different natural history, both empirically and in our simulations. Our results show that diseases with longer incubation periods, such as Ebola, where infected individuals can travel farther before becoming infectious, result in more long-distance sparking events and less predictable disease trajectories, as compared to the more predictable wave-like spread of diseases with shorter incubation periods, such as cholera.
Abstract There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce …
Abstract There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce an analytically tractable model that enables one to connect two layers in a multilayer network by controlling the locality of coupling. In particular we introduce a tractable model for embedding one network (A) into another (B), focusing on the case where network A has many more nodes than network B. In our model, nodes in network A are assigned, or embedded, to the nodes in network B using an assignment rule where the extent of node localization is controlled by a single parameter. We start by mapping an unassigned “source” node in network A to a randomly chosen “target” node in network B. We then assign the neighbors of the source node to the neighborhood of the target node using a random walk starting at the target node and with a per-step stopping probability q . By varying the parameter q , we are able to produce a range of embeddings from local ( q = 1) to global ( q → 0). The simplicity of the model allows us to calculate key quantities, making it a useful starting point for more realistic models.
Abstract Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements …
Abstract Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements as disease spread is influenced by numerous factors, including the pathogen’s underlying transmission parameters and epidemiological dynamics, social networks and population connectivity, and environmental conditions. Here, using data from Sierra Leone we analyze the spatiotemporal dynamics of recent cholera and Ebola outbreaks and compare and contrast the spread of these two pathogens in the same population. We develop a simulation model of the spatial spread of an epidemic in order to examine the impact of a pathogen’s incubation period on the dynamics of spread and the predictability of outbreaks. We find that differences in the incubation period alone can determine the limits of predictability for diseases with different natural history, both empirically and in our simulations. Our results show that diseases with longer incubation periods, such as Ebola, where infected individuals can travel further before becoming infectious, result in more long-distance sparking events and less predictable disease trajectories, as compared to the more predictable wave-like spread of diseases with shorter incubation periods, such as cholera. Significance statement Understanding how infectious diseases spread is critical for preventing and containing outbreaks. While advances have been made in forecasting epidemics, much is still unknown. Here we show that the incubation period – the time between exposure to a pathogen and onset of symptoms – is an important factor in predicting spatiotemporal spread of disease and provides one explanation for the different trajectories of the recent Ebola and cholera outbreaks in Sierra Leone. We find that outbreaks of pathogens with longer incubation periods, such as Ebola, tend to have less predictable spread, whereas pathogens with shorter incubation periods, such as cholera, spread in a more predictable, wavelike pattern. These findings have implications for the scale and timing of reactive interventions, such as vaccination campaigns.
We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. …
We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. We model extinctions as node or interaction removals. For node removal, we consider random, directed and sequential extinctions; for interaction removal, we consider random extinctions. The bipartite network reorganizes showing an increase of the effective modularity and a fast decrease of the persistence of the species in the original communities with increasing number of extinction events. Second, we compare extinctions in a real mutualistic network with the growth of a bipartite network model. The modularity reaches a stationary value and nodes remain in the same community after joining the network. Our results show that perturbations and disruptive events affect the connectivity pattern of mutualistic networks at the mesoscale level. The increase of the effective modularity observed in some scenarios could provide some protection to the remaining ecosystem.
Models of social diffusion reflect processes of how new products, ideas or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition …
Models of social diffusion reflect processes of how new products, ideas or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition of the number of adopters as a function of a control parameter. We explore a simple model of social adoption where the agents can be in two states, either adopters or non-adopters, and can switch between these two states interacting with other agents through a network. The probability of an agent to switch from non-adopter to adopter depends on the number of adopters in her network neighborhood, the adoption threshold $T$ and the adoption coefficient $a$, two parameters defining a Hill function. In contrast, the transition from adopter to non-adopter is spontaneous at a certain rate $\mu$. In a mean-field approach, we derive the governing ordinary differential equations and show that the nature of the transition between the global non-adoption and global adoption regimes depends mostly on the balance between the probability to adopt with one and two adopters. The transition changes from continuous, via a transcritical bifurcation, to discontinuous, via a combination of a saddle-node and a transcritical bifurcation, through a supercritical pitchfork bifurcation. We characterize the full parameter space. Finally, we compare our analytical results with Montecarlo simulations on annealed and quenched degree regular networks, showing a better agreement for the annealed case. Our results show how a simple model is able to capture two seemingly very different types of transitions, i.e., continuous and discontinuous and thus unifies underlying dynamics for different systems. Furthermore the form of the adoption probability used here is based on empirical measurements.
We present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. We initially …
We present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. We initially consider the phenomenon of bipartisanship breakdown by analyzing spatial distributions of several bipartisanship indices. We find that such breakdown is more prominently close to cosmopolite and largely populated areas and less important in rural areas where bipartisanship still prevails, and its evolution mildly consolidates in the 2016 round, with some evidence of bipartisanship reinforcement which we hypothesize to be due to psychological mechanisms of risk aversion. Subsequently, a functional network analysis detects an effective partition of municipalities which remarkably coincides with the first‐level political and administrative division of autonomous communities. Finally, we explore to which extent vote data are faithful by applying forensic techniques to vote statistics. Results based on deviation from Benford’s law are mixed and vary across different levels of aggregation. As a complementary metric, we further explore the cooccurring statistics of vote share and turnout, finding a mild tendency in the clusters of the conservative party to smear out towards the area of high turnout and vote share, what has been previously interpreted as a possible sign of incremental fraud.
There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce an …
There has lately been increased interest in describing complex systems not merely as single networks but rather as collections of networks that are coupled to one another. We introduce an analytically tractable model that enables one to connect two layers in a multilayer network by controlling the locality of coupling. In particular we introduce a tractable model for embedding one network (A) into another (B), focusing on the case where network A has many more nodes than network B. In our model, nodes in network A are assigned, or embedded, to the nodes in network B using an assignment rule where the extent of node localization is controlled by a single parameter. We start by mapping an unassigned `source' node in network A to a randomly chosen `target' node in network B. We then assign the neighbors of the source node to the neighborhood of the target node using a random walk starting at the target node and with a per-step stopping probability $q$. By varying the parameter $q$, we are able to produce a range of embeddings from local ($q = 1$) to global ($q \to 0$). The simplicity of the model allows us to calculate key quantities, making it a useful starting point for more realistic models.
Abstract The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications …
Abstract The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update their state decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in single-layer complex networks. In this work, we investigate how a multilayer structure affects the dynamics of the ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q *. Above it, the voter model always orders to an absorbing configuration. While below it a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking. In this latter case, the majority opinion in the different layers takes opposite signs and the arrival at the absorbing state is indefinitely delayed due to ageing.
The growing number of large databases of animal tracking provides an opportunity for analyses of movement patterns at the scales of populations and even species. We used analytical approaches, developed …
The growing number of large databases of animal tracking provides an opportunity for analyses of movement patterns at the scales of populations and even species. We used analytical approaches, developed to cope with big data, that require no a priori assumptions about the behaviour of the target agents, to analyse a pooled tracking dataset of 272 elephant seals (Mirounga leonina) in the Southern Ocean, that was comprised of >500,000 location estimates collected over more than a decade. Our analyses showed that the displacements of these seals were described by a truncated power law distribution across several spatial and temporal scales, with a clear signature of directed movement. This pattern was evident when analysing the aggregated tracks despite a wide diversity of individual trajectories. We also identified marine provinces that described the migratory and foraging habitats of these seals. Our analysis provides evidence for the presence of intrinsic drivers of movement, such as memory, that cannot be detected using common models of movement behaviour. These results highlight the potential for big data techniques to provide new insights into movement behaviour when applied to large datasets of animal tracking.
The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for …
The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in complex networks. Additionally, multilayer networks produce profound changes in the dynamics of models. In this work, we investigate how a multilayer structure affects the dynamics of an ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While, below, a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking in which the majority opinion in the different layers takes opposite signs and that due to the ageing indefinitely delay the arrival at the absorbing state.
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June …
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. Vote counts are extracted at the level of municipalities, yielding an unusually high resolution dataset with over 8000 samples. We initially consider the phenomenon of Bipartisanship breakdown by analysing spatial distributions of several Bipartisanship indices. We find that such breakdown is more prominent close to cosmopolite and largely populated areas and less important in rural areas where Bipartisanship still prevails, and its evolution mildly consolidates in the 2016 round, with some evidence of Bipartisanship reinforcement which we hypothesize to be due to psychological mechanisms of risk aversion. On a third step we explore to which extent vote data are faithful by applying forensic techniques to vote statistics. We first explore the conformance of first digit distributions to Benford's law for each of the main political parties. The results and interpretations are mixed and vary across different levels of aggregation, finding a general good quantitative agreement at the national scale for both municipalities and precincts but finding systematic nonconformance at the level of individual precincts. As a complementary metric, we further explore the co-occurring statistics of voteshare and turnout, finding a mild tendency in the clusters of the conservative party to smear out towards the area of high turnout and voteshare, what has been previously interpreted as a possible sign of incremental fraud. In every case results are qualitatively similar between 2015 and 2016 elections.
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June …
In this paper we present a social network and forensic analysis of the vote counts of Spanish national elections that took place in December 2015 and their sequel in June 2016. Vote counts are extracted at the level of municipalities, yielding an unusually high resolution dataset with over 8000 samples. We initially consider the phenomenon of Bipartisanship breakdown by analysing spatial distributions of several Bipartisanship indices. We find that such breakdown is more prominent close to cosmopolite and largely populated areas and less important in rural areas where Bipartisanship still prevails, and its evolution mildly consolidates in the 2016 round, with some evidence of Bipartisanship reinforcement which we hypothesize to be due to psychological mechanisms of risk aversion. On a third step we explore to which extent vote data are faithful by applying forensic techniques to vote statistics. We first explore the conformance of first digit distributions to Benford's law for each of the main political parties. The results and interpretations are mixed and vary across different levels of aggregation, finding a general good quantitative agreement at the national scale for both municipalities and precincts but finding systematic nonconformance at the level of individual precincts. As a complementary metric, we further explore the co-occurring statistics of voteshare and turnout, finding a mild tendency in the clusters of the conservative party to smear out towards the area of high turnout and voteshare, what has been previously interpreted as a possible sign of incremental fraud. In every case results are qualitatively similar between 2015 and 2016 elections.
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, …
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds. In many situations, agents choose between discrete options. We analyze experimental data on binary opinion choices in humans. The data consists of two separate experiments in which humans answer questions with a binary response, where one is correct and the other is incorrect. The questions are answered without and with information on the answers of some previous participants. We find that a Bayesian approach captures the probability of choosing one of the answers. The influence of peers is uncorrelated with the difficulty of the question. The data is inconsistent with Weber's law, which states that the probability of choosing an option depends on the proportion of previous answers choosing that option and not on the total number of those answers. Last, the present Bayesian model fits reasonably well to the data as compared to some other previously proposed functions although the latter sometime perform slightly better than the Bayesian model. The asset of the present model is the simplicity and mechanistic explanation of the behavior.
The voter model has been studied extensively as a paradigmatic opinion dynamics model. However, its ability to model real opinion dynamics has not been addressed. We introduce a noisy voter …
The voter model has been studied extensively as a paradigmatic opinion dynamics model. However, its ability to model real opinion dynamics has not been addressed. We introduce a noisy voter model (accounting for social influence) with recurrent mobility of agents (as a proxy for social context), where the spatial and population diversity are taken as inputs to the model. We show that the dynamics can be described as a noisy diffusive process that contains the proper anisotropic coupling topology given by population and mobility heterogeneity. The model captures statistical features of U.S. presidential elections as the stationary vote-share fluctuations across counties and the long-range spatial correlations that decay logarithmically with the distance. Furthermore, it recovers the behavior of these properties when the geographical space is coarse grained at different scales---from the county level through congressional districts, and up to states. Finally, we analyze the role of the mobility range and the randomness in decision making, which are consistent with the empirical observations.
Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the …
Motivated by the idea that some characteristics are specific to the relations between individuals and not of the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model on fully connected networks, square lattices and Erd \"os-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link-dynamics have no counterpart under traditional node dynamics in the same topologies.
We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state …
We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully-connected, random and scale free networks with an update probability inversely proportional to the persistence, that is, the time since the last event. We find that in the thermodynamic limit, at variance with standard updates, the system orders slowly. The approach to the absorbing state is characterized by a power law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined.