arXiv subjects

Takayuki Hiraoka

Publications and source records attributed to Takayuki Hiraoka.

At least 19 recordsLinked to original sources

arXiv2026

Disentangling epidemics and percolation

Non-recurrent epidemics on complex networks, such as the paradigmatic susceptible-infected-recovered (SIR) model, are often studied by mapping the model to bond percolation. However, the conditions under which this identification is justified have not been fully understood, except in specific cases. Here, we systematically determine when this mapping can be applied, starting from minimal assumptions on the epidemic model and the underlying network. Specifically, we discuss the conditions for three different forms of equivalence between a general non-recurrent epidemic model and Bernoulli bond percolation: isomorphism, equality of marginal infection probabilities, and equality of expected epidemic size. We numerically demonstrate the validity of our findings and examine how epidemiological outcomes are affected when these equivalences are not upheld. Our results establish the methodological basis and limitations of a common tool for analyzing epidemic processes on networks.

physics.soc-ph↗

arXiv2026

Coevolution of epidemic dynamics and network topology driven by disease fatality and waning immunity

Epidemics on complex networks have been shown to exhibit dynamics that are strongly influenced by the topology of the network. However, it remains unclear how the topology of the network is influenced by epidemic properties, such as waning immunity and disease fatality, coupled with demographic changes. To explore the interplay between epidemic dynamics and network topology, we develop an agent-based model of a fatal infectious disease with an imperfect immunity on an initially scale-free network that evolves via demographic and epidemic-induced changes. We show that this model undergoes an epidemic transition between a phase in which the disease eventually dies out and a phase in which it becomes endemic. Moreover, the network may lose its scale-free property as a result of the epidemic spreading, giving rise to a topological transition from a power-law to a non-power-law degree distribution. We validate our findings using heterogeneous mean-field approximations of the agent-based model. These results highlight the importance of accounting for network evolution in epidemic models and advance our understanding of coevolving dynamical systems, in which disease dynamics and network topology continuously shape one another.

physics.soc-ph↗

arXiv2026

Message passing and cyclicity transition

Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation remains elusive. We show that the message passing solutions commonly associated with the probability of belonging to the giant component actually identify reachability from cycles. This interpretation generally applies to bond and site percolation on any directed or undirected networks. Our findings highlight the distinction between transition in cyclicity and the emergence of the giant component.

physics.soc-ph↗

arXiv2026

Epidemic reproduction numbers in spatial networks

The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not hold in real-world populations where the contact patterns deviate from that assumption. In this paper, we present a network-based framework to compare reproduction numbers in populations with and without spatial structure, while other parameters of the disease remain fixed. Using this framework, we show that in homogeneously mixed populations, in the absence of external interventions, the effective reproduction number decreases exponentially as the susceptible population declines. In contrast, in spatially structured populations, the basic reproduction number is smaller, and the effective reproduction number initially decreases faster but eventually converges to unity. We show that the reproduction number is determined by the level of competition between infectious nodes, which is governed by the network structure. Our results suggest that without knowledge of the network structure, reproduction numbers may not be informative for parameterizing the contagiousness of the disease or predicting the behavior of epidemic spreading.

q-bio.PE↗

arXiv2025

Hierarchical organization of bursty trains in event sequences

Temporal sequences of discrete events that describe natural and social processes are often driven by non-Poisson dynamics. In addition to a heavy-tailed interevent time distribution, which primarily captures the deviation from a Poisson process, a heavy tail in the distribution of bursty train sizes is frequently observed, which implies the presence of higher-order temporal correlations that extend beyond interevent times. Here, we study empirical event sequences from different domains to show that the bursty trains in these processes are hierarchically structured across different timescales, and that such hierarchical organization gives rise to the higher-order temporal correlations. We propose a dynamic algorithm that generates event sequences with hierarchical structures with arbitrary precision. The algorithm successfully reproduces the features of real-world phenomena, implying the presence of memory mechanisms embedded in system dynamics across multiple timescales.

physics.soc-ph↗

arXiv2025

Block-corrected Modularity for Community Detection

Unknown node attributes in complex networks may introduce community structures that are important to distinguish from those driven by known attributes. We propose a block-corrected modularity that discounts given block structures present in the network to reveal communities masked by them. We show analytically how the proposed modularity finds the community structure driven by an unknown attribute in a simple network model. Further, we observe that the block-corrected modularity finds the underlying community structure on a number of simple synthetic network models while methods using different null models fail. We develop an efficient spectral method as well as two Louvain-inspired fine-tuning algorithms to maximize the proposed modularity and demonstrate their performance on several synthetic network models. Finally, we assess our methodology on various real-world citation networks built using the OpenAlex data by correcting for the temporal citation patterns.

physics.soc-ph↗

arXiv2025

Strength and weakness of disease-induced herd immunity in networks

When a fraction of a population becomes immune to an infectious disease, the population-wide infection risk decreases nonlinearly due to collective protection, known as herd immunity. Some studies based on mean-field models suggest that natural infection in a heterogeneous population may induce herd immunity more efficiently than homogeneous immunization. However, we theoretically show that this is not necessarily the case when the population is modeled as a network instead of using the mean-field approach. We identify two competing mechanisms driving disease-induced herd immunity in networks: the biased distribution of immunity toward socially active individuals enhances herd immunity, while the topological localization of immune individuals weakens it. The effect of localization is stronger in networks embedded in a low-dimensional space, which can make disease-induced immunity less effective than random immunization. Our results highlight the role of networks in shaping herd immunity and call for a careful examination of model predictions that inform public health policies.

physics.soc-ph↗

arXiv2025

Geospatial analysis of toponyms in geotagged social media posts

Place names, or toponyms, play an integral role in human representation and communication of geographic space. In particular, how people relate each toponym with particular locations in geographic space should be indicative of their spatial perception. Here, we make use of an extensive dataset of georeferenced social media posts, retrieved from Twitter, to perform a statistical analysis of the geographic distribution of toponyms and uncover the relationship between toponyms and geographic space. We show that the occurrence of toponyms is characterized by spatial inhomogeneity, giving rise to patterns that are distinct from the distribution of common nouns. Using simple models, we quantify the spatial specificity of toponym distributions and identify their core-periphery structures. In particular, we find that toponyms are used with a probability that decays as a power law with distance from the geographic center of their occurrence. Our findings highlight the potential of social media data to explore linguistic patterns in geographic space, paving the way for comprehensive analyses of human spatial representations.

physics.soc-ph↗

arXiv2022

Herd Immunity and Epidemic Size in Networks with Vaccination Homophily

We study how the herd immunity threshold and the expected epidemic size depend on homophily with respect to vaccine adoption. We find that the presence of homophily considerably increases the critical vaccine coverage needed for herd immunity and that strong homophily can push the threshold entirely out of reach. The epidemic size monotonically increases as a function of homophily strength for a perfect vaccine, while it is maximized at a nontrivial level of homophily when the vaccine efficacy is limited. Our results highlight the importance of vaccination homophily in epidemic modeling.

physics.soc-ph↗

arXiv2021

Adaptive and optimized COVID-19 vaccination strategies across geographical regions and age groups

We evaluate the efficiency of various heuristic strategies for allocating vaccines against COVID-19 and compare them to strategies found using optimal control theory. Our approach is based on a mathematical model which tracks the spread of disease among different age groups and across different geographical regions, and we introduce a method to combine age-specific contact data to geographical movement data. As a case study, we model the epidemic in the population of mainland Finland utilizing mobility data from a major telecom operator. Our approach allows to determine which geographical regions and age groups should be targeted first in order to minimize the number of deaths. In the scenarios that we test, we find that distributing vaccines demographically and in an age-descending order is not optimal for minimizing deaths and the burden of disease. Instead, more lives could potentially be saved by using strategies which emphasize high-incidence regions and distribute vaccines in parallel to multiple age groups. The level of emphasis that high-incidence regions should be given depends on the overall transmission rate in the population. This observation highlights the importance of updating the vaccination strategy when the effective reproduction number changes due to the general contact patterns changing and new virus variants entering.

q-bio.PE↗

arXiv2021

Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history

The origin of non-Poissonian or bursty temporal patterns observed in various datasets for human social dynamics has been extensively studied, yet its understanding still remains incomplete. Considering the fact that humans are social beings, a fundamental question arises: Is the bursty human dynamics dominated by individual characteristics or by interaction between individuals? In this paper we address this question by analyzing the Wikipedia edit history to see how spontaneous individual editors are in initiating bursty periods of editing, i.e., individual-driven burstiness, and to what extent such editors' behaviors are driven by interaction with other editors in those periods, i.e., interaction-driven burstiness. We quantify the degree of initiative (DoI) of an editor of interest in each Wikipedia article by using the statistics of bursty periods containing the editor's edits. The integrated value of the DoI over all relevant timescales reveals which is dominant between individual-driven and interaction-driven burstiness. We empirically find that this value tends to be larger for weaker temporal correlations in the editor's editing behavior and/or stronger editorial correlations. These empirical findings are successfully confirmed by deriving an analytic form of the DoI from a model capturing the essential features of the edit sequence. Thus our approach provides a deeper insight into the origin and underlying mechanisms of bursts in human social dynamics.

physics.soc-ph↗

arXiv2020

Waiting-time paradox in 1922

We present an English translation and discussion of an essay that a Japanese physicist, Torahiko Terada, wrote in 1922. In the essay, he described the waiting-time paradox, also called the bus paradox, which is a known mathematical phenomenon in queuing theory, stochastic processes, and modern temporal network analysis. He also observed and analyzed data on Tokyo City trams to verify the relevance of the waiting-time paradox to busy passengers in Tokyo at the time. This essay seems to be one of the earliest documentations of the waiting-time paradox in a sufficiently scientific manner.

physics.soc-ph↗

arXiv2019

Modeling temporal networks with bursty activity patterns of nodes and links

The concept of temporal networks provides a framework to understand how the interaction between system components changes over time. In empirical communication data, we often detect non-Poissonian, so-called bursty behavior in the activity of nodes as well as in the interaction between nodes. However, such reconciliation between node burstiness and link burstiness cannot be explained if the interaction processes on different links are independent of each other. This is because the activity of a node is the superposition of the interaction processes on the links incident to the node and the superposition of independent bursty point processes is not bursty in general. Here we introduce a temporal network model based on bursty node activation and show that it leads to heavy-tailed inter-event time distributions for both node dynamics and link dynamics. Our analysis indicates that activation processes intrinsic to nodes give rise to dynamical correlations across links. Our framework offers a way to model competition and correlation between links, which is key to understanding dynamical processes in various systems.

physics.soc-ph↗

arXiv2019

Copula-based algorithm for generating bursty time series

Dynamical processes in various natural and social phenomena have been described by a series of events or event sequences showing non-Poissonian, bursty temporal patterns. Temporal correlations in such bursty time series can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. Modeling and simulating various dynamical processes requires us to generate event sequences with a heavy-tailed IET distribution and memory effects between IETs. For this, we propose a Farlie-Gumbel-Morgenstern copula-based algorithm for generating event sequences with correlated IETs when the IET distribution and the memory coefficient between two consecutive IETs are given. We successfully apply our algorithm to the cases with heavy-tailed IET distributions. We also compare our algorithm to the existing shuffling method to find that our algorithm outperforms the shuffling method for some cases. Our copula-based algorithm is expected to be used for more realistic modeling of various dynamical processes.

physics.soc-ph↗

arXiv2019

Burst-tree decomposition of time series reveals the structure of temporal correlations

Comprehensive characterization of non-Poissonian, bursty temporal patterns observed in various natural and social processes is crucial to understand the underlying mechanisms behind such temporal patterns. Among them bursty event sequences have been studied mostly in terms of interevent times (IETs), while the higher-order correlation structure between IETs has gained very little attention due to the lack of a proper characterization method. In this paper we propose a method of decomposing an event sequence into a set of IETs and a burst tree, which exactly captures the structure of temporal correlations that is entirely missing in the analysis of IET distributions. We apply the burst-tree decomposition method to various datasets and analyze the structure of the revealed burst trees. In particular, we observe that event sequences show similar burst-tree structure, such as heavy-tailed burst size distributions, despite of very different IET distributions. The burst trees allow us to directly characterize the preferential and assortative mixing structure of bursts responsible for the higher-order temporal correlations. We also show how to use the decomposition method for the systematic investigation of such higher-order correlations captured by the burst trees in the framework of randomized reference models. Finally, we devise a simple kernel-based model for generating event sequences showing appropriate higher-order temporal correlations. Our method is a tool to make the otherwise overwhelming analysis of higher-order correlations in bursty time series tractable by turning it into the analysis of a tree structure.

physics.data-an↗

arXiv2019

Bursty time series analysis for temporal networks

Characterizing bursty temporal interaction patterns of temporal networks is crucial to investigate the evolution of temporal networks as well as various collective dynamics taking place in them. The temporal interaction patterns have been described by a series of interaction events or event sequences, often showing non-Poissonian or bursty nature. Such bursty event sequences can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. The heterogeneities of IETs have been extensively studied in recent years, while the correlations between IETs are far from being fully explored. In this Chapter, we introduce various measures for bursty time series analysis, such as the IET distribution, the burstiness parameter, the memory coefficient, the bursty train sizes, and the autocorrelation function, to discuss the relation between those measures. Then we show that the correlations between IETs can affect the speed of spreading taking place in temporal networks. Finally, we discuss possible research topics regarding bursty time series analysis for temporal networks.

physics.soc-ph↗

arXiv2018

Correlated bursts in temporal networks slow down spreading

Spreading dynamics has been considered to take place in temporal networks, where temporal interaction patterns between nodes show non-Poissonian bursty nature. The effects of inhomogeneous interevent times (IETs) on the spreading have been extensively studied in recent years, yet little is known about the effects of correlations between IETs on the spreading. In order to investigate those effects, we study two-step deterministic susceptible-infected (SI) and probabilistic SI dynamics when the interaction patterns are modeled by inhomogeneous and correlated IETs, i.e., correlated bursts. By analyzing the transmission time statistics in a single-link setup and by simulating the spreading in Bethe lattices and random graphs, we conclude that the positive correlation between IETs slows down the spreading. We also argue that the shortest transmission time from one infected node to its susceptible neighbors can successfully explain our numerical results.

physics.soc-ph↗

arXiv2018

Limits of memory coefficient in measuring correlated bursts

Temporal inhomogeneities in event sequences of natural and social phenomena have been characterized in terms of interevent times and correlations between interevent times. The inhomogeneities of interevent times have been extensively studied, while the correlations between interevent times, often called correlated bursts, are far from being fully understood. For measuring the correlated bursts, two relevant approaches were suggested, i.e., memory coefficient and burst size distribution. Here a burst size denotes the number of events in a bursty train detected for a given time window. Empirical analyses have revealed that the larger memory coefficient tends to be associated with the heavier tail of burst size distribution. In particular, empirical findings in human activities appear inconsistent, such that the memory coefficient is close to $0$, while burst size distributions follow a power law. In order to comprehend these observations, by assuming the conditional independence between consecutive interevent times, we derive the analytical form of the memory coefficient as a function of parameters describing interevent time and burst size distributions. Our analytical result can explain the general tendency of the larger memory coefficient being associated with the heavier tail of burst size distribution. We also find that the apparently inconsistent observations in human activities are compatible with each other, indicating that the memory coefficient has limits to measure the correlated bursts.

physics.soc-ph↗