arXiv subjects

Naoki Masuda

Publications and source records attributed to Naoki Masuda.

At least 19 recordsLinked to original sources

arXiv2026

Early warning signals for synchronization transitions from partial observations

Anticipating the onset of collective synchronization is important in many networked systems, yet observing every oscillator is often impractical. We investigate whether synchronization transitions can be detected from a small set of monitored, or sentinel, nodes. Using a stochastic Kuramoto model on networks, we numerically compare three early warning signals: the local order parameter, its temporal variance, and the variance of individual oscillator phases after removing their mean rotational trends. We also compare sentinel-selection strategies based on node dynamics, degree, and random sampling. We show that, under partial observation, the local order parameter and the variance of detrended phases provide substantially stronger warning signals than the variance of the local order parameter. Selecting nodes according to their dynamical behavior near the transition consistently improves performance over other sentinel-selection methods. With only $\lfloor\ln N\rfloor$ dynamically selected sentinels, two success indicators approach the performance obtained by observing all $N$ nodes. These results demonstrate that synchronization transitions can be anticipated from sparse observations when the warning signal and monitored nodes are chosen appropriately.

physics.soc-ph↗

arXiv2026

A theory of spatial early warning signals for tipping points on complex networks

Spatial early warning signals (EWSs) seek evidence of an approaching tipping point from a single snapshot of many interacting elements. Existing theory largely assumes spatial homogeneity, whereas networks introduce systematic differences among nodes that may obscure fluctuation-based warning signals. We develop a mathematical framework for spatial EWSs in stochastic dynamical systems on networks. We find that the expected spatial variance, a popular spatial EWS, decomposes exactly into a structural contribution from heterogeneity in the equilibrium state and a fluctuation contribution determined by the stationary covariance. Near a simple steady-state bifurcation, the potentially divergent covariance concentrates along the critical eigendirection: the left eigenvector determines how strongly noise excites the critical fluctuation, while the right eigenvector determines its spatial pattern. Consequently, the spatial variance has a divergent fluctuation contribution when the limiting critical eigendirection is noise-excited and spatially nonuniform after centering. In contrast, the spatial coefficient of variation generally saturates, while skewness, kurtosis, and Moran's $I$ approach network-dependent limits without a universal warning direction. We also derive results for homogeneous networks, node-wise baseline subtraction as preprocessing, and Hopf bifurcations, for which the limiting distributions are qualitatively different. These results clarify when spatial EWSs provide reliable warnings and why their performance depends on network structure, noise, and preprocessing.

physics.soc-ph↗

arXiv2026

Baseline-referenced spatial early warning signals for tipping points on heterogeneous networks

Anticipating tipping points in complex systems is difficult because many early warning signals require long time series, which are often unavailable in practice. Spatial early warning signals offer an alternative by using a single snapshot across many interacting elements, or nodes. However, their performance in heterogeneous systems is often inconsistent because raw node states reflect both dynamical changes associated with an approaching transition and static heterogeneity induced by network structure. Here, we propose a baseline-referenced framework for spatial early warning signals. The method compares each node's state with its own baseline far from the tipping point before computing a spatial statistic, thus reducing network-structure-induced variation. We evaluate baseline-referenced variants of five classical spatial early warning signals across diverse tipping scenarios and networks, and find that baseline referencing markedly improves variance-based spatial signals. The best variants increase consistently and progressively toward tipping points across different scenarios, outperform a single-node temporal variance that requires long time series, and retain high performance even when up to 80% of nodes are omitted from observation. These results provide a practical route for using spatial early warning signals in heterogeneous networked systems when dense temporal monitoring or complete network-wide observation is infeasible, as is often the case in real applications.

physics.soc-ph↗

arXiv2026

Dimensional reduction of dynamical systems on graphons

Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves key properties of the original dynamics such as bifurcation structure. A class of such methods proposed in network science research entails finding a one- (or low-) dimensional system that a particular weighted average of the state variables of all nodes in the network approximately obeys. We formulate and mathematically analyze this dimension reduction technique for dynamical systems on dense graphons, or the limiting, infinite-dimensional object of a sequence of graphs with an increasing number of nodes. We first theoretically justify the continuum limit for a nonlinear dynamical system of our interest, and the existence and uniqueness of the solution of graphon dynamical systems. We then derive the reduced one-dimensional system on graphons and prove its convergence properties. Finally, we perform numerical simulations for various graphons and dynamical system models to assess the accuracy of the one-dimensional approximation.

math.DS↗

arXiv2026

Using covariance of node states to design early warning signals for network dynamics

Real-life systems often experience regime shifts. An early warning signal (EWS) is a quantity that attempts to anticipate such a regime shift. Because complex systems of practical interest showing regime shifts are often dynamics on networks, a research interest is to design EWSs for networks, including determining sentinel nodes that are useful for constructing high-quality EWSs. Previous work has shown that the sample variance is a viable EWS including in the case of networks. We explore the use of the sample covariance of two nodes, or sentinel node pairs, for improving EWSs for networks. We perform analytical calculations in four-node networks and numerical simulations in larger networks to find that the sample covariance and its combination over node pairs is inferior to the sample variance and its combination over nodes; the latter are previously proposed EWSs based on sentinel node selection. The present results support the predominant use of diagonal entries of the covariance matrix (i.e., variance) as opposed to off-diagonal entries in EWS construction.

physics.soc-ph↗

arXiv2026

Detecting and forecasting tipping points from sample variance alone

Anticipating tipping points in complex systems is a fundamental challenge across domains. Traditional early warning signals (EWSs) based on critical slowing down, such as increasing sample variance, are widely used, but their ability to reliably indicate imminent bifurcations and forecast their timing remains limited. Here, we introduce TIPMOC (TIpping via Power-law fits and MOdel Comparison), a parametric framework designed to statistically detect the approach of a bifurcation and estimate its future location using only the sample variance. TIPMOC exploits the mathematical property that variance diverges with a characteristic power-law form near codimension-one bifurcations. By sequentially monitoring system variance as a control parameter changes, TIPMOC statistically adjudicates between linear and power-law divergence at each step. When evidence favors power-law divergence, TIPMOC forecasts the impending tipping point and estimates its position; otherwise, it avoids false positives. Through numerical simulations, we demonstrate TIPMOC's robustness and accuracy in both detection and timing prediction across different types of dynamics and bifurcation, whereas the accuracy of timing prediction is limited. TIPMOC shows low false positive rates and performs well even with uneven sampling and colored noise. This method thus enhances the interpretability and practical utility of classical EWSs, serving as both a transparent add-on and a stand-alone statistical tool for forecasting regime shifts in diverse complex systems.

physics.soc-ph↗

arXiv2026

Quantifying concurrency in event-based temporal network and hypergraph data

Many social, biological, and technological systems are recorded as sequences of time-stamped interactions. In such systems, concurrency, i.e., the tendency for an individual to participate in multiple interactions approximately at the same time, can strongly affect processes such as epidemic or information spreading. However, concurrency measures for event-based temporal network data are not established. We introduce edge-event correlation (EEC), a simple and interpretable measure that quantifies how similarly two connections are active over time. We apply EEC to empirical temporal networks and temporal hypergraphs, the latter allowing single events to involve more than two nodes. Across most datasets, pairs of edges or hyperedges that share a node show higher concurrency than pairs that do not. We further find that this elevated concurrency is mainly driven by pairs embedded in closed local structures, such as triangles in the aggregated network. EEC provides a practical tool for quantifying concurrency in event-based temporal data and may help identify network structures that facilitate rapid spreading or collective dynamics.

physics.soc-ph↗

arXiv2026

Modeling non-Poissonian temporal hypergraphs by Markovian node dynamics

Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce node-driven temporal hypergraph models in which each node stochastically alternates between low- and high-activity states, and a hyperedge produces time-stamped events with a probability that depends on the number of high-state nodes in the hyperedge. For two event-generation rules, we analytically derive interevent time distributions and autocorrelation functions of event sequences, both for hyperedges and nodes. Despite Markovian node-state dynamics, the induced event processes become mixtures of Poissonian, short-tailed components, resulting in longer-tailed interevent time distributions and slowly decaying autocorrelation. The theory further shows the dependence of these features on the size of hyperedge, which largely agrees with various empirical data. We expect our models to provide a simple, interpretable framework for connecting individual-level activity fluctuations to the timing patterns observed in real group interactions.

physics.soc-ph↗

arXiv2026

Non-dilemmatic social dynamics promote cooperation in multilayer networks

Various theoretical and empirical studies have accounted for why humans cooperate in competitive environments. Although prior work has revealed that network structure and multiplex interactions can promote cooperation, most theory assumes that individuals play similar dilemma games in all social contexts. However, real-world agents may participate in a diversity of interactions, not all of which present dilemmas. We develop an evolutionary game model on multilayer networks in which one layer supports the prisoner's dilemma game, while the other follows constant-selection dynamics, representing biased but non-dilemmatic competition, akin to opinion or fad spreading. Our theoretical analysis reveals that coupling a social dilemma layer to a non-dilemmatic constant-selection layer robustly enhances cooperation in many cases, across different multilayer networks, updating rules, and payoff schemes. These findings suggest that embedding individuals within diverse networked settings -- even those unrelated to direct social dilemmas -- can be a principled approach to engineering cooperation in socio-ecological and organizational systems.

physics.soc-ph↗

arXiv2025

Observing network dynamics through sentinel nodes

A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex networks, in which nodes may be extremely diverse, and no single component can truly represent the state of the entire system. It seems, therefore, that to observe the dynamics of social, biological or technological networks, one must extract the dynamic states of a large number of nodes -- a task that is often practically prohibitive. Theoretical tools are also highly restrictive, given the analytically impenetrable combination of complex heterogeneous networks with nonlinear, often hidden, dynamics. To overcome this challenge, we use machine learning techniques to detect the network's sentinel nodes, a set of network components whose combined states can help approximate the average dynamics of the entire network. The method allows us to assess the equilibrium state of a large complex system by tracking just a small number of carefully selected nodes. We find that the sentinels are mainly determined by the network structure such that they can be extracted even with little knowledge of the system's specific interaction dynamics. Therefore, the network's sentinels offer a natural probe by which to observe the system's dynamic states. Intriguingly, sentinels tend to avoid the highly central nodes such as the hubs.

physics.soc-ph↗

arXiv2025

Introduction to correlation networks: Interdisciplinary approaches beyond thresholding

Many empirical networks originate from correlational data, arising in domains as diverse as psychology, neuroscience, genomics, microbiology, finance, and climate science. Specialized algorithms and theory have been developed in different application domains for working with such networks, as well as in statistics, network science, and computer science, often with limited communication between practitioners in different fields. This leaves significant room for cross-pollination across disciplines. A central challenge is that it is not always clear how to best transform correlation matrix data into networks for the application at hand, and probably the most widespread method, i.e., thresholding on the correlation value to create either unweighted or weighted networks, suffers from multiple problems. In this article, we review various methods of constructing and analyzing correlation networks, ranging from thresholding and its improvements to weighted networks, regularization, dynamic correlation networks, threshold-free approaches, comparison with null models, and more. Finally, we propose and discuss recommended practices and a variety of key open questions currently confronting this field.

physics.soc-ph↗

arXiv2025

Temporal Motifs for Financial Networks: A Study on Mercari, JPMC, and Venmo Platforms

Understanding the dynamics of financial transactions among people is critical for various applications such as fraud detection. One important aspect of financial transaction networks is temporality. The order and repetition of transactions can offer new insights when considered within the graph structure. Temporal motifs, defined as a set of nodes that interact with each other in a short time period, are a promising tool in this context. In this work, we study three unique temporal financial networks: transactions in Mercari, an online marketplace, payments in a synthetic network generated by J.P. Morgan Chase, and payments and friendships among Venmo users. We consider the fraud detection problem on the Mercari and J.P. Morgan Chase networks, for which the ground truth is available. We show that temporal motifs offer superior performance to several baselines, including a previous method that considers simple graph features and two node embedding techniques (LINE and node2vec), while being practical in terms of runtime performance. For the Venmo network, we investigate the interplay between financial and social relations on three tasks: friendship prediction, vendor identification, and analysis of temporal cycles. For friendship prediction, temporal motifs yield better results than general heuristics, such as Jaccard and Adamic-Adar measures. We are also able to identify vendors with high accuracy and observe interesting patterns in rare motifs, such as temporal cycles. We believe that the analysis, datasets, and lessons from this work will be beneficial for future research on financial transaction networks.

cs.SI↗

arXiv2025

Source Detection in Hypergraph Epidemic Dynamics using a Higher-Order Dynamic Message Passing Algorithm

Source detection is crucial for capturing the dynamics of real-world infectious diseases and informing effective containment strategies. Most existing approaches to source detection focus on conventional pairwise networks, whereas recent efforts on both mathematical modeling and analysis of contact data suggest that higher-order (e.g., group) interactions among individuals may both account for a large fraction of infection events and change our understanding of how epidemic spreading proceeds in empirical populations. In the present study, we propose a message-passing algorithm, called the HDMPN, for source detection for a stochastic susceptible-infectious dynamics on hypergraphs. By modulating the likelihood maximization method by the fraction of infectious neighbors, HDMPN aims to capture the influence of higher-order structures and do better than the conventional likelihood maximization. We numerically show that, in most cases, HDMPN outperforms benchmarks including the likelihood maximization method without modification.

physics.soc-ph↗

arXiv2025

To Be a Truster or Not to Be: Evolutionary Dynamics of a Symmetric N-Player Trust Game in Well-Mixed and Networked Populations

Trust and reciprocation of it form the foundation of economic, social and other interactions. While the Trust Game is widely used to study these concepts for interactions between two players, often alternating different roles (i.e., investor and trustee), its extensions to multi-player scenarios have been restricted to instances where players assume only one role. We propose a symmetric N-player Trust Game, in which players alternate between two roles, and the payoff of the player is defined as the average across their two roles and drives the evolutionary game dynamics. We find that prosocial strategies are harder to evolve with the present symmetric N-player Trust Game than with the Public Goods Game, which is well studied. In particular, trust fails to evolve regardless of payoff function nonlinearity in well-mixed populations in the case of the symmetric N-player trust game. In structured populations, nonlinear payoffs can have strong impacts on the evolution of trust. The same nonlinearity can yield substantially different outcomes, depending on the nature of the underlying network. Our results highlight the importance of considering both payoff structures and network topologies in understanding the emergence and maintenance of prosocial behaviours.

physics.soc-ph↗

arXiv2025

Scalar embedding of temporal network trajectories

A temporal network -- a collection of snapshots recording the evolution of a network whose links appear and disappear dynamically -- can be interpreted as a trajectory in graph space. In order to characterize the complex dynamics of such trajectory via the tools of time series analysis and signal processing, it is sensible to preprocess the trajectory by embedding it in a low-dimensional Euclidean space. Here we argue that, rather than the topological structure of each network snapshot, the main property of the trajectory that needs to be preserved in the embedding is the relative graph distance between snapshots. This idea naturally leads to dimensionality reduction approaches that explicitly consider relative distances, such as Multidimensional Scaling (MDS) or identifying the distance matrix as a feature matrix in which to perform Principal Component Analysis (PCA). This paper provides a comprehensible methodology that illustrates this approach. Its application to a suite of generative network trajectory models and empirical data certify that nontrivial dynamical properties of the network trajectories are preserved already in their scalar embeddings, what enables the possibility of performing time series analysis in temporal networks.

physics.soc-ph↗

arXiv2025

Applicability of spatial early warning signals to complex network dynamics

Early warning signals (EWSs) for complex dynamical systems aim to anticipate tipping points before they occur. While signals computed from time series data, such as temporal variance, are useful for this task, they are costly to obtain in practice because they need many samples over time to calculate. Spatial EWSs use just a single sample per spatial location and aggregate the samples over space rather than time to try to mitigate this limitation. However, although many complex systems in nature and society form diverse networks, the performance of spatial EWSs is mostly unknown for general networks because the vast majority of studies of spatial EWSs have been on regular lattice networks. Therefore, we have carried out a comprehensive investigation of six major spatial EWSs on various networks. We find that the winning EWS depends on tipping scenarios, although the coefficient of variation and spatial skewness tend to outperform alternative EWSs. We also find that spatial EWSs behave in a drastically different manner between the square lattice and complex networks and tend to be more reliable for the latter than the former. The present results encourage further studies of spatial EWSs on complex networks.

physics.soc-ph↗

arXiv2025

Energy landscape analysis based on the Ising model: Tutorial review

We review a class of energy landscape analysis method that uses the Ising model and takes multivariate time series data as input. The method allows one to capture dynamics of the data as trajectories of a ball from one basin to a different basin to yet another, constrained on the energy landscape specified by the estimated Ising model. While this energy landscape analysis has mostly been applied to functional magnetic resonance imaging (fMRI) data from the brain for historical reasons, there are emerging applications outside fMRI data and neuroscience. To inform such applications in various research fields, this review paper provides a detailed tutorial on each step of the analysis, terminologies, concepts underlying the method, and validation, as well as recent developments of extended and related methods.

cond-mat.dis-nn↗

arXiv2025

Spline tie-decay temporal networks

Increasing amounts of data are available on temporal, or time-varying, networks. There have been various representations of temporal network data each of which has different advantages for downstream tasks such as mathematical analysis, visualizations, agent-based and other dynamical simulations on the temporal network, and discovery of useful structure. The tie-decay network is a representation of temporal networks whose advantages include the capability of generating continuous-time networks from discrete time-stamped contact event data with mathematical tractability and a low computational cost. However, the current framework of tie-decay networks is limited in terms of how each discrete contact event can affect the time-dependent tie strength (which we call the kernel). Here we extend the tie-decay network model in terms of the kernel. Specifically, we use a cubic spline function for modeling short-term behavior of the kernel and an exponential decay function for long-term behavior, and graft them together. This spline version of tie-decay network enables delayed and $C^1$-continuous interaction rates between two nodes while it only marginally increases the computational and memory burden relative to the conventional tie-decay network. We show mathematical properties of the spline tie-decay network and numerically showcase it with three tasks: network embedding, a deterministic opinion dynamics model, and a stochastic epidemic spreading model.

physics.soc-ph↗