arXiv subjects

Naoki Masuda

Publications and source records attributed to Naoki Masuda.

At least 91 records · Page 5Linked to original sources

arXiv2020

SI-spreading-based network embedding in static and temporal networks

Link prediction can be used to extract missing information, identify spurious interactions as well as forecast network evolution. Network embedding is a methodology to assign coordinates to nodes in a low dimensional vector space. By embedding nodes into vectors, the link prediction problem can be converted into a similarity comparison task. Nodes with similar embedding vectors are more likely to be connected. Classic network embedding algorithms are random-walk-based. They sample trajectory paths via random walks and generate node pairs from the trajectory paths. The node pair set is further used as the input for a Skip-Gram model, a representative language model that embeds nodes (which are regarded as words) into vectors. In the present study, we propose to replace random walk processes by a spreading process, namely the susceptible-infected (SI) model, to sample paths. Specifically, we propose two SI-spreading-based algorithms, SINE and TSINE, to embed static and temporal networks, respectively. The performance of our algorithms is evaluated by the missing link prediction task in comparison with state-of-the-art static and temporal network embedding algorithms. Results show that SINE and TSINE outperform the baselines across all six empirical datasets. We further find that the performance of SINE is mostly better than TSINE, suggesting that temporal information does not necessarily improve the embedding for missing link prediction. Moreover, we study the effect of the sampling size, quantified as the total length of the trajectory paths, on the performance of the embedding algorithms. The better performance of SINE and TSINE requires a smaller sampling size in comparison with the baseline algorithms. Hence, SI-spreading-based embedding tends to be more applicable to large-scale networks.

cs.SI↗

arXiv2020

Random walks and diffusion on networks

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

physics.soc-ph↗

arXiv2020

Small inter-event times govern epidemic spreading on temporal networks

Just like the degrees of human and animal interaction networks, the distribution of the times between interactions is known to often be right-skewed and fat-tailed. Both these distributions affect epidemic dynamics strongly, but, as we show in this Letter, for very different reasons. Whereas the high degrees of the tail are critical for facilitating epidemics, it is the small interevent times that control the dynamics of epidemics. We investigate this effect both analytically and numerically for different versions of the Susceptible-Infected-Recovered model on different types of networks.

q-bio.PE↗

arXiv2020

Long-tailed distributions of inter-event times as mixtures of exponential distributions

Inter-event times of various human behavior are apparently non-Poissonian and obey long-tailed distributions as opposed to exponential distributions, which correspond to Poisson processes. It has been suggested that human individuals may switch between different states in each of which they are regarded to generate events obeying a Poisson process. If this is the case, inter-event times should approximately obey a mixture of exponential distributions with different parameter values. In the present study, we introduce the minimum description length principle to compare mixtures of exponential distributions with different numbers of components (i.e., constituent exponential distributions). Because these distributions violate the identifiability property, one is mathematically not allowed to apply the Akaike or Bayes information criteria to their maximum likelihood estimator to carry out model selection. We overcome this theoretical barrier by applying a minimum description principle to joint likelihoods of the data and latent variables. We show that mixtures of exponential distributions with a few components are selected as opposed to more complex mixtures in various data sets and that the fitting accuracy is comparable to that of state-of-the-art algorithms to fit power-law distributions to data. Our results lend support to Poissonian explanations of apparently non-Poissonian human behavior.

physics.soc-ph↗

arXiv2020

A Gillespie algorithm for non-Markovian stochastic processes

The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on social networks. Empirically, the inter-event times of various phenomena obey long-tailed distributions. The Gillespie algorithm and its variants either assume Poisson processes (i.e., exponentially distributed inter-event times), use particular functions for time courses of the event rate, or work for non-Poissonian renewal processes, including the case of long-tailed distributions of inter-event times, but at a high computational cost. In the present study, we propose an innovative Gillespie algorithm for renewal processes on the basis of the Laplace transform. The algorithm makes use of the fact that a class of point processes is represented as a mixture of Poisson processes with different event rates. The method is applicable to multivariate renewal processes whose survival function of inter-event times is completely monotone. It is an exact algorithm and works faster than a recently proposed Gillespie algorithm for general renewal processes, which is exact only in the limit of infinitely many processes. We also propose a method to generate sequences of event times with a tunable amount of positive correlation between inter-event times. We demonstrate our algorithm with exact simulations of epidemic processes on networks, finding that a realistic amount of positive correlation in inter-event times only slightly affects the epidemic dynamics.

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

Dynamical stability of water distribution networks

Water distribution networks are hydraulic infrastructures that aim to meet water demands at their various nodes. Water flows through pipes in the network create nonlinear dynamics on networks. A desirable feature of water distribution networks is high resistance to failures and other shocks given to the system. Such threats would at least transiently change the flow rate in various pipes, potentially undermining the functionality of the whole water distribution system. Here we carry out a linear stability analysis for a nonlinear dynamical system representing the flow rate through pipes that are interconnected through an arbitrary pipe network with reservoirs and consumer nodes. We show that the steady state is always locally stable and develop a method to calculate the eigenvalue that corresponds to the mode that decays the most slowly towards the equilibrium, which we use as an index for resilience of the system. We show that the proposed index is positively correlated with the recovery rate of the pipe network, which was derived from a realistic and industrially popular simulator. The present analytical framework is expected to be useful for deploying tools from nonlinear dynamics and network analysis to designing, resilience managements and scenario testings of water distribution networks.

physics.soc-ph↗

arXiv2019

Constructing networks by filtering correlation matrices: A null model approach

Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there have been criticisms on this thresholding approach such as an inability to filter out spurious correlations, which have led to proposals of alternative methods to overcome some of the problems. We propose a method to create networks from correlation matrices based on optimisation with regularization, where we lay an edge between each pair of nodes if and only if the edge is unexpected from a null model. The proposed algorithm is advantageous in that it can be combined with different types of null models. Moreover, the algorithm can select the most plausible null model from a set of candidate null models using a model selection criterion. For three economic data sets, we find that the configuration model for correlation matrices is often preferred to standard null models. For country-level product export data, the present method better predicts main products exported from countries than sample correlation matrices do.

physics.soc-ph↗

arXiv2019

Detecting sequences of system states in temporal networks

Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained description of these systems by proposing a method to assign discrete states to the systems and inferring the sequence of such states from the data. Such states could, for example, correspond to a mental state (as inferred from neuroimaging data) or the operational state of an organization (as inferred by interpersonal communication). Our method combines a graph distance measure and hierarchical clustering. Using several empirical data sets of social temporal networks, we show that our method is capable of inferring the system's states such as distinct activities in a school and a weekday state as opposed to a weekend state. We expect the methods to be equally useful in other settings such as temporally varying protein interactions, ecological interspecific interactions, functional connectivity in the brain and adaptive social networks.

cs.SI↗

arXiv2019

Multiscale core-periphery structure in a global liner shipping network

Maritime transport accounts for a majority of trades in volume, of which 70% in value is carried by container ships that transit regular routes on fixed schedules in the ocean. In the present paper, we analyse a data set of global liner shipping as a network of ports. In particular, we construct the network of the ports as the one-mode projection of a bipartite network composed of ports and ship routes. Like other transportation networks, global liner shipping networks may have core-periphery structure, where a core and a periphery are groups of densely and sparsely interconnected nodes, respectively. Core-periphery structure may have practical implications for understanding the robustness, efficiency and uneven development of international transportation systems. We develop an algorithm to detect core-periphery pairs in a network, which allows one to find core and peripheral nodes on different scales and uses a configuration model that accounts for the fact that the network is obtained by the one-mode projection of a bipartite network. We also found that most ports are core (as opposed to peripheral) ports and that ports in some countries in Europe, America and Asia belong to a global core-periphery pair across different scales, whereas ports in other countries do not.

physics.soc-ph↗

arXiv2018

Modelling project failure and its mitigation in a time-stamped network of interrelated tasks

Resolving major societal challenges, such as stagnated economic growth or wasted resources, heavily relies on successful project delivery. However, projects are notoriously hard to deliver successfully, partly due to their interconnected nature which makes them prone to cascading failures. We deploy a model of cascading failure to temporal network data obtained from an engineering project, where tasks constituting the entire project and inter-dependencies between tasks correspond to time-stamped nodes and edges, respectively. We numerically evaluate the performance of six strategies to mitigate cascading failures. It is assumed that increased time between a pair of inter-connected tasks acts as a buffer, preventing a failure to propagate from one task to another. We show that, in a majority of cases that we explored, temporal properties of the activities (i.e., start and end date of each task in the project) are more relevant than their structural properties (i.e., out-degree and the size of the out-component of the task) to preventing large-scale cascading failures. Our results suggest potential importance of changing timings of tasks, apart from the static structure of the same network of tasks, for containing project failure.

cs.SI↗

arXiv2018

Configuration model for correlation matrices preserving the node strength

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, such as those derived from random matrix theory, that partially preserve properties of the original matrix. We propose a model to generate such reference correlation and covariance matrices for the given matrix. Correlation matrices are often analysed as networks, which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node. Given this background, the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes, akin to configuration models for conventional networks. Our algorithm is derived from the maximum entropy principle. We will apply the proposed algorithm to measurement of clustering coefficients and community detection, both of which require a null model to assess the statistical significance of the obtained results.

physics.soc-ph↗

arXiv2018

Clustering coefficients for correlation networks

The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighbouring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients are useful in characterising individual nodes. In contrast, the conventional local clustering coefficients were strongly correlated with and therefore may be confounded by the node's connectivity.

physics.soc-ph↗

arXiv2018

A generalised significance test for individual communities in networks

Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks, communities are generally heterogeneous in various aspects such as the size, density of edges, connectivity to other communities and significance. In the present study, we propose a method to statistically test the significance of individual communities in a given network. Compared to the previous methods, the present algorithm is unique in that it accepts different community-detection algorithms and the corresponding quality function for single communities. The present method requires that a quality of each community can be quantified and that community detection is performed as optimisation of such a quality function summed over the communities. Various community detection algorithms including modularity maximisation and graph partitioning meet this criterion. Our method estimates a distribution of the quality function for randomised networks to calculate a likelihood of each community in the given network. We illustrate our algorithm by synthetic and empirical networks.

physics.soc-ph↗

arXiv2018

Core-periphery structure requires something else in the network

A network with core-periphery structure consists of core nodes that are densely interconnected. In contrast to community structure, which is a different meso-scale structure of networks, core nodes can be connected to peripheral nodes and peripheral nodes are not densely interconnected. Although core-periphery structure sounds reasonable, we argue that it is merely accounted for by heterogeneous degree distributions, if one partitions a network into a single core block and a single periphery block, which the famous Borgatti-Everett algorithm and many succeeding algorithms assume. In other words, there is a strong tendency that high-degree and low-degree nodes are judged to be core and peripheral nodes, respectively. To discuss core-periphery structure beyond the expectation of the node's degree (as described by the configuration model), we propose that one needs to assume at least one block of nodes apart from the focal core-periphery structure, such as a different core-periphery pair, community or nodes not belonging to any meso-scale structure. We propose a scalable algorithm to detect pairs of core and periphery in networks, controlling for the effect of the node's degree. We illustrate our algorithm using various empirical networks.

physics.soc-ph↗

arXiv2018

Effects of the distant population density on spatial patterns of demographic dynamics

Spatiotemporal patterns of population changes within and across countries have various implications. Different geographical, demographic and econo-societal factors seem to contribute to migratory decisions made by individual inhabitants. Focussing on internal (i.e., domestic) migration, we ask whether individuals may take into account the information on the population density in distant locations to make migratory decisions. We analyse population census data in Japan recorded with a high spatial resolution (i.e., cells of size 500 m $\times$ 500 m) for the entirety of the country and simulate demographic dynamics induced by the gravity model and its variants. We show that, in the census data, the population growth rate in a cell is positively correlated with the population density in nearby cells up to a radius of 20 km as well as that of the focal cell. The ordinary gravity model does not capture this empirical observation. We then show that the empirical observation is better accounted for by extensions of the gravity model such that individuals are assumed to perceive the attractiveness, approximated by the population density, of the source or destination cell of migration as the spatial average over a radius of $\approx 1$ km.

physics.soc-ph↗

arXiv2018

Optimal Containment of Epidemics over Temporal Activity-Driven Networks

In this paper, we study the dynamics of epidemic processes taking place in temporal and adaptive networks. Building on the activity-driven network model, we propose an adaptive model of epidemic processes, where the network topology dynamically changes due to both exogenous factors independent of the epidemic dynamics as well as endogenous preventive measures adopted by individuals in response to the state of the infection. A direct analysis of the model using Markov processes involves the spectral analysis of a transition probability matrix whose size grows exponentially with the number of nodes. To overcome this limitation, we derive an upper-bound on the decay rate of the number of infected nodes in terms of the eigenvalues of a $2 \times 2$ matrix. Using this upper bound, we propose an efficient algorithm to tune the parameters describing the endogenous preventive measures in order to contain epidemics over time. We confirm our theoretical results via numerical simulations.

cs.SI↗

arXiv2018

Structural changes in the interbank market across the financial crisis from multiple core-periphery analysis

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank markets seem better characterised by a bipartite structure with more core-periphery connections than inside the core. Using a novel core-periphery detection method on the eMID interbank market, we enrich this picture by showing that the network is actually characterised by multiple core-periphery pairs. Moreover, a transition from core-periphery to bipartite structures occurs by shortening the temporal scale of data aggregation. We further show how the global financial crisis transformed the market, in terms of composition, multiplicity and internal organisation of core-periphery pairs. By unveiling such a fine-grained organisation and transformation of the interbank market, our method can find important applications in the understanding of how distress can propagate over financial networks.

q-fin.RM↗