Research projects

For my research intersets, see About Naoki.

The following showcases my recent work across different topics.

Dynamics of system states in temporal networks

Keywords: network, time series, algorithm, clustering

Networks often vary over time. Data of such temporal (i.e., time-varying) networks abound, and a key question is how to understand empirical temporal networks that are both complex in structure and time-dependent. To address this broad question, we developed a method to coarse grain temporal network data by identifying a relatively small number of discrete states of the network and view the given temporal network as a state-transition dynamics among the inferred states [Masuda & Holme. Sci Rep (2019)]. For example, the figure to the left below shows state-transition dynamics of a temporal network composed of four persons. Each shaded box corresponds to a network of the four persons, which defines a network state. Therefore, there are four states in this example. The dynamics of the network are equivalent to transitions from one state (i.e., one four-person network) to another. The thickness of the arrow between shaded boxes represents the frequency of the associated state transition.

Figure: Left: Dynamics of the system state of a temporal network composed of four nodes. Right: State dynamics of a temporal network in a primary school in Europe. Discrete times 1 to 25 correspond to the first day, and 26 to 50 correspond to the second day. In each day, a clear lunch-time state (state 2 in the bottom panel) is detected. The data originate from the SocioPatterns project, and the details including the precise credit to the data source are found in our paper.

Our method, which is computational rather than mathematical, combines a graph distance measure and hierarchical clustering. It is capable of inferring network states such as distinct activities in a school, i.e., the class-time state and the lunch-time state (the right panel of the figure). Note that these states cannot be found if we only look at simple measures such as the gross frequency of inter-personal contacts (middle panel in the right figure). We expect that the method is equally useful in other settings such as temporally varying protein interactions, ecological interspecific interactions, functional connectivity in the brain, and different operational states of an organization. We want to look for such applications as well as further develop this line of methods.

Core-periphery structure of networks

Keywords: network, meso-scale structure, algorithm

Here is our research.

Gillespie algorithm

Keywords: network, time series, point process, Laplace transform

Social networks we form and other networks often change over time, and such networks are analysed under the umbrella term temporal networks. Many temporal networks have burstiness. Suppose you meet somebody and have discrete conversation events. Your conversation events would not occur uniformly at random. A chunk of events tends to occur in a burst, which occurs in an intermittent manner (Figure). In technical terms, the inter-event times obey a long-tailed distribution.

Fig: A bursty time series. The vertical bar represents the time a conversation event happens e.g. between two particular persons.

Before burstiness was known, it had been common to assum that conversation events occur as if people arrive at a sales counter sporadically and completely randomly, lacking burstiness (technically, exponential-like distribution of inter-event times). Now we know that this is an oversimplification in many cases.

The Gillespie algorithm, invented in 1970s, is a mathematical/computational technique with which one can numerically simulate systems of interacting event sequences (e.g. a population of humans or molecules) efficiently and without error. In the original form, this algorithm generates non-bursty event sequences. We invented a new variant of the Gillespie algorithm to be able to generate bursty event sequences [Masuda & Rocha. SIAM Rev (2018)]. We used mathematical tools so-called the Laplace transform and completely monotone functions.

Football managers as reinforcement learner

Keywords: reinforcement learning, sports, data

Managerial decisions should be important for the performance of the team. Using football data in Japan and Germany, we examined the following two hypotheses [Tamura & Masuda, EPJ Data Science (2015)].

  • Hypothesis 1: Managers adopt reinforcement learning in deciding on the starting formation (see the figure below) in each game.
  • Hypothesis 2: Reinforcement learning results in a high performance of the team.
Fig: Schematic of the formation in football. We extracted the starting formation from such image data to be submitted to the analysis.

Reinforcement learning implies that, if you are successul you would stick to the same behaviour next time, and if you are unsuccessful you would switch to a different behaviour. In this way one expects to get a higher reward than before as the learning goes on. In the context of the present data analysis, the manager would change the starting formation in the next game if the team is defeated, and he would stick to the same formation if the team wins.

We used the data on starting formation simply because such data were available online (free of charge). The analysis was conducted using standard statistical methods such as multivariate linear regression.

Our data analysis supported hypothesis 1 but not 2. In other words, we found evidence that the managers' behaviour was consistent with reinforcement learning, but it did not mean a high winning rate for the team. It may not be nice to switch from one strategy to another every time the team is lost.

Reinforcement learning accounts for human conditional cooperation

Keywords: cooperation, reinforcement learning, network

How can we cooperate in social dilemma situations, where not to cooperate apparently seems optimal behavior? How does our society sustain cooperation? This is really a big question. Evolutionary game theory has played a huge role in revealing various mechanisms to enable cooperation. In the context of our daily life, evolutionary game theory is basically saying that we imitate successful others. Though this sounds reasonable, real human behavior is often far from what evolutionary game theory predicts. For example, evolutionary game theory predicts that wiring people in a fixed social network enhances cooperation, whereas this has been disproved by multiple experiments. As another example, humans often show "conditional cooperation" behavior, where they cooperate if many others did so the last time. In addition, human cooperation also depends on what the same individual did the last time, in which sense conditional cooperation is moody.

Instead of evolutionary game theory, we illuminated a behavioral rule called reinforcement learning, often employed in psychology, neuroscience, autonomous vehicle control, finance, robotics, video games and more. A reinforcement learner does not care how others are doing (different from the evolutionary game approach) and cares only the rewards that the learner gains. If the received reward is large, reinforce the current behavior. If the reward is small, try something different. Using computational modelling, we have shown that reinforcement learning (as opposed to evolutionary game theory) explains conditional cooperation and its moody couzin fairly well [Ezaki et al. PLOS Comput Biol (2016)].

Our other reinforcement learning approaches to cooperation: Masuda, Ohtsuki. Bull Math Biol (2009); Masuda, Nakamura. J Theor Biol (2011); Tanabe, Masuda. J Theor Biol (2011)

Brain dynamics during bistable perception

Keywords: neuroscience, fMRI, energy landscape, multistability, Ising model, attractor dynamics

Optical illusion is a phenomenon in which percept switches from one to another while one is looking at the same stimulus. Rubin's vase, in which a vase is one percept and two heads facing each other are another percept, is a classical example of it. An often made theoretical account for such bistable perception is that the brain state wanders in an energy landscape which looks like two basins connected to each other. One basin corresponds to one percept, and the brain state is represented by a moving ball on the energy landscape. The height of the basin represents the energy, and the bottom of the basin corresponds to a brain state with a local minimum of energy. However, no empirical data exists to support this energy landscape explanation.

We analyzed fMRI signals obtained from participants performing a visual bistable perception task. We used the maximum entropy model [Watanabe et al. Nat Comm (2013)] to construct energy landscapes of the brain and analyzed dynamics of the brain state in the energy landscape. We found three attractive basins (figure below), and the meaning of the attractive basin was different from the implications of the previous studies. In the basin shown in magenta in the figure, activity of visual areas was dominant and represented stabilization of a perception. In the basin shown in blue, activity of frontal areas was dominant and represented switching from one percept to another [Watanabe et al. Nat Comm (2014)].

Fig: Schematics of brain dynamics during bistable perception. Magenta: visual-area state. Blue: frontal-area state. Yellow: intermediate state. A colored circle represents activity of regions of interest in each of the three attractive basins (red: high, blue: low). The green curve represents brain dynamics.

In-group favoritism

Keywords: evolutionary game, cooperation, community structure, reputation

Humans often help others belonging to the same group more strongly than those belonging to different groups. This phenomenon is called in-group favoritism. In fact, theoretical mechanisms underlying it have not been well understood (see [Masuda, Fu. F1000Prime Reports (2015)] for a survey of theoretical models of in-group favoritism). We provided reputation-based accounts (i.e., people care about their own reputations, so-called reputation-based indirect reciprocity) for in-group favoritism [Masuda, Ohtsuki. Proc R Soc B (2007); Masuda. J Theor Biol (2012); Nakamura, Masuda. BMC Evol Biol (2012)].

Fig: In-group favoritism. A circle represents a group. The thickness of arrow represents the strength of cooperation.

Dominance networks of ant workers

Keywords: network, hierarchy, social insects
[Shimoji, Abe, Tsuji, Masuda. J R Soc Interface (2014)]

Dominance hierarchy among animals is widespread in various species and believed to regulate resource allocation within an animal group. Here, we analyse dominance hierarchies formed by worker ants as directed networks, in which a directed link (arrow) emanates from the attacking to attacked workers. The observed dominance networks are perfect or approximate directed acyclic graphs, consistent with perfect hierarchy (see the figure below). They are also sparse and random. In addition, the number of workers that the focal worker attacks is fairly heterogeneously distributed, and those attacking excessively many others are located near the top, but not the top, of the hierarchy.

Fig: A dominance network of ants. A circle represents an ant worker. Each line is actually an arrow directed downwards.

Temporal networks

Keywords: network, time series, point processes, epidemic

Temporal network is an emerging concept in network science in which the timing of interaction between two nodes is taken into account. In the conventional, static network viewpoints, a link in a social network, for example, represents dyadic relationship between the two individuals such as friendship. However, when dynamical processes such as epidemic spreading occurs on real networks, we in fact have to take into account the fact that the link is not always open. In other words, infection can occur between a pair of individuals only when the two individuals face each other. Even if they are close friends, they may be away from each other for most of the time. As network data with time stamps of events are increasingly available, we need develop computational tools to analyze them and theoretical models to understand implications of the temporal network data. The completed projects include

  • We theoretically showed that temporal networks, as compared to static networks, slow down diffusive dynamics (and synchronisation dynamics) on networks [Masuda, Klemm, Eguíluz. Phys Rev Lett (2013)].
  • Importance of events: Some conversation events are more important than others. Even events between the same two individuals may have different importance values. Here, we defined an event to be important when it is effective at connecting a chain of communication from one person to another. We showed, for example, that only a small fraction of events is important [Takaguchi et al. New J Phys (2012)].
  • Predictability of conversation partners: If you have talked with a specific peer, then you will not entirely randomly select a next conversation partner. There is a hidden pattern in your partner choice [Takaguchi et al. Phys Rev X (2011)].
  • Dynamic sports ranking: In professional tennis, for example, it is impossible for all the pairs of players to fight against each other. The results of the matches can be summarized as a directed network in which a link emanates from the winner to loser of a single game. A missing element in network-based ranking systems is the time component; winning against Roger Federer in 2011 and in 1999 would have different values. We proposed a network-based ranking system that take into account the dynamics of players' strengths [Motegi, Masuda. Sci Rep (2012)].

Neural mechanisms of two types of indirect reciprocity

Keywords: evolutionary game, neuroscience, cooperation, reputation, pay-it-forward, empathy

See a popular summary ("Significance") available at the following journal's website: Watanabe et al. PNAS (2014).
To note, this is a purely experimental study motivated by previous theoretical studies by myself and many other people.

Theoretical underpinning of indirect reciprocity

Keywords: evolutionary game, cooperation, reputation, pay-it-forward

In our daily lives and also in behavioral experiments, nonkin individuals pretty often cooperative with each other in social dilemma situations, i.e., situations in which defection rather than cooperation is apparently lucrative. Indirect reciprocity is a mechanism for cooperation in which cooperative individuals will be cooperated by somebody else. Although indirect reciprocity has been theoretically analyzed since 1990s, there are still important key questions to be answered. Our completed projects on this topic include

  • Partial observation: How does the information about individuals' reputations, which is an essential ingredient of the most popular type of indirect reciprocity, can propagate to the entire population? It seems difficult for everybody to share the information about others' reputations, except in online marketplaces or similar. Gossiping may have limited reliability, either. We analyzed the situation in which observation of others' reputations is incomplete, i.e., sometimes the observation cannot be made. We clarified the conditions under which cooperation based on reputation-based indirect reciprocity survives given incomplete observation [Nakamura, Masuda. PLOS Comput Biol (2011)].
    Fig: Seven reputation assignment rules that make cooperation viable. C: cooperation, D: defection, G: good reputation, B: bad reputation, U: unknown reputation.
  • Pay-it-forward reciprocity: Humans often help others after they have been helped. In such a case, individuals are not using reputations of other players. We analysed models of such indirect reciprocity to find that emergence of cooperation by this mechanism required other cooperation-enhancing assumptions (e.g., social network structure) [Iwagami, Masuda. J Theor Biol (2010); Masuda, PLOS ONE (2011)].

Resting-state brain networks

Keywords: neuroscience, network, fMRI, default mode network, Ising model, log-linear model

The resting-state brain networks (RSNs) underlie fundamental human cognitive functions such as memory. We revealed that a relatively simple second-order statistical model called the pairwise maximum entropy model was nicely fitted to activity patterns of RSNs and predictive of anatomical connectivity between brain regions [Watanabe et al. Nat Comm (2013); Watanabe et al. Front Neuroinfo (2014)]. We also applied the same methods to human sleep data to reveal dynamics of functional connectivity during sleep, which depended on the sleep stage (i.e., slow-wave sleep versus rapid-eye-movement sleep) and resting-state network (i.e., default mode network versus fronto-parietal network) [Watanabe et al. NeuroImage (2014)].

Suicide in online social networks

Keywords: network, social networking service, logistic regression

We analyzed a data set provided by a Japanese social networking service to explore network (and other) correlates of suicide ideation of users [Masuda, Kurahashi, Onari. PLOS ONE (2013)]. See the following articles that feature our paper:

Special individuals in collective dynamics

Keywords: network, evolutionary game, voter model, partisan, cooperation

Heterogeneous and partisan voter models: We proposed and analyzed heterogeneous and partisan voter models in which the rate at which an agent changes opinion or the preference of either of the two opinions depends on agents. We quantified how much the consensus time is lengthened by these properties. In addition, a small fraction of stubborn agents can convert the opinion of the rest of the population with weak preferences against the stubborn agents' opinion [Masuda, Gibert, Redner. Phys Rev E (2010); Masuda, Redner. J Stat Mech (2011)].

We analysed effects of zealous players in evolutionary game dynamics. In particular, only a small fraction of zealous cooperators can elicit cooperation of many others who in fact feel that non-cooperation is more lucrative [Masuda. Sci Rep (2012); Nakajima, Masuda. J Math Biol (2014)].

Precision of network oscillation

Keywords: network, synchronisation, oscillation, coupled phase oscillators, clock, Laplacian

Biological cellular networks often create very regular rhythms in spite that each constituent cell is subjected to environmental and internal noise. Synchronisation of cells does not imply a high precision of rhythmic activity; synchronous rhythm can be even arrhythmic. In experiments, the precision of collective oscillations is enhanced by coupling between cells. However, whether networks of cells realize a higher precision than single oscillatory cells had been an unanswered question. We built a minimal coupled phase oscillator model on networks to clarify this issue. In terms of the left eigenvector of the Laplacian matrix representing the network, we related the precision of synchronous oscillations to the network structure, coupling strength, and noise intensity. Democratic networks including undirected networks realize the most precise rhythms. Autocratic networks, or equivalently, feedforward networks, realize the least precise rhythms [Masuda, Kawamura, Kori. New J Phys (2010); Kori, Kawamura, Masuda. J Theor Biol (2012)].

Network epidemiology

Keywords: network, community structure, SIR model, SIS model, percolation, phase transition

Epidemic spreading is one of the most important and examined phenomena that can occur on networks. Clarifying conditions under which a large-scale outbreak occurs and establishing intervention methods to suppress or enhance epidemic spreading have various practical implications. Examples include human infectious diseases, Internet security related to computer viruses, and viral marketing. The completed projects include

  • Nosocomial infection: Using medical records collected in a community hospital in Japan, we constructed social networks within the hospital composed of resident doctors, nurses, and hospitalized patients (see the figure below). By numerically simulating epidemic processes on the social networks, we revealed that medical doctors, in particular resident doctors, rather than nurses and patients, were likely to be responsible for propagating diseases within the hospital. Intervention methods targeting medical doctors would be efficient [Ueno, Masuda. J Theor Biol (2008)].
  • Preparatory immunization protocols (deciding on which nodes should be treated first) given the fact that most social networks have community structure (i.e., group structure) [Masuda. New J Phys (2009)].
  • Antivirus, which is activated to kill viruses when viruses are detected, may be an effective means to make networks resistant against endemicity. We analyzed a model of virus and antivirus to clarify the effectiveness of antivirus and its dependence on network structure [Ahn et al. Phys Rev E (2006)].

Who is important in collective opinion formation?

Keywords: network, Laplacian, voter model, PageRank, random-walk, spanning tree, synchronisation

In social networks, some individuals seem to play important roles in collective opinion formation, whereas others not. Hubs, or those connected to many others, may be such "central" individuals, but the answer is not that trivial because hubs may be influenced by, while influencing, many others. Using the voter model, a traditional opinion formation model used in statistical physics, mathematical probability theory etc., and random-walk techniques, we addressed to the following issues:

  • On directed networks (links have directionality, from the influencer to the influenced), the probability that a new opinion injected at a node prevails the population depends on the initial node (surprisingly, such an intuitive dependence is absent on undirected networks). We determined this so-called fixation probability for each node, which can be viewed as a ranking of nodes and closely related to the PageRank used in Google search. Spreading of a new opinion would be enhanced if a high ranked node is targeted for injection [Masuda, Ohtsuki. New J Phys (2009)].
  • Quantification of the strength of groups of nodes [Masuda, Kawamura, Kori. New J Phys (2009)].
  • Calculation of the node's importance using directed spanning trees [Masuda, Kawamura, Kori. Phys Rev E (2009)]
  • Case in which one opinion is inherently stronger than the other [Masuda, J Theor Biol (2009)]
  • Case in which directed networks have multiple roots (top nodes) and dangling nodes (bottom nodes) [Masuda, Kori. Phys Rev E (2010)]

Synchronisation on networks

Apart from collective fluctuations and precision of oscillators on networks, mechanisms and phenomenology of synchronisation have been a stimulating research topic which find applications in biological rhythms, ecology, social dynamics, and so on. We are investigating theoretical aspects of synchronisation on networks. The completed projects on this topic include

  • Synchronisation and network formation under spike-timing-dependent plasticity (STDP): Excitatory synapses often show STDP in which the synapse is potentiated (depressed) when the postsynaptic neuron spikes shortly after (before) the presynaptic neuron does. Computational implications of STDP for fully recurrent neural networks had not been well understood. We showed that STDP leads to the formation of feedforward networks on the basis of theory of coupled phase oscillators and numerical simulations [Masuda, Kori. J Comput Neurosci (2007); Takahashi, Kori, Masuda. Phys Rev E (2009)].
  • Many neural networks have the so-called small-world property, i.e., the short average path length and a large clustering coefficient in the terminology of network science. We showed that chaotic dynamics appears for oscillators coupled on model networks with the small-world property, even if the oscillator at each node is not chaotic [Tönjes, Masuda, Kori. Chaos (2010)].

Gamma oscillations and selective attention

Rhythmic brain activity is considered to be a critical component of neural processing. In particular, stimulus induced oscillations in the gamma-frequency band (30-80 Hz) are common. Although the neural mechanisms of such oscillations are well understood, both in theory and experiments, the beneficial role of gamma activity in neural processing had been rarely questioned. By using computational models, we showed that the gamma rhythmicity in a population of spiking neurons drastically reduces the response variability when a preferred stimulus is present. This reduction enhances stimulus discrimination and can increase the overall information throughput in sensory cortex [Masuda, Doiron. PLOS Comput Biol (2007); Masuda. Neural Comput (2009)].