My research interests contain network science, evolutionary games (in particular, mechanisms of cooperation in social dilemma situations), modeling of (other) social dynamics, and computational neuroscience. These different topics often intersect each other. In each topic, my interest ranges from mathematical modeling to data analysis. Although my coverage may seem too broad, the general goal of my research is to understand social systems, may they be systems of networked agents, social dilemma situations, or others, by mathematics, physics, numerical methods, and the knowledge of brain science. The following is a summary of my recent accomplishments.
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
- 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, Sato, Yano, and Masuda, New Journal of Physics, 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, Nakamura, Sato, Yano, and Masuda, Physical Review 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 and Masuda, Scientific Reports, 2012].
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
- 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 Journal of Physics, 2009].
- Nosocomial infection: Using medical records collected in a community hospital in Japan, we revealed that medical doctors, in particular resident doctors, rather than nurses and hospitalized patients, were likely to be responsible for propagating diseases within the hospital. Intervention methods targeting medical doctors are expected to be efficient [Ueno and Masuda, Journal of Theoretical Biology, 2008].
- 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, Jeong, Masuda, and Noh, Physical Review E, 2006].
Random walk and opinion formation
Irrespective of whether network structure is assumed or not, questions regarding opinion formation models such as the probability that a consensus is reached and the time to consensus can be often answered through the analysis of appropriate random walk models. Therefore, we are investigating opinion formation models with and without network structure, random walks on their own, and related dynamics. Completed projects include
- 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 to the stubborn agents' opinion [Masuda, Gibert, and Redner, Physical Review E, 2010; Masuda and Redner, Journal of Statistical Mechanics, 2011; Masuda, Scientific Reports, 2012].
- Random walks on directed networks. In the voter model, the probability that a new opinion injected at a node prevails the population depends on the initial node. We determined this so-called fixation probability for each node, which can be viewed as a ranking of nodes. Spreading of a new opinion would be enhanced if a high ranked node is targeted. In addition, the fixation probability is closely related to the PageRank [Masuda, Kawamura, and Kori, New Journal of Physics, 2009; Physical Review E, 2009; Masuda and Kori, Physical Review E, 2010].
- Analysis of a priority queue model in which tasks to be executed arrive in a bursty manner. The problem can be mapped to a first-passage problem of a one-dimensional random walk [Masuda, Kim, and Kahng, Physical Review E, 2009].
- Avalanche and self-organized criticality on scale-free networks [Masuda, Goh, and Kahng, Physical Review E, 2005].
- Analytical estimation of the return time of the random walk on scale-free networks [Masuda and Konno, Physical Review E, 2004].
Precision of network oscillation
Biological cellular networks often create very regular rhythms in spite that each constituent cell is subjected to environmental and internal noise. Synchronization 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, and Kori, New Journal of Physics, 2010; Kori, Kawamura, and Masuda, Journal of Theoretical Biology, 2012].
Synchronization on networks
Apart from collective fluctuations and precision of oscillators on networks, mechanisms and phenomenology of synchronization have been a stimulating research topic which find applications in biological rhythms, ecology, social dynamics, and so on. We are investigating theoretical aspects of synchronization on networks. The completed projects on this topic include
- Synchronization 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 and Kori, Journal of Computational Neuroscience, 2007; Takahashi, Kori, and Masuda, Physical Review 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 [Toenjes, Masuda, and Kori, Chaos, 2010].
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 and Masuda, PLoS Computational Biology, 2011].
- Trinary reputation: Most theoretical work on the reputation-based indirect reciprocity is based on the assumption of binary (i.e., good or bad) reputation, presumably because of mathematical tractability. We analyzed a trinary reputation model. Although it is a mere extension of the original model, what occurs in the population is often not simply captured as an extension of the results obtained from the binary reputation model [Tanabe, Suzuki, and Masuda, Journal of Theoretical Biology, 2013].
- Humans often help others after they have been helped. In such a case, individuals are not using reputations of other players. We analyzed models of such indirect reciprocity to find that emergence of cooperation by this mechanism requires other cooperation-enhancing assumptions (e.g., network structure) [Iwagami and Masuda, Journal of Theoretical Biology, 2010; Masuda, PLoS ONE, 2011].
- Humans often help others belonging to the same group, but not those belonging to different groups. The mechanisms underlying such ingroup favoritism have not been well understood. We provided reputation-based accounts for ingroup favoritism [Masuda and Ohtsuki, Proceedings of the Royal Society B, 2007; Masuda, Journal of Theoretical Biology, 2012; Nakamura and Masuda, BMC Evolutionary Biology, 2012].
Analysis of brain networks
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. (Masuda being the last and corresponding author), Nature Communications, 2013].
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 and Doiron, PLoS Computational Biology, 2007; Masuda, Neural Computation, 2009].