arXiv subjects

Takehisa Hasegawa

Publications and source records attributed to Takehisa Hasegawa.

At least 37 records · Page 2Linked to original sources

arXiv2016

Outbreaks in susceptible-infected-removed epidemics with multiple seeds

We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.

physics.soc-ph↗

arXiv2014

Discontinuous Transition of a Multistage Independent Cascade Model on Networks

We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability $T_1$ that a node adopting a fad increases the awareness of a neighboring susceptible node, and the probability $T_2$ that an adopter directly causes a susceptible node to adopt the fad. We formulate a tree approximation for the MIC model on an uncorrelated network with an arbitrary degree distribution $p_k$. Applied on a random regular network with degree $k=6$, this model exhibits a rich phase diagram, including continuous and discontinuous transition lines for fad percolation, and a continuous transition line for the percolation of susceptible nodes. In particular, the percolation transition of fads is discontinuous (continuous) when $T_1$ is larger (smaller) than a certain value. A similar discontinuous transition is also observed in random graphs and scale-free networks. Furthermore, assigning a finite fraction of initial adopters dramatically changes the phase boundaries.

physics.soc-ph↗

arXiv2014

Critical Phase in Complex Networks: a Numerical Study

We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and percolating phase at the critical point. The critical point is stretched to a finite region, called the critical phase, on nonamenable graphs. To investigate the critical phase, we introduce a fractal exponent, which characterizes a subextensive order of the system. We perform the Monte Carlo simulations for percolation on two nonamenable graphs - the binary tree and the enhanced binary tree. The former shows the nonpercolating phase and the critical phase, whereas the latter shows all three phases. We also examine the possibility of critical phase in complex networks. Our conjecture is that networks with a growth mechanism have only the critical phase and the percolating phase. We study percolation on a stochastically growing network with and without a preferential attachment mechanism, and a deterministically growing network, called the decorated flower, to show that the critical phase appears in those models. We provide a finite-size scaling by using the fractal exponent, which would be a powerful method for numerical analysis of the phase transition involving the critical phase.

cond-mat.dis-nn↗

arXiv2014

Suppressing epidemics on networks by exploiting observer nodes

To control infection spreading on networks, we investigate the effect of observer nodes that recognize infection in a neighboring node and make the rest of the neighbor nodes immune. We numerically show that random placement of observer nodes works better on networks with clustering than on locally treelike networks, implying that our model is promising for realistic social networks. The efficiency of several heuristic schemes for observer placement is also examined for synthetic and empirical networks. In parallel with numerical simulations of epidemic dynamics, we also show that the effect of observer placement can be assessed by the size of the largest connected component of networks remaining after removing observer nodes and links between their neighboring nodes.

physics.soc-ph↗

arXiv2014

Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network

We study bond percolation on a one-parameter family of hierarchical small-world network, and find a meta-transition between the inverted BKT transition and the abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and fractal exponent is discontinuous in the inverted BKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and fractal exponent in each transition go to vanish as approaching the meta-transition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this meta-transition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation.

cond-mat.stat-mech↗

arXiv2014

Generalized scaling theory for critical phenomena including essential singularity and infinite dimensionality

We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.

cond-mat.stat-mech↗

arXiv2013

Hierarchical scale-free network is fragile against random failure

We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev- Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the percolating phase when the occupation probability is less than 1. The present result is contrasted to bond percolation in the same network of which the percolation threshold is zero. We also show that the percolation threshold of intentional attacks is 1. Our results suggest that this hierarchical scale-free network is very fragile against both random failure and intentional attacks. Such a structural defect is common in many hierarchical network models.

cond-mat.dis-nn↗

arXiv2013

Profile and scaling of the fractal exponent of percolations in complex networks

We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical simulations to determine the transition point precisely. Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite size scaling technique does not work. In our finite size scaling, the forms of the scaling functions for the order parameter and the fractal exponent determine the transition point and critical exponents numerically for an infinite order transition as well as a standard second order transition. We confirm the validity of our scaling hypothesis through Monte-Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where an infinite order transition occurs, and the configuration model, where a second order transition occurs.

cond-mat.dis-nn↗

arXiv2013

Observability transitions in correlated networks

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components comprising the observable nodes is a major concern of the model. We analyze this model in random heterogeneous networks with degree correlation. With numerical simulations and analytical arguments based on generating functions, we find that negative degree correlation makes networks more observable. This result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors. Finally, we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component. Optimized networks have negative degree correlation induced by the resulting hub-repulsive structure; the largest hubs are rarely connected to each other, in contrast to the rich-club phenomenon of networks.

physics.soc-ph↗

arXiv2013

Absence of the non-percolating phase for percolation on the non-planar Hanoi network

We investigate bond percolation on the non-planar Hanoi network (HN-NP), which was studied in [Boettcher et al. Phys. Rev. E 80 (2009) 041115]. We calculate the fractal exponent of a subgraph of the HN-NP, which gives a lower bound for the fractal exponent of the original graph. This lower bound leads to the conclusion that the original system does not have a non-percolating phase, where only finite size clusters exist, for p>0, or equivalently, that the system exhibits either the critical phase, where infinitely many infinite clusters exist, or the percolating phase, where a unique giant component exists. Monte Carlo simulations support our conjecture.

cond-mat.dis-nn↗

arXiv2012

Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network

We study the Ising model in a hierarchical small-world network by renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.

cond-mat.stat-mech↗

arXiv2012

Robustness of correlated networks against propagating attacks

We investigate robustness of correlated networks against propagating attacks modeled by a susceptible-infected-removed model. By Monte-Carlo simulations, we numerically determine the first critical infection rate, above which a global outbreak of disease occurs, and the second critical infection rate, above which disease disintegrates the network. Our result shows that correlated networks are robust compared to the uncorrelated ones, regardless of whether they are assortative or disassortative, when a fraction of infected nodes in an initial state is not too large. For large initial fraction, disassortative network becomes fragile while assortative network holds robustness. This behavior is related to the layered network structure inevitably generated by a rewiring procedure we adopt to realize correlated networks.

physics.soc-ph↗

arXiv2012

Phase transition without global ordering in a hierarchical scale-free network

We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites. Surprisingly, when each site is unoccupied even with a small probability, the system permits neither the percolating phase nor the nonpercolating phase, but rather only critical phases. Although the order parameter always remains zero, a transition still exists between the critical phases that is characterized by the value of the fractal exponent, which measures the degree of criticality; the system changes from one critical state to another with the jump of the fractal exponent at the transition point. The phase boundary depends on the fraction of occupied sites. When the fraction of unoccupied sites exceeds a certain value, the transition line between the critical phases disappears, and a unique critical phase remains.

cond-mat.dis-nn↗

arXiv2011

Robustness of networks against propagating attacks under vaccination strategies

We study the effect of vaccination on robustness of networks against propagating attacks that obey the susceptible-infected-removed model.By extending the generating function formalism developed by Newman (2005), we analytically determine the robustness of networks that depends on the vaccination parameters. We consider the random defense where nodes are vaccinated randomly and the degree-based defense where hubs are preferentially vaccinated. We show that when vaccines are inefficient, the random graph is more robust against propagating attacks than the scale-free network. When vaccines are relatively efficient, the scale-free network with the degree-based defense is more robust than the random graph with the random defense and the scale-free network with the random defense.

physics.soc-ph↗

arXiv2011

Numerical study of a three-state host-parasite system on the square lattice

We numerically study the phase diagram of a three-state host-parasite model on the square lattice motivated by population biology. The model is an extension of the contact process, and the three states correspond to an empty site, a host, and a parasite. We determine the phase diagram of the model by scaling analysis. In agreement with previous results, three phases are identified: the phase in which both hosts and parasites are extinct (S_{0}), the phase in which hosts survive but parasites are extinct (S_{01}), and the phase in which both hosts and parasites survive (S_{012}). We argue that both the S_{0}-S_{01} and S_{01}-S_{012} boundaries belong to the directed percolation class. In this model, it has been suggested that an excessively large reproduction rate of parasites paradoxically extinguishes hosts and parasites and results in S_{0}. We show that this paradoxical extinction is a finite size effect; the corresponding parameter region is likely to disappear in the limit of infinite system size.

cond-mat.stat-mech↗

arXiv2010

Generating-function approach for bond percolations in hierarchical networks

We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts $\tilde{p}$ and that of the ordinary bonds $p$. The system has a critical phase in which the percolating probability $P$ takes an intermediate value $0<P<1$. Using generating function approach, we calculate the fractal exponent $ψ$ of the root clusters to show that $ψ$ varies continuously with $\tilde{p}$ in the critical phase. We confirm numerically that the distribution $n_s$ of cluster size $s$ in the critical phase obeys a power law $n_s \propto s^{-τ}$, where $τ$ satisfies the scaling relation $τ=1+ψ^{-1}$. In addition the critical exponent $β(\tilde{p})$ of the order parameter varies as $\tilde{p}$, from $β\simeq 0.164694$ at $\tilde{p}=0$ to infinity at $\tilde{p}=\tilde{p}_c=5/32$.

cond-mat.dis-nn↗

arXiv2010

Critical Phase of Bond Percolations on Growing Networks

The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^ψ$ and the mean number of clusters with size $s$ per node follows a power function $n_s \propto s^{-τ}$ in the whole range of open bond probability $p$. The exponent $τ$ and the fractal exponent $ψ$ are also derived as a function of $p$ and the degree exponent $γ$, and are found to satisfy the scaling relation $τ=1+ψ^{-1}$. Numerical results with several network sizes are quite well fitted by a finite size scaling for a wide range of $p$ and $γ$, which gives a clear evidence for the existence of a critical phase.

cond-mat.dis-nn↗

arXiv2009

Reply to Comment on `Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees'

We discuss the nature of the two-stage percolation transition on the enhanced binary tree in order to explain the disagreement in the estimation of the second transition probability between the one in our recent paper (J. Phys. A:Math. Theor. 42 (2009) 145001) and the one in the comment to it from Baek, Minnhagen and Kim. We point out some reasons that the finite size scaling analysis used by them is not proper for the enhanced tree due to its nonamenable nature, which is verified by some numerical results.

cond-mat.stat-mech↗