Influence of initiators on the tipping point in the extended Watts model
Takehisa Hasegawa; Shinji Nishioka, 筆頭著者, Elsevier BV
Physica A: Statistical Mechanics and its Applications, 2024年11月, ［査読有り］

Robustness of random networks with selective reinforcement against attacks
Tomoyo Kawasumi; Takehisa Hasegawa, ラスト(シニア)オーサー, Elsevier BV
Physica A: Statistical Mechanics and its Applications, 2024年09月, ［査読有り］

Cascading Behavior of an Extended Watts Model on Networks
Shinji Nishioka; Takehisa Hasegawa., ラスト(シニア)オーサー
Journal of the Physical Society of Japan, 2022年11月30日, ［査読有り］

Synergistic epidemic spreading in correlated networks
Shogo Mizutaka; Kizashi Mori; Takehisa Hasegawa, ラスト(シニア)オーサー
Physical Review E, 2022年09月06日, ［査読有り］

Impact of assortative mixing by mask-wearing on the propagation of epidemics in networks
Hiromu Watanabe; Takehisa Hasegawa, ラスト(シニア)オーサー
Physica A: Statistical Mechanics and its Applications, 2022年06月18日, ［査読有り］

Revisiting finite size effect of percolation in degree correlated networks
Shogo Mizutaka; Takehisa Hasegawa, ラスト(シニア)オーサー
Journal of the Physical Society of Japan, 2022年03月02日, ［査読有り］

Observability transitions in clustered networks
筆頭著者
Physica A: Statistical Mechanics and its Applications, 2021年07月01日, ［査読有り］

Emergence of long-range correlations in random networks
Shogo Mizutaka; Takehisa Hasegawa, ラスト(シニア)オーサー, We perform an analysis of the long-range degree correlation of the giant component (GC) in an uncorrelated random network by employing generating functions. By introducing a characteristic length, we find that a pair of nodes in the GC is negatively degree-correlated within the characteristic length and uncorrelated otherwise. At the critical point, where the GC becomes fractal, the characteristic length diverges and the negative long-range degree correlation emerges. We further propose a correlation function for degrees of two nodes separated by the shortest path length l, which behaves as an exponentially decreasing function of distance in the off-critical region. The correlation function obeys a power-law with an exponential cutoff near the critical point. The Erdös-Rényi random graph is employed to confirm this critical behavior.
Journal of Physics: Complexity, 2020年09月21日, ［査読有り］

Structure of percolating clusters in random clustered networks
Takehisa Hasegawa; Shogo Mizutaka, 筆頭著者, We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We analytically and numerically show that the PC in the highly clustered networks is clustered even at the percolation threshold. The assortativity of the PC depends on the details of the RCN. The PC at the percolation threshold is disassortative when the numbers of edges and triangles of each node are assigned by Poisson distributions, but assortative when each node in an RCN has the same small number of edges, most of which form triangles. This result seemingly contradicts the disassortativity of fractal networks, although the renormalization scheme unveils the disassortative nature of a fractal PC.
Physical Review E, 2020年06月22日, ［査読有り］

Percolation on a maximally disassortative network
Shogo Mizutaka and Takehisa Hasegawa, We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation critical behaviors. Using the generating function method for bipartite networks, we analytically derive the percolation threshold and the order parameter critical exponent, β. For the MD scale-free networks, whose degree distribution is, we show that the exponent, β, for the MD networks and corresponding uncorrelated networks are the same for &IMG ALIGN="MIDDLE" ALT="$\gamma>3$ " SRC="epl19938ieqn2.gif"/; but are different for &IMG ALIGN="MIDDLE" ALT="$2<\gamma<3$ " SRC="epl19938ieqn3.gif"/;. A strong degree-degree correlation significantly affects the percolation critical behavior in heavy-Tailed scale-free networks. Our analytical results for the critical exponents are numerically confirmed by a finite-size scaling argument.
EPL (Europhysics Letters), 2020年01月31日, ［査読有り］

Disassortativity of percolating clusters in random networks
Shogo Mizutaka; Takehisa Hasegawa, ラスト(シニア)オーサー, We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the assortativity of a giant component, r, which is defined as Pearson's correlation coefficient for degrees of directly connected nodes. For uncorrelated random networks in which the third moment for the degree distribution is finite, we prove the following two points: (1) Assortativity r satisfies the relation r≤0 for p≥pc. (2) The average degree of nodes adjacent to degree k nodes at the percolation threshold is proportional to k-1 independently of the degree distribution function. These results claim that disassortativity emerges in giant components near the percolation threshold. The accuracy of the analytical treatment is confirmed by extensive Monte Carlo simulations.
Physical Review E, 2018年12月18日, ［査読有り］

Sudden spreading of infections in an epidemic model with a finite seed fraction
Takehisa Hasegawa; Koji Nemoto, We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small., Springer Heidelberg
European Physical Journal B, 2018年03月01日, ［査読有り］

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks
Takehisa Hasegawa; Koji Nemoto, This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2017年08月, ［査読有り］

Local cluster-size statistics in the critical phase of bond percolation on the Cayley tree
Tomoaki Nogawa; Takehisa Hasegawa; Koji Nemoto, We study bond percolation of the Cayley tree (CT) by focusing on the probability distribution function (PDF) of a local variable, namely, the size of the cluster including a selected vertex. Because the CT does not have a dominant bulk region, which is free from the boundary effect, even in the large-size limit, the phase of the system on it is not well defined. We herein show that local observation is useful to define the phase of such a system in association with the well-defined phase of the system on the Bethe lattice, that is, an infinite regular tree without boundary. Above the percolation threshold, the PDFs of the vertex at the center of the CT (the origin) and of the vertices near the boundary of the CT (the leaves) have different forms, which are also dissimilar to the PDF observed in the ordinary percolating phase of a Euclidean lattice. The PDF for the origin of the CT is bimodal: a decaying exponential function and a system-size-dependent asymmetric peak, which obeys a finite-size-scaling law with a fractal exponent. These modes are respectively related to the PDFs of the finite and infinite clusters in the nonuniqueness phase of the Bethe lattice. On the other hand, the PDF for the leaf of the CT is a decaying power function. This is similar to the PDF observed at a critical point of a Euclidean lattice but is attributed to the nesting structure of the CT around the boundary., IOP PUBLISHING LTD
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2016年05月, ［査読有り］

Outbreaks in susceptible-infected-removed epidemics with multiple seeds
Takehisa Hasegawa; Koji Nemoto, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2016年03月, ［査読有り］

Advantage or disadvantage of migration in a prey-predator system　　　　　　　　　　　　　　　
Kazunori Sato; Takehisa Hasegawa; Satoru Morita; Jin Yoshimura; Kei-ichi Tainaka
Far East Journal of Applied Mathematics, 2015年, ［査読有り］

Discontinuous transition of a multistage independent cascade model on networks
Takehisa Hasegawa; Koji Nemoto, 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 observed in random graphs and scale-free networks. Furthermore, assigning a finite fraction of initial adopters dramatically changes the phase boundaries., IOP PUBLISHING LTD
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2014年11月, ［査読有り］

Suppressing epidemics on networks by exploiting observer nodes
Taro Takaguchi; Takehisa Hasegawa; Yuichi Yoshida, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2014年07月, ［査読有り］

Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network
Tomoaki Nogawa; Takehisa Hasegawa, We study the bond percolation on a one-parameter family of a hierarchical small-world network and find the metatransition between an inverted Berezinskii-Kosterlitz-Thouless (iBKT) transition and an abrupt transition driven by changing the network topology. It is found that the order parameter is continuous and the fractal exponent is discontinuous in the iBKT transition, and oppositely, the former is discontinuous and the latter is continuous in the abrupt transition. The gaps of the order parameter and the fractal exponent in each transition vanish as they approach the metatransition point. This point corresponds to a marginal power-law transition. In the renormalization group formalism, this metatransition corresponds to the transition between transcritical and saddle-node bifurcations of the fixed point via a pitchfork bifurcation., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2014年04月, ［査読有り］

Critical phase in complex networks: A numerical study
Takehisa Hasegawa; Tomoaki Nogawa; Koji Nemoto, 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., L and H Scientific Publishing, LLC
Discontinuity, Nonlinearity, and Complexity, 2014年, ［査読有り］

Hierarchical scale-free network is fragile against random failure
Takehisa Hasegawa; Koji Nemoto, 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. © 2013 American Physical Society., American Physical Society
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2013年12月06日, ［査読有り］

Observability transitions in correlated networks
Takehisa Hasegawa; Taro Takaguchi; Naoki Masuda, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2013年10月, ［査読有り］

Profile and scaling of the fractal exponent of percolations in complex networks
T. Hasegawa; T. Nogawa; K. Nemoto, 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. Copyright (C) EPLA, 2013, EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY
EPL, 2013年10月, ［査読有り］

Absence of the nonpercolating phase for percolation on the nonplanar Hanoi network
Takehisa Hasegawa; Tomoaki Nogawa, We investigate bond percolation on the nonplanar Hanoi network (HN-NP), which was studied previously [Boettcher et al. Phys. Rev. E 80, 041115 (2009)]. 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 nonpercolating 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. DOI:10.1103/PhysRevE.87.032810, AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2013年03月, ［査読有り］

Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network
Tomoaki Nogawa; Takehisa Hasegawa; Koji Nemoto, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2012年09月, ［査読有り］

Robustness of correlated networks against propagating attacks
T. Hasegawa; K. Konno; K. Nemoto, 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., SPRINGER
EUROPEAN PHYSICAL JOURNAL B, 2012年08月, ［査読有り］

Generalized Scaling Theory for Critical Phenomena Including Essential Singularities and Infinite Dimensionality
Tomoaki Nogawa; Takehisa Hasegawa; Koji Nemoto, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW LETTERS, 2012年06月, ［査読有り］

Phase transition without global ordering in a hierarchical scale-free network
Takehisa Hasegawa; Masataka Sato; Koji Nemoto, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2012年01月, ［査読有り］

Robustness of networks against propagating attacks under vaccination strategies
Takehisa Hasegawa; Naoki Masuda, We study the effect of vaccination on the robustness of networks against propagating attacks that obey the susceptible-infected-removed model. By extending the generating function formalism developed by Newman (2005 Phys. Rev. Lett. 95 108701), 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., IOP PUBLISHING LTD
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2011年09月, ［査読有り］

Numerical study of a three-state host-parasite system on the square lattice
Takehisa Hasegawa; Norio Konno; Naoki Masuda, 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., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2011年04月, ［査読有り］

An Introduction to Complex Networks
HASEGAWA Takehisa, GSIS SELECTED LECTURES: Exploring Collaborative Mathematics, The Editorial Committee of the Interdisciplinary Information Sciences
Interdisciplinary Information Sciences, 2011年, ［査読有り］

Generating-function approach for bond percolation in hierarchical networks
Takehisa Hasegawa; Masataka Sato; Koji Nemoto, We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts (p) over tilde 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 psi of the root clusters to show that psi varies continuously with (p) over tilde 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)proportional to s(-tau), where tau satisfies the scaling relation tau = 1+psi(-1). In addition the critical exponent beta((p) over tilde) of the order parameter varies as (p) over tilde, from beta similar or equal to 0.164 694 at (p) over tilde = 0 to infinity at (p) over tilde = (p) over tilde(c)=5/32., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2010年10月, ［査読有り］

Critical phase of bond percolation on growing networks
Takehisa Hasegawa; Koji Nemoto, 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(psi) and the mean number of clusters with size s per node follows a power function n(s)proportional to s(-tau) in the whole range of open bond probability p. The exponent tau and the fractal exponent psi are also derived as a function of p and the degree exponent gamma and are found to satisfy the scaling relation tau=1 + psi(-1). Numerical results with several network sizes are quite well fitted by a finite-size scaling for a wide range of p and gamma, which gives a clear evidence for the existence of a critical phase., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2010年05月, ［査読有り］

Reply to the comment on ‘Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees’
Tomoaki Nogawa; Takehisa Hasegawa, IOP Publishing
Journal of Physics A: Mathematical and Theoretical, 2009年11月27日

Ferromagnetic Ising spin systems on the growing random tree
Takehisa Hasegawa; Koji Nemoto, We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel A(k)=k+alpha. We derive an estimate of the divergent temperature T(s) below which the zero-field susceptibility of the system diverges. Our result shows that T(s) is related to alpha as tanh(J/T(s))=alpha/[2(alpha+1)], where J is the ferromagnetic interaction. An analysis of exactly solvable limit for the model and numerical calculation supports the validity of this estimate., AMER PHYSICAL SOC
PHYSICAL REVIEW E, 2009年08月, ［査読有り］

Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees
Tomoaki Nogawa; Takehisa Hasegawa, We perform Monte Carlo simulations to study the Bernoulli (p) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two distinct percolation thresholds pc1 and pc2. The mean cluster size diverges as p approaches pc1 from below. The system is critical at all the points in the intermediate phase (pc1 < p < pc2) and there exist infinitely many infinite clusters. In this phase, the corresponding fractal exponent continuously increases with p from zero to unity. Above pc2 the system has a unique infinite cluster., IOP PUBLISHING LTD
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009年04月, ［査読有り］

Susceptibility of the Ising model on the scale-free network with a Cayley tree-like structure
Takehisa Hasegawa; Koji Nemoto, We derive the exact expression for the zero-field susceptibility of each spin of the Ising model on the scale-free (SF) network having the degree distribution P(k) alpha k(-gamma) with the Cayley tree-like structure. The system shows that: (i) the zero-field susceptibility of a spin in the interior part diverges below the transition temperature of the SF network with the Bethe lattice-like structure T-c for gamma > 3, while it diverges at any finite temperature for gamma <= 3, and (ii) the surface part diverges below the divergence temperature of the SF network with the Cayley tree-like structure T-s for gamma > 3, while it diverges at any finite temperature for y <= 3. (c) 2007 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2008年02月, ［査読有り］

Ising model on the scale-free network with a Cayley-tree-like structure
Takehisa Hasegawa; Koji Nemoto, We derive an exact expression for the magnetization and the zero-field susceptibility of the Ising model on a random graph with degree distribution P(k)proportional to k(-gamma) and with a boundary consisting of leaves, that is, vertices whose degree is 1. The system has no magnetization at any finite temperature, and the susceptibility diverges below a certain temperature T-s depending on the exponent gamma. In particular, T-s reaches infinity for gamma <= 4. These results are completely different from those of the case having no boundary, indicating the nontrivial roles of the leaves in the networks., AMERICAN PHYSICAL SOC
PHYSICAL REVIEW E, 2007年02月, ［査読有り］

Real Space Renormalization Group Analysis with the Replica Method for the Two Dimensional Ising Edwards–Anderson Model
Hasegawa Takehisa; Nemoto Koji, We apply the real space renormalization group (RG) to the replica Hamiltonian of the two dimensional Ising Edwards–Anderson model to discuss the existence of the spin glass (SG) phase. We derive the RG equations under the replica symmetric (RS) ansatz and the resulting flow diagram indicates the existence of the SG phase. The critical exponent for the SG transition has a plausible value while that of the multicritical point (MCP) is a complex number. We consider that this failure at the MCP is due to not taking the RS breaking into account. Indeed we find that the RS breaking parameter is relevant both at the SG critical point and the MCP, indicating the nontriviality of the SG phase of this model., THE PHYSICAL SOCIETY OF JAPAN
Journal of the Physical Society of Japan, 2006年07月, ［査読有り］

複雑ネットワークのパーコレーション：非フラクタルな世界の自己相似性　　　　　　　　　　　　　　　
長谷川雄央
第二回数理物理工学研究会「不規則・複雑系物理学とその周辺〜複雑さに潜む美しさの探求〜」, 2025年03月, ［招待有り］
20250314, 20250316

複雑ネットワークについて私が知っている二、三の事柄　　　　　　　　　　　　　　　
長谷川雄央
統計物理の進展と応用2025, 2025年03月
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fractal scale-free treeとsmall-world scale-free tree上のパーコレーションについて　　　　　　　　　　　　　　　
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流行具合の動的変化を組み込んだSARモデルのEBCMによる解析　　　　　　　　　　　　　　　
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ネットワーク科学研究会2024, 2025年03月
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SHMネットワーク上のイジングモデルのダイナミクス　　　　　　　　　　　　　　　
綿谷和紀; 長谷川雄央
ネットワーク科学研究会2024, 2025年03月
20250304, 20250305

複雑ネットワークにおけるパーコレートクラスターサイズの非ガウス極限分布　　　　　　　　　　　　　　　
能川知昭; 長谷川雄央
ネットワーク科学研究会2024, 2025年03月
20250304, 20250305

ネットワークの双曲性とパーコレーションの相図の関係についてII　　　　　　　　　　　　　　　
長谷川雄央; 能川知昭
日本物理学会第79回年次大会, 2024年09月
20240916, 20240919

ネットワーク上のSIRモデルにおける回復過程の詳細と終状態の関係　　　　　　　　　　　　　　　
能川知昭; 長谷川雄央
日本物理学会第79回年次大会, 2024年09月
20240916, 20240919

複雑ネットワークの関節点統計とその応用　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会第79回年次大会, 2024年09月
20240916, 20240919

一般化Song-Havlin-Makse model上のパーコレーションと緩和ダイナミクスについて　　　　　　　　　　　　　　　
綿谷和紀; 長谷川雄央
日本物理学会第79回年次大会, 2024年09月
20240916, 20240919

ネットワーク上の感染症モデルの機械学習による次元縮約 II　　　　　　　　　　　　　　　
能川知昭; 長谷川雄央
日本物理学会2024年春季大会, 2024年03月
20240318, 20240321

fractal scale-free treeとsmall-world scale-free tree上のパーコレーションについて　　　　　　　　　　　　　　　
綿谷和紀; 長谷川雄央
ネットワーク科学研究会2023, 2023年12月
20231223, 20231224

ネットワーク上の感染症モデルの機械学習による次元縮約　　　　　　　　　　　　　　　
能川知昭; 長谷川雄央
日本物理学会第78回年次大会, 2023年09月16日
20230916, 20230919

ネットワークの双曲性とパーコレーションの相図の関係について　　　　　　　　　　　　　　　
長谷川雄央; 能川知昭
日本物理学会第78回年次大会, 2023年09月16日
20230916, 20230919

ランダムネットワークにおけるマスク着用の混合パターン付き感染症モデルの解析　　　　　　　　　　　　　　　
渡邉大夢; 長谷川雄央
2022年度MIMS現象数理学研究拠点共同研究集会「社会物理学とその周辺」, 2022年12月10日
20221210, 20221210

相乗効果付感染症モデルにおける次数揺らぎの影響　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会2022年秋季大会, 2022年09月
20220912, 20220915

選択的に補強されたランダムネットワークの攻撃に対する頑強性　　　　　　　　　　　　　　　
川澄知代; 長谷川雄央
ネットワーク科学研究会2022, 2022年08月
20220823, 20220825

ネットワークの双曲性とパーコレーション転移の関係について　　　　　　　　　　　　　　　
長谷川雄央
ネットワーク科学研究会2022, 2022年08月
20220823, 20220825

選択的に補強されたランダムネットワークの攻撃に対する頑強性　　　　　　　　　　　　　　　
川澄知代; 長谷川雄央
日本物理学会第77回年次大会, 2022年03月15日
20220315, 20220318

ネットワーク上の多状態パーコレーション過程　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会第77回年次大会, 2022年03月15日
20220315, 20220318

Impact of assortative mixing by mask-wearing on epidemic spreadings in networks　　　　　　　　　　　　　　　
渡邉大夢; 長谷川雄央
ネットワーク科学研究会2021, 2021年12月11日
20211211, 20211212

ランダムグラフにおける長距離次数相関　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会2021年秋季大会, 2021年09月
20210920, 20210923

ネットワーク上の感染症におけるマスク着用の混合パターンの効果　　　　　　　　　　　　　　　
渡邉大夢; 長谷川雄央
日本物理学会2021年秋季大会, 2021年09月
20210920, 20210923

結合写像で動くエージェントモデルの軌道の統計的性質　　　　　　　　　　　　　　　
増山佑輔; 長谷川雄央
2021年度日本数理生物学会年会, 2021年09月
20210913, 20210915

ネットワーク上の感染症におけるマスク着用の混合パターンの効果　　　　　　　　　　　　　　　
渡邉大夢; 長谷川雄央
2021年度日本数理生物学会年会, 2021年09月
20210913, 20210915

隣接次数相関ネットワーク上のパーコレーション問題再訪　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会第76回年次大会, 2021年03月12日

ネットワーク上の拡張Wattsモデルのカスケード現象Ⅱ　　　　　　　　　　　　　　　
西岡伸二; 長谷川雄央
日本物理学会第76回年次大会, 2021年03月12日

長時間シミュレーションからみるcoupled chaos agentモデルの統計的性質　　　　　　　　　　　　　　　
増山佑輔; 長谷川雄央
ネットワーク科学セミナー2020, 2020年12月17日
20201217, 20201218

拡張Wattsモデルにおけるカスケードダイナミクスのseed割合依存性　　　　　　　　　　　　　　　
西岡伸二; 長谷川雄央
ネットワーク科学セミナー2020, 2020年12月17日
20201217, 20201218

Double explosive spreadings of synergistic SIS model on correlated bimodal networks　　　　　　　　　　　　　　　
森萌; 水高将吾; 長谷川雄央
ネットワーク科学セミナー2020, 2020年12月17日
20201217, 20201218

ランダムグラフにおける長距離次数相関　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
ネットワーク科学セミナー2020, 2020年12月17日
20201217, 20201218

correlated bimodal network上の相乗効果付SISモデルの振舞い　　　　　　　　　　　　　　　
森萌; 水高将吾; 長谷川雄央
日本物理学会2020年秋季大会, 2020年09月

巨大連結成分の統計的性質：次数相関　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会2020年秋季大会, 2020年09月

ネットワーク上の拡張Wattsモデルのカスケード現象　　　　　　　　　　　　　　　
西岡伸二; 長谷川雄央
日本物理学会2020年秋季大会, 2020年09月

Negative degree correlations of percolating clusters in random networks　　　　　　　　　　　　　　　
Shogo Mizutaka; Takehisa Hasegawa
Critical and Collective Effects in Graphs and Networks 2019 (CCEGN2019), 2019年05月
20200505, 20200510

Long-range degree correlations of fractal clusters in random networks　　　　　　　　　　　　　　　
Shogo Mizutaka; Takehisa Hasegawa
COMPLEX NETWORKS 2019, 2019年12月
20191210, 20191212

Degree correlations of percolating clusters in random networks　　　　　　　　　　　　　　　
Shogo Mizutaka; Takehisa Hasegawa
the 27th International Conference on Statistical Physics (StatPhys 27), 2019年07月

Inevitable Fragility of Hierarchical Networks against Random Node Failures　　　　　　　　　　　　　　　
Takehisa Hasegawa; Tomoaki Nogawa
the 27th International Conference on Statistical Physics (StatPhys 27), 2019年07月

最大負次数相関がパーコレーションの臨界特性に与える影響　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会第74回年次大会, 2019年03月

configuration modelにおける連結成分の統計的性質について　　　　　　　　　　　　　　　
長谷川雄央; 岩瀬優太; 五十嵐有美; 尾畑伸明
日本物理学会第74回年次大会, 2019年03月

パーコレーション問題における最大連結成分の負次数相関性　　　　　　　　　　　　　　　
水高将吾; 長谷川雄央
日本物理学会2018年秋季大会, 2018年09月

クラスター性のあるネットワークの連結成分の統計的性質　　　　　　　　　　　　　　　
長谷川雄央; 水高将吾
日本物理学会2018年秋季大会, 2018年09月

複雑な接触伝播モデルの初期状態依存性II　　　　　　　　　　　　　　　
長谷川雄央; 根本幸児
日本物理学会2018年秋季大会, 2018年09月

ランダムウォークで重み付けられたネットワークのバックボーン　　　　　　　　　　　　　　　
岩瀬優太; 長谷川雄央; 水高将吾
日本物理学会2018年秋季大会, 2018年09月

複雑な接触伝播モデルの初期状態依存性　　　　　　　　　　　　　　　
長谷川雄央; 根本幸児
日本物理学会2017年秋季大会, 2017年09月

複雑ネットワーク上のパーコレーションにおける二段相転移の解析　　　　　　　　　　　　　　　
浮田裕基; 根本幸児; 長谷川雄央
日本物理学会2017年秋季大会, 2017年09月

ランダムウォークモデルによるネットワークの辺の重みづけ　　　　　　　　　　　　　　　
岩瀬優太; 長谷川雄央
日本物理学会2017年秋季大会, 2017年09月

階層スモールワールドネットワーク上の確率過程におけるロバストな臨界性II　　　　　　　　　　　　　　　
能川知昭; 長谷川雄央
日本物理学会第72回年次大会, 2017年03月

Link Salienceによる日本航空路線ネットワークの辺の分類　　　　　　　　　　　　　　　
岩瀬優太; 長谷川雄央
日本物理学会第72回年次大会, 2017年03月

Outbreaks in the SIR epidemics with multiple seeds - a statistical physics approach　　　　　　　　　　　　　　　
Takehisa Hasegawa
The 2016 (26th) annual meeting of the Japanese Society for Mathematical Biology (JSMB2016), 2016年09月

ネットワーク上の感染症における隔離対策の効果　　　　　　　　　　　　　　　
長谷川雄央; 根本幸児
日本物理学会2016年秋季大会, 2016年09月

複数の感染源が引き起こす感染症の爆発的拡がり　　　　　　　　　　　　　　　
根本幸児; 長谷川雄央
日本物理学会2016年秋季大会, 2016年09月

階層スモールワールドネットワーク上の確率過程におけるロバストな臨界性　　　　　　　　　　　　　　　
能川知昭; 長谷川雄央
日本物理学会2016年秋季大会, 2016年09月

極大独立集合の状態数　　　　　　　　　　　　　　　
中井直人; 根本幸児; 長谷川雄央
日本物理学会2015年秋季大会, 2015年09月

意見共有とネットワークの共進化ダイナミクスにおけるリンク繋ぎ替えの効果　　　　　　　　　　　　　　　
羽刕勝紀; 根本幸児; 長谷川雄央
日本物理学会2015年秋季大会, 2015年09月

複数の感染源を持つSIRモデルが起こすパーコレーション転移　　　　　　　　　　　　　　　
長谷川雄央; 根本幸児
日本物理学会2015年秋季大会, 2015年09月

Recent Problems of Network Science　　　　　　　　　　　　　　　
Takehisa Hasegawa
The 8th International Congress on Industrial and Applied Mathematics (ICIAM2015), 2015年08月

複数の感染源を持つSIRモデルが起こすパーコレーション転移　　　　　　　　　　　　　　　
根本幸児; 長谷川雄央
統計物理の新展開2015, 2015年06月

プログラミングA　　　　　　　　　　　　　　　
茨城大学理学部

物理学特別講義A　　　　　　　　　　　　　　　
北海道大学理学部

情報科学特別講義 III　　　　　　　　　　　　　　　
東北大学大学院情報科学研究科

情報科学特別講義 II　　　　　　　　　　　　　　　
東北大学大学院情報科学研究科

情報科学特別講義 I　　　　　　　　　　　　　　　
東北大学大学院情報科学研究科

主題別ゼミナール　　　　　　　　　　　　　　　
茨城大学理学部

数理モデル特論Ⅱ　　　　　　　　　　　　　　　
茨城大学大学院理工学研究科

数理モデル特論Ｉ　　　　　　　　　　　　　　　
茨城大学大学院理工学研究科

ネットワーク演習　　　　　　　　　　　　　　　
茨城大学理学部

ネットワーク概論　　　　　　　　　　　　　　　
茨城大学理学部

情報基礎　　　　　　　　　　　　　　　
茨城大学理学部

日本物理学会

日本数理生物学会

複雑ネットワークの構造とロバストな臨界性の関係解明
基盤研究(C)
茨城大学
2024年04月 - 2027年03月

複雑ネットワーク構造がもたらすロバスト臨界性の解明　　　　　　　　　　　　　　　
基盤研究(C)
2019年04月 - 2024年03月

複雑ネットワーク理論に基づく人工物システムの頑健性評価と強化　　　　　　　　　　　　　　　
基盤研究(C)
2018年07月 - 2021年03月

非ユークリッド的グラフにおける確率モデルの多重相転移　　　　　　　　　　　　　　　
若手研究（Ｂ）
2015年04月 - 2018年03月

複雑ネットワーク上の感染症ダイナミクスの解析と動的ワクチン接種法の提案　　　　　　　　　　　　　　　
若手研究（Ｂ）
2012年04月 - 2015年03月