arXiv subjects

M. O. Hase

Publications and source records attributed to M. O. Hase.

17 recordsLinked to original sources

arXiv2026

Susceptible-Infected-Susceptible Model with Mitigation on Scale-Free Networks

We investigate infectious disease spreading on scale-free networks using a heterogeneous mean-field approach applied to the susceptible-infected-susceptible model, incorporating a mitigation factor. Individual heterogeneity is incorporated through a power-law distribution, while a mitigation factor accounts for behavioral responses and external effects that effectively reduce transmission from infected individuals. This mechanism, inspired by Malthus-Verhulst-type constraints, introduces a nonlinear saturation effect that encodes self-limiting dynamics in a tractable way. Analytical results are supported by stochastic simulations. We find that the mitigation factor induces a nontrivial behavior in the probability that a link points to an infected node, which develops a maximum at finite infection rates. In contrast, the overall prevalence remains a monotonically increasing function of the transmission rate. Additionally, the mitigation mechanism leads to an inversion in the dependence of epidemic observables on the degree exponent at sufficiently high transmission rates. While in the standard model smaller exponents yield higher endemic prevalence, in the modified model this trend reverses, with larger exponents producing higher prevalence and increased infection probability along network links.

cond-mat.stat-mech↗

arXiv2025

Annealing approximation in master-node network model

This paper investigates absorbing-state phase transitions in opinion dynamics through a master-node network model analyzed using annealing approximation. We develop a theoretical framework examining three fundamental regimes: systems converging to complete disagreement, complete consensus, or both states depending on initial conditions. The phase behavior is governed by two key chiral parameters: $R$ measuring right-oriented influence and $L$ measuring left-oriented influence in the network interactions. Our analysis reveals a rich phase diagram featuring both continuous and discontinuous transitions between disordered and ordered phases. The discontinuous transition emerges in systems with two absorbing states, where the final configuration depends critically on initial opinion distributions. The annealing approximation provides fundamental insights into how asymmetric social influences (chirality) shape collective opinion formation, acting as a symmetry-breaking element that drives the system toward polarization or consensus.

physics.soc-ph↗

arXiv2025

Annealed mean-field epidemiological model on scale-free networks with a mitigating factor

An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate a scale-free network, and we have adjusted the number of connections to produce a sparse network. Specifically, the model's behavior near the infection threshold is examined, as well as the behavior of the stationary prevalence and the probability that a connection between individuals encounters an infected one. We found that these functions display a monotonically increasing dependence on the infection rate. Subsequently, a modification that mimics the mitigation in the probability of encountering an infected individual is introduced, following an old idea rooted in the Malthus-Verhulst model. We found that this modification drastically changes the probability that a connection meets an infected individual. However, despite this change, it does not alter the monotonically increasing behavior of the stationary prevalence.

q-bio.PE↗

arXiv2025

Susceptible-Infected-Susceptible dynamics with mitigation in connection of infected population

The susceptible-infected-susceptible epidemic model is analyzed through a degree-based mean-field approach. In this work, a mitigation factor is introduced in the probability of finding an infected individual following an edge. This modification simulates situations where the infected population reduces its participation in the dynamics of disease propagation, as may happen with the seclusion or hospitalization of infected individuals. A detailed investigation of this new model and its comparison to the original one (without the mitigation factor) was performed on the Barabási-Albert network, where some important results were analytically accessible.

cond-mat.stat-mech↗

arXiv2022

First-passage process in degree space for the time-dependent Erdős-Rényi and Watts-Strogatz models

In this work, we investigate the temporal evolution of the degree of a given vertex in a network by mapping the dynamics into a random walk problem in degree space. We analyze when the degree approximates a pre-established value through a parallel with the first-passage problem of random walks. The method is illustrated on the time-dependent versions of the Erdős-Rényi and Watts-Strogatz models, which originally were formulated as static networks. We have succeeded in obtaining an analytic form for the first and the second moments of the first-passage time and showing how they depend on the size of the network. The dominant contribution for large networks with $N$ vertices indicates that these quantities scale on the ratio $N/p$, where $p$ is the linking probability.

cond-mat.stat-mech↗

arXiv2021

Weakening connections in heterogeneous mean-field models

Two versions of the susceptible-infected-susceptible epidemic model, which have different transmission rules, are analysed. Both models are considered on a weighted network to simulate a mitigation in the connection between the individuals. The analysis is performed through a heterogeneous mean-field approach on a scale-free network. For a suitable choice of the parameters, both models exhibit a positive infection threshold, when they share the same critical exponents associated with the behaviour of the prevalence against the infection rate. Nevertheless, when the infection threshold vanishes, the prevalence of these models display different algebraic decays to zero for low values of the infection rate.

cond-mat.stat-mech↗

arXiv2017

Random walk in degree space and the time-dependent Watts-Strogatz model

In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erdös-Rényi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.

physics.soc-ph↗

arXiv2016

Carrying capacity in growing networks

In this work, a growing network model that can generate a random network with finite degree in infinite time is studied. The dynamics are governed by a rule where the degree increases under a scheme similar to the Malthus-Verhulst model in the context of population growth. The degree distribution is analysed in both stationary and time-dependent regimes through some exact results and simulations, and a scaling behaviour is found in asymptotically large time. For finite times, the time-dependent degree distribution displays an accumulation of hubs as a result of competition between attractive and repulsive terms in linking probability.

physics.soc-ph↗

arXiv2015

Entropy production for asymmetric diffusion of particles

We analyse a non-equilibrium exclusion process in which particles are created and annihilated in pairs and hop to the the right or to the left with different transition rates, $p$ and $q$, respectively. We have studied the dynamics of a single particle, and exactly determined the entropy, entropy production rate and entropy flux as functions of time. In the system of many particles, we have characterised the system by its probability distribution, as well as the entropy production rate in close forms, provided that $p+q$ equals the sum of dimers creation and annihilation rates. The general case, where this constraint is absent, was considered at pair approximation level; the time-dependent behaviour of the system was analysed, and the stationary entropy production was determined. In all cases, in the stationary regime, we showed that the entropy production rate is a bilinear form in the current of particles and the force $\ln(p/q)$.

cond-mat.stat-mech↗

arXiv2012

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that $w=1/2$, correponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase ($w<1/2$) from a region with spin-glass, ferromagnetic, mixed, and paramagnetic phases ($w>1/2$).

cond-mat.dis-nn↗

arXiv2011

Irreversible spherical model and its stationary entropy production rate

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.

cond-mat.stat-mech↗

arXiv2010

Aging and fluctuation-dissipation ratio in a nonequilibrium $q$-state lattice model

A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

cond-mat.stat-mech↗

arXiv2008

Solvable Metric Growing Networks

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen to be embedded in a metric arrangement, where the geographic distance between vertices plays a crucial role. The present work proposes a model for growing network that takes into account the geographic distance between vertices: the probability that they are connected is higher if they are located nearer than farther. In this framework, the mean degree of vertices, degree distribution and shortest path length between two randomly chosen vertices are analysed.

cond-mat.stat-mech↗

arXiv2007

Diluted antiferromagnet in a ferromagnetic enviroment

The question of robustness of a network under random ``attacks'' is treated in the framework of critical phenomena. The persistence of spontaneous magnetization of a ferromagnetic system to the random inclusion of antiferromagnetic interactions is investigated. After examing the static properties of the quenched version (in respect to the random antiferromagnetic interactions) of the model, the persistence of the magnetization is analysed also in the annealed approximation, and the difference in the results are discussed.

cond-mat.dis-nn↗

arXiv2006

Dynamics of a mean spherical model with competing interactions

The Langevin dynamics of a $d$-dimensional mean spherical model with competing interactions along $m\leq d$ directions of a hypercubic lattice is analysed. After a quench at high temperatures, the dynamical behaviour is characterized by two distinct time scales associated with stationary and aging regimes. The asymptotic expressions for the autocorrelation and response functions, in supercritical, critical, and subcritical cases, were calculated. Aging effects, which are known to be present in the ferromagnetic version of this model system, are not affected by the introduction of competing interactions.

cond-mat.soft↗

arXiv2006

The fluctuation-dissipation theorem and the linear Glauber model

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.

cond-mat.stat-mech↗

arXiv2006

Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field.

cond-mat.dis-nn↗