A wide range of interacting systems can be described by complex networks. A common feature of such networks is that they consist of several communities or modules, the degree of which may quantified as the modularity. However, even a random uncorrelated network, which has no obvious modular structure, has a finite modularity due to the quenched disorder. For this reason, the modularity of a given network is meaningful only when it is compared with that of a randomized network with the same degree distribution. In this context, it is important to calculate the modularity of a random uncorrelated network with an arbitrary degree distribution. The modularity of a random network has been calculated [Reichardt and Bornholdt, Phys. Rev. E 76, 015102 (2007)]; however, this was limited to the case whereby the network was assumed to have only two communities, and it is evident that the modularity should be calculated in general with $q(\ge 2)$ communities. Here we calculate the modularity for $q$ communities by evaluating the ground-state energy of the $q$-state Potts Hamiltonian, based on replica symmetric solutions assuming that the mean degree is large. We found that the modularity is proportional to $\langle \sqrt{k}\rangle /\langle k\rangle$ regardless of $q$ and that only the coefficient depends on $q$. In particular, when the degree distribution follows a power law, the modularity is proportional to ${\langle k\rangle }^{-1/2}$. Our analytical results are confirmed by comparison with numerical simulations. Therefore, our results can be used as reference values for real-world networks.

The purpose of this paper is to provide a new formula for the effective diffusion coefficient of a generalized Fick-Jacobs equation for narrow three-dimensional channels. The generalized Fick-Jacobs equation is obtained by projecting the three-dimensional diffusion equation along the normal directions of a curve in three-dimensional space that roughly resembles the narrow channel. The projection (or dimensional reduction) is achieved by integrating the diffusion equation along the cross sections of the channel contained in the planes orthogonal to the curve. We show that the resulting formula for the associated effective diffusion coefficient can be expressed in terms of the geometric moments of the channel's cross sections and the curve's curvature. We show the effect that a rotating cross section with offset has on the effective diffusion coefficient.

We revisit the self-contained quantum refrigerator in the strong-internal-coupling regime by employing the quantum optical master equation. It is shown that strong internal coupling reduces the cooling ability of the refrigerator. In contrast to the weak-coupling case, strong internal coupling could lead to quite different and even converse thermodynamic behaviors.

We use large scale computer simulations of a glass-forming liquid in which a fraction $c$ of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on $c$. This result can be rationalized by assuming that the configurational entropy of the pinned liquid decreases linearly upon increasing of $c$. This behavior is discussed in the context of thermodynamic theories for the glass transition, notably the Adam-Gibbs picture and the random first order transition theory. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing $c$, results which indicate that in glass-forming liquids there is a dynamic crossover at which the shape of the relaxing entities changes.

The swimming behavior of bacteria and other microorganisms is sensitive to the physical properties of the fluid in which they swim. Mucus, biofilms, and artificial liquid-crystalline solutions are all examples of fluids with some degree of anisotropy that are also commonly encountered by bacteria. In this article, we study how liquid-crystalline order affects the swimming behavior of a model swimmer. The swimmer is a one-dimensional version of G. I. Taylor's swimming sheet: an infinite line undulating with small-amplitude transverse or longitudinal traveling waves. The fluid is a two-dimensional hexatic liquid-crystalline film. We calculate the power dissipated, swimming speed, and flux of fluid entrained as a function of the swimmer's wave form as well as properties of the hexatic film, such as the rotational and shear viscosity, the Frank elastic constant, and the anchoring strength. The departure from isotropic behavior is greatest for large rotational viscosity and weak anchoring boundary conditions on the orientational order at the swimmer surface. We even find that if the rotational viscosity is large enough, the transverse-wave swimmer moves in the opposite direction relative to a swimmer in an isotropic fluid.

The identification of the topological structures of complex networks from dynamical information is a significant inverse problem. How to infer the information of network topology from short-time dynamical data is a challenging topic. The presence of synchronization among nodes makes the identification of network topology difficult. In this paper we present an efficient method called the repeated-drive adaptive feedback scheme to reveal the network connectivity from short-time dynamics. By applying the short asynchronous transient data as a repeated drive, the adjacency matrix can be successfully determined in terms of the modified adaptive feedback scheme. This improved scheme is valid for both synchronous and asynchronous cases of the network and is especially efficient in the presence of global or local synchronization, where the transient drive can be obtained by perturbing the system to get a very short asynchronous transient. The detection speed of our scheme exhibits the optimized effect by adjusting the time-series segment length and the coupling strength among nodes in the network.

We propose and study a dissatisfied adaptive snowdrift game with a payoff parameter $r$ that incorporates a cost for rewiring a connection. An agent, facing adverse local environment, may switch action without a cost or rewire an existing link with a cost $a$ so as to attain a better competing environment. Detailed numerical simulations reveal nontrivial and nonmonotonic dependence of the frequency of cooperation and the densities of different types of links on $a$ and $r$. A theory that treats the cooperative and noncooperative agents separately and accounts for spatial correlation up to neighboring agents is formulated. The theory gives results that are in good agreement with simulations. The frequency of cooperation $f_C$ is enhanced (suppressed) at high rewiring cost relative to that at low rewiring cost when $r$ is small (large). For a given value of $r$, there exists a critical value of the rewiring cost below which the system evolves into a phase of frozen dynamics with isolated noncooperative agents segregated from a cluster of cooperative agents, and above which the system evolves into a connected population of mixed actions with continual dynamics. The phase boundary on the $a\text{−}r$ phase space that separates the two phases with distinct structural, population and dynamical properties is mapped out. The phase diagram reveals that, as a general feature, for small $r$ (small $a$), the disconnected and segregated phase can survive over a wider range of $a\left(r\right)$.

Many work extraction or information erasure processes in the literature involve the raising and lowering of energy levels via external fields. But even if the actual system is treated quantum mechanically, the field is assumed to be classical and of infinite strength, hence not developing any correlations with the system or experiencing back-actions. We extend these considerations to a fully quantum mechanical treatment by studying a spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-$l$ system, which models an external field. With this concrete model together with a bosonic thermal bath, we analyze the back-action a finite-size field suffers during a quantum-mechanical work extraction process and the effect this has on the extractable work and highlight a range of assumptions commonly made when considering such processes. The well-known semiclassical treatment of work extraction from a pure qubit predicts a maximum extractable work $W=kTlog2$ for a quasistatic process, which holds as a strict upper bound in the fully quantum mechanical case and is attained only in the classical limit. We also address the problem of emergent local time dependence in a joint system with a globally fixed Hamiltonian.

Spectral fluctuations of a system of $N$ weakly interacting bosons in an isotropic harmonic trap are studied, with the focus on the deviations from Poisson spectral statistics, typical of a quantum integrable systems. We have utilized the ideas formulated by Makino et al. [Phys. Rev. E 67, 066205 (2003)] who have extended the approach of Berry and Robnik [J. Phys. A 17, 2413 (1984)]. Earlier investigations of the Berry conjecture [Proc. R. Soc. London, Ser. A 356, 375 (1977)] of Poisson spectral statistics mainly considered quantum systems whose classical counterparts are integrable. However, the system of $N$ weakly interacting bosons in the external trap has no classical counterpart. Also, it is a realistic and experimentally achievable system with close relation to Bose-Einstein condensation. Thus, a stringent analysis of the applicability of the Berry conjecture to this kind of systems is indeed required. We observe that for small boson number, the system is close to integrability and the nearest-neighbor level spacing distribution and the level number variance exhibit deviations from Poisson statistics similar to those of rational rectangular billiards.

A lattice model of critical dense polymers $\mathrm{O}\left(n\right)$ is considered for finite cylinder geometry. Due to the presence of noncontractible loops with a fixed fugacity $\xi$, the model at $n=0$ is a generalization of the critical dense polymers solved by Pearce, Rasmussen, and Villani. We found the free energy for any height $N$ and circumference $L$ of the cylinder. The density $\rho$ of noncontractible loops is obtained for $N\to \infty$ and large $L$. The results are compared with those found for the anisotropic quantum chain with twisted boundary conditions. Using the latter method, we derived $\rho$ for any $\mathrm{O}\left(n\right)$ model and an arbitrary fugacity.

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition-state theory. Which expression should be used depends on the strength of the interparticle interactions. Analytical expressions for the self- and transport diffusion are derived when correlations, caused by memory effects in the environment, are neglected. The diffusive behavior is studied numerically with kinetic Monte Carlo (kMC) simulations, which reproduces the diffusion including correlations. The effect of correlations is studied by comparing the analytical expressions with the kMC simulations. It is found that the Maxwell-Stefan diffusion can exceed the self-diffusion. To our knowledge, this is the first time this is observed. The diffusive behavior in one-dimensional and higher-dimensional systems is qualitatively the same, with the effect of correlations decreasing for increasing dimension. The length dependence of both the self- and transport diffusion is studied for one-dimensional systems. For long lengths the self-diffusion shows a $1/L$ dependence. Finally, we discuss when agreement with experiments and simulations can be expected. The assumption that particles in different cavities do not interact is expected to hold quantitatively at low and medium particle concentrations if the particles are not strongly interacting.

Chromatin remodeling factors are enzymes being able to alter locally chromatin structure at the nucleosomal level and they actively participate in the regulation of gene expression. Using simple rules for individual nucleosome motion induced by a remodeling factor, we designed simulations of the remodeling of oligomeric chromatin, in order to address quantitatively collective effects in DNA accessibility upon nucleosome mobilization. Our results suggest that accessibility profiles are inhomogeneous thanks to borders effects like protein binding. Remarkably, we show that the accessibility lifetime of DNA sequence is roughly doubled in the vicinity of borders as compared to its value in bulk regions far from the borders. These results are quantitatively interpreted as resulting from the confined diffusion of a large nucleosome depleted region.

The diffusion processes on complex networks may be described by different Laplacian matrices due to heterogeneous connectivity. Here we investigate the random walks of blind ants and myopic ants on heterogeneous networks: While a myopic ant hops to a neighbor node every step, a blind ant may stay or hop with probabilities that depend on node connectivity. By analyzing the trajectories of blind ants, we show that the asymptotic behaviors of both random walks are related by rescaling time and probability with node connectivity. Using this result, we show how the small eigenvalues of the Laplacian matrices generating the two random walks are related. As an application, we show how the return-to-origin probability of a myopic ant can be used to compute the scaling behaviors of the Edwards-Wilkinson model, a representative model of load balancing on networks.

We consider a dual model of decision making, in which an individual forms its opinion based on contrasting mechanisms of imitation and rational calculation. The decision-making model (DMM) implements imitating behavior by means of a network of coupled two-state master equations that undergoes a phase transition at a critical value of a control parameter. The evolutionary spatial game, being a generalization of the prisoner's dilemma game, is used to determine in objective fashion the cooperative or anticooperative strategy adopted by individuals. Interactions between two sources of dynamics increases the domain of initial states attracted to phase transition dynamics beyond that of the DMM network in isolation. Additionally, on average the influence of the DMM on the game increases the final observed fraction of cooperators in the system.

The minority game is a well-known agent-based model with no explicit interaction among its agents. However, it is known that they interact through the global magnitudes of the model and through their strategies. In this work we have attempted to formalize the implicit interactions among minority game agents as if they were links on a complex network. We have defined the link between two agents by quantifying the similarity between them. This link definition is based on the information of the instance of the game (the set of strategies assigned to each agent at the beginning) without any dynamic information on the game and brings about a static, unweighed and undirected network. We have analyzed the structure of the resulting network for different parameters, such as the number of agents $\left(N\right)$ and the agent's capacity to process information $\left(m\right)$, always taking into account games with two strategies per agent. In the region of crowd effects of the model, the resulting networks structure is a small-world network, whereas in the region where the behavior of the minority game is the same as in a game of random decisions, networks become a random network of Erdos-Renyi. The transition between these two types of networks is slow, without any peculiar feature of the network in the region of the coordination among agents. Finally, we have studied the resulting static networks for the full strategy minority game model, a maximal instance of the minority game in which all possible agents take part in the game. We have explicitly calculated the degree distribution of the full strategy minority game network and, on the basis of this analytical result, we have estimated the degree distribution of the minority game network, which is in accordance with computational results.

In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbors, as introduced by Bagnoli et al. [Phys. Rev. E 76, 061904 (2007)]. We rederive previous results using a self-organized method that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by physical contacts in real life but often gather information from an information network, which may be quite different from the physical ones. The similarity between the physical and the information networks determines the possibility of stopping the infection for a sufficiently high precaution level: if the networks are too different, there is no means of avoiding the epidemics.

In this paper we investigate how the complexity of chaotic phase spaces affect the efficiency of importance sampling Monte Carlo simulations. We focus on flat-histogram simulations of the distribution of finite-time Lyapunov exponent in a simple chaotic system and obtain analytically that the computational effort: (i) scales polynomially with the finite time, a tremendous improvement over the exponential scaling obtained in uniform sampling simulations; and (ii) the polynomial scaling is suboptimal, a phenomenon known as critical slowing down. We show that critical slowing down appears because of the limited possibilities to issue a local proposal in the Monte Carlo procedure when it is applied to chaotic systems. These results show how generic properties of chaotic systems limit the efficiency of Monte Carlo simulations.

We study models with three coupled vector fields characterized by $O\left(N_1\right)\oplus O\left(N_2\right)\oplus O\left(N_3\right)$ symmetry. Using the nonperturbative functional renormalization group, we derive $\beta$ functions for the couplings and anomalous dimensions in $d$ dimensions. Specializing to the case of three dimensions, we explore interacting fixed points that generalize the $O\left(N\right)$ Wilson-Fisher fixed point. We find a symmetry-enhanced isotropic fixed point, a large class of fixed points with partial symmetry enhancement, as well as partially and fully decoupled fixed-point solutions. We discuss their stability properties for all values of $N_1,N_2$, and $N_3$, emphasizing important differences to the related two-field models. For small numbers of field components, we find no stable fixed-point solutions, and we argue that this can be attributed to the presence of a large class of possible (mixed) couplings in the three-field and multifield models. Furthermore, we contrast different mechanisms for stability interchange between fixed points in the case of the two- and three-field models, which generically proceed through fixed-point collisions.

We analyze the dynamics of a two-dimensional system of interacting active dumbbells. We characterize the mean-square displacement, linear response function, and deviation from the equilibrium fluctuation-dissipation theorem as a function of activity strength, packing fraction, and temperature for parameters such that the system is in its homogeneous phase. While the diffusion constant in the last diffusive regime naturally increases with activity and decreases with packing fraction, we exhibit an intriguing nonmonotonic dependence on the activity of the ratio between the finite-density and the single-particle diffusion constants. At fixed packing fraction, the time-integrated linear response function depends nonmonotonically on activity strength. The effective temperature extracted from the ratio between the integrated linear response and the mean-square displacement in the last diffusive regime is always higher than the ambient temperature, increases with increasing activity, and, for small active force, monotonically increases with density while for sufficiently high activity it first increases and next decreases with the packing fraction. We ascribe this peculiar effect to the existence of finite-size clusters for sufficiently high activity and density at the fixed (low) temperatures at which we worked. The crossover occurs at lower activity or density the lower the external temperature. The finite-density effective temperature is higher (lower) than the single dumbbell one below (above) a crossover value of the Péclet number.

The observation of quantum coherence in pigment-protein complexes has attracted considerable interest. One such endeavor entails applying a quantum heat engine to model the photosynthetic reaction center, but the definition of work used is inconsistent with that defined in quantum thermodynamics. Using the definition of work proposed in Weimer et al. [Europhys. Lett. 83, 30008 (2008)], we investigated two proposals for enhancing the performance of the photosynthetic reaction center. In proposal A, which is similar to that in Dorfman et al. [Proc. Natl. Acad. Sci. USA 110, 2746 (2013)], we found that the power and current-voltage characteristic of the heat engine can be increased by Fano interference but the efficiency cannot. In proposal B, which is similar to that in Creatore et al. [Phys. Rev. Lett. 111, 253601 (2013)], we found that the mechanism of strengthening the performance of the heat engine is invalid; i.e., the dipole-dipole interaction between two electron donors could not increase the power, efficiency, or current-voltage characteristic.