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While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at achieving explainable AI, namely the Gradient-weighted Class Activation Map (Grad-CAM), to investigate how deep learning (implemented by ResNets) recognizes the distinctive features of a particular anomalous diffusion model from the raw trajectory data. Our results show that Grad-CAM reveals the portions of the trajectory that hold crucial information about the underlying mechanism of anomalous diffusion, which can be utilized to enhance the robustness of the trained classifier against the measurement noise. Moreover, we observe that deep learning distills unique statistical characteristics of different diffusion mechanisms at various spatiotemporal scales, with larger-scale (smaller-scale) features identified at higher (lower) layers., Comment: 14 pages, 12 figures

Unlike traditional media, online news platforms allow users to consume content that suits their tastes and to facilitate interactions with other people. However, as more personalized consumption of information and interaction with like-minded users increase, ideological bias can inadvertently increase and contribute to the formation of echo chambers, reinforcing the polarization of opinions. Although the structural characteristics of polarization among different ideological groups in online spaces have been extensively studied, research into how these groups emotionally interact with each other has not been as thoroughly explored. From this perspective, we investigate both structural and affective polarization between news media user groups on Naver News, South Korea's largest online news portal, during the period of 2022 Korean presidential election. By utilizing the dataset comprising 333,014 articles and over 36 million user comments, we uncover two distinct groups of users characterized by opposing political leanings and reveal significant bias and polarization among them. Additionally, we reveal the existence of echo chambers within co-commenting networks and investigate the asymmetric affective interaction patterns between the two polarized groups. Classification task of news media articles based on the distinct comment response patterns support the notion that different political groups may employ distinct communication strategies. Our approach based on network analysis on large-scale comment dataset offers novel insights into characteristics of user polarization in the online news platforms and the nuanced interaction nature between user groups., Comment: 21 pages, 6 figures

Giving up and starting over may seem wasteful in many situations such as searching for a target or training deep neural networks (DNNs). Our study, though, demonstrates that resetting from a checkpoint can significantly improve generalization performance when training DNNs with noisy labels. In the presence of noisy labels, DNNs initially learn the general patterns of the data but then gradually memorize the corrupted data, leading to overfitting. By deconstructing the dynamics of stochastic gradient descent (SGD), we identify the behavior of a latent gradient bias induced by noisy labels, which harms generalization. To mitigate this negative effect, we apply the stochastic resetting method to SGD, inspired by recent developments in the field of statistical physics achieving efficient target searches. We first theoretically identify the conditions where resetting becomes beneficial, and then we empirically validate our theory, confirming the significant improvements achieved by resetting. We further demonstrate that our method is both easy to implement and compatible with other methods for handling noisy labels. Additionally, this work offers insights into the learning dynamics of DNNs from an interpretability perspective, expanding the potential to analyze training methods through the lens of statistical physics., Comment: 26 pages, 11 figures

Bridging the gap between the practical performance of deep learning and its theoretical foundations often involves analyzing neural networks through stochastic gradient descent (SGD). Expanding on previous research that focused on modeling structured inputs under a simple Gaussian setting, we analyze the behavior of a deep learning system trained on inputs modeled as Gaussian mixtures to better simulate more general structured inputs. Through empirical analysis and theoretical investigation, we demonstrate that under certain standardization schemes, the deep learning model converges toward Gaussian setting behavior, even when the input data follow more complex or real-world distributions. This finding exhibits a form of universality in which diverse structured distributions yield results consistent with Gaussian assumptions, which can support the theoretical understanding of deep learning models., Comment: Accepted for Bridging the Gap Between Practice and Theory in Deep Learning (BGPT) Workshop at ICLR 2024, [v1] 23 pages, 16 figures

The economic success of individuals is often determined by a combination of talent, luck, and assistance from others. We introduce a new agent-based model that simultaneously considers talent, luck, and social interaction. This model allows us to explore how network structure (how agents interact) and talent distribution among agents affect the dynamics of capital accumulation through analytical and numerical methods. We identify a phenomenon as ``talent configuration effect", which refers to the influence of how talent is allocated to individuals (nodes) in the network. We analyze this effect through two key properties: talent assortativity (TA) and talent-degree correlation (TD). In particular, we focus on three economic indicators: growth rate ($n_{\rm rate}$), Gini coefficient (inequality: $n_{\rm Gini}$), and meritocratic fairness ($n_{LT}$). This investigation helps us understand the interplay between talent configuration and network structure on capital dynamics. We find that, in the short term, positive correlations exist between TA and TD for all three economic indicators. Furthermore, the dominant factor influencing capital dynamics depends on the network topology. In scale-free networks, TD has a stronger influence on the economic indices than TA. Conversely, in lattice-like networks, TA plays a more significant role. Our findings address that high socioeconomic homophily can create a dilemma between growth and equality, and that hub monopolization by few highly talented agents makes economic growth strongly dependent on their performances., Comment: 20 pages = (12 pages, 6 figures, and 1 table in main text and Appendix A-D) + (8 pages, 8 figures and 1 table as Supplemental Material); Published version with extra typo correction

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling predictions of their temporal evolution and analyses of thermodynamic quantities, including absorbed heat, work done on the system, and entropy production. However, inferring the Langevin equation from observed trajectories remains challenging, particularly for nonlinear and high-dimensional systems. In this study, we present a comprehensive framework that employs Bayesian neural networks for inferring Langevin equations in both overdamped and underdamped regimes. Our framework first provides the drift force and diffusion matrix separately and then combines them to construct the Langevin equation. By providing a distribution of predictions instead of a single value, our approach allows us to assess prediction uncertainties, which can prevent potential misunderstandings and erroneous decisions about the system. We demonstrate the effectiveness of our framework in inferring Langevin equations for various scenarios including a neuron model and microscopic engine, highlighting its versatility and potential impact., Comment: 30 pages, 17 figures

Hidden geometry enables the investigation of complex networks at different scales. Extending this framework to multiplex networks, we uncover a novel kind of mesoscopic organization in real multiplex systems, named $\textit{clan}$, a group of nodes that preserve their local geometric arrangement across layers. Furthermore, we reveal the intimate relationship between the unfolding of clan structure and mutual percolation against targeted attacks, leading to an ambivalent role of clans: making a system fragile yet less prone to complete shattering. Finally, we confirm the correlation between the multiscale nature of geometric organization and the overall robustness. Our findings expand the significance of hidden geometry in network function, while also highlighting potential pitfalls in evaluating and controlling catastrophic failure of multiplex systems.

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the system domain, where the type of system remains consistent and thus cannot ensure the adaptation to new, or unseen physical systems governed by different laws. For instance, a neural network trained on a mass-spring system cannot guarantee accurate predictions for the behavior of a two-body system or any other system with different physical laws. In this work, we take a significant leap forward by targeting cross domain generalization within the field of Hamiltonian dynamics. We model our system with a graph neural network (GNN) and employ a meta learning algorithm to enable the model to gain experience over a distribution of systems and make it adapt to new physics. Our approach aims to learn a unified Hamiltonian representation that is generalizable across multiple system domains, thereby overcoming the limitations of system-specific models. We demonstrate that the meta-trained model captures the generalized Hamiltonian representation that is consistent across different physical domains. Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning., Comment: Conference paper at ICLR 2024

Dynamical systems with interacting agents are universal in nature, commonly modeled by a graph of relationships between their constituents. Recently, various works have been presented to tackle the problem of inferring those relationships from the system trajectories via deep neural networks, but most of the studies assume binary or discrete types of interactions for simplicity. In the real world, the interaction kernels often involve continuous interaction strengths, which cannot be accurately approximated by discrete relations. In this work, we propose the relational attentive inference network (RAIN) to infer continuously weighted interaction graphs without any ground-truth interaction strengths. Our model employs a novel pairwise attention (PA) mechanism to refine the trajectory representations and a graph transformer to extract heterogeneous interaction weights for each pair of agents. We show that our RAIN model with the PA mechanism accurately infers continuous interaction strengths for simulated physical systems in an unsupervised manner. Further, RAIN with PA successfully predicts trajectories from motion capture data with an interpretable interaction graph, demonstrating the virtue of modeling unknown dynamics with continuous weights., Comment: 14 pages, 8 figures

How have individuals of social animals in nature evolved to learn from each other, and what would be the optimal strategy for such learning in a specific environment? Here, we address both problems by employing a deep reinforcement learning model to optimize the social learning strategies (SLSs) of agents in a cooperative game in a multi-dimensional landscape. Throughout the training for maximizing the overall payoff, we find that the agent spontaneously learns various concepts of social learning, such as copying, focusing on frequent and well-performing neighbors, self-comparison, and the importance of balancing between individual and social learning, without any explicit guidance or prior knowledge about the system. The SLS from a fully trained agent outperforms all of the traditional, baseline SLSs in terms of mean payoff. We demonstrate the superior performance of the reinforcement learning agent in various environments, including temporally changing environments and real social networks, which also verifies the adaptability of our framework to different social settings., Comment: Main manuscript : 11 pages, 6 figures. Supplementary information : 7 pages, 7 figures

Exploitation universally emerges in various decision-making contexts, e.g., animals foraging, web surfing, the evolution of scientists' research topics, and our daily lives. Despite its ubiquity, exploitation, which refers to the behavior of revisiting previous experiences, has often been considered to delay the search process of finding a target. In this paper, we investigate how exploitation affects search performance by applying a non-Markovian random walk model, where a walker randomly revisits a previously visited node using long-term memory. We analytically study two broad forms of network structures, namely (i) clique-like networks and (ii) lollipop-like networks, and find that exploitation can significantly improve search performance in lollipop-like networks whereas it hinders target search in clique-like networks. Moreover, we numerically verify that exploitation can reduce the time needed to fully explore the underlying networks by using $550$ diverse real-world networks. Based on the analytic result, we define the lollipop-likeness of a network and observe a positive relationship between the advantage of exploitation and lollipop-likeness., Comment: 12 pages, 7 figures

Team chemistry is the holy grail of understanding collaborative human behavior, yet its quantitative understanding remains inconclusive. To reveal the presence and mechanisms of team chemistry in scientific collaboration, we reconstruct the publication histories of 560,689 individual scientists and 1,026,196 duos of scientists. We identify ability discrepancies between teams and their members, enabling us to evaluate team chemistry in a way that is robust against prior experience of collaboration and inherent randomness. Furthermore, our network analysis uncovers a nontrivial modular structure that allows us to predict team chemistry between scientists who have never collaborated before. Research interest is the highest correlated ingredient of team chemistry among six personal characteristics that have been commonly attributed as the keys to successful collaboration, yet the diversity of the characteristics cannot completely explain team chemistry. Our results may lead to unlocking the hidden potential of collaboration by the matching of well-paired scientists.

Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path probability distribution, many methods have been developed to estimate EP from only trajectory data. However, estimating the EP of a system with odd-parity variables, which prevails in nonequilibrium systems, has not been covered. In this study, we develop a machine learning method for estimating the EP in a stochastic system with odd-parity variables through multiple neural networks. We demonstrate our method with two systems, an underdamped bead-spring model and a one-particle odd-parity Markov jump process., Comment: 6 pages, 3 figures

Quantifying entropy production (EP) is essential to understand stochastic systems at mesoscopic scales, such as living organisms or biological assemblies. However, without tracking the relevant variables, it is challenging to figure out where and to what extent EP occurs from recorded time-series image data from experiments. Here, applying a convolutional neural network (CNN), a powerful tool for image processing, we develop an estimation method for EP through an unsupervised learning algorithm that calculates only from movies. Together with an attention map of the CNN's last layer, our method can not only quantify stochastic EP but also produce the spatiotemporal pattern of the EP (dissipation map). We show that our method accurately measures the EP and creates a dissipation map in two nonequilibrium systems, the bead-spring model and a network of elastic filaments. We further confirm high performance even with noisy, low spatial resolution data, and partially observed situations. Our method will provide a practical way to obtain dissipation maps and ultimately contribute to uncovering the nonequilibrium nature of complex systems., Comment: 15 pages, 8 figures

Invariants and conservation laws convey critical information about the underlying dynamics of a system, yet it is generally infeasible to find them from large-scale data without any prior knowledge or human insight. We propose ConservNet to achieve this goal, a neural network that spontaneously discovers a conserved quantity from grouped data where the members of each group share invariants, similar to a general experimental setting where trajectories from different trials are observed. As a neural network trained with a novel and intuitive loss function called noise-variance loss, ConservNet learns the hidden invariants in each group of multi-dimensional observables in a data-driven, end-to-end manner. Our model successfully discovers underlying invariants from the simulated systems having invariants as well as a real-world double pendulum trajectory. Since the model is robust to various noises and data conditions compared to baseline, our approach is directly applicable to experimental data for discovering hidden conservation laws and further, general relationships between variables., Comment: 12 pages, 9 figures

The recent interest into the Brownian gyrator has been confined chiefly to the analysis of Brownian dynamics both in theory and experiment despite the applicability of general cases with definite mass. Considering mass explicitly in the solution of the Fokker--Planck equation and Langevin dynamics simulations, we investigate how inertia can change the dynamics and energetics of the Brownian gyrator. In the Langevin model, the inertia reduces the nonequilibrium effects by diminishing the declination of the probability density function and the mean of a specific angular momentum, $j_\theta$, as a measure of rotation. Another unique feature of the Langevin description is that rotation is maximized at a particular anisotropy while the stability of the rotation is minimized at a particular anisotropy or mass. Our results suggest that the Langevin dynamics description of the Brownian gyrator is intrinsically different from that with Brownian dynamics. In addition, $j_\theta$ is proven to be essential and convenient for estimating stochastic energetics such as heat currents and entropy production even in the underdamped regime., Comment: 12 pages, 7 figures

A collective flashing ratchet transports Brownian particles using a spatially periodic, asymmetric, and time-dependent on-off switchable potential. The net current of the particles in this system can be substantially increased by feedback control based on the particle positions. Several feedback policies for maximizing the current have been proposed, but optimal policies have not been found for a moderate number of particles. Here, we use deep reinforcement learning (RL) to find optimal policies, with results showing that policies built with a suitable neural network architecture outperform the previous policies. Moreover, even in a time-delayed feedback situation where the on-off switching of the potential is delayed, we demonstrate that the policies provided by deep RL provide higher currents than the previous strategies., Comment: 6 + 4 pages, 3 + 2 figures

To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. This implies that another modified TUR is required to cover the finite-time Otto cycle. Finally, we discuss the possible origin of this violation in terms of the uncertainty products of the thermodynamic quantities and the relative error near resonance conditions., Comment: 12 pages, 12 figures

Interactions between elements, which are usually represented by networks, have to delineate potentially unequal relationships in terms of their relative importance or direction. The intrinsic unequal relationships of such kind, however, are opaque or hidden in numerous real systems. For instance, when a node in a network with limited interaction capacity spends its capacity to its neighboring nodes, the allocation of the total amount of interactions to them can be vastly diverse. Even if such potentially heterogeneous interactions epitomized by weighted networks are observable, as a result of the aforementioned ego-centric allocation of interactions, the relative importance or dependency between two interacting nodes can only be implicitly accessible. In this work, we precisely pinpoint such relative dependency by proposing the framework to discover hidden dependent relations extracted from weighted networks. For a given weighted network, we provide a systematic criterion to select the most essential interactions for individual nodes based on the concept of information entropy. The criterion is symbolized by assigning the effective number of neighbors or the effective out-degree to each node, and the resultant directed subnetwork decodes the hidden dependent relations by leaving only the most essential directed interactions. We apply our methodology to two time-stamped empirical network data, namely the international trade relations between nations in the world trade web (WTW) and the network of people in the historical record of Korea, Annals of the Joseon Dynasty (AJD). Based on the data analysis, we discover that the properties of mutual dependency encoded in the two systems are vastly different., Comment: 20 pages, 15 figures

The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading failure of the power grid to chronic pain or epileptic seizure in the brain. Furthermore, networks provide a powerful model to understand and predict the properties of a diverse range of real-world complex systems. Recently, a multilayer network has been realized as a better suited framework for the representation of complex systems having multiple types of interactions among the same set of constituents. This article shows that by tuning the properties of one layer (network) of a multilayer network, one can regulate the dynamical behavior of another layer (network). By taking an example of a multiplex network comprising two different types of networked Kuramoto oscillators representing two different layers, this article attempts to provide a glimpse of opportunities and emerging phenomena multiplexing can induce which is otherwise not possible for a network in isolation. Here we consider explosive synchronization to demonstrate the potential of multilayer networks framework. To the end, we discuss several possible extensions of the model considered here by incorporating real-world properties., Comment: 11 pages, 8 figures

This Letter presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories of relevant variables without detailed information on the system dynamics. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides stochastic EP by optimizing the objective function proposed here. We verify the NEEP with the stochastic processes of the bead-spring and discrete flashing ratchet models, and also demonstrate that our method is applicable to high-dimensional data and can provide coarse-grained EP for Markov systems with unobservable states., Comment: 6+8 pages, 4+8 figures

Dynamics of complex social systems has often been described in the framework of temporal networks, where links are considered to exist only at the moment of interaction between nodes. Such interaction patterns are not only driven by internal interaction mechanisms, but also affected by environmental changes. To investigate the impact of the environmental changes on the dynamics of temporal networks, we analyze several face-to-face interaction datasets using the multiscale entropy (MSE) method to find that the observed temporal correlations can be categorized according to the environmental similarity of datasets such as classes and break times in schools. By devising and studying a temporal network model considering a periodically changing environment as well as a preferential activation mechanism, we numerically show that our model could successfully reproduce various empirical results by the MSE method in terms of multiscale temporal correlations. Our results demonstrate that the environmental changes can play an important role in shaping the dynamics of temporal networks when the interactions between nodes are influenced by the environment of the systems., Comment: 10 pages, 8 figures

Rich phenomena from complex systems have long intrigued researchers, and yet modeling system micro-dynamics and inferring the forms of interaction remain challenging for conventional data-driven approaches, being generally established by human scientists. In this study, we propose AgentNet, a model-free data-driven framework consisting of deep neural networks to reveal and analyze the hidden interactions in complex systems from observed data alone. AgentNet utilizes a graph attention network with novel variable-wise attention to model the interaction between individual agents, and employs various encoders and decoders that can be selectively applied to any desired system. Our model successfully captured a wide variety of simulated complex systems, namely cellular automata (discrete), the Vicsek model (continuous), and active Ornstein--Uhlenbeck particles (non-Markovian) in which, notably, AgentNet's visualized attention values coincided with the true interaction strength and exhibited collective behavior that was absent in the training data. A demonstration with empirical data from a flock of birds showed that AgentNet could identify hidden interaction ranges exhibited by real birds, which cannot be detected by conventional velocity correlation analysis. We expect our framework to open a novel path to investigating complex systems and to provide insight into general process-driven modeling., Comment: 17 pages, 8 figures, 3 tables

In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called `friction'. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the Otto efficiency, and the power of the Lindbladian engine can be nonzero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that even with an equilibrium bath, a nonequilibrium working fluid brings on the higher performance than what an equilibrium working fluid does., Comment: 10 pages, 5 figures (main) with additional 3 figures (appendix); published version

To provide a comprehensive view for dynamics of and on many real-world temporal networks, we investigate the interplay of temporal connectivity patterns and spreading phenomena, in terms of the susceptible-infected-removed (SIR) model on the modified activity-driven temporal network (ADTN) with memory. In particular, we focus on how the epidemic threshold of the SIR model is affected by the heterogeneity of nodal activities and the memory strength in temporal and static regimes, respectively. While strong ties (memory) between nodes inhibit the spread of epidemic to be localized, the heterogeneity of nodal activities enhances it to be globalized initially. Since the epidemic threshold of the SIR model is very sensitive to the degree distribution of nodes in static networks, we test the SIR model on the modified ADTNs with the possible set of the activity exponents and the memory exponents that generates the same degree distributions in temporal networks. We also discuss the role of spatiotemporal scaling properties of the largest cluster and the maximum degree in the epidemic threshold. It is observed that the presence of highly active nodes enables to trigger the initial spread of epidemic in a short period of time, but it also limits its final spread to the entire network. This implies that there is the trade-off between the spreading time of epidemic and its outbreak size. Finally, we suggest the phase diagram of the SIR model on ADTNs and the optimal condition for the spread of epidemic under the circumstances., Comment: 7 pages, 6 figures (published version)

The spread of behavior in a society has two major features: the synergy of multiple spreaders and the dominance of hubs. While strong synergy is known to induce mixed-order transitions (MOTs) at percolation, the effects of hubs on the phenomena are yet to be clarified. By analytically solving the generalized epidemic process on random scale-free networks with the power-law degree distribution $p_k \sim k^{-\alpha}$, we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for $\alpha < 4$, an abundance of hubs drive MOTs, even if a synergistic spreading event requires an arbitrarily large number of adjacent spreaders. In particular, for $2 < \alpha < 3$, we find that a global cascade is possible even when only synergistic spreading events are allowed. These transition properties are substantially different from those of cooperative contagions, which are another class of synergistic cascading processes exhibiting MOTs., Comment: 5 + 7 pages, 3 + 3 figures

Popularity describes the dynamics of mass attention, and is a part of a broader class of population dynamics in ecology and social science literature. Studying accurate model of popularity is important for quantifying spreading of novelty, memes, and influences in human society. Although logistic equation and similar class of nonlinear differential equation formulates traditional population dynamics well, part of the deviation in long-term prediction is stated, yet fully understood. Recently, several studies hinted a long-term memory effect on popularity whose response function follows a power-law, especially that appears on online mass media such as YouTube, Twitter, or Amazon book sales. Here, we investigate the ranking of most popular music, \textit{the Billboard Hot 100 chart}, which is one of the largest popularity dataset spanning several decades. Using a popularity model that comprises logistic growth and a power-law decaying long-term memory, we showed that rank history is mainly characterized by initial popularity and memory strength. With this framework, we investigated temporal development of long-term memory on the whole popularity dynamics. As a result, abrupt emergence of long-term memory and broad initial popularity is illustrated, which was not clearly detected by time-independent measures. We emphasize not only development of the mass media, but also the difference of spreading and accumulated popularity affect dynamics significantly when the popularity has long-term memory., Comment: 9 pages, 11 figures

We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim \textit{et al.}, Eur. Phys. J. B {\bf 88}, 315 (2015)]. Particularly, we focus on the interplay of the time resolution and memory in dynamic topologies. Through the random walk (RW) process, we investigate diffusion properties and topological changes as the time resolution increases. Our results with memory are compared to those of the memoryless case. Based on the temporal percolation concept, we derive scaling exponents in the dynamics of the largest cluster and the coverage of the RW process in time-varying networks. We find that the time resolution in the time-accumulated network determines the effective size of the network, while memory affects relevant scaling properties at the crossover from the dynamic regime to the static one. The origin of memory-dependent scaling behaviors is the dynamics of the largest cluster, which depends on temporal degree distributions. Finally, we conjecture of the extended finite-size scaling ansatz for dynamic topologies and the fundamental property of temporal networks, which are numerically confirmed., Comment: 11 pages, 8 figures (8 pdf files); pulished version

We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially-condensed phase is the most interesting, compared to that in the original SB problem., Comment: 12 pages, 10 figures (10 pdf files); published version

Painting is an art form that has long functioned as a major channel for the creative expression and communication of humans, its evolution taking place under an interplay with the science, technology, and social environments of the times. Therefore, understanding the process based on comprehensive data could shed light on how humans acted and manifested creatively under changing conditions. Yet, there exist few systematic frameworks that characterize the process for painting, which would require robust statistical methods for defining painting characteristics and identifying human's creative developments, and data of high quality and sufficient quantity. Here we propose that the color contrast of a painting image signifying the heterogeneity in inter-pixel chromatic distance can be a useful representation of its style, integrating both the color and geometry. From the color contrasts of paintings from a large-scale, comprehensive archive of 179,853 high-quality images spanning several centuries we characterize the temporal evolutionary patterns of paintings, and present a deep study of an extraordinary expansion in creative diversity and individuality that came to define the modern era., Comment: 11 pages, 7 figures

We perform an in-depth analysis on the inequality in 863 Wikimedia projects. We take the complete editing history of 267,304,095 Wikimedia items until 2016, which not only covers every language edition of Wikipedia, but also embraces the complete versions of Wiktionary, Wikisource, Wikivoyage, etc. Our findings of common growth pattern described by the interrelations between four characteristic growth yardsticks suggest a universal law of communal data formation. In this encyclopaedic data set, we observe the interplay between the number of edits and the degree of inequality. In particular, the rapid increase in the Gini coefficient suggests that this entrenched inequality stems from the nature of such open-editing communal data sets, namely the abiogenesis of the supereditors' oligopoly. We show that these supereditor groups were created at the early stages of these open-editing media and are still active. Furthermore, our model considers both short-term and long-term memories to successfully elucidate the underlying mechanism of the establishment of oligarchy in Wikipedia. Our results anticipate a noticeable prospect of such communal databases in the future: the disparity will not be resolved spontaneously., Comment: 20 pages of main text including 4 figures + 35 pages of supplementary information including 28 supplementary figures and 7 supplementary tables

The slow-bond problem is a long-standing question about the minimal strength $\epsilon_\mathrm{c}$ of a local defect with global effects on the Kardar--Parisi--Zhang (KPZ) universality class. A consensus on the issue has been delayed due to the discrepancy between various analytical predictions claiming $\epsilon_\mathrm{c} = 0$ and numerical observations claiming $\epsilon_\mathrm{c} > 0$. We revisit the problem via finite-size scaling analyses of the slow-bond effects, which are tested for different boundary conditions through extensive Monte Carlo simulations. Our results provide evidence that the previously reported nonzero $\epsilon_\mathrm{c}$ is an artifact of a crossover phenomenon, which logarithmically converges to zero as the system size goes to infinity., Comment: 8 pages, 6 figures (6 pdf files); published version

We consider inventions as novel combinations of existing technological capabilities. Patent data allow us to explicitly identify such combinatorial processes in invention activities. Unconsidered in the previous research, not every new combination is novel to the same extent. Some combinations are naturally anticipated based on patent activities in the past or mere random choices, and some appear to deviate exceptionally from existing invention pathways. We calculate a relative likelihood that each pair of classification codes is put together at random, and a deviation from the empirical observation so as to assess the overall novelty (or conventionality) that the patent brings forth at each year. An invention is considered as unconventional if a pair of codes therein is unlikely to be used together given the statistics in the past. Temporal evolution of the distribution indicates that the patenting activities become more conventional with occasional cross-over combinations. Our analyses show that patents introducing novelty on top of the conventional units would receive higher citations, and hence have higher impact., Comment: 20 pages, 7 figures

We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and discontinuous transitions with tricriticality in between. With the help of a comprehensive finite-size scaling theory, we numerically confirm static and dynamic scaling behaviors of the GEP near continuous phase transitions and at tricriticality, which verifies the field-theoretical results of previous studies. We also propose a proper criterion for the discontinuous transition line, which is shown to coincide with the bond percolation threshold., Comment: 7 pages, 6 figures, 1 table; published version

Wikipedia is a free Internet encyclopedia with an enormous amount of content. This encyclopedia is written by volunteers with various backgrounds in a collective fashion; anyone can access and edit most of the articles. This open-editing nature may give us prejudice that Wikipedia is an unstable and unreliable source; yet many studies suggest that Wikipedia is even more accurate and self-consistent than traditional encyclopedias. Scholars have attempted to understand such extraordinary credibility, but usually used the number of edits as the unit of time, without consideration of real time. In this work, we probe the formation of such collective intelligence through a systematic analysis using the entire history of 34,534,110 English Wikipedia articles, between 2001 and 2014. From this massive data set, we observe the universality of both timewise and lengthwise editing scales, which suggests that it is essential to consider the real-time dynamics. By considering real time, we find the existence of distinct growth patterns that are unobserved by utilizing the number of edits as the unit of time. To account for these results, we present a mechanistic model that adopts the article editing dynamics based on both editor-editor and editor-article interactions. The model successfully generates the key properties of real Wikipedia articles such as distinct types of articles for the editing patterns characterized by the interrelationship between the numbers of edits and editors, and the article size. In addition, the model indicates that infrequently referred articles tend to grow faster than frequently referred ones, and articles attracting a high motivation to edit counterintuitively reduce the number of participants. We suggest that this decay of participants eventually brings inequality among the editors, which will become more severe with time., Comment: 12 pages, 9 figures

The formation of network structure is mainly influenced by an individual node's activity and its memory, where activity can usually be interpreted as the individual inherent property and memory can be represented by the interaction strength between nodes. In our study, we define the activity through the appearance pattern in the time-aggregated network representation, and quantify the memory through the contact pattern of empirical temporal networks. To address the role of activity and memory in epidemics on time-varying networks, we propose temporal-pattern coarsening of activity-driven growing networks with memory. In particular, we focus on the relation between time-scale coarsening and spreading dynamics in the context of dynamic scaling and finite-size scaling. Finally, we discuss the universality issue of spreading dynamics on time-varying networks for various memory-causality tests., Comment: 8 pages, 10 figures (published version)

We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent $1/2$ even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions., Comment: 7 pages, 5 figures (5 eps files); published version

The quest for historically impactful science and technology provides invaluable insight into the innovation dynamics of human society, yet many studies are limited to qualitative and small-scale approaches. Here, we investigate scientific evolution through systematic analysis of a massive corpus of digitized English texts between 1800 and 2008. Our analysis reveals great predictability for long-prevailing scientific concepts based on the levels of their prior usage. Interestingly, once a threshold of early adoption rates is passed even slightly, scientific concepts can exhibit sudden leaps in their eventual lifetimes. We developed a mechanistic model to account for such results, indicating that slowly-but-commonly adopted science and technology surprisingly tend to have higher innate strength than fast-and-commonly adopted ones. The model prediction for disciplines other than science was also well verified. Our approach sheds light on unbiased and quantitative analysis of scientific evolution in society, and may provide a useful basis for policy-making., Comment: Supplementary material attached

The investigation of random walks is central to a variety of stochastic processes in physics, chemistry, and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability $p$, and stops to change the direction with $1-p$. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return., Comment: 4 pages, 2 figures

Recently, Kawaguchi and Nakayama (KN) [Phys. Rev. E {\bf 88}, 022147 (2013)] showed that the hidden entropy production associated with a coarse-graining procedure obeys the integral fluctuation theorem (IFT) if the original process does not involve any odd-parity variable that changes its sign under time reversal. This was interpreted as the evidence that odd-parity variables play an important role in the derivation of irreversible stochastic dynamics from time-reversible deterministic dynamics. In this Comment, we show that KN's approach is inadequate for describing the origin of irreversible stochastic dynamics, which calls into question whether odd-parity variables are required for the emergence of macroscopic irreversibility., Comment: 3 pages

Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process on modular networks with equal-sized finite communities and adjustable modularity. Using the analytical approach originally applied to clique-based random networks, we show that the system exhibits a bond-percolation type continuous phase transition for weak social reinforcement, whereas a discontinuous phase transition occurs for sufficiently strong social reinforcement. Our findings are numerically verified using the finite-size scaling analysis and the crossings of the bimodality coefficient., Comment: 8 pages, 8 figures (9 eps files); published version