Human mobility description by physical analogy of electric circuit network based on GPS data.

Human mobility in an urban area is complicated; the origins, destinations, and transportation modes of each person differ. The quantitative description of urban human mobility has recently attracted the attention of researchers, and it highly related to urban science problems. Herein, combined with physics inspiration, we introduce a revised electric circuit model (RECM) in which moving people are regarded as charged particles and analogical concepts of electromagnetism such as human conductivity and human potential enable us to capture the characteristics of urban human mobility. We introduce the unit system, ensure the uniqueness of the calculation result, and reduce the computation cost of the algorithm to 1/10,000 compared with the original ECM, making the model more universal and easier to use. We compared features including human conductivity and potential between different major cities in Japan to show our improvement of the universality and the application range of the model. Furthermore, based on inspiration of physics, we propose a route generation model (RGM) to simulate a human flow pattern that automatically determines suitable routes between a given origin and destination as a source and sink, respectively. These discoveries are expected to lead to new approaches to the solution of urban science problems.

A Markov network approach for reproducing purchase behaviours observed in convenience stores.

The convenience store industry in Japan holds immense significance, making a thorough comprehension of customer purchase behaviour invaluable for companies aiming to gain insights into their customer base. In this paper, we propose a novel application of a Markov network model to simulate purchases guided by stopping probabilities calculated from real data. Each node in the Markov network represents different product categories available for purchase. Additionally, we introduce the concept of a "driving force," quantifying the influence of purchasing product A on the likelihood of purchasing product B, compared to random purchasing. For instance, our analysis reveals that the inclusion of nutrient bars in a purchase set leads to, on average, a 13% reduction in tobacco purchases compared to random patterns. To validate our approach, we compare the simulated macro-level purchase behaviours with real point of Sale (POS) data obtained from a prominent convenience store giant, 7-Eleven. The dataset is comprised of roughly 54 million receipts, in which we focus on the product categories existing in this dataset rather than individual products. Our model successfully replicates the purchase size distribution for 99.9% of all purchases and the purchase counts across various product categories, demonstrating its efficacy in capturing broad purchase patterns.

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws.

We develop a single two-layered model framework that captures and replicates both the statistical properties of the network as well as those of the intrinsic quantities of the agents. Our model framework consists of two distinct yet connected elements that were previously only studied in isolation, namely methods related to temporal network structures and those associated with money transport flows. Within this context, the network structure emerges from the first layer and its topological structure is transferred to the second layer associated with the money transactions. In this manner, we can explain how the micro-level dynamics of the agents within the network lead to the exogenous manifestation of the aggregated system statistical data en-wrapping the very same agents within the system. This is done by capturing the essential dynamics of collective motion in complex networks that enable the simultaneous emergence of tent-shaped distributions in growth rates within the agents, together with the emergence of scaling properties within the network in the study. We can validate the model framework and dynamics by applying these to the context of the real-world inter-firm trading network of firms in Japan and comparing the results of the statistical distributions at both network and agent levels in a temporal manner. In particular, we compare our results to the fundamental quantities supporting the seven empirical laws observed in data: the degree distribution, the mean degree growth rate over time, the age distribution of the firms, the preferential attachment, the sales distribution in steady states, their growth rates, their scaling relations generated by the model. We find these results to be nearly identical to the real-world data. The framework has the potential to be transformed into a forecasting tool to support decision-makers on financial and prudential policies.

Scale-dependent power law properties in hashtag usage time series of Weibo.

We analyze the time series of hashtag numbers of social media data. We observe that the usage distribution of hashtags is characterized by a fat-tailed distribution with a size-dependent power law exponent and we find that there is a clear dependency between the growth rate distributions of hashtags and size of hashtags usage. We propose a generalized random multiplicative process model with a theory that explains the size dependency of the fat-tailed distribution. Numerical simulations show that our model reproduces these size-dependent properties nicely. We expect that our model is useful for understanding the mechanism of fat-tailed distributions in various fields of science and technology.

Extraction of Important Factors in a High-Dimensional Data Space: An Application for High-Growth Firms.

We introduce a new non-black-box method of extracting multiple areas in a high-dimensional big data space where data points that satisfy specific conditions are highly concentrated. First, we extract one-dimensional areas where the data that satisfy specific conditions are mostly gathered by using the Bayesian method. Second, we construct higher-dimensional areas where the densities of focused data points are higher than the simple combination of the results for one dimension, and then we verify the results through data validation. Third, we apply this method to estimate the set of significant factors shared in successful firms with growth rates in sales at the top 1% level using 156-dimensional data of corporate financial reports for 12 years containing about 320,000 firms. We also categorize high-growth firms into 15 groups of different sets of factors.

Direct modelling from GPS data reveals daily-activity-dependency of effective reproduction number in COVID-19 pandemic.

During the COVID-19 pandemic, governments faced difficulties in implementing mobility restriction measures, as no clear quantitative relationship between human mobility and infection spread in large cities is known. We developed a model that enables quantitative estimations of the infection risk for individual places and activities by using smartphone GPS data for the Tokyo metropolitan area. The effective reproduction number is directly calculated from the number of infectious social contacts defined by the square of the population density at each location. The difference in the infection rate of daily activities is considered, where the 'stay-out' activity, staying at someplace neither home nor workplace, is more than 28 times larger than other activities. Also, the contribution to the infection strongly depends on location. We imply that the effective reproduction number is sufficiently suppressed if the highest-risk locations or activities are restricted. We also discuss the effects of the Delta variant and vaccination.

Potential fields and fluctuation-dissipation relations derived from human flow in urban areas modeled by a network of electric circuits.

Owing to the big data the extension of physical laws on nonmaterial has seen numerous successes, and human mobility is one of the scientific frontier topics. Recent GPS technology has made it possible to trace detailed trajectories of millions of people, macroscopic approaches such as the gravity law for human flow between cities and microscopic approaches of individual origin-destination distributions are attracting much attention. However, we need a more general basic model with wide applicability to realize traffic forecasting and urban planning of metropolis fully utilizing the GPS data. Here, based on a novel idea of treating moving people as charged particles, we introduce a method to map macroscopic human flows into currents on an imaginary electric circuit defined over a metropolitan area. Conductance is found to be nearly proportional to the maximum current in each location and synchronized human flows in the morning and evening are well described by the temporal changes of electric potential. Surprisingly, the famous fluctuation-dissipation theorem holds, namely, the variances of currents are proportional to the conductivities akin to an ordinary material.

Classification of endogenous and exogenous bursts in collective emotions based on Weibo comments during COVID-19.

Bursts and collective emotion have been widely studied in social physics field where researchers use mathematical models to understand human social dynamics. However, few researches recognize and separately analyze the internal and external influence on burst behaviors. To bridge this gap, we introduce a non-parametric approach to classify an interevent time series into five scenarios: random arrival, endogenous burst, endogenous non-burst, exogenous burst and exogenous non-burst. In order to process large-scale social media data, we first segment the interevent time series into sections by detecting change points. Then we use the rule-based algorithm to classify the time series based on its distribution. To validate our model, we analyze 27.2 million COVID-19 related comments collected from Chinese social media between January to October 2020. We adopt the emotion category called Profile of Mood States which consists of six emotions: Anger, Depression, Fatigue, Vigor, Tension and Confusion. This enables us to compare the burst features of different collective emotions during the COVID-19 period. The burst detection and classification approach introduced in this paper can also be applied to analyzing other complex systems, including but not limited to social media, financial market and signal processing.

Analysis of Individual High-Frequency Traders' Buy-Sell Order Strategy Based on Multivariate Hawkes Process.

Traders who instantly react to changes in the financial market and place orders in milliseconds are called high-frequency traders (HFTs). HFTs have recently become more prevalent and attracting attention in the study of market microstructures. In this study, we used data to track the order history of individual HFTs in the USD/JPY forex market to reveal how individual HFTs interact with the order book and what strategies they use to place their limit orders. Specifically, we introduced an 8-dimensional multivariate Hawkes process that included the excitations due to the occurrence of limit orders, cancel orders, and executions in the order book change, and performed maximum likelihood estimations of the limit order processes for 134 HFTs. As a result, we found that the limit order generation processes of 104 of the 134 HFTs were modeled by a multivariate Hawkes process. In this analysis of the EBS market, the HFTs whose strategies were modeled by the Hawkes process were categorized into three groups according to their excitation mechanisms: (1) those excited by executions; (2) those that were excited by the occurrences or cancellations of limit orders; and (3) those that were excited by their own orders.

Data-driven stochastic simulation leading to the allometric scaling laws in complex systems.

We propose a data-driven stochastic method that allows the simulation of a complex system's long-term evolution. Given a large amount of historical data on trajectories in a multi-dimensional phase space, our method simulates the time evolution of a system based on a random selection of partial trajectories in the data without detailed knowledge of the system dynamics. We apply this method to a large data set of time evolution of approximately one million business firms for a quarter century. Accordingly, from simulations starting from arbitrary initial conditions, we obtain a stationary distribution in three-dimensional log-size phase space, which satisfies the allometric scaling laws of three variables. Furthermore, universal distributions of fluctuation around the scaling relations are consistent with the empirical data.

Universal scaling of human flow remain unchanged during the COVID-19 pandemic.

To prevent the spread of the COVID-19 pandemic, governments in various countries have severely restricted the movement of people. The large amount of detailed human location data obtained from mobile phone users is useful for understanding the change of flow patterns of people under the effect of pandemic. In this paper, we observe the synchronized human flow during the COVID-19 pandemic using Global Positioning System data of about 1 million people obtained from mobile phone users. We apply the drainage basin analysis method which we introduced earlier for characterization of macroscopic human flow patterns to observe the effect of the spreading pandemic. Before the pandemic the afternoon basin size distribution has been approximated by an exponential distribution, however, the distribution of Tokyo and Sapporo, which were most affected by the first wave of COVID-19, deviated significantly from the exponential distribution. On the other hand, during the morning rush hour, the scaling law holds universally, i.e., in all cities, even though the number of moving people in the basin has decreased significantly. The fact that these scaling laws, which are closely related to the three-dimensionality structure of the city and the fractal structure of the transportation network, have not changed indicates that the macroscopic human flow features are determined mainly by the means of transport and the basic structure of cities which are invariant of the pandemic.

Sigma-Pi Structure with Bernoulli Random Variables: Power-Law Bounds for Probability Distributions and Growth Models with Interdependent Entities.

The Sigma-Pi structure investigated in this work consists of the sum of products of an increasing number of identically distributed random variables. It appears in stochastic processes with random coefficients and also in models of growth of entities such as business firms and cities. We study the Sigma-Pi structure with Bernoulli random variables and find that its probability distribution is always bounded from below by a power-law function regardless of whether the random variables are mutually independent or duplicated. In particular, we investigate the case in which the asymptotic probability distribution has always upper and lower power-law bounds with the same tail-index, which depends on the parameters of the distribution of the random variables. We illustrate the Sigma-Pi structure in the context of a simple growth model with successively born entities growing according to a stochastic proportional growth law, taking both Bernoulli, confirming the theoretical results, and half-normal random variables, for which the numerical results can be rationalized using insights from the Bernoulli case. We analyze the interdependence among entities represented by the product terms within the Sigma-Pi structure, the possible presence of memory in growth factors, and the contribution of each product term to the whole Sigma-Pi structure. We highlight the influence of the degree of interdependence among entities in the number of terms that effectively contribute to the total sum of sizes, reaching the limiting case of a single term dominating extreme values of the Sigma-Pi structure when all entities grow independently.

Robust Characterization of Multidimensional Scaling Relations between Size Measures for Business Firms.

Although the sizes of business firms have been a subject of intensive research, the definition of a "size" of a firm remains unclear. In this study, we empirically characterize in detail the scaling relations between size measures of business firms, analyzing them based on allometric scaling. Using a large dataset of Japanese firms that tracked approximately one million firms annually for two decades (1994-2015), we examined up to the trivariate relations between corporate size measures: annual sales, capital stock, total assets, and numbers of employees and trading partners. The data were examined using a multivariate generalization of a previously proposed method for analyzing bivariate scalings. We found that relations between measures other than the capital stock are marked by allometric scaling relations. Power-law exponents for scalings and distributions of multiple firm size measures were mostly robust throughout the years but had fluctuations that appeared to correlate with national economic conditions. We established theoretical relations between the exponents. We expect these results to allow direct estimation of the effects of using alternative size measures of business firms in regression analyses, to facilitate the modeling of firms, and to enhance the current theoretical understanding of complex systems.

Universal scaling laws of collective human flow patterns in urban regions.

Detail observation of human locations became available recently by the development of information technology such as mobile phones with GPS (Global Positioning System). We analyzed temporal changes of global human flow patterns in urban regions based on mobile phones' GPS data in 9 large cities in Japan. By applying a new concept of drainage basins in analogous to river flow patterns, we discovered several universal scaling relations. These include, the number of moving people in a drainage basin of diameter L is proportional to [Formula: see text] in the morning rush hour, which is surprisingly different from reasonable intuition of proportionality to the 2 dimensional area, [Formula: see text]. We show that this unexpected 3 dimensional feature is related to the strong attraction of the city center to become a 3 dimensional structure due skyscrapers.

Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach.

Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.

Metabolic Dynamics of Ecosystems Realizing Steady Log-Uniform Distributions: The Case of Commodities in Shops.

From the viewpoint of statistical physics, ecosystems in the real world are very attractive targets of research as examples of far-from thermal equilibrium systems where various kinds of components are coming in and out continuously while keeping the whole systems quasi-stationary. As a fortunate example of a fully-observable ecosystem, we analyzed the comprehensive data of convenience stores where approximately 5% of the commodity species is replaced by new ones daily. The share of stores for each species fluctuates significantly; however, the entire distribution of shares is fairly stationary and follows the log-uniform distribution, that is, the power law distribution with exponent 0. We introduce an empirical time evolution model of shares and firstly deduce that the key mechanism of realizing this stationary distribution is random multiplicative diffusion in finite size spaces. Our model based on the general stochastic process is expected to be applicable to various dynamic systems, especially complex systems with highly nonlinear interactions.

Segmentation of time series in up- and down-trends using the epsilon-tau procedure with application to USD/JPY foreign exchange market data.

We propose the epsilon-tau procedure to determine up- and down-trends in a time series, working as a tool for its segmentation. The method denomination reflects the use of a tolerance level ε for the series values and a patience level τ in the time axis to delimit the trends. We first illustrate the procedure in discrete random walks, deriving the exact probability distributions of trend lengths and trend amplitudes, and then apply it to segment and analyze the trends of U.S. dollar (USD)/Japanese yen (JPY) market time series from 2015 to 2018. Besides studying the statistics of trend lengths and amplitudes, we investigate the internal structure of the trends by grouping trends with similar shapes and selecting clusters of shapes that rarely occur in the randomized data. Particularly, we identify a set of down-trends presenting similar sharp appreciation of the yen that are associated with exceptional events such as the Brexit Referendum in 2016.

The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets.

Foreign exchange rates movements exhibit significant cross-correlations even on very short time-scales. The effect of these statistical relationships become evident during extreme market events, such as flash crashes. Although a deep understanding of cross-currency correlations would be clearly beneficial for conceiving more stable and safer foreign exchange markets, the microscopic origins of these interdependencies have not been extensively investigated. This paper introduces an agent-based model which describes the emergence of cross-currency correlations from the interactions between market makers and an arbitrager. The model qualitatively replicates the time-scale vs. cross-correlation diagrams observed in real trading data, suggesting that triangular arbitrage plays a primary role in the entanglement of the dynamics of different foreign exchange rates. Furthermore, the model shows how the features of the cross-correlation function between two foreign exchange rates, such as its sign and value, emerge from the interplay between triangular arbitrage and trend-following strategies. In particular, the interaction of these trading strategies favors certain combinations of price trend signs across markets, thus altering the probability of observing two foreign exchange rates drifting in the same or opposite direction. Ultimately, this entangles the dynamics of foreign exchange rate pairs, leading to cross-correlation functions that resemble those observed in real trading data.

Dynamics of essential interaction between firms on financial reports.

Companies tend to publish financial reports in order to articulate strategies, disclose key performance measurements as well as summarise the complex relationships with external stakeholders as a result of their business activities. Therefore, any major changes to business models or key relationships will be naturally reflected within these documents, albeit in an unstructured manner. In this research, we automatically scan through a large and rich database, containing over 400,000 reports of companies in Japan, in order to generate structured sets of data that capture the essential features, interactions and resulting relationships among these firms. In doing so, we generate a citation type network where we empirically observe that node creation, annihilation and link rewiring to be the dominant processes driving its structure and formation. These processes prompt the network to rapidly evolve, with over a quarter of the interactions between firms being altered within every single calendar year. In order to confirm our empirical observations and to highlight and replicate the essential dynamics of each of the three processes separately, we borrow inspiration from ecosystems and evolutionary theory. Specifically, we construct a network evolutionary model where we adapt and incorporate the concept of fitness within our numerical analysis to be a proxy real measure of a company's importance. By making use of parameters estimated from the real data, we find that our model reliably replicates degree distributions and motif formations of the citation network, and therefore reproducing both macro as well as micro, local level, structural features. This is done with the exception of the real frequency of bidirectional links, which are primarily formed as a result of an entirely separate and distinct process, namely the equity investments from one company into another.