^{1}

^{*}

^{2}

^{1}

^{2}

Edited by: Isamu Okada, Sōka University, Japan

Reviewed by: Francisco Welington Lima, Federal University of Piauí, Brazil; Reik Donner, Potsdam-Institut für Klimafolgenforschung (PIK), Germany

This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

As a method of analyzing and predicting social phenomena using social media as data, we present analyses based on the mathematical model of the hit phenomenon, which is one of the established models of sociophysics. The dynamics of the number of social media posts for movies, events, and a YouTube movie are explained. For entertainment topics, the direct communication strength, “D,” indicates the satisfaction of the current interested people or supporters, whereas the indirect communication strength, “P,” indicates the power to acquire a new support layer. Thus, this is effective not only for the analysis of entertainment and marketing strategy but also for burst analysis on the social media.

In the present age, where consumer behavior remains on record through the internet, the purchase and action records of numerous consumers are available. Analyses reveal that there are many cases, where it is possible to incorporate natural science methodology, such as physics, apart from conventional social science. Therefore, sociophysics, which studies society using physics, has developed significantly, of late [

As a sociophysics theory for analyzing society based on social media writing, a mathematical model for the hit phenomenon has been developed by Ishii et al. [

In the mathematical theory of the hit phenomenon, the effect of advertisement and the propagation of reputation and rumors by human communication are incorporated into the statistical physics of human dynamics. The propagation of information, reputation, and rumors has been studied in several works. For example, the SIR model is a simple mathematical model for epidemics [

The other famous model for the spread of information is the Bass model [

There are several problems in the above two models. In the SIR model, the spread of information is assumed to happen as communication between an adopter and non-adopter, and the mass media effects are not included. Moreover, the exchange of WOM communication is assumed to be proportional to the number of adopters. In the Bass model, it is assumed that once a consumer adopts a new product, he influences other non-adopters to adopt the product at all later times. In order to overcome these disadvantages, the Bass-SIR model was presented [

Another similar mathematical model for calculating the spread of information is the opinion dynamics model by Galam [_{i} = ±1, represents the choice of agents, I, with Yes = 1 and No = −1. Galam expressed the group conflict function, G, as

Our approach is different. Here, we use the mathematical model of the hit phenomenon [

The target of the mathematical model of the hit phenomenon is the “hits” phenomenon. The hits on social media are similar to the burst phenomenon, which is found to evolve through non-Poissonian dynamics [

There many investigations on the hit phenomenon, other than our works [

In this paper, after screening a movie/ drama and expanding the topic of the social incident using the mathematical model of the hit phenomenon, which is modified slightly from the original model of Ishii et al. [

The mathematical model of the hit phenomenon within a society is presented as a stochastic process of the interaction of human dynamics as in the many-body theory in physics [

Here, we introduce the intention of a person, “i,” as _{i}(_{i}(_{ij}_{ijk}, and _{i}_{p}. Considering the effect of direct communication, indirect communication, and the decline of the audience, we obtain the above equation for the mathematical model of the hit phenomenon. The advertisement and publicity effect for each person can be described as the mean field value of the random external force effect, <_{i}

Generally, information spreads through WOM, which sometimes has a significant effect on the spread of topics. The WOM effect can be distinguished into two types: WOM direct from friends and indirect WOM as rumors. We call the WOM effect between friends “_{ij}_{j}(_{j}(_{ij} is the coefficient of direct communication. Thus, we can describe the effect of direct communication as follows:

In this paper, the rumor is called _{jk}_{j}(_{k}(_{ijk}_{jk}_{j}(_{k}(_{ijk} is the coefficient of indirect effect to _{ijk} = _{ijk}_{jk}.

Equation (1) is for individuals; however, it is not convenient for analysis. Thus, we consider the ensemble average of the purchase intention of individuals, as follows:
_{i}

For the ensemble average of Equation (1), we obtain for the left-hand side,

For the fourth term, which is the random effect term, we consider that the random effect can be divided into two parts: the collective and individual effects:
_{i}(_{i}(^{2}_{ξ}, should be determined separately. Thus, if the number of media is one, the number of parameters that should be adjusted using real data is only three.

In the following calculation, coefficients

The advertisement and publicity effects are included in _{ξ}(

The advertisement and publicity effects are obtained from M Data Co. Ltd (

For reliability, we introduce the “R-factor” (reliability factor), which is well-known in the field of low-energy electron diffraction (LEED) [

For our purpose, we define the R-factor as follows:

In the real calculation, for adjusting parameters _{ξ},

Although parameters _{ξ}, _{ξ},

In this section, we present the analysis results of social-media posts, using the mathematical model of the hit phenomenon. The actual analysis of the direct and indirect communication are presented, which are critical in the mathematical model of the hit phenomenon. Other examples include Japanese group events, reputation of popular videos, and the results before the conclusion of event-ticket reservation.

In Figure

Calculated and observed data for Japanese Famous Food WOM of “Case A” in 2014/1/1–2014/12/31. The histograms are the daily total advertisements on TV (Green) and the internet (Purple). The blue curve corresponds to the observed number of daily Blog postings and the red curve is our calculation.

A movie example is shown in Figure

Calculated and observed data for the movie, “Case B” in Japan. The histogram indicates [ADV (s)] is the number of daily exposures on TV information about “Case B” in seconds. The blue curve corresponds to the observed number of daily Twitter postings and the red curve is our calculation.

In the analysis, we present an example, where indirect communication, which is a characteristic action in the mathematical model of the hit phenomenon, has significant effect. According to the mathematical-model analysis of the hit phenomenon, several movies show large indirect communication. The results for movies, “Case C” and “Case D,” are depicted in Figure

Reputation of films

Another typical break is “Case E,” a Japanese Tarent who became a hit in September 2016. Figure

Analysis of “Case E.” The red curve is our calculation using the model, the blue curve is the observed daily number of postings in blogs, in Japanese language, and the histograms are the daily total advertisements on TV (Orange) and the internet (Green).

Figure

Observed parameters “P,” “D,” and C_{adv} for TV, and C_{adv} for the internet, as per the calculations in of Figure

On the other hand, the direct communication strength, “

The following example is of the reputation of the Japanese Famous group, “Case F” for event. We analyzed the reputation, before and after event held in summer 2015, using the mathematical model of the hit phenomenon [

Analysis of the “Case F,” before and after event in Japan, in the summer of 2016.

Several Famous groups participated in this event and gathered a vast audience. Before event, the indirect communication strength, “P,” was large, whereas that of the direct communication, “D,” increased, after the event. Indirect communication shows the strength with which people, other than the interested people, are interested and direct communication indicates the interest of interested people. In the “Case F,” it appears that those who were interested, before the event, became core interested people of “Case F,” after the event.

In hit contents, indirect communication increases after publication. The “Case E” epidemic is consistent with the increase in break and indirect communication. Hence, the reputation breaks, when indirect communication increases rapidly. Additionally, convergence occurs, when indirect communication decreases.

On the other hand, the strength of direct communication shows the enthusiasm of core interested people but does not imply that there are numerous core interested people. The increase in direct communication, after the event at “Case F,” indicates an increase in the number of enthusiastic interested people. However, the fact that there is no increase in direct communication in the “Case E” indicates that “Case E” is only a topicality and there is no increase in “Case E” 's core interested people.

Using the mathematical model of the hit phenomenon, we analyzed the reputations of a movie, a YouTube movie that became a global topic, and the popular event trend in Japanese. Important factors in the mathematical model of the hit phenomenon include the direct communication strength, “D,” the indirect communication strength, “P,” and the coefficient, “C,” of the media response strength.

The results indicate that for the reputation of “Case E” 's movie, the indirect communication strength, “P,” increased, with the world-wide reputation. “P” tends to be large, for hit movies also. Therefore, the indirect communication strength, “P,” was found to be related to the wide propagation of the topic.

On the other hand, the comparison of the reputation, before and after the group event, shows that the direct communication strength, “D,” appears to be the satisfaction level of the support layer.

Hence, “D” indicates whether the current support layer is satisfied, and P indicates the power to acquire a new support layer. This can be said to be effective not only for the analysis of entertainment and marketing strategy but also for political election analysis.

As the mathematical model of the hit phenomenon is a theory of sociophysics, it is possible to describe how a person in society causes interest, and follow the time change of this interest. Therefore, expansion is easy. For example, to determine which among two competing topics shows interest, a theory has already been proposed, which generates two mathematical models of the hit phenomenon simultaneously [

In addition, it is possible to solve the influence of social media on the market share of products by the simultaneous theory of the market share, in economics, and the mathematical model of the hit phenomenon [

The hits on social media are similar to the burst phenomenon, which evolves through non-Poissonian dynamics.

In this paper, using the mathematical model of the hit phenomenon, which is one of the theories of sociophysics, the rise of topics and convergence in society were calculated, even for movies, and events, and the reputation of a YouTube movie that became a global topic. This establishes that the mathematical model of the hit phenomenon can explain the spread of topics as a social phenomenon. Using this model, it can be determined whether the topic is spread beyond clusters by social dynamics; if the indirect communication is considerable, it becomes a hit. Additionally, it is possible to quantitatively analyze the propagation mechanism of popular topics, using the mathematical model of the hit phenomenon. It may be possible to clarify the mechanism for information propagation as a social epidemic phenomenon, according to the utilization of the corresponding parameter.

AI consider the model and select the target. YK do actual computation.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.