Pub Date : 2021-11-01DOI: 10.1080/0022250X.2021.1981311
Peng Lu, Dianhan Chen
ABSTRACT The life cycle pattern is pervasive for both natural and social sciences, from human behaviors to social systems. Based on the life cycle model of collective actions, the man–land relationship governs the rise and fall cycles, namely dynastic cycles. We combine agent-based modeling, systemic dynamics, and numerical simulations, to build the life cycle model of empires. It aims to investigate the rise and fall process of 18 major dynasties (empires) in history of China, from BC 221 to AD 1912. The core aim is to find optimal solutions, which achieve the best matching between simulations and real history. According to our algorithm, the optimal solutions can be obtained, when we have the minimal span differences (gaps) between simulated and real empires. First, we traverse all related parameters, and select simulations with 18 empires. Second, we select the cases with the total ticks between 2122 and 2132 years (ticks). Third, we select cases whose differences (gaps) are within 20 years. Finally, we obtain three optimal solutions (combinations of parameters) whose validity (100 simulations) and robustness (1000 simulations) have been checked. It seems that our life cycle model has achieved the best fitness to real empires in the history of China. For distributive matching of durations (spans), both discrete and continuous forms can be matched. Besides, the simulate and real durations can be matched as well, under counterfactual inferences of 16–17, 18 & 19–20 pairs. Based on our model, the whole history process of China can be back-calculated. Therefore, it seems that the trend of human history (society) may be an automatic process, which cannot be altered by man’s will.
{"title":"The life cycle model of chinese empire dynamics (221 BC–1912 AD)","authors":"Peng Lu, Dianhan Chen","doi":"10.1080/0022250X.2021.1981311","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1981311","url":null,"abstract":"ABSTRACT The life cycle pattern is pervasive for both natural and social sciences, from human behaviors to social systems. Based on the life cycle model of collective actions, the man–land relationship governs the rise and fall cycles, namely dynastic cycles. We combine agent-based modeling, systemic dynamics, and numerical simulations, to build the life cycle model of empires. It aims to investigate the rise and fall process of 18 major dynasties (empires) in history of China, from BC 221 to AD 1912. The core aim is to find optimal solutions, which achieve the best matching between simulations and real history. According to our algorithm, the optimal solutions can be obtained, when we have the minimal span differences (gaps) between simulated and real empires. First, we traverse all related parameters, and select simulations with 18 empires. Second, we select the cases with the total ticks between 2122 and 2132 years (ticks). Third, we select cases whose differences (gaps) are within 20 years. Finally, we obtain three optimal solutions (combinations of parameters) whose validity (100 simulations) and robustness (1000 simulations) have been checked. It seems that our life cycle model has achieved the best fitness to real empires in the history of China. For distributive matching of durations (spans), both discrete and continuous forms can be matched. Besides, the simulate and real durations can be matched as well, under counterfactual inferences of 16–17, 18 & 19–20 pairs. Based on our model, the whole history process of China can be back-calculated. Therefore, it seems that the trend of human history (society) may be an automatic process, which cannot be altered by man’s will.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46181589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1080/0022250X.2021.1988946
Andreas Tutić
ABSTRACT We study the evolution of cooperation in the Volunteer’s Dilemma using the stochastic Moran process, which models a birth/death dynamic on a finite population. Each period one player dies and is replaced by a copy of a player. Players are either matched in pairs or matched in groups to play the Volunteer’s Dilemma and their payoffs affect their probabilities of reproduction. This set-up allows to study how selection pressure, initial number of cooperators as well as the size of the groups playing the Volunteer’s Dilemma influence the evolution of cooperation. Our main result is that given sufficiently high selection pressure an equilibrium of full cooperation is certain in pairwise interactions but an impossibility in group interactions.
{"title":"Stochastic evolutionary dynamics in the Volunteer’s Dilemma","authors":"Andreas Tutić","doi":"10.1080/0022250X.2021.1988946","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1988946","url":null,"abstract":"ABSTRACT We study the evolution of cooperation in the Volunteer’s Dilemma using the stochastic Moran process, which models a birth/death dynamic on a finite population. Each period one player dies and is replaced by a copy of a player. Players are either matched in pairs or matched in groups to play the Volunteer’s Dilemma and their payoffs affect their probabilities of reproduction. This set-up allows to study how selection pressure, initial number of cooperators as well as the size of the groups playing the Volunteer’s Dilemma influence the evolution of cooperation. Our main result is that given sufficiently high selection pressure an equilibrium of full cooperation is certain in pairwise interactions but an impossibility in group interactions.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49072327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-05DOI: 10.1080/0022250X.2021.1973456
E. Dil, E. Dil
ABSTRACT In order to model the income data, the physical distributions of Fermi-Dirac and Bose-Einstein families have already been proposed in the literature. In this study, we generalize Fermi-Dirac distribution by using a q,p-deformed version of Fermi-Dirac distribution which provides the advantage of working with flexible free q, p deformation parameters as the regression parameters for modeling the income data. We analyze the accuracy of the generalized version, q,p-deformed Fermi-Dirac distribution, on describing the data of income share held by quintiles for countries, and household income for the states of U.S.A. in 2018. We also use minimization routine for modeling the data which leads to the best fit parameters for the deformation parameters q and p. Subsequently, we plot the fitted q,p-deformed Fermi-Dirac distribution as income distribution with the obtained deformation parameters, then find the statistical confidence values from the fitted curve. We figure out that our model properly describes the income data for the systems experiencing a high level of income inequality, and also values are correlated with the Gini index for those of considered systems.
{"title":"Sociophysics of income distributions modeled by deformed fermi-dirac distributions","authors":"E. Dil, E. Dil","doi":"10.1080/0022250X.2021.1973456","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1973456","url":null,"abstract":"ABSTRACT In order to model the income data, the physical distributions of Fermi-Dirac and Bose-Einstein families have already been proposed in the literature. In this study, we generalize Fermi-Dirac distribution by using a q,p-deformed version of Fermi-Dirac distribution which provides the advantage of working with flexible free q, p deformation parameters as the regression parameters for modeling the income data. We analyze the accuracy of the generalized version, q,p-deformed Fermi-Dirac distribution, on describing the data of income share held by quintiles for countries, and household income for the states of U.S.A. in 2018. We also use minimization routine for modeling the data which leads to the best fit parameters for the deformation parameters q and p. Subsequently, we plot the fitted q,p-deformed Fermi-Dirac distribution as income distribution with the obtained deformation parameters, then find the statistical confidence values from the fitted curve. We figure out that our model properly describes the income data for the systems experiencing a high level of income inequality, and also values are correlated with the Gini index for those of considered systems.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49103316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-08DOI: 10.1080/0022250X.2021.1981310
E. Iacomini, P. Vellucci
ABSTRACT In recent months, the figure of Greta Thunberg and the theme of climate changings quickly became the focus of the debate. This has led to a polarization effect in opinion forming about the climate subject. Starting from the analysis of this phenomenon, we develop an opinion dynamics model in which several types of contrarian agents are considered. Each agent is supposed to have an opinion on several topics related to each other; thus, the opinions being formed on these topics are also mutually dependent. The aim of the paper is to investigate the indirect effects of contrarian agents on the collective opinion about these topics. Several numerical tests are presented in order to highlight the main features of the model.
{"title":"Contrarian effect in opinion forming: Insights from Greta Thunberg phenomenon","authors":"E. Iacomini, P. Vellucci","doi":"10.1080/0022250X.2021.1981310","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1981310","url":null,"abstract":"ABSTRACT In recent months, the figure of Greta Thunberg and the theme of climate changings quickly became the focus of the debate. This has led to a polarization effect in opinion forming about the climate subject. Starting from the analysis of this phenomenon, we develop an opinion dynamics model in which several types of contrarian agents are considered. Each agent is supposed to have an opinion on several topics related to each other; thus, the opinions being formed on these topics are also mutually dependent. The aim of the paper is to investigate the indirect effects of contrarian agents on the collective opinion about these topics. Several numerical tests are presented in order to highlight the main features of the model.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45849029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-17eCollection Date: 2022-01-01DOI: 10.1080/0022250X.2021.1929968
Tanzhe Tang, Amineh Ghorbani, Caspar G Chorus
In the field of opinion dynamics, the hiding of opinions is routinely modeled as staying silent. However, staying silent is not always feasible. In situations where opinions are indirectly expressed by one's observable actions, people may however try to hide their opinions via a more complex and intelligent strategy called obfuscation, which minimizes the information disclosed to others. This study proposes a formal opinion dynamics model to study the hitherto unexplored effect of obfuscation on public opinion formation based on the recently developed Action-Opinion Inference Model. For illustration purposes, we use our model to simulate two cases with different levels of complexity, highlighting that the effect of obfuscation largely depends on the subtle relations between actions and opinions.
{"title":"Hiding opinions by minimizing disclosed information: an obfuscation-based opinion dynamics model.","authors":"Tanzhe Tang, Amineh Ghorbani, Caspar G Chorus","doi":"10.1080/0022250X.2021.1929968","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1929968","url":null,"abstract":"<p><p>In the field of opinion dynamics, the hiding of opinions is routinely modeled as staying silent. However, staying silent is not always feasible. In situations where opinions are indirectly expressed by one's observable actions, people may however try to hide their opinions via a more complex and intelligent strategy called obfuscation, which minimizes the information disclosed to others. This study proposes a formal opinion dynamics model to study the hitherto unexplored effect of obfuscation on public opinion formation based on the recently developed Action-Opinion Inference Model. For illustration purposes, we use our model to simulate two cases with different levels of complexity, highlighting that the effect of obfuscation largely depends on the subtle relations between actions and opinions.</p>","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ftp.ncbi.nlm.nih.gov/pub/pmc/oa_pdf/62/1f/GMAS_46_1929968.PMC9487867.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33482572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-27DOI: 10.1080/0022250X.2021.1956918
S. Westenberger
ABSTRACT What causes turnover on the Billboard charts? The neutral model of cultural evolution, which assumes that taste is transmitted via an unbiased copying process, provides precise predictions regarding expected popularity distributions and turnover within a popularity-ranked list. Recent advances in this line make it possible to characterize the likelihood of music taste transmission mechanisms by investigating departures of observed turnover rates from neutral model predictions. Here, I bias the neutral model to investigate four alternative conceptions of individual music taste transmission (song quality, individual status, social network, and anticonformist) and use agent-based simulations to examine the impact on turnover. I then compare modeled with empirical turnover data from the Billboard Hot 100 over the period from 1958 to 2021 and find that observed turnover patterns are reproduced only in an anticonformist model simulating the systematic rejection of the most popular songs. This finding was unexpected and challenges the notion of a generalized “preference for the popular.” Overall, this study contributes to ongoing debates regarding the mechanisms involved in the transmission of taste and the mechanics of fashion change.
摘要：是什么导致了公告牌排行榜上的营业额？文化进化的中性模型假设品味是通过无偏见的复制过程传播的，它提供了关于受欢迎程度排名列表中预期受欢迎程度分布和营业额的精确预测。这一领域的最新进展使得通过研究观察到的更替率与中性模型预测的偏差来表征音乐品味传播机制的可能性成为可能。在这里，我偏向中性模型来研究个人音乐品味传播的四个替代概念（歌曲质量、个人地位、社交网络和反信息主义者），并使用基于代理的模拟来检验对营业额的影响。然后，我将1958年至2021年期间Billboard Hot 100的建模营业额数据与实证营业额数据进行了比较，发现观察到的营业额模式仅在模拟对最受欢迎歌曲的系统拒绝的反信息主义模型中再现。这一发现出乎意料，并挑战了普遍“偏爱大众”的概念。总的来说，这项研究有助于就品味传递机制和时尚变化机制进行持续的辩论。
{"title":"Drifting to the top? Disentangling mechanisms influencing the turnover rate of popular music","authors":"S. Westenberger","doi":"10.1080/0022250X.2021.1956918","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1956918","url":null,"abstract":"ABSTRACT What causes turnover on the Billboard charts? The neutral model of cultural evolution, which assumes that taste is transmitted via an unbiased copying process, provides precise predictions regarding expected popularity distributions and turnover within a popularity-ranked list. Recent advances in this line make it possible to characterize the likelihood of music taste transmission mechanisms by investigating departures of observed turnover rates from neutral model predictions. Here, I bias the neutral model to investigate four alternative conceptions of individual music taste transmission (song quality, individual status, social network, and anticonformist) and use agent-based simulations to examine the impact on turnover. I then compare modeled with empirical turnover data from the Billboard Hot 100 over the period from 1958 to 2021 and find that observed turnover patterns are reproduced only in an anticonformist model simulating the systematic rejection of the most popular songs. This finding was unexpected and challenges the notion of a generalized “preference for the popular.” Overall, this study contributes to ongoing debates regarding the mechanisms involved in the transmission of taste and the mechanics of fashion change.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2021.1956918","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43153590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-06DOI: 10.1080/0022250X.2021.1941002
Avneet Kaur, M. Sadhwani, S Z Abbas
ABSTRACT This paper intends to simulate a simple artificial society divided into two populations: criminal and non-criminal. The time evolution of the system is modeled using a set of differential equations, borrowing relevant features from the prey-predator, epidemic spread, and harvesting models. Each population can switch type upon interaction. The stability and equilibrium points of this system are examined, concluding that harvesting and interaction rates play an important role in the evolution of the system toward different stable equilibria between populations, which eventually coalesce into one. The results indicate that as long as the harvesting and conversion rates remain sufficiently small, the criminal population thrives. However, when either of the two crosses a certain value, the criminal population becomes extinct.
{"title":"Law Enforcement: The key to a Crime-free Society","authors":"Avneet Kaur, M. Sadhwani, S Z Abbas","doi":"10.1080/0022250X.2021.1941002","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1941002","url":null,"abstract":"ABSTRACT This paper intends to simulate a simple artificial society divided into two populations: criminal and non-criminal. The time evolution of the system is modeled using a set of differential equations, borrowing relevant features from the prey-predator, epidemic spread, and harvesting models. Each population can switch type upon interaction. The stability and equilibrium points of this system are examined, concluding that harvesting and interaction rates play an important role in the evolution of the system toward different stable equilibria between populations, which eventually coalesce into one. The results indicate that as long as the harvesting and conversion rates remain sufficiently small, the criminal population thrives. However, when either of the two crosses a certain value, the criminal population becomes extinct.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2021.1941002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43641049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-06DOI: 10.1080/0022250X.2021.1931173
H. Ashi, Raneah Al-Maalwi, Sarah Al-Sheikh
ABSTRACT One problem that has become a concern for governments around the world is unemployment. We illustrate the problem using a nonlinear system of differential equations considering three dynamical variables: the number of unemployed people, the number of employees and the number of available vacancies. We find that the system possesses one positive equilibrium point which is locally and globally stable under certain conditions. We identify the employment rate and the rate of creating new vacancies that is required to reach the unemployment rate of 7% in agreement with the efforts of governments to attain low unemployment levels.keywords: Unemployment; Stability; Routh Hurwitz; Lyapunov function; Numerical simulation
{"title":"Study of the unemployment problem by mathematical modeling: Predictions and controls","authors":"H. Ashi, Raneah Al-Maalwi, Sarah Al-Sheikh","doi":"10.1080/0022250X.2021.1931173","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1931173","url":null,"abstract":"ABSTRACT One problem that has become a concern for governments around the world is unemployment. We illustrate the problem using a nonlinear system of differential equations considering three dynamical variables: the number of unemployed people, the number of employees and the number of available vacancies. We find that the system possesses one positive equilibrium point which is locally and globally stable under certain conditions. We identify the employment rate and the rate of creating new vacancies that is required to reach the unemployment rate of 7% in agreement with the efforts of governments to attain low unemployment levels.keywords: Unemployment; Stability; Routh Hurwitz; Lyapunov function; Numerical simulation","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2021.1931173","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49327020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-04DOI: 10.1080/0022250X.2021.1972417
Atsushi Ishida
ABSTRACT People’s evaluation of the relative position of their income is not as accurate as the relative income hypothesis assumes. It is observed from empirical survey data that income evaluation is concentrated in the middle. We develop a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation. We conduct theoretical analysis and empirical parameter estimation using Bayesian statistical modeling. The theoretical analysis shows that the centralization of income evaluation distribution occurs when the subjective reference distribution is more dispersed than the objective distribution. Empirical analysis using Japanese data from 2015 shows that the relationship between subjective and objective distributions differed depending on social categories with different social experiences. Women had a more ambiguous distribution than men. Among men, those aged 45–54 had a subjective distribution closest to the objective distribution. Thus, the subjective reference income distributions that potentially define people’s evaluation of their income and their differences based on social category were only clarified by constructing the model.
{"title":"A model of income evaluation: income comparison on subjective reference income distribution","authors":"Atsushi Ishida","doi":"10.1080/0022250X.2021.1972417","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1972417","url":null,"abstract":"ABSTRACT People’s evaluation of the relative position of their income is not as accurate as the relative income hypothesis assumes. It is observed from empirical survey data that income evaluation is concentrated in the middle. We develop a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation. We conduct theoretical analysis and empirical parameter estimation using Bayesian statistical modeling. The theoretical analysis shows that the centralization of income evaluation distribution occurs when the subjective reference distribution is more dispersed than the objective distribution. Empirical analysis using Japanese data from 2015 shows that the relationship between subjective and objective distributions differed depending on social categories with different social experiences. Women had a more ambiguous distribution than men. Among men, those aged 45–54 had a subjective distribution closest to the objective distribution. Thus, the subjective reference income distributions that potentially define people’s evaluation of their income and their differences based on social category were only clarified by constructing the model.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45150422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-03DOI: 10.1080/0022250X.2021.1917928
B. Cornwell, Jake Burchard
Theorem 3.1 and Corollary 3.1.1 in the article are false. While Theorem 3.1 correctly states that κ N ð Þ � k, the reverse inequality is not necessarily true (a family of counterexamples can be produced to show this). It should be noted that these statements, while false, are nevertheless tangential to the main emphasis of the paper, which is that cohesion in two-mode networks should be studied without one-mode projections, and that this can be done using both what we call “two-sided” and “onesided” approaches. We have replaced Theorem 3.1 and Corollary 3.1.1 with the following new, correct theorems and accompanying text.
本文中的定理3.1和推论3.1.1为假。虽然定理3.1正确地陈述了κ N ð Þ ø k，但反向不等式不一定是正确的(可以产生一系列反例来证明这一点)。应该指出的是，这些陈述虽然是错误的，但与本文的主要重点无关，即双模网络中的内聚应该在没有单模预测的情况下进行研究，并且这可以使用我们称之为“双面”和“片面”的方法来完成。我们将定理3.1和推论3.1.1替换为以下新的、正确的定理和相应的文本。
{"title":"Correction","authors":"B. Cornwell, Jake Burchard","doi":"10.1080/0022250X.2021.1917928","DOIUrl":"https://doi.org/10.1080/0022250X.2021.1917928","url":null,"abstract":"Theorem 3.1 and Corollary 3.1.1 in the article are false. While Theorem 3.1 correctly states that κ N ð Þ � k, the reverse inequality is not necessarily true (a family of counterexamples can be produced to show this). It should be noted that these statements, while false, are nevertheless tangential to the main emphasis of the paper, which is that cohesion in two-mode networks should be studied without one-mode projections, and that this can be done using both what we call “two-sided” and “onesided” approaches. We have replaced Theorem 3.1 and Corollary 3.1.1 with the following new, correct theorems and accompanying text.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2021.1917928","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45977764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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