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Computers
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Computational Modeling of Social Processes and Social Networks
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Computational Modeling of Social Processes and Social Networks

A special issue of Computers (ISSN 2073-431X).

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 11021

Special Issue Editors

Dr. Ivan Kozitsin

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Guest Editor
Institute of Control Sciences, Russian Academy of Sciences, Moscow 117997, Russia
Interests: opinion formation models; temporal networks; information dissemination
Dr. Anastasia Peshkovskaya

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Guest Editor
Neuroscience Center, Tomsk State University, Tomsk Oblast 634050, Russia
Interests: collective action; eye tracking; decision making; cooperation; social networking; social media use behavior
Dr. Alexander Petrov

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Guest Editor
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow 125047, Russia
Interests: mathematical modeling; social movements; information dissemination
Prof. Dr. Gholamreza Jafari

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Guest Editor
1. Department of Physics, Institute for Cognitive Science and Brian, Shahid Beheshti University, Tehran19839-63113, Iran
2. Institute of Information Technology and Data Science, Irkutsk National Research Technical University, Irkutsk Oblast 664074, Russia
Interests: complex networks; social media; statistical physics cognitive science; collective actions

Special Issue Information

Dear Colleagues,

The field of computational social science is currently going through a crucial period of development. The growing availability of data on social dynamics provide more opportunities to apply methods from mathematical modeling, statistical physics, social psychology, behavioral economics, and network theory and to thus elaborate upon comprehensive analytical descriptions of social phenomena. Nonetheless, all of these approaches still find it difficult to capture the complexity of social systems. There is no doubt that there is a need for further theoretical and empirical research aimed at exploring how people’s opinions and behavior change over time, how social networks (both real-world and online) self-organize and evolve, and why echo chambers persist in the online environment. Furthermore, this knowledge has to be instrumentalized so as to combat the dissemination of misinformation and dangerous content, mitigate polarization between and within nations, and provide and sustain cooperation in the face of current and future global challenges.

This Special Issue intends to publish original research whereby different computational methods are applied to investigate a range of social phenomena, such as collective action and prosocial behavior, opinion formation, information dissemination, and social network evolution. Both theoretical and empirical studies are encouraged. In our opinion, special attention should be devoted to linking the theoretical and empirical aspects of modeling the role of social media platforms in social dynamics as well as to studying the impact of ranking algorithms on the organization of information environment. Research on opinion mining and sentiment analysis are also welcome.

Dr. Ivan Kozitsin
Dr. Anastasia Peshkovskaya
Dr. Alexander Petrov
Prof. Dr. Gholamreza Jafari
Guest Editors

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Keywords

  • opinion formation models
  • temporal networks
  • ranking algorithms
  • social movements
  • big data
  • artificial societies
  • social contagion
  • social networks
  • collective action
  • cooperation
  • computational social science

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Published Papers (5 papers)

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24 pages, 485 KiB  
Article
Modeling Seasonality of Emotional Tension in Social Media
by Alexey Nosov, Yulia Kuznetsova, Maksim Stankevich, Ivan Smirnov and Oleg Grigoriev
Computers 2024, 13(1), 3; https://doi.org/10.3390/computers13010003 - 22 Dec 2023
Viewed by 1815
Abstract
Social media has become an almost unlimited resource for studying social processes. Seasonality is a phenomenon that significantly affects many physical and mental states. Modeling collective emotional seasonal changes is a challenging task for the technical, social, and humanities sciences. This is due [...] Read more.
Social media has become an almost unlimited resource for studying social processes. Seasonality is a phenomenon that significantly affects many physical and mental states. Modeling collective emotional seasonal changes is a challenging task for the technical, social, and humanities sciences. This is due to the laboriousness and complexity of obtaining a sufficient amount of data, processing and evaluating them, and presenting the results. At the same time, understanding the annual dynamics of collective sentiment provides us with important insights into collective behavior, especially in various crises or disasters. In our study, we propose a scheme for identifying and evaluating signs of the seasonal rise and fall of emotional tension based on social media texts. The analysis is based on Russian-language comments in VKontakte social network communities devoted to city news and the events of a small town in the Nizhny Novgorod region, Russia. Workflow steps include a statistical method for categorizing data, exploratory analysis to identify common patterns, data aggregation for modeling seasonal changes, the identification of typical data properties through clustering, and the formulation and validation of seasonality criteria. As a result of seasonality modeling, it is shown that the calendar seasonal model corresponds to the data, and the dynamics of emotional tension correlate with the seasons. The proposed methodology is useful for a wide range of social practice issues, such as monitoring public opinion or assessing irregular shifts in mass emotions. Full article
(This article belongs to the Special Issue Computational Modeling of Social Processes and Social Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>This histogram visualizes the proximity of the dataset to a normal distribution. The MATLAB Distribution Fitter was used to fit the normal distributions to the data with Parameter Estimate: mu = 1.20889 (Std. Err. 0.00361506) and sigma = 0.123707 (Std. Err. 0.00255787).</p> Full article ">Figure 2
<p>The samples were based on records from 1 March 2020 to 28 February 2023. In the chart, the numbers at the ends of the bars indicate the deviation in the white-to-black ratios from the Base Level (<math display="inline"><semantics> <mrow> <mi>B</mi> <mi>W</mi> <mo>−</mo> <mi>B</mi> <mi>L</mi> </mrow> </semantics></math>). The seasonal samples from 2020 to 2023 show an alternation in white-to-black ratios, with black dominance in the spring and fall and white dominance in the winter and summer.</p> Full article ">Figure 3
<p>The samples are based on records from 1 January 2020 to 31 December 2022. In the graph, the numbers at the ends of the bars indicate the deviation of the white-to-black ratios from the Base Level (<math display="inline"><semantics> <mrow> <mi>B</mi> <mi>W</mi> <mo>−</mo> <mi>B</mi> <mi>L</mi> </mrow> </semantics></math>). The quarterly samples from 2020 to 2022 show an alternation in white-to-black ratios, with black dominance in the second and fourth quarters and white dominance in the first and third quarters. From the first to the third quarter, the amplitude of deviations increases and falls sharply in the fourth quarter.</p> Full article ">Figure 4
<p>The samples were based on records from 1 February 2020 to 31 January 2023. The numbers at the ends of the bars indicate the deviation in white-to-black ratios from the Base Level (<math display="inline"><semantics> <mrow> <mi>B</mi> <mi>W</mi> <mo>−</mo> <mi>B</mi> <mi>L</mi> </mrow> </semantics></math>). In the off-season samples, the alternation in the white-to-black ratio was broken. The predominance of white over black began in August and continued until January.</p> Full article ">Figure 5
<p>The samples were based on records from 1 March 2020 to 28 February 2023. The seasonal alternation in white-to-black ratios (<math display="inline"><semantics> <mrow> <mi>B</mi> <mi>W</mi> </mrow> </semantics></math>) was typical from spring 2020 to spring 2021. The intervals from summer 2021 to autumn 2021 were approximately equal. Winter 2022 was an exception, after which the alternation was restored.</p> Full article ">Figure 6
<p>The samples were based on records from 1 January 2020 to 31 December 2022. The quarterly alternation in white-to-black ratios (<math display="inline"><semantics> <mrow> <mi>B</mi> <mi>W</mi> </mrow> </semantics></math>) was typical from the first quarter of 2020 to the fourth quarter of 2021. The alternation sequence was broken from the fourth quarter of 2021 to the second quarter of 2022. The alternation was restored from the second quarter of 2022 to the fourth quarter of 2022, but with a noticeably smaller amplitude.</p> Full article ">Figure 7
<p>The centroid was an array <math display="inline"><semantics> <mrow> <mo>(</mo> <msubsup> <mrow> <mover accent="true"> <mi>y</mi> <mo stretchy="false">^</mo> </mover> </mrow> <mn>1</mn> <mrow> <mspace width="0.166667em"/> <mi>c</mi> </mrow> </msubsup> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msubsup> <mrow> <mover accent="true"> <mi>y</mi> <mo stretchy="false">^</mo> </mover> </mrow> <mi>k</mi> <mrow> <mspace width="0.166667em"/> <mi>c</mi> </mrow> </msubsup> <mo>)</mo> </mrow> </semantics></math>, the values of the components of which were determined by the formula (<a href="#FD13-computers-13-00003" class="html-disp-formula">13</a>) by averaging the white and black levels for all the models from the set <math display="inline"><semantics> <mi mathvariant="script">L</mi> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math>. Therefore, the <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>-</mo> </mrow> </semantics></math>axis shows the indices of the array elements, and the <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>-</mo> </mrow> </semantics></math>axis shows the values of the array elements. For each index <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>k</mi> </mrow> </semantics></math>, the value of the array element <math display="inline"><semantics> <msubsup> <mrow> <mover accent="true"> <mi>y</mi> <mo stretchy="false">^</mo> </mover> </mrow> <mi>i</mi> <mrow> <mspace width="0.166667em"/> <mi>c</mi> </mrow> </msubsup> </semantics></math> was a pair consisting of white and black values corresponding to this index.</p> Full article ">Figure 8
<p>Black and white ratios on the <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>-</mo> </mrow> </semantics></math>intervals. The <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>-</mo> </mrow> </semantics></math>axis shows the intervals <math display="inline"><semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics></math> corresponding to the model, and the <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>-</mo> </mrow> </semantics></math>axis shows the white and black levels for <math display="inline"><semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics></math>, which was determined by Formula (<a href="#FD2-computers-13-00003" class="html-disp-formula">2</a>). (<b>a</b>) Model with parameter value <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>; (<b>b</b>) model with parameter value <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mo>−</mo> <mn>5</mn> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>Comparative behavior of the intervals from <math display="inline"><semantics> <msub> <mi>T</mi> <mn>5</mn> </msub> </semantics></math> to <math display="inline"><semantics> <msub> <mi>T</mi> <mn>8</mn> </msub> </semantics></math>. Values of the white levels in the output components <math display="inline"><semantics> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mn>5</mn> <mrow> <mspace width="0.166667em"/> <mi>l</mi> </mrow> </msubsup> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msubsup> <mi>y</mi> <mn>8</mn> <mrow> <mspace width="0.166667em"/> <mi>l</mi> </mrow> </msubsup> <mo>)</mo> </mrow> </semantics></math> in the points <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mn>5</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>T</mi> <mn>8</mn> </msub> </mrow> </semantics></math> for all <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>∈</mo> <mi mathvariant="script">L</mi> </mrow> </semantics></math>. Some of the lines overlapped each other, so there appeared to be fewer than thirteen lines.</p> Full article ">Figure 10
<p>Seasonal pattern according to the calendar seasonal model across the dataset based on records from 21 December 2019 to 5 March 2023.</p> Full article ">
31 pages, 4302 KiB  
Article
Investigation of the Gender-Specific Discourse about Online Learning during COVID-19 on Twitter Using Sentiment Analysis, Subjectivity Analysis, and Toxicity Analysis
by Nirmalya Thakur, Shuqi Cui, Karam Khanna, Victoria Knieling, Yuvraj Nihal Duggal and Mingchen Shao
Computers 2023, 12(11), 221; https://doi.org/10.3390/computers12110221 - 31 Oct 2023
Cited by 2 | Viewed by 2207
Abstract
This paper presents several novel findings from a comprehensive analysis of about 50,000 Tweets about online learning during COVID-19, posted on Twitter between 9 November 2021 and 13 July 2022. First, the results of sentiment analysis from VADER, Afinn, and TextBlob show that [...] Read more.
This paper presents several novel findings from a comprehensive analysis of about 50,000 Tweets about online learning during COVID-19, posted on Twitter between 9 November 2021 and 13 July 2022. First, the results of sentiment analysis from VADER, Afinn, and TextBlob show that a higher percentage of these Tweets were positive. The results of gender-specific sentiment analysis indicate that for positive Tweets, negative Tweets, and neutral Tweets, between males and females, males posted a higher percentage of the Tweets. Second, the results from subjectivity analysis show that the percentage of least opinionated, neutral opinionated, and highly opinionated Tweets were 56.568%, 30.898%, and 12.534%, respectively. The gender-specific results for subjectivity analysis indicate that females posted a higher percentage of highly opinionated Tweets as compared to males. However, males posted a higher percentage of least opinionated and neutral opinionated Tweets as compared to females. Third, toxicity detection was performed on the Tweets to detect different categories of toxic content—toxicity, obscene, identity attack, insult, threat, and sexually explicit. The gender-specific analysis of the percentage of Tweets posted by each gender for each of these categories of toxic content revealed several novel insights related to the degree, type, variations, and trends of toxic content posted by males and females related to online learning. Fourth, the average activity of males and females per month in this context was calculated. The findings indicate that the average activity of females was higher in all months as compared to males other than March 2022. Finally, country-specific tweeting patterns of males and females were also performed which presented multiple novel insights, for instance, in India, a higher percentage of the Tweets about online learning during COVID-19 were posted by males as compared to females. Full article
(This article belongs to the Special Issue Computational Modeling of Social Processes and Social Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>The variation of social media use by gender from the findings of a survey conducted by the Pew Research Center from 2005 to 2021.</p> Full article ">Figure 2
<p>A flowchart representing the working of Algorithm 1 to Algorithm 6 for the development of the master dataset.</p> Full article ">Figure 3
<p>A pie chart to represent different genders from the “Gender” attribute.</p> Full article ">Figure 4
<p>A pie chart to represent the distribution of positive, negative, and neutral sentiments (as per VADER) in the Tweets.</p> Full article ">Figure 5
<p>A pie chart to represent the distribution of positive, negative, and neutral sentiments (as per Afinn) in the Tweets.</p> Full article ">Figure 6
<p>A pie chart to represent the distribution of positive, negative, and neutral sentiments (as per TextBlob) in the Tweets.</p> Full article ">Figure 7
<p>A pie chart to represent the results of subjectivity analysis using TextBlob.</p> Full article ">Figure 8
<p>Representation of the variation of different categories of toxic content present in the Tweets.</p> Full article ">Figure 9
<p>A graphical representation of the variation of the intensities of different categories of toxic content on a monthly basis in Tweets about online learning during COVID-19.</p> Full article ">Figure 10
<p>A graphical representation of the variation of the intensity of toxicity on a monthly basis by different genders in Tweets about online learning during COVID-19.</p> Full article ">Figure 11
<p>A graphical representation of the variation of the intensity of obscene content on a monthly basis by different genders in Tweets about online learning during COVID-19.</p> Full article ">Figure 12
<p>A graphical representation of the variation of the intensity of identity attacks on a monthly basis by different genders in Tweets about online learning during COVID-19.</p> Full article ">Figure 13
<p>A graphical representation of the variation of the intensity of insult on a monthly basis by different genders in Tweets about online learning during COVID-19.</p> Full article ">Figure 14
<p>A graphical representation of the variation of the intensity of threat on a monthly basis by different genders in Tweets about online learning during COVID-19.</p> Full article ">Figure 15
<p>A graphical representation of the variation of the intensity of sexually explicit content on a monthly basis by different genders in Tweets about online learning during COVID-19.</p> Full article ">Figure 16
<p>A graphical representation of the variation of the average activity on Twitter (in the context of tweeting about online learning during COVID-19) on a monthly basis.</p> Full article ">Figure 17
<p>Representation of the trends in Tweets about online learning during COVID-19 posted by males from different countries of the world.</p> Full article ">Figure 18
<p>Representation of the trends in Tweets about online learning during COVID-19 posted by females from different countries of the world.</p> Full article ">Figure A1
<p>A word cloud-based representation of the 100 most frequently used in positive Tweets.</p> Full article ">Figure A2
<p>A word cloud-based representation of the 100 most frequently used in negative Tweets.</p> Full article ">Figure A3
<p>A word cloud-based representation of the 100 most frequently used in neutral Tweets.</p> Full article ">Figure A4
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that were highly opinionated.</p> Full article ">Figure A5
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that were least opinionated.</p> Full article ">Figure A6
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that were categorized as having a neutral opinion.</p> Full article ">Figure A7
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that belonged to the toxicity category.</p> Full article ">Figure A8
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that belonged to the obscene category.</p> Full article ">Figure A9
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that belonged to the identity attack category.</p> Full article ">Figure A10
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that belonged to the insult category.</p> Full article ">Figure A11
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that belonged to the threat category.</p> Full article ">Figure A12
<p>A word cloud-based representation of the 100 most frequently used words in Tweets that belonged to the sexually explicit category.</p> Full article ">
19 pages, 8953 KiB  
Article
The Effects of Individuals’ Opinion and Non-Opinion Characteristics on the Organization of Influence Networks in the Online Domain
by Vladislav N. Gezha and Ivan V. Kozitsin
Computers 2023, 12(6), 116; https://doi.org/10.3390/computers12060116 - 2 Jun 2023
Cited by 4 | Viewed by 1778
Abstract
The opinion dynamics literature argues that the way people perceive social influence depends not only on the opinions of interacting individuals, but also on the individuals’ non-opinion characteristics, such as age, education, gender, or place of residence. The current paper advances this line [...] Read more.
The opinion dynamics literature argues that the way people perceive social influence depends not only on the opinions of interacting individuals, but also on the individuals’ non-opinion characteristics, such as age, education, gender, or place of residence. The current paper advances this line of research by studying longitudinal data that describe the opinion dynamics of a large sample (~30,000) of online social network users, all citizens of one city. Using these data, we systematically investigate the effects of users’ demographic (age, gender) and structural (degree centrality, the number of common friends) properties on opinion formation processes. We revealed that females are less easily influenced than males. Next, we found that individuals that are characterized by similar ages have more chances to reach a consensus. Additionally, we report that individuals who have many common peers find an agreement more often. We also demonstrated that the impacts of these effects are virtually the same, and despite being statistically significant, are far less strong than that of opinion-related features: knowing the current opinion of an individual and, what is even more important, the distance in opinions between this individual and the person that attempts to influence the individual is much more valuable. Next, after conducting a series of simulations with an agent-based model, we revealed that accounting for non-opinion characteristics may lead to not very sound but statistically significant changes in the macroscopic predictions of the populations of opinion camps, primarily among the agents with radical opinions (≈3% of all votes). In turn, predictions for the populations of neutral individuals are virtually the same. In addition, we demonstrated that the accumulative effect of non-opinion features on opinion dynamics is seriously moderated by whether the underlying social network correlates with the agents’ characteristics. After applying the procedure of random shuffling (in which the agents and their characteristics were randomly scattered over the network), the macroscopic predictions have changed by ≈9% of all votes. What is interesting is that the population of neutral agents was again not affected by this intervention. Full article
(This article belongs to the Special Issue Computational Modeling of Social Processes and Social Networks)
►▼ Show Figures

Figure 1

Figure 1
<p>The workflow of the analysis.</p> Full article ">Figure 2
<p>We demonstrate the organization of the matrix <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo>=</mo> <msub> <mrow> <mfenced close="]" open="["> <mrow> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfenced> </mrow> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> <mo>∈</mo> <mfenced close="]" open="["> <mi>m</mi> </mfenced> </mrow> </msub> </mrow> </semantics></math> for a fixed <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>∈</mo> <mfenced close="]" open="["> <mi>m</mi> </mfenced> </mrow> </semantics></math>. Each of its rows sums up to one as it covers all possible alternatives. Let us consider the <math display="inline"><semantics> <mi>l</mi> </semantics></math>-th row that outlines how individuals with opinion <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mi>s</mi> </msub> </mrow> </semantics></math> react to opinion <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mi>l</mi> </msub> </mrow> </semantics></math>. Overall, there are <math display="inline"><semantics> <mi>m</mi> </semantics></math> possible alternatives: <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mi>s</mi> </msub> <mo>→</mo> <msub> <mo>Ξ</mo> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mo>Ξ</mo> <mi>s</mi> </msub> <mo>→</mo> <msub> <mo>Ξ</mo> <mi>m</mi> </msub> </mrow> </semantics></math>. The resulting estimated probabilities of these alternatives are described by the quantities <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>l</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math>. Other rows are elaborated analogously. We would like to emphasize that row <math display="inline"><semantics> <mi>s</mi> </semantics></math> stands for the situations when the influence comes from the coherent opinion <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mi>s</mi> </msub> </mrow> </semantics></math>, whereas column <math display="inline"><semantics> <mi>s</mi> </semantics></math> contains the probabilities of holding the current opinion <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mi>s</mi> </msub> </mrow> </semantics></math>. In this regard, the elements of the <math display="inline"><semantics> <mi>s</mi> </semantics></math>-th column (the quantities <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>) represent how stubborn are individuals with opinion <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mi>s</mi> </msub> </mrow> </semantics></math>. According to the previous empirical research [<a href="#B5-computers-12-00116" class="html-bibr">5</a>,<a href="#B9-computers-12-00116" class="html-bibr">9</a>,<a href="#B16-computers-12-00116" class="html-bibr">16</a>], we should expect that this column will dominate the others. In matrix <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, the components standing for positive and negative opinion shifts are easily located. The zone of positive shifts is defined as follows: <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mi>p</mi> </msub> <mo>=</mo> <mfenced close="}" open="{"> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> <mo> </mo> <mo>|</mo> <mo> </mo> <mi>l</mi> <mo>&lt;</mo> <mi>s</mi> <mo>,</mo> <mi>k</mi> <mo>&lt;</mo> <mi>s</mi> </mrow> </mfenced> <mo>∪</mo> <mfenced close="}" open="{"> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> <mo> </mo> <mfenced close="&#x232A;" open="|"> <mrow> <mo> </mo> <mi>l</mi> </mrow> </mfenced> <mi>s</mi> <mo>,</mo> <mi>k</mi> <mo>&gt;</mo> <mi>s</mi> </mrow> </mfenced> </mrow> </semantics></math>, where <math display="inline"><semantics> <mi>l</mi> </semantics></math> and <math display="inline"><semantics> <mi>k</mi> </semantics></math> are the row and column indices, respectively. In other words, <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mi>p</mi> </msub> </mrow> </semantics></math> is the union of the second and fourth “quadrants”, given that the origin of coordinates is located at <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mi>k</mi> <mo>=</mo> <mi>s</mi> </mrow> </semantics></math> (the component <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>). Correspondingly, the zone of negative shifts is the union of the first and third “quadrants”: <math display="inline"><semantics> <mrow> <msub> <mi>D</mi> <mi>n</mi> </msub> <mo>=</mo> <mfenced close="}" open="{"> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> <mo> </mo> <mo>|</mo> <mrow> <mo> </mo> <mi>l</mi> </mrow> <mo>&gt;</mo> <mi>s</mi> <mo>,</mo> <mi>k</mi> <mo>&lt;</mo> <mi>s</mi> </mrow> </mfenced> <mo>∪</mo> <mfenced close="}" open="{"> <mrow> <mi>l</mi> <mo>,</mo> <mi>k</mi> <mo> </mo> <mo>|</mo> <mo> </mo> <mi>l</mi> <mo>&lt;</mo> <mrow> <mi>s</mi> <mo>,</mo> <mi>k</mi> </mrow> <mo>&gt;</mo> <mi>s</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>These heatmaps represent the estimated matrices <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>P</mi> <mn>5</mn> </msub> </mrow> </semantics></math> that were computed after the opinion scale <math display="inline"><semantics> <mrow> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math> had been discretized into five subintervals <math display="inline"><semantics> <mrow> <msub> <mo>Ξ</mo> <mn>1</mn> </msub> <mo>=</mo> <mfenced close=")" open="["> <mrow> <mn>0</mn> <mo>,</mo> <mo> </mo> <mn>0.2</mn> </mrow> </mfenced> <mo>,</mo> <msub> <mo>Ξ</mo> <mn>2</mn> </msub> <mo>=</mo> <mfenced close=")" open="["> <mrow> <mn>0.2</mn> <mo>,</mo> <mo> </mo> <mn>0.4</mn> </mrow> </mfenced> <mo>,</mo> <msub> <mo>Ξ</mo> <mn>3</mn> </msub> <mo>=</mo> <mfenced close=")" open="["> <mrow> <mn>0.4</mn> <mo>,</mo> <mo> </mo> <mn>0.6</mn> </mrow> </mfenced> <mo>,</mo> <msub> <mo>Ξ</mo> <mn>4</mn> </msub> <mo>=</mo> <mfenced close=")" open="["> <mrow> <mn>0.6</mn> <mo>,</mo> <mo> </mo> <mn>0.8</mn> </mrow> </mfenced> <mo>,</mo> <msub> <mo>Ξ</mo> <mn>5</mn> </msub> <mo>=</mo> <mfenced close="]" open="["> <mrow> <mn>0.8</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> </mrow> </mfenced> </mrow> </semantics></math>. The values are presented to three decimal places.</p> Full article ">Figure 4
<p>The values of the estimated OLS regression coefficients (see <a href="#computers-12-00116-t003" class="html-table">Table 3</a>) plotted with the corresponding 95% confidence intervals. Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘ ’ 1.</p> Full article ">Figure 5
<p>The figure demonstrates the averaged dynamics of the populations of leftists (upper panels) and rightists (bottom panels) across Scenarios 1–4 (marked with different colors). For each Scenario, the colored area is formed by the upper and lower contours of the corresponding simulations, and the curve represents the trajectory averaged over simulations. The left panels depict the time span <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mn>500,000</mn> </mrow> </semantics></math>; the right panels investigate the range <math display="inline"><semantics> <mrow> <mn>500,000</mn> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mn>4,000,000</mn> </mrow> </semantics></math>. The final populations of leftists and rightists are depicted on the right side of the figure in absolute and normalized (in brackets) values.</p> Full article ">Figure A1
<p>This transition matrix was estimated based on the empirical data (non-opinion covariates are ignored).</p> Full article ">Figure A2
<p>This transition matrix was estimated based on the empirical data (type 1—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a> and formula (A2)).</p> Full article ">Figure A3
<p>This transition matrix was estimated based on the empirical data (type 2—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A4
<p>This transition matrix was estimated based on the empirical data (type 3—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A5
<p>This transition matrix was estimated based on the empirical data (type 4—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A6
<p>This transition matrix was estimated based on the empirical data (type 5—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A7
<p>This transition matrix was estimated based on the empirical data (type 6—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A8
<p>This transition matrix was estimated based on the empirical data (type 7—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A9
<p>This transition matrix was estimated based on the empirical data (type 8—see <a href="#computers-12-00116-t004" class="html-table">Table 4</a>).</p> Full article ">Figure A10
<p>These histograms show the structure of the dataset. The histograms that represent the age, gender, and opinion distributions are borrowed from the Ref. [<a href="#B28-computers-12-00116" class="html-bibr">28</a>].</p> Full article ">
16 pages, 2492 KiB  
Article
Disparity of Density in the Age of Mobility: Analysis by Opinion Formation Model
by Shiro Horiuchi
Computers 2023, 12(5), 94; https://doi.org/10.3390/computers12050094 - 1 May 2023
Cited by 1 | Viewed by 1800
Abstract
High mobility has promoted the concentration of people’s aggregation in urban areas. As people pursue areas with higher density, gentrification and sprawl become more serious. Disadvantaged people are then pushed out of urban centers. Conversely, as mobility increases, the disadvantaged may also migrate [...] Read more.
High mobility has promoted the concentration of people’s aggregation in urban areas. As people pursue areas with higher density, gentrification and sprawl become more serious. Disadvantaged people are then pushed out of urban centers. Conversely, as mobility increases, the disadvantaged may also migrate in pursuit of their desired density. As a result, disparities relative to density and housing may shrink. Hence, migration is a complex system. Understanding the effects of migration on disparities intuitively is difficult. This study explored the effects of mobility on disparity using an agent-based model of opinion formation. We find that as mobility increases, disparities between agents in density and diversity widen, but as mobility increases further, the disparities shrink, and then widen again. Our results present possibilities for a just city in the age of mobility. Full article
(This article belongs to the Special Issue Computational Modeling of Social Processes and Social Networks)
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Figure 1

Figure 1
<p>Screenshot of the initial condition by NetLogo. In histogram red bars represent opinions, yellow bars represent diversity of agents.</p> Full article ">Figure 2
<p>The procedure of the ABM.</p> Full article ">Figure 3
<p>Trends in the mean values of <span class="html-italic">density</span>, <span class="html-italic">opinion</span>, and <span class="html-italic">diversity</span>. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0.001. The value of <span class="html-italic">mobility</span> = (<b>a</b>) 0, (<b>b</b>) 1, and (<b>c</b>) ∞.</p> Full article ">Figure 4
<p>Distribution of agents after 1000 turns. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0.001. The value of <span class="html-italic">mobility</span> = (<b>a</b>) 0, (<b>b</b>) 0.5, (<b>c</b>) 1, (<b>d</b>) 2, (<b>e</b>) 4, (<b>f</b>) 8, (<b>g</b>) 64, and (<b>h</b>) ∞.</p> Full article ">Figure 5
<p>Box plot for the mean values of (<b>a</b>) density, (<b>b</b>) opinion, and (<b>c</b>) diversity for mobility (x-axes) after 1000 turns with 100 trials; 999 in the x-axis represents ∞ and ◦ represents outliers. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0.001.</p> Full article ">Figure 6
<p>Box plots for Pearson’s correlation coefficients for (<b>a</b>) resource–density, (<b>b</b>) resource–opinion, and (<b>c</b>) resource–diversity at each mobility after 1000 turns with 100 trials; 999 in the x-axis represents ∞ and ◦ represents outliers. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0.001.</p> Full article ">Figure 7
<p>Trends in the mean values of <span class="html-italic">density</span>, <span class="html-italic">opinion</span>, and <span class="html-italic">diversity</span>. The values of <span class="html-italic">δ</span> = 0.001 and <span class="html-italic">ε</span> = 0.01. The value of <span class="html-italic">mobility</span> = (<b>a</b>) 0, (<b>b</b>) 1, and (<b>c</b>) ∞.</p> Full article ">Figure 8
<p>Box plot for the mean values of (<b>a</b>) density, (<b>b</b>) opinion, and (<b>c</b>) diversity at each mobility after 1000 turns with 100 trials; 999 in the x-axis represents ∞ and ◦ represents outliers. The values of <span class="html-italic">δ</span> = 0.001 and <span class="html-italic">ε</span> = 0.01.</p> Full article ">Figure 9
<p>Box plots of Pearson’s correlation coefficients for (<b>a</b>) resource–density, (<b>b</b>) resource–opinion, and (<b>c</b>) resource–diversity at each mobility after 1000 turns with 100 trials; 999 in the x-axis represents ∞ and ◦ represents outliers. The values of <span class="html-italic">δ</span> = 0.001 and <span class="html-italic">ε</span> = 0.01.</p> Full article ">Figure 10
<p>Trends in the mean values of <span class="html-italic">density</span>, <span class="html-italic">opinion</span>, and <span class="html-italic">diversity</span>. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0. The value of <span class="html-italic">mobility</span> = (<b>a</b>) 0, (<b>b</b>) 1, and (<b>c</b>) ∞.</p> Full article ">Figure 11
<p>Box plot for the mean values of (<b>a</b>) density, (<b>b</b>) opinion, and (<b>c</b>) diversity at each mobility after 1000 turns with 100 trials; 999 in the x-axis represents ∞ and ◦ represents outliers. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0.</p> Full article ">Figure 12
<p>Box plots for Pearson’s correlation coefficients (<b>a</b>) resource–density, (<b>b</b>) resource–opinion, and (<b>c</b>) resource–diversity at each mobility after 1000 turns with 100 trials for each mobility; 999 in the x-axis represents ∞ and ◦ represents outliers. The values of <span class="html-italic">δ</span> = 0.01 and <span class="html-italic">ε</span> = 0.</p> Full article ">

Review

Jump to: Research

15 pages, 813 KiB  
Review
Simulation Models for Suicide Prevention: A Survey of the State-of-the-Art
by Ryan Schuerkamp, Luke Liang, Ketra L. Rice and Philippe J. Giabbanelli
Computers 2023, 12(7), 132; https://doi.org/10.3390/computers12070132 - 29 Jun 2023
Cited by 4 | Viewed by 2067
Abstract
Suicide is a leading cause of death and a global public health problem, representing more than one in every 100 deaths in 2019. Modeling and Simulation (M&S) is widely used to address public health problems, and numerous simulation models have investigated the complex, [...] Read more.
Suicide is a leading cause of death and a global public health problem, representing more than one in every 100 deaths in 2019. Modeling and Simulation (M&S) is widely used to address public health problems, and numerous simulation models have investigated the complex, dependent, and dynamic risk factors contributing to suicide. However, no review has been dedicated to these models, which prevents modelers from effectively learning from each other and raises the risk of redundant efforts. To guide the development of future models, in this paper we perform the first scoping review of simulation models for suicide prevention. Examining ten articles, we focus on three practical questions. First, which interventions are supported by previous models? We found that four groups of models collectively support 53 interventions. We examined these interventions through the lens of global recommendations for suicide prevention, highlighting future areas for model development. Second, what are the obstacles preventing model application? We noted the absence of cost effectiveness in all models reviewed, meaning that certain simulated interventions may be infeasible. Moreover, we found that most models do not account for different effects of suicide prevention interventions across demographic groups. Third, how much confidence can we place in the models? We evaluated models according to four best practices for simulation, leading to nuanced findings that, despite their current limitations, the current simulation models are powerful tools for understanding the complexity of suicide and evaluating suicide prevention interventions. Full article
(This article belongs to the Special Issue Computational Modeling of Social Processes and Social Networks)
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Figure 1

Figure 1
<p>The continuum of conceptual, mathematical, and simulation models.</p> Full article ">Figure 2
<p>An example ABM depicting agents, their connections, and their access to care. Agents that are farther away have greater difficulty in accessing care.</p> Full article ">Figure 3
<p>A simple System Dynamics model diagram for determining the number of suicidal ideations (i.e., suicidal thoughts).</p> Full article ">Figure 4
<p>An example social network demonstrating the spread of care-seeking behavior.</p> Full article ">
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