Pub Date : 2022-03-03DOI: 10.1142/s0219525922500023
M. Gaudiano, Carlos M. Lucca, J. Revelli
In this work, we study the hierarchical properties observed in temporal patterns of public transport strike records of Córdoba city, Argentina. We show how a previously developed entropy-based methodology can be applied here to unveil different strike regimes, to which particular political uncontrollability degrees can be naturally associated. From data analysis, a successive increment in the uncontrollability of the public transport system can be quantitatively inferred. The proposed analysis turns out to be easily generalizable to other contexts, providing a theoretical framework for contrasting the intensity of the strikes, independently of its nature, city and/or historical time.
{"title":"Entropic Analysis of Public transport System Strikes","authors":"M. Gaudiano, Carlos M. Lucca, J. Revelli","doi":"10.1142/s0219525922500023","DOIUrl":"https://doi.org/10.1142/s0219525922500023","url":null,"abstract":"In this work, we study the hierarchical properties observed in temporal patterns of public transport strike records of Córdoba city, Argentina. We show how a previously developed entropy-based methodology can be applied here to unveil different strike regimes, to which particular political uncontrollability degrees can be naturally associated. From data analysis, a successive increment in the uncontrollability of the public transport system can be quantitatively inferred. The proposed analysis turns out to be easily generalizable to other contexts, providing a theoretical framework for contrasting the intensity of the strikes, independently of its nature, city and/or historical time.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79587954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-25DOI: 10.1142/s0219525922500011
Jun Su, Pengcheng Zhou
Music listening is one of the most enigmatic of human mental phenomena; it not only triggers emotions but also changes our behavior. During the music session many people are observed to exhibit varying emotional response, which can be influenced by diverse factors such as music genre and instrument as well as the personal attributes of audiences. In this study, we assume that there is an intrinsic, complex and implicit relationship between the basic sound features of music and human emotional response to the music. The response levels of 12 individuals to a representative repertoire of 36 classical/popular Chinese traditional music (CTM) are systematically analyzed using the chills as a quantitative indicator, totally resulting in 432 ([Formula: see text]) CTM–individual pairs that define a systematic individual-to-music response profile (SPTMRP). Gaussian process (GP) is then employed to model the multivariate correlation of SPTMRP profile with 15 sound features (including 5 Timbres, 4 Rhythms and 6 Pitchs) and 5 individual features in a supervised manner, which is also improved by genetic algorithm (GA) feature selection and compared with other machine learning methods. It is shown that the built GP regression model possesses a strong internal fitting ability ([Formula: see text]) and a good external predictive power ([Formula: see text]), which performed much better than linear PLS and nonlinear SVM and RF, confirming that the human emotional response to music can be quantitatively explained by GP methodology. Statistical examination of the GP model reveals that the sound features contribute more significantly to emotional response than individual features; their importance increases in the order: [Formula: see text], in which the spectral centroid (SC), relative amplitude of salient peaks (RASP), ratio of peak amplitudes (RPA), sum of all rhythm histograms (SARH) and period of unfolded maximum peak (PUMP) as well as gender are primarily responsible for the response.
{"title":"Use of Gaussian Process to Model, predict and Explain Human Emotional response to Chinese Traditional Music","authors":"Jun Su, Pengcheng Zhou","doi":"10.1142/s0219525922500011","DOIUrl":"https://doi.org/10.1142/s0219525922500011","url":null,"abstract":"Music listening is one of the most enigmatic of human mental phenomena; it not only triggers emotions but also changes our behavior. During the music session many people are observed to exhibit varying emotional response, which can be influenced by diverse factors such as music genre and instrument as well as the personal attributes of audiences. In this study, we assume that there is an intrinsic, complex and implicit relationship between the basic sound features of music and human emotional response to the music. The response levels of 12 individuals to a representative repertoire of 36 classical/popular Chinese traditional music (CTM) are systematically analyzed using the chills as a quantitative indicator, totally resulting in 432 ([Formula: see text]) CTM–individual pairs that define a systematic individual-to-music response profile (SPTMRP). Gaussian process (GP) is then employed to model the multivariate correlation of SPTMRP profile with 15 sound features (including 5 Timbres, 4 Rhythms and 6 Pitchs) and 5 individual features in a supervised manner, which is also improved by genetic algorithm (GA) feature selection and compared with other machine learning methods. It is shown that the built GP regression model possesses a strong internal fitting ability ([Formula: see text]) and a good external predictive power ([Formula: see text]), which performed much better than linear PLS and nonlinear SVM and RF, confirming that the human emotional response to music can be quantitatively explained by GP methodology. Statistical examination of the GP model reveals that the sound features contribute more significantly to emotional response than individual features; their importance increases in the order: [Formula: see text], in which the spectral centroid (SC), relative amplitude of salient peaks (RASP), ratio of peak amplitudes (RPA), sum of all rhythm histograms (SARH) and period of unfolded maximum peak (PUMP) as well as gender are primarily responsible for the response.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88266935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-24DOI: 10.1142/s0219525921500119
Guang Zeng, Jun Zhang, Rui Ye, A. Schadschneider, Shuchao Cao, Qiao Wang, Weiguo Song
Large crowds are challenging the comfort and safety level of big cities, while music may be a potential method to improve pedestrian flow. This paper focuses on the influence of different tempos and types of background music on pedestrian dynamics. Three tempos (90[Formula: see text]beats/min (BPM), 120[Formula: see text]BPM and 150[Formula: see text]BPM) and two types (pure music and metronome stimuli) of music are considered. It is found that more frequent stop-and-go behaviors emerge with rhythms. Compared with that under a low tempo (90[Formula: see text]BPM) of rhythm condition, stopping is more frequent with a high tempo one (120[Formula: see text]BPM or 150[Formula: see text]BPM). The number of stopping pedestrians per unit time increases 68.57%, 376.00%, 298.29%, 224.00%, 438.29% and 393.71% with 90 BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM music, 90[Formula: see text]BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM metronome, compared with that without any rhythm, respectively. The velocity and flow are lower, and higher local densities appear with background music. The step frequency at high density with rhythms ([Formula: see text], [Formula: see text] and [Formula: see text][Formula: see text]Hz for 90[Formula: see text]BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM music; [Formula: see text], [Formula: see text] and [Formula: see text][Formula: see text]Hz for 90[Formula: see text]BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM metronome) is lower than that without any rhythm ([Formula: see text][Formula: see text]Hz). Pedestrians need more time to avoid collisions and to step under background music conditions, because they are influenced by the music and not fully focusing on walking. As a result, step frequency decreases and stopping behavior is more frequent. This in turn leads to the decrease of the velocity and flow and the emergence of higher local densities. Our study will be helpful for understanding the effect of background music on pedestrian dynamics.
{"title":"Pedestrian dynamics in single-File movement under Background Music with Different Tempos","authors":"Guang Zeng, Jun Zhang, Rui Ye, A. Schadschneider, Shuchao Cao, Qiao Wang, Weiguo Song","doi":"10.1142/s0219525921500119","DOIUrl":"https://doi.org/10.1142/s0219525921500119","url":null,"abstract":"Large crowds are challenging the comfort and safety level of big cities, while music may be a potential method to improve pedestrian flow. This paper focuses on the influence of different tempos and types of background music on pedestrian dynamics. Three tempos (90[Formula: see text]beats/min (BPM), 120[Formula: see text]BPM and 150[Formula: see text]BPM) and two types (pure music and metronome stimuli) of music are considered. It is found that more frequent stop-and-go behaviors emerge with rhythms. Compared with that under a low tempo (90[Formula: see text]BPM) of rhythm condition, stopping is more frequent with a high tempo one (120[Formula: see text]BPM or 150[Formula: see text]BPM). The number of stopping pedestrians per unit time increases 68.57%, 376.00%, 298.29%, 224.00%, 438.29% and 393.71% with 90 BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM music, 90[Formula: see text]BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM metronome, compared with that without any rhythm, respectively. The velocity and flow are lower, and higher local densities appear with background music. The step frequency at high density with rhythms ([Formula: see text], [Formula: see text] and [Formula: see text][Formula: see text]Hz for 90[Formula: see text]BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM music; [Formula: see text], [Formula: see text] and [Formula: see text][Formula: see text]Hz for 90[Formula: see text]BPM, 120[Formula: see text]BPM and 150[Formula: see text]BPM metronome) is lower than that without any rhythm ([Formula: see text][Formula: see text]Hz). Pedestrians need more time to avoid collisions and to step under background music conditions, because they are influenced by the music and not fully focusing on walking. As a result, step frequency decreases and stopping behavior is more frequent. This in turn leads to the decrease of the velocity and flow and the emergence of higher local densities. Our study will be helpful for understanding the effect of background music on pedestrian dynamics.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90113622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1142/S0219525922500059
Arvind Upreti, V. Sridhar
{"title":"The dynamics of Task Automation and Worker Adjustment in Labor Markets: an Agent-based Approach","authors":"Arvind Upreti, V. Sridhar","doi":"10.1142/S0219525922500059","DOIUrl":"https://doi.org/10.1142/S0219525922500059","url":null,"abstract":"","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78398980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1142/S0219525922400021
Filippo Gusella
This paper proposes a macroeconometric analysis to depict and measure possible nancial cycles that emerge due to the dynamic interaction between heterogeneous market participants. We consider 2-type heterogeneous speculative agents: Trend followers tend to follow the price trend while contrarians go against the wind. As agents' beliefs are unobserved variables, we construct a state-space model where heuristics are considered as unobserved state components and from which the conditions for endogenous cycles can be mathematically derived and empirically tested. Further, we speci cally measure the length of endogenous nancial cycles. The model is estimated using the equity price index for the 196
{"title":"Detecting and Measuring Financial cycles in Heterogeneous Agents Models: an Empirical Analysis","authors":"Filippo Gusella","doi":"10.1142/S0219525922400021","DOIUrl":"https://doi.org/10.1142/S0219525922400021","url":null,"abstract":"This paper proposes a macroeconometric analysis to depict and measure possible nancial cycles that emerge due to the dynamic interaction between heterogeneous market participants. We consider 2-type heterogeneous speculative agents: Trend followers tend to follow the price trend while contrarians go against the wind. As agents' beliefs are unobserved variables, we construct a state-space model where heuristics are considered as unobserved state components and from which the conditions for endogenous cycles can be mathematically derived and empirically tested. Further, we speci cally measure the length of endogenous nancial cycles. The model is estimated using the equity price index for the 196","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88855052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-29DOI: 10.1142/s0219525921500107
Ricardo Simão, Francisco Rosendo, L. Wardil
The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.
{"title":"The Talent versus luck Model as an Ensemble of One-dimensional Random Walks","authors":"Ricardo Simão, Francisco Rosendo, L. Wardil","doi":"10.1142/s0219525921500107","DOIUrl":"https://doi.org/10.1142/s0219525921500107","url":null,"abstract":"The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78572690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-15DOI: 10.25088/complexsystems.30.4.483
J. Treur
In this paper, a self-modeling mental network model is presented for cognitive analysis and support processes for a human. These cognitive analysis and support processes are modeled by internal mental models. At the base level, the model is able to perform the analysis and support processes based on these internal mental models. To obtain adaptation of these internal mental models, a first-order self-model is included in the network model. In addition, to obtain control of this adaptation, a second-order self-model is included. This makes the network model a second-order self-modeling network model. The adaptive network model is illustrated for a number of realistic scenarios for a supported car driver.
{"title":"A Self-Modeling Network Model Addressing Controlled Adaptive Mental Models for Analysis and Support Processes","authors":"J. Treur","doi":"10.25088/complexsystems.30.4.483","DOIUrl":"https://doi.org/10.25088/complexsystems.30.4.483","url":null,"abstract":"In this paper, a self-modeling mental network model is presented for cognitive analysis and support processes for a human. These cognitive analysis and support processes are modeled by internal mental models. At the base level, the model is able to perform the analysis and support processes based on these internal mental models. To obtain adaptation of these internal mental models, a first-order self-model is included in the network model. In addition, to obtain control of this adaptation, a second-order self-model is included. This makes the network model a second-order self-modeling network model. The adaptive network model is illustrated for a number of realistic scenarios for a supported car driver.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80452314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-15DOI: 10.25088/complexsystems.30.4.539
A. Bramson, Kazuto Okamoto, Megumi Hori
Walkability analyses have gained increased attention for economic, environmental and health reasons, but the methods for assessing walkability have yet to be broadly evaluated. In this paper, five methods for calculating walkability scores are described: in-radius, circle buffers, road network node buffers, road network edge buffers and a fully integrated network approach. Unweighted and various weighted versions are analyzed to capture levels of preference for walking longer distances. The methods are evaluated via an application to train stations in central Tokyo in terms of accuracy, similarity and algorithm performance. The fully integrated network method produces the most accurate results in the shortest amount of processing time, but requires a large upfront investment of time and resources. The circle buffer method runs a bit slower, but does not require any network information and when properly weighted yields walkability scores very similar to the integrated network approach.
{"title":"Comparing Methods for Measuring Walkability","authors":"A. Bramson, Kazuto Okamoto, Megumi Hori","doi":"10.25088/complexsystems.30.4.539","DOIUrl":"https://doi.org/10.25088/complexsystems.30.4.539","url":null,"abstract":"Walkability analyses have gained increased attention for economic, environmental and health reasons, but the methods for assessing walkability have yet to be broadly evaluated. In this paper, five methods for calculating walkability scores are described: in-radius, circle buffers, road network node buffers, road network edge buffers and a fully integrated network approach. Unweighted and various weighted versions are analyzed to capture levels of preference for walking longer distances. The methods are evaluated via an application to train stations in central Tokyo in terms of accuracy, similarity and algorithm performance. The fully integrated network method produces the most accurate results in the shortest amount of processing time, but requires a large upfront investment of time and resources. The circle buffer method runs a bit slower, but does not require any network information and when properly weighted yields walkability scores very similar to the integrated network approach.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75771224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-15DOI: 10.25088/complexsystems.30.4.457
Sebastian Mežnar, N. Lavrač, Blaž Škrlj
Understanding how information propagates in real-life complex networks yields a better understanding of dynamic processes such as misinformation or epidemic spreading. The recently introduced branch of machine learning methods for learning node representations offers many novel applications, one of them being the task of spreading prediction addressed in this paper. We explore the utility of the state-of-the-art node representation learners when used to assess the effects of spreading from a given node, estimated via extensive simulations. Further, as many real-life networks are topologically similar, we systematically investigate whether the learned models generalize to previously unseen networks, showing that in some cases very good model transfer can be obtained. This paper is one of the first to explore transferability of the learned representations for the task of node regression; we show there exist pairs of networks with similar structure between which the trained models can be transferred (zero-shot) and demonstrate their competitive performance. To our knowledge, this is one of the first attempts to evaluate the utility of zero-shot transfer for the task of node regression.
{"title":"Transfer Learning for Node Regression Applied to Spreading Prediction","authors":"Sebastian Mežnar, N. Lavrač, Blaž Škrlj","doi":"10.25088/complexsystems.30.4.457","DOIUrl":"https://doi.org/10.25088/complexsystems.30.4.457","url":null,"abstract":"Understanding how information propagates in real-life complex networks yields a better understanding of dynamic processes such as misinformation or epidemic spreading. The recently introduced branch of machine learning methods for learning node representations offers many novel applications, one of them being the task of spreading prediction addressed in this paper. We explore the utility of the state-of-the-art node representation learners when used to assess the effects of spreading from a given node, estimated via extensive simulations. Further, as many real-life networks are topologically similar, we systematically investigate whether the learned models generalize to previously unseen networks, showing that in some cases very good model transfer can be obtained. This paper is one of the first to explore transferability of the learned representations for the task of node regression; we show there exist pairs of networks with similar structure between which the trained models can be transferred (zero-shot) and demonstrate their competitive performance. To our knowledge, this is one of the first attempts to evaluate the utility of zero-shot transfer for the task of node regression.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76766391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-15DOI: 10.25088/complexsystems.30.4.525
A. Faragó
Random graphs are frequently used models of real-life random networks. The classical Erdös–Rényi random graph model is very well explored and has numerous nontrivial properties. In particular, a good number of important graph parameters that are hard to compute in the deterministic case often become much easier in random graphs. However, a fundamental restriction in the Erdös–Rényi random graph is that the edges are required to be probabilistically independent. This is a severe restriction, which does not hold in most real-life networks. We consider more general random graphs in which the edges may be dependent. Specifically, two models are analyzed. The first one is called a p-robust random graph. It is defined by the requirement that each edge exist with probability at least p, no matter how we condition on the presence/absence of other edges. It is significantly more general than assuming independent edges existing with probability p, as exemplified via several special cases. The second model considers the case when the edges are positively correlated, which means that the edge probability is at least p for each edge, no matter how we condition on the presence of other edges (but absence is not considered). We prove some interesting, nontrivial properties about both models.
{"title":"The Impact of Edge Correlations in Random Networks","authors":"A. Faragó","doi":"10.25088/complexsystems.30.4.525","DOIUrl":"https://doi.org/10.25088/complexsystems.30.4.525","url":null,"abstract":"Random graphs are frequently used models of real-life random networks. The classical Erdös–Rényi random graph model is very well explored and has numerous nontrivial properties. In particular, a good number of important graph parameters that are hard to compute in the deterministic case often become much easier in random graphs. However, a fundamental restriction in the Erdös–Rényi random graph is that the edges are required to be probabilistically independent. This is a severe restriction, which does not hold in most real-life networks. We consider more general random graphs in which the edges may be dependent. Specifically, two models are analyzed. The first one is called a p-robust random graph. It is defined by the requirement that each edge exist with probability at least p, no matter how we condition on the presence/absence of other edges. It is significantly more general than assuming independent edges existing with probability p, as exemplified via several special cases. The second model considers the case when the edges are positively correlated, which means that the edge probability is at least p for each edge, no matter how we condition on the presence of other edges (but absence is not considered). We prove some interesting, nontrivial properties about both models.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72378638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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