Pub Date : 2021-10-12DOI: 10.1142/s0219525921500090
Giulia Braghini, F. Salvarani
{"title":"Effects of Hidden Opinion manipulation in Microblogging Platforms","authors":"Giulia Braghini, F. Salvarani","doi":"10.1142/s0219525921500090","DOIUrl":"https://doi.org/10.1142/s0219525921500090","url":null,"abstract":"","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"98 1","pages":"2150009:1-2150009:26"},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90985061","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 : 2021-10-01DOI: 10.1142/s0219525921500089
A. M. Jaramillo, Mariana Macedo, R. Menezes
{"title":"Reaching to the Top: the Gender effect in Highly-Ranked academics in Computer Science","authors":"A. M. Jaramillo, Mariana Macedo, R. Menezes","doi":"10.1142/s0219525921500089","DOIUrl":"https://doi.org/10.1142/s0219525921500089","url":null,"abstract":"","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"29 1","pages":"2150008:1-2150008:18"},"PeriodicalIF":0.4,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87021426","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 : 2021-09-30DOI: 10.1142/s021952592150003x
WILMER LEAL, GUILLERMO RESTREPO, PETER F. STADLER, JÜRGEN JOST
Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array of statistics has been devised to gauge different aspects of their structures. Hypergraphs lack behind in this respect. The Forman–Ricci curvature is a statistics for graphs based on Riemannian geometry, which stresses the relational character of vertices in a network by focusing on the edges rather than on the vertices. Despite many successful applications of this measure to graphs, Forman–Ricci curvature has not been introduced for hypergraphs. Here, we define the Forman–Ricci curvature for directed and undirected hypergraphs such that the curvature for graphs is recovered as a special case. It quantifies the trade-off between hyperedge (arc) size and the degree of participation of hyperedge (arc) vertices in other hyperedges (arcs). Here, we determine upper and lower bounds for Forman–Ricci curvature both for hypergraphs in general and for graphs in particular. The measure is then applied to two large networks: the Wikipedia vote network and the metabolic network of the bacterium Escherichia coli. In the first case, the curvature is governed by the size of the hyperedges, while in the second example, it is dominated by the hyperedge degree. We found that the number of users involved in Wikipedia elections goes hand-in-hand with the participation of experienced users. The curvature values of the metabolic network allowed detecting redundant and bottle neck reactions. It is found that ADP phosphorylation is the metabolic bottle neck reaction but that the reverse reaction is not similarly central for the metabolism. Furthermore, we show the utility of the Forman–Ricci curvature for quantification of assortativity in hypergraphs and illustrate the idea by investigating three metabolic networks.
{"title":"FORMAN–RICCI CURVATURE FOR HYPERGRAPHS","authors":"WILMER LEAL, GUILLERMO RESTREPO, PETER F. STADLER, JÜRGEN JOST","doi":"10.1142/s021952592150003x","DOIUrl":"https://doi.org/10.1142/s021952592150003x","url":null,"abstract":"Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array of statistics has been devised to gauge different aspects of their structures. Hypergraphs lack behind in this respect. The Forman–Ricci curvature is a statistics for graphs based on Riemannian geometry, which stresses the relational character of vertices in a network by focusing on the edges rather than on the vertices. Despite many successful applications of this measure to graphs, Forman–Ricci curvature has not been introduced for hypergraphs. Here, we define the Forman–Ricci curvature for directed and undirected hypergraphs such that the curvature for graphs is recovered as a special case. It quantifies the trade-off between hyperedge (arc) size and the degree of participation of hyperedge (arc) vertices in other hyperedges (arcs). Here, we determine upper and lower bounds for Forman–Ricci curvature both for hypergraphs in general and for graphs in particular. The measure is then applied to two large networks: the Wikipedia vote network and the metabolic network of the bacterium <italic>Escherichia coli</italic>. In the first case, the curvature is governed by the size of the hyperedges, while in the second example, it is dominated by the hyperedge degree. We found that the number of users involved in Wikipedia elections goes hand-in-hand with the participation of experienced users. The curvature values of the metabolic network allowed detecting redundant and bottle neck reactions. It is found that ADP phosphorylation is the metabolic bottle neck reaction but that the reverse reaction is not similarly central for the metabolism. Furthermore, we show the utility of the Forman–Ricci curvature for quantification of assortativity in hypergraphs and illustrate the idea by investigating three metabolic networks.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"325 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515760","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 : 2021-09-25DOI: 10.1142/s0219525921500041
Shaoping Xiao, B. She, S. Mehta, Z. Kan
In many engineered and natural networked systems, there has been great interest in leader selection and/or edge assignment during the optimal design of controllable networks. In this paper, we present our pioneering work in leader–follower network design via memetic algorithms, which focuses on minimizing the number of leaders or the amount of control energy while ensuring network controllability. We consider three problems in this paper: (1) selecting the minimum number of leaders in a pre-defined network with guaranteed network controllability; (2) selecting the leaders in a pre-defined network with the minimum control energy; and (3) assigning edges (interactions) between nodes to form a controllable leader–follower network with the minimum control energy. The proposed framework can be applied in designing signed, unsigned, directed, or undirected networks. It should be noted that this work is the first to apply memetic algorithms in the design of controllable networks. We chose memetic algorithms because they have been shown to be more efficient and more effective than the standard genetic algorithms in solving some optimization problems. Our simulation results provide an additional demonstration of their efficiency and effectiveness.
{"title":"Design of controllable Leader-follower Networks via Memetic Algorithms","authors":"Shaoping Xiao, B. She, S. Mehta, Z. Kan","doi":"10.1142/s0219525921500041","DOIUrl":"https://doi.org/10.1142/s0219525921500041","url":null,"abstract":"In many engineered and natural networked systems, there has been great interest in leader selection and/or edge assignment during the optimal design of controllable networks. In this paper, we present our pioneering work in leader–follower network design via memetic algorithms, which focuses on minimizing the number of leaders or the amount of control energy while ensuring network controllability. We consider three problems in this paper: (1) selecting the minimum number of leaders in a pre-defined network with guaranteed network controllability; (2) selecting the leaders in a pre-defined network with the minimum control energy; and (3) assigning edges (interactions) between nodes to form a controllable leader–follower network with the minimum control energy. The proposed framework can be applied in designing signed, unsigned, directed, or undirected networks. It should be noted that this work is the first to apply memetic algorithms in the design of controllable networks. We chose memetic algorithms because they have been shown to be more efficient and more effective than the standard genetic algorithms in solving some optimization problems. Our simulation results provide an additional demonstration of their efficiency and effectiveness.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"1 1","pages":"2150004:1-2150004:29"},"PeriodicalIF":0.4,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90666540","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 : 2021-09-15DOI: 10.25088/complexsystems.30.3.415
B. Chakraborty, M. Dalui, B. Sikdar
This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.
{"title":"Synthesis of Scalable Single Length Cycle, Single Attractor Cellular Automata in Linear Time","authors":"B. Chakraborty, M. Dalui, B. Sikdar","doi":"10.25088/complexsystems.30.3.415","DOIUrl":"https://doi.org/10.25088/complexsystems.30.3.415","url":null,"abstract":"This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"92 1","pages":"415-439"},"PeriodicalIF":0.4,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80452367","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 : 2021-09-15DOI: 10.25088/complexsystems.30.3.347
Jayati Deshmukh, S. Srinivasa, Sridhar Mandyam
Managing diversity is a challenging problem for organizations and governments. Diversity in a population may be of two kinds—acquired and innate. The former refers to diversity acquired by pre-existing social or organizational environments, attracting employees or immigrants because of their wealth and opportunities. Innate diversity, on the other hand, refers to a collection of pre-existing communities having to interact with one another and to build an overarching social or organizational identity. While acquired diversity has a prior element of common identity, innate diversity needs to build a common identity from a number of disparate regional or local identities. Diversity in any large population may have different extents of acquired and innate elements. In this paper, innate and acquired diversity are modeled in terms of two factors, namely: insularity and homophily, respectively. Insularity is the tendency of agents to act cooperatively only with others from the same community, which is often the primary challenge of innate diversity; while homophily is the tendency of agents to prefer members from their own community to start new social or business connections, which is often the primary challenge in acquired diversity. The emergence of network structure is studied when insularity and homophily are varied. In order to promote cooperation in a diverse population, the role played by a subset of agents called “global” agents who are not affected by homophily and insularity considerations is also studied. Simulation results show several interesting emergent properties. While the global agents are shown to acquire high betweenness, they are by no means the wealthiest or the most powerful in the network. However, the presence of global agents is important for the regional agents whose own wealth prospects increase because of their interaction with global agents.
{"title":"What Keeps a Vibrant Population Together?","authors":"Jayati Deshmukh, S. Srinivasa, Sridhar Mandyam","doi":"10.25088/complexsystems.30.3.347","DOIUrl":"https://doi.org/10.25088/complexsystems.30.3.347","url":null,"abstract":"Managing diversity is a challenging problem for organizations and governments. Diversity in a population may be of two kinds—acquired and innate. The former refers to diversity acquired by pre-existing social or organizational environments, attracting employees or immigrants because of their wealth and opportunities. Innate diversity, on the other hand, refers to a collection of pre-existing communities having to interact with one another and to build an overarching social or organizational identity. While acquired diversity has a prior element of common identity, innate diversity needs to build a common identity from a number of disparate regional or local identities. Diversity in any large population may have different extents of acquired and innate elements. In this paper, innate and acquired diversity are modeled in terms of two factors, namely: insularity and homophily, respectively. Insularity is the tendency of agents to act cooperatively only with others from the same community, which is often the primary challenge of innate diversity; while homophily is the tendency of agents to prefer members from their own community to start new social or business connections, which is often the primary challenge in acquired diversity. The emergence of network structure is studied when insularity and homophily are varied. In order to promote cooperation in a diverse population, the role played by a subset of agents called “global” agents who are not affected by homophily and insularity considerations is also studied. Simulation results show several interesting emergent properties. While the global agents are shown to acquire high betweenness, they are by no means the wealthiest or the most powerful in the network. However, the presence of global agents is important for the regional agents whose own wealth prospects increase because of their interaction with global agents.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"37 1","pages":"347-373"},"PeriodicalIF":0.4,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80588174","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 : 2021-09-15DOI: 10.25088/complexsystems.30.3.297
Shaoping Xiao, Ruicheng Liu
An agent-based model was developed to study outbreaks and outbreak control for COVID-19, mainly in urban communities. Rules for people’s interactions and virus infectiousness were derived based on previous sociology studies and recently published data-driven analyses of COVID-19 epidemics. The calculated basic reproduction number of epidemics from the developed model coincided with reported values. There were three control measures considered in this paper: social distancing, self-quarantine and community quarantine. Each control measure was assessed individually at first. Later on, an artificial neural network was used to study the effects of different combinations of control measures. To help quantify the impacts of self-quarantine and community quarantine on outbreak control, both were scaled respectively. The results showed that self-quarantine was more effective than the others, but any individual control measure was ineffective in controlling outbreaks in urban communities. The results also showed that a high level of self-quarantine and general community quarantine, assisted with social distancing, would be recommended for outbreak control.
{"title":"Studies of COVID-19 Outbreak Control Using Agent-Based Modeling","authors":"Shaoping Xiao, Ruicheng Liu","doi":"10.25088/complexsystems.30.3.297","DOIUrl":"https://doi.org/10.25088/complexsystems.30.3.297","url":null,"abstract":"An agent-based model was developed to study outbreaks and outbreak control for COVID-19, mainly in urban communities. Rules for people’s interactions and virus infectiousness were derived based on previous sociology studies and recently published data-driven analyses of COVID-19 epidemics. The calculated basic reproduction number of epidemics from the developed model coincided with reported values. There were three control measures considered in this paper: social distancing, self-quarantine and community quarantine. Each control measure was assessed individually at first. Later on, an artificial neural network was used to study the effects of different combinations of control measures. To help quantify the impacts of self-quarantine and community quarantine on outbreak control, both were scaled respectively. The results showed that self-quarantine was more effective than the others, but any individual control measure was ineffective in controlling outbreaks in urban communities. The results also showed that a high level of self-quarantine and general community quarantine, assisted with social distancing, would be recommended for outbreak control.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"106 1","pages":"297-321"},"PeriodicalIF":0.4,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79860914","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 : 2021-09-15DOI: 10.25088/complexsystems.30.3.323
F. Pazos, F. Felicioni
The recent worldwide epidemic of COVID-19 disease, for which there are no medications to cure it and the vaccination is still at an early stage, led to the adoption of public health measures by governments and populations in most of the affected countries to avoid the contagion and its spread. These measures are known as nonpharmaceutical interventions (NPIs), and their implementation clearly produces social unrest as well as greatly affects the economy. Frequently, NPIs are implemented with an intensity quantified in an ad hoc manner. Control theory offers a worthwhile tool for determining the optimal intensity of the NPIs in order to avoid the collapse of the healthcare system while keeping them as low as possible, yielding concrete guidance to policymakers. A simple controller, which generates a control law that is easy to calculate and to implement is proposed. This controller is robust to large parametric uncertainties in the model used and to some level of noncompliance with the NPIs.
{"title":"A Control Approach to Guide Nonpharmaceutical Interventions in the Treatment of COVID-19 Disease Using a SEIHRD Dynamical Model","authors":"F. Pazos, F. Felicioni","doi":"10.25088/complexsystems.30.3.323","DOIUrl":"https://doi.org/10.25088/complexsystems.30.3.323","url":null,"abstract":"The recent worldwide epidemic of COVID-19 disease, for which there are no medications to cure it and the vaccination is still at an early stage, led to the adoption of public health measures by governments and populations in most of the affected countries to avoid the contagion and its spread. These measures are known as nonpharmaceutical interventions (NPIs), and their implementation clearly produces social unrest as well as greatly affects the economy. Frequently, NPIs are implemented with an intensity quantified in an ad hoc manner. Control theory offers a worthwhile tool for determining the optimal intensity of the NPIs in order to avoid the collapse of the healthcare system while keeping them as low as possible, yielding concrete guidance to policymakers. A simple controller, which generates a control law that is easy to calculate and to implement is proposed. This controller is robust to large parametric uncertainties in the model used and to some level of noncompliance with the NPIs.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"1 1","pages":"323-346"},"PeriodicalIF":0.4,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84776439","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 : 2021-09-15DOI: 10.25088/complexsystems.30.3.375
Rade Vuckovac
A puzzle lies behind password authentication (PA) and blockchain proof of work (PoW). A cryptographic hash function is commonly used to implement them. The potential problem with secure hash functions is their complexity and rigidity. We explore the use of complex systems constructs such as a cellular automaton (CA) to provide puzzle functionality. The analysis shows that computational irreducibility and sensitivity to initial state phenomena are enough to create simple puzzle systems that can be used for PA and PoW. Moreover, we present puzzle schemata using CA and n-body problems.
{"title":"Cryptographic Puzzles and Complex Systems","authors":"Rade Vuckovac","doi":"10.25088/complexsystems.30.3.375","DOIUrl":"https://doi.org/10.25088/complexsystems.30.3.375","url":null,"abstract":"A puzzle lies behind password authentication (PA) and blockchain proof of work (PoW). A cryptographic hash function is commonly used to implement them. The potential problem with secure hash functions is their complexity and rigidity. We explore the use of complex systems constructs such as a cellular automaton (CA) to provide puzzle functionality. The analysis shows that computational irreducibility and sensitivity to initial state phenomena are enough to create simple puzzle systems that can be used for PA and PoW. Moreover, we present puzzle schemata using CA and n-body problems.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"61 1","pages":"375-390"},"PeriodicalIF":0.4,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83933788","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 : 2021-09-15DOI: 10.25088/complexsystems.30.3.273
M. Cirunay, R. Batac
We compare the statistical distributions of the geometrical properties of road networks for two representative datasets under different levels of planning: the cities comprising Metropolitan Manila show the conditions under bottom-up self-organized growth, while Brasilia and the Australian Capital Territory centered at Canberra represent the case of strict top-down planning. The distribution of segmented areas of the cities shows a dual power-law behavior, with the larger areas following the ∼1.9 scaling exponent observed in other cities, while the smaller areas show a lower exponent of ∼0.5, believed to be due to practical considerations. While all cities are found to favor the formation of straight road segments, the planned city roads have a preponderance of sinuous roads, with sinuosities approaching π. A simple model based on a nearest-neighbor directed branching coupled with sectional grid formations is proposed to capture the nontrivial statistical features observed.
{"title":"Spatial Signatures of Road Network Growth for Different Levels of Global Planning","authors":"M. Cirunay, R. Batac","doi":"10.25088/complexsystems.30.3.273","DOIUrl":"https://doi.org/10.25088/complexsystems.30.3.273","url":null,"abstract":"We compare the statistical distributions of the geometrical properties of road networks for two representative datasets under different levels of planning: the cities comprising Metropolitan Manila show the conditions under bottom-up self-organized growth, while Brasilia and the Australian Capital Territory centered at Canberra represent the case of strict top-down planning. The distribution of segmented areas of the cities shows a dual power-law behavior, with the larger areas following the ∼1.9 scaling exponent observed in other cities, while the smaller areas show a lower exponent of ∼0.5, believed to be due to practical considerations. While all cities are found to favor the formation of straight road segments, the planned city roads have a preponderance of sinuous roads, with sinuosities approaching π. A simple model based on a nearest-neighbor directed branching coupled with sectional grid formations is proposed to capture the nontrivial statistical features observed.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"67 1","pages":"273-296"},"PeriodicalIF":0.4,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75567472","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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