Pub Date : 2023-10-17DOI: 10.1088/2632-072x/ad00f7
Marco Alberto Javarone, Gabriele Di Antonio, Gianni Valerio Vinci, Raffaele Cristodaro, Claudio J. Tessone, Luciano Pietronero
Abstract The behaviour of Bitcoin owners is reflected in the structure and the number of bitcoin transactions encoded in the Blockchain. Likewise, the behaviour of Bitcoin traders is reflected in the formation of bullish and bearish trends in the crypto market. In light of these observations, we wonder if human behaviour underlies some relationship between the Blockchain and the crypto market. To address this question, we map the Blockchain to a spin-lattice problem, whose configurations form ordered and disordered patterns, representing the behaviour of Bitcoin owners. This novel approach allows us to obtain time series suitable to detect a causal relationship between the dynamics of the Blockchain and market trends of the Bitcoin and to find that disordered patterns in the Blockchain precede Bitcoin panic selling. Our results suggest that human behaviour underlying Blockchain evolution and the crypto market brings out a fascinating connection between disorder and panic in Bitcoin dynamics.
{"title":"Disorder Unleashes Panic in Bitcoin Dynamics","authors":"Marco Alberto Javarone, Gabriele Di Antonio, Gianni Valerio Vinci, Raffaele Cristodaro, Claudio J. Tessone, Luciano Pietronero","doi":"10.1088/2632-072x/ad00f7","DOIUrl":"https://doi.org/10.1088/2632-072x/ad00f7","url":null,"abstract":"Abstract The behaviour of Bitcoin owners is reflected in the structure and the number of bitcoin transactions encoded in the Blockchain. Likewise, the behaviour of Bitcoin traders is reflected in the formation of bullish and bearish trends in the crypto market. In light of these observations, we wonder if human behaviour underlies some relationship between the Blockchain and the crypto market. To address this question, we map the Blockchain to a spin-lattice problem, whose configurations form ordered and disordered patterns, representing the behaviour of Bitcoin owners. This novel approach allows us to obtain time series suitable to detect a causal relationship between the dynamics of the Blockchain and market trends of the Bitcoin and to find that disordered patterns in the Blockchain precede Bitcoin panic selling. Our results suggest that human behaviour underlying Blockchain evolution and the crypto market brings out a fascinating connection between disorder and panic in Bitcoin dynamics.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-16DOI: 10.1088/2632-072x/ad0390
Melvyn Tyloo
Abstract For many coupled dynamical systems, the interaction is the outcome of the measurement that each unit has of the others as e.g. in modern inverter-based power grids, autonomous vehicular platoons or swarms of drones, or it is the results of physical flows. Synchronization among all the components of these systems is of primal importance to avoid failures. The overall operational state of these systems therefore crucially depends on the correct and reliable functioning of the individual elements as well as the information they transmit through the network. Here, we investigate the effect of Byzantine attacks where one unit does not behave as expected, but is controlled by an external attacker. For such attacks, we assess the impact on the global collective behavior of nonlinearly coupled phase oscillators. We relate the synchronization error induced by the input signal to the properties of the attacked node. This allows to anticipate the potential of an attacker and identify which network components to secure.
{"title":"Assessing the impact of Byzantine attacks on coupled phase oscillators","authors":"Melvyn Tyloo","doi":"10.1088/2632-072x/ad0390","DOIUrl":"https://doi.org/10.1088/2632-072x/ad0390","url":null,"abstract":"Abstract For many coupled dynamical systems, the interaction is the outcome of the measurement that each unit has of the others as e.g. in modern inverter-based power grids, autonomous vehicular platoons or swarms of drones, or it is the results of physical flows. Synchronization among all the components of these systems is of primal importance to avoid failures. The overall operational state of these systems therefore crucially depends on the correct and reliable functioning of the individual elements as well as the information they transmit through the network. Here, we investigate the effect of Byzantine attacks where one unit does not behave as expected, but is controlled by an external attacker. For such attacks, we assess the impact on the global collective behavior of nonlinearly coupled phase oscillators. We relate the synchronization error induced by the input signal to the properties of the attacked node. This allows to anticipate the potential of an attacker and identify which network components to secure.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1088/2632-072x/ad0017
Rima Hazra, Mayank Singh, Pawan Goyal, Bibhas Adhikari, Animesh Mukherjee
Abstract Interdisciplinarity has over the recent years have gained tremendous importance and has become one of the key ways of doing cutting edge research. In this paper we attempt to model the citation flow across three different fields—physics (PHY), mathematics (MA) and computer science (CS). For instance, is there a specific pattern in which these fields cite one another? We carry out experiments on a dataset comprising more than 1.2 million articles taken from these three fields. We quantify the citation interactions among these three fields through temporal bucket signatures . We present numerical models based on variants of the recently proposed relay-linking framework to explain the citation dynamics across the three disciplines. These models make a modest attempt to unfold the underlying principles of how citation links could have been formed across the three fields over time.
{"title":"Modeling interdisciplinary interactions among Physics, Mathematics and Computer Science","authors":"Rima Hazra, Mayank Singh, Pawan Goyal, Bibhas Adhikari, Animesh Mukherjee","doi":"10.1088/2632-072x/ad0017","DOIUrl":"https://doi.org/10.1088/2632-072x/ad0017","url":null,"abstract":"Abstract Interdisciplinarity has over the recent years have gained tremendous importance and has become one of the key ways of doing cutting edge research. In this paper we attempt to model the citation flow across three different fields—physics (PHY), mathematics (MA) and computer science (CS). For instance, is there a specific pattern in which these fields cite one another? We carry out experiments on a dataset comprising more than 1.2 million articles taken from these three fields. We quantify the citation interactions among these three fields through temporal bucket signatures . We present numerical models based on variants of the recently proposed relay-linking framework to explain the citation dynamics across the three disciplines. These models make a modest attempt to unfold the underlying principles of how citation links could have been formed across the three fields over time.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135804578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1088/2632-072x/ad0208
Jiafeng Xiao, Linjie Liu, Xiaojie Chen, Attila Szolnoki
Abstract A social dilemma implies that individuals will choose the defection strategy to maximize their individual gains. Reward is a powerful motivator to promote the evolution of cooperation, thus addressing the social dilemma. Nevertheless, it is costly since we need to monitor all participants in the game. Inspired by these observations, we here propose an inexpensive protocol, a so-called sampling reward mechanism, and apply it to social dilemmas, including public goods game and collective-risk social dilemma. More precisely, the actual usage of reward depends on the portion of cooperators in the sample. We show that the average cooperation level can be effectively improved under high reward threshold and high reward intensity, albeit at the expense of reward cost. It is intriguing to discover that for the latter aspect, there is a critical threshold at which further increases in reward intensity have no significant effect on improving the cooperation level. Moreover, we find that the small sample size favors the evolution of cooperation while an intermediate sample size always results in a lower reward cost. We also demonstrate that our findings are robust and remain valid for both types of social dilemma.
{"title":"Evolution of cooperation driven by sampling reward","authors":"Jiafeng Xiao, Linjie Liu, Xiaojie Chen, Attila Szolnoki","doi":"10.1088/2632-072x/ad0208","DOIUrl":"https://doi.org/10.1088/2632-072x/ad0208","url":null,"abstract":"Abstract A social dilemma implies that individuals will choose the defection strategy to maximize their individual gains. Reward is a powerful motivator to promote the evolution of cooperation, thus addressing the social dilemma. Nevertheless, it is costly since we need to monitor all participants in the game. Inspired by these observations, we here propose an inexpensive protocol, a so-called sampling reward mechanism, and apply it to social dilemmas, including public goods game and collective-risk social dilemma. More precisely, the actual usage of reward depends on the portion of cooperators in the sample. We show that the average cooperation level can be effectively improved under high reward threshold and high reward intensity, albeit at the expense of reward cost. It is intriguing to discover that for the latter aspect, there is a critical threshold at which further increases in reward intensity have no significant effect on improving the cooperation level. Moreover, we find that the small sample size favors the evolution of cooperation while an intermediate sample size always results in a lower reward cost. We also demonstrate that our findings are robust and remain valid for both types of social dilemma.
","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/2632-072x/acff33
Gaia Colombani, Giulia Bertagnolli, Oriol Artime
Abstract The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modeling a plethora of relevant aspects in network science, such as network navigability, robustness and resilience. We analytically characterize self-avoiding random walkers that evolve on complex networks and whose memory suffers stochastic resetting, that is, at each step, with a certain probability, they forget their previous trajectory and start free diffusion anew. Several out-of-equilibrium properties are addressed, such as the time-dependent position of the walker, the time-dependent degree distribution of the non-visited network and the first-passage time distribution, and its moments, to target nodes. We examine these metrics for different resetting parameters and network topologies, both synthetic and empirical, and find a good agreement with simulations in all cases. We also explore the role of resetting on network exploration and report a non-monotonic behavior of the cover time: frequent memory resets induce a global minimum in the cover time, significantly outperforming the well-known case of the pure random walk, while reset events that are too spaced apart become detrimental for the network discovery. Our results provide new insights into the profound interplay between topology and dynamics in complex networks, and shed light on the fundamental properties of SARWs in nontrivial environments.
{"title":"Efficient network exploration by means of resetting self-avoiding random walkers","authors":"Gaia Colombani, Giulia Bertagnolli, Oriol Artime","doi":"10.1088/2632-072x/acff33","DOIUrl":"https://doi.org/10.1088/2632-072x/acff33","url":null,"abstract":"Abstract The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modeling a plethora of relevant aspects in network science, such as network navigability, robustness and resilience. We analytically characterize self-avoiding random walkers that evolve on complex networks and whose memory suffers stochastic resetting, that is, at each step, with a certain probability, they forget their previous trajectory and start free diffusion anew. Several out-of-equilibrium properties are addressed, such as the time-dependent position of the walker, the time-dependent degree distribution of the non-visited network and the first-passage time distribution, and its moments, to target nodes. We examine these metrics for different resetting parameters and network topologies, both synthetic and empirical, and find a good agreement with simulations in all cases. We also explore the role of resetting on network exploration and report a non-monotonic behavior of the cover time: frequent memory resets induce a global minimum in the cover time, significantly outperforming the well-known case of the pure random walk, while reset events that are too spaced apart become detrimental for the network discovery. Our results provide new insights into the profound interplay between topology and dynamics in complex networks, and shed light on the fundamental properties of SARWs in nontrivial environments.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-04DOI: 10.1088/2632-072x/ad0018
Caterina A M La Porta, Stefano Zapperi
Abstract Inequalities in wealth, income, access to food and healthcare have been rising worldwide in the past decades, approaching levels seen in the early 20th century. Here we study the relationships between wealth inequality and mobility for different segments of the population, comparing longitudinal surveys conducted in the USA and in Italy. The larger wealth inequality observed in the USA is reflected by poorer health conditions than in Italy. We also find that in both countries wealth mobility becomes slower at the two extremes of the wealth distribution. Households trapped in a state of persistent lack of wealth are generally experiencing greater food insecurity and poorer health than the general population. We interpret the observed association between inequality and immobility using a simple agent based model of wealth condensation driven by random returns and exchanges. The model describes well survey data on a qualitative level, but the mobility is generally overestimated by the model. We trace back this discrepancy to the way income is generated for low-wealth households which is not correctly accounted by the model. On the other hand, the model is excellent in describing the wealth dynamics within a restricted class of ultra-wealthy, as we demonstrate by analyzing billionaires lists. Our results suggest that different forms of inequality are intertwined and should therefore be addressed together.
{"title":"Unraveling the dynamics of wealth inequality and the impact on social mobility and health disparities","authors":"Caterina A M La Porta, Stefano Zapperi","doi":"10.1088/2632-072x/ad0018","DOIUrl":"https://doi.org/10.1088/2632-072x/ad0018","url":null,"abstract":"Abstract Inequalities in wealth, income, access to food and healthcare have been rising worldwide in the past decades, approaching levels seen in the early 20th century. Here we study the relationships between wealth inequality and mobility for different segments of the population, comparing longitudinal surveys conducted in the USA and in Italy. The larger wealth inequality observed in the USA is reflected by poorer health conditions than in Italy. We also find that in both countries wealth mobility becomes slower at the two extremes of the wealth distribution. Households trapped in a state of persistent lack of wealth are generally experiencing greater food insecurity and poorer health than the general population. We interpret the observed association between inequality and immobility using a simple agent based model of wealth condensation driven by random returns and exchanges. The model describes well survey data on a qualitative level, but the mobility is generally overestimated by the model. We trace back this discrepancy to the way income is generated for low-wealth households which is not correctly accounted by the model. On the other hand, the model is excellent in describing the wealth dynamics within a restricted class of ultra-wealthy, as we demonstrate by analyzing billionaires lists. Our results suggest that different forms of inequality are intertwined and should therefore be addressed together.
","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135549048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-18DOI: 10.1088/2632-072x/acfadd
Robin Delabays, Laurent Pagnier, Benjamin Schäfer, Melvyn Tyloo, Dirk Witthaut
Abstract The ongoing rapid transformation of our energy supply challenges the operation and stability of electric power grids and other supply networks. This focus issue comprises new ideas and concepts in the monitoring and control of complex networks to address these challenges.
{"title":"Focus on Monitoring and Control of Complex Supply Systems","authors":"Robin Delabays, Laurent Pagnier, Benjamin Schäfer, Melvyn Tyloo, Dirk Witthaut","doi":"10.1088/2632-072x/acfadd","DOIUrl":"https://doi.org/10.1088/2632-072x/acfadd","url":null,"abstract":"Abstract The ongoing rapid transformation of our energy supply challenges the operation and stability of electric power grids and other supply networks. This focus issue comprises new ideas and concepts in the monitoring and control of complex networks to address these challenges.
","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135149935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1088/2632-072x/acf6a4
Ruben Interian, Francisco Aparecido Rodrigues
The erosion of social cohesion and polarization is one of the topmost societal risks. In this work, we investigated the evolution of polarization, influence, and domination in online interaction networks using a large Twitter dataset collected before and during the 2022 Brazilian elections. From a theoretical perspective, we develop a methodology called d-modularity that allows discovering the contribution of specific groups to network polarization using the well-known modularity measure. While the overall network modularity (somewhat unexpectedly) decreased, the proposed group-oriented approach reveals that the contribution of the right-leaning community to this modularity increased, remaining very high during the analyzed period. Our methodology is general enough to be used in any situation when the contribution of specific groups to overall network modularity and polarization is needed to investigate. Moreover, using the concept of partial domination, we are able to compare the reach of sets of influential profiles from different groups and their ability to accomplish coordinated communication inside their groups and across segments of the entire network. We show that in the whole network, the left-leaning high-influential information spreaders dominated, reaching a substantial fraction of users with fewer spreaders. However, when comparing domination inside the groups, the results are inverse. Right-leaning spreaders dominate their communities using few nodes, showing as the most capable of accomplishing coordinated communication. The results bring evidence of extreme isolation and the ease of accomplishing coordinated communication that characterized right-leaning communities during the 2022 Brazilian elections, which likely influenced the subsequent coup events in Brasilia.
{"title":"Group polarization, influence, and domination in online interaction networks: A case study of the 2022 Brazilian elections","authors":"Ruben Interian, Francisco Aparecido Rodrigues","doi":"10.1088/2632-072x/acf6a4","DOIUrl":"https://doi.org/10.1088/2632-072x/acf6a4","url":null,"abstract":"The erosion of social cohesion and polarization is one of the topmost societal risks. In this work, we investigated the evolution of polarization, influence, and domination in online interaction networks using a large Twitter dataset collected before and during the 2022 Brazilian elections. From a theoretical perspective, we develop a methodology called d-modularity that allows discovering the contribution of specific groups to network polarization using the well-known modularity measure. While the overall network modularity (somewhat unexpectedly) decreased, the proposed group-oriented approach reveals that the contribution of the right-leaning community to this modularity increased, remaining very high during the analyzed period. Our methodology is general enough to be used in any situation when the contribution of specific groups to overall network modularity and polarization is needed to investigate. Moreover, using the concept of partial domination, we are able to compare the reach of sets of influential profiles from different groups and their ability to accomplish coordinated communication inside their groups and across segments of the entire network. We show that in the whole network, the left-leaning high-influential information spreaders dominated, reaching a substantial fraction of users with fewer spreaders. However, when comparing domination inside the groups, the results are inverse. Right-leaning spreaders dominate their communities using few nodes, showing as the most capable of accomplishing coordinated communication. The results bring evidence of extreme isolation and the ease of accomplishing coordinated communication that characterized right-leaning communities during the 2022 Brazilian elections, which likely influenced the subsequent coup events in Brasilia.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"08 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135098462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1088/2632-072x/acf90b
Shogo Mizutaka
Abstract A recent study (Chiyomaru and Takemoto 2022 Phys. Rev. E 106 014301) considered adversarial attacks conducted to distort voter model dynamics in networks. This method intervenes in the interaction patterns of individuals and induces them to be in a target opinion state through a small perturbation ε . In this study, we investigate adversarial attacks on voter dynamics in random networks of finite size n . The exit probability P +1 to reach the target absorbing state and the mean time τ n to reach consensus are analyzed in the mean-field approximation. Given ε > 0, the exit probability P +1 converges asymptotically to unity as n increases. The mean time τ n to reach consensus scales as <?CDATA $(ln epsilon n)/epsilon$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ln</mml:mi> <mml:mi>ϵ</mml:mi> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>/</mml:mo> <mml:mi>ϵ</mml:mi> </mml:mrow> </mml:math> for homogeneous networks with a large finite n . By contrast, it scales as <?CDATA $(ln (epsilonmu_1^2n/mu_2))/epsilon$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mo form="prefix">ln</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ϵ</mml:mi> <mml:msubsup> <mml:mi>μ</mml:mi> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>ϵ</mml:mi> </mml:math> for heterogeneous networks with a large finite n , where µ 1 and µ 2 represent the first and second moments of the degree distribution, respectively. Moreover, we observe the crossover phenomenon of τ n from a linear scale to a logarithmic scale and find <?CDATA $n_{mathrm{co}}sim epsilon^{-1/alpha}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> <mml:mi mathvariant="normal">o</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> </mml:math> above which the state of all nodes becomes the target state in logarithmic time. Here, α = 1 for homogeneous networks and <?CDATA $alpha = (gamma-1)/2$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> for scale-free networks with a degree exponent <?CDATA $2ltgammalt3$?> <mml:math xmlns:mml="ht
{"title":"Crossover phenomenon in adversarial attacks on voter model","authors":"Shogo Mizutaka","doi":"10.1088/2632-072x/acf90b","DOIUrl":"https://doi.org/10.1088/2632-072x/acf90b","url":null,"abstract":"Abstract A recent study (Chiyomaru and Takemoto 2022 Phys. Rev. E 106 014301) considered adversarial attacks conducted to distort voter model dynamics in networks. This method intervenes in the interaction patterns of individuals and induces them to be in a target opinion state through a small perturbation ε . In this study, we investigate adversarial attacks on voter dynamics in random networks of finite size n . The exit probability P +1 to reach the target absorbing state and the mean time τ n to reach consensus are analyzed in the mean-field approximation. Given ε > 0, the exit probability P +1 converges asymptotically to unity as n increases. The mean time τ n to reach consensus scales as <?CDATA $(ln epsilon n)/epsilon$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ln</mml:mi> <mml:mi>ϵ</mml:mi> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>/</mml:mo> <mml:mi>ϵ</mml:mi> </mml:mrow> </mml:math> for homogeneous networks with a large finite n . By contrast, it scales as <?CDATA $(ln (epsilonmu_1^2n/mu_2))/epsilon$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mo form=\"prefix\">ln</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ϵ</mml:mi> <mml:msubsup> <mml:mi>μ</mml:mi> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>ϵ</mml:mi> </mml:math> for heterogeneous networks with a large finite n , where µ 1 and µ 2 represent the first and second moments of the degree distribution, respectively. Moreover, we observe the crossover phenomenon of τ n from a linear scale to a logarithmic scale and find <?CDATA $n_{mathrm{co}}sim epsilon^{-1/alpha}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"normal\">c</mml:mi> <mml:mi mathvariant=\"normal\">o</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> </mml:math> above which the state of all nodes becomes the target state in logarithmic time. Here, α = 1 for homogeneous networks and <?CDATA $alpha = (gamma-1)/2$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> for scale-free networks with a degree exponent <?CDATA $2ltgammalt3$?> <mml:math xmlns:mml=\"ht","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135255215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-21DOI: 10.1088/2632-072X/acf264
A. Ramezanpour, A. Mashaghi
Biochemical reaction networks are expected to encode an efficient representation of the function of cells in a variable environment. It is thus important to see how these networks do learn and implement such representations. The first step in this direction is to characterize the function and learning capabilities of basic artificial reaction networks. In this study, we consider multilayer networks of reversible reactions that connect two layers of signal and response species through an intermediate layer of hidden species. We introduce a stochastic learning algorithm that updates the reaction rates based on the correlation values between reaction products and responses. Our findings indicate that the function of networks with random reaction rates, as well as their learning capacity for random signal-response activities, are critically determined by the number of reactants and reaction products. Moreover, the stored patterns exhibit different levels of robustness and qualities as the reaction rates deviate from their optimal values in a stochastic model of defect evolution. These findings can help suggest network modules that are better suited to specific functions, such as amplifiers or dampeners, or to the learning of biologically relevant signal-response activities.
{"title":"Learning capacity and function of stochastic reaction networks","authors":"A. Ramezanpour, A. Mashaghi","doi":"10.1088/2632-072X/acf264","DOIUrl":"https://doi.org/10.1088/2632-072X/acf264","url":null,"abstract":"Biochemical reaction networks are expected to encode an efficient representation of the function of cells in a variable environment. It is thus important to see how these networks do learn and implement such representations. The first step in this direction is to characterize the function and learning capabilities of basic artificial reaction networks. In this study, we consider multilayer networks of reversible reactions that connect two layers of signal and response species through an intermediate layer of hidden species. We introduce a stochastic learning algorithm that updates the reaction rates based on the correlation values between reaction products and responses. Our findings indicate that the function of networks with random reaction rates, as well as their learning capacity for random signal-response activities, are critically determined by the number of reactants and reaction products. Moreover, the stored patterns exhibit different levels of robustness and qualities as the reaction rates deviate from their optimal values in a stochastic model of defect evolution. These findings can help suggest network modules that are better suited to specific functions, such as amplifiers or dampeners, or to the learning of biologically relevant signal-response activities.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48587367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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