Pub Date : 2024-07-04DOI: 10.1088/2632-072x/ad5cb9
Silvia Muñoz-Álvarez, Carlos Gracia-Lázaro and Yamir Moreno
The sustainable exploitation of natural resources constitutes a real-world problem of interest for many fields. In this work, we study those situations in which the exploiting agents have information about the state of the resource and their own benefits and costs but not about the behavior or performance of the rest of the agents. Cognitive Hierarchy Theory provides a framework for those low-information scenarios by focusing on the assumptions that agents make about other individuals’ behavior. Motivated by this theory, we introduce a theoretical agent-based model in which agents exhibit varying degrees of rationalization when exploiting the resource, and this resource’s evolution is driven by a differential equation that mirrors the dynamics of real-world resource growth. Our results show that, although most regimes imply depletion, higher benefits and sustainability are obtained when agents assume overexploitation by the rest and try to compensate for it. Furthermore, many exploiting agents and a long-term perspective also involve a better resource state, reaching the optimal exploitation level when all these factors come together.
{"title":"Modeling natural resources exploitation in low-information environments","authors":"Silvia Muñoz-Álvarez, Carlos Gracia-Lázaro and Yamir Moreno","doi":"10.1088/2632-072x/ad5cb9","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5cb9","url":null,"abstract":"The sustainable exploitation of natural resources constitutes a real-world problem of interest for many fields. In this work, we study those situations in which the exploiting agents have information about the state of the resource and their own benefits and costs but not about the behavior or performance of the rest of the agents. Cognitive Hierarchy Theory provides a framework for those low-information scenarios by focusing on the assumptions that agents make about other individuals’ behavior. Motivated by this theory, we introduce a theoretical agent-based model in which agents exhibit varying degrees of rationalization when exploiting the resource, and this resource’s evolution is driven by a differential equation that mirrors the dynamics of real-world resource growth. Our results show that, although most regimes imply depletion, higher benefits and sustainability are obtained when agents assume overexploitation by the rest and try to compensate for it. Furthermore, many exploiting agents and a long-term perspective also involve a better resource state, reaching the optimal exploitation level when all these factors come together.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"36 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548382","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 : 2024-07-04DOI: 10.1088/2632-072x/ad5cba
Nirbhay Patil, Fabián Aguirre-López and Jean-Philippe Bouchaud
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.
{"title":"The spectral boundary of block structured random matrices","authors":"Nirbhay Patil, Fabián Aguirre-López and Jean-Philippe Bouchaud","doi":"10.1088/2632-072x/ad5cba","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5cba","url":null,"abstract":"Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"31 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548383","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 : 2024-06-20DOI: 10.1088/2632-072x/ad577f
Carlos Gracia-Lázaro, Alexis R Hernández, Felipe Maciel-Cardoso and Yamir Moreno
We present an agent-based model that explores the intricate relationship between pro-family and prosocial behaviors and their impact on settlement formation. The objective is to investigate how the technological level and various constraints influence the transition from pro-family to prosocial behavior. The model incorporates factors such as the specialization requirements of the technology, societal tolerance, and dynamic interactions within a synthetic population, where individuals may prioritize either their family or their own settlement. Agents’ fitness is determined by two components: the proportion of pro-family agents within their family and the fraction of prosocial agents in their settlement, along with its size. Our findings reveal that (i) the technological level drives the transition from pro-family to prosocial behavior, and (ii) the developmental requirements of the technology shape the smoothness of this transition, ranging from abrupt to gradual. These results emphasize the significance of considering the interplay between the technological level, the nature of the technology, and cultural influences when examining settlement patterns and the dynamics of pro-family and prosocial behaviors in human societies.
{"title":"Exploring the interplay of technology, pro-family and prosocial behavior in settlement formation","authors":"Carlos Gracia-Lázaro, Alexis R Hernández, Felipe Maciel-Cardoso and Yamir Moreno","doi":"10.1088/2632-072x/ad577f","DOIUrl":"https://doi.org/10.1088/2632-072x/ad577f","url":null,"abstract":"We present an agent-based model that explores the intricate relationship between pro-family and prosocial behaviors and their impact on settlement formation. The objective is to investigate how the technological level and various constraints influence the transition from pro-family to prosocial behavior. The model incorporates factors such as the specialization requirements of the technology, societal tolerance, and dynamic interactions within a synthetic population, where individuals may prioritize either their family or their own settlement. Agents’ fitness is determined by two components: the proportion of pro-family agents within their family and the fraction of prosocial agents in their settlement, along with its size. Our findings reveal that (i) the technological level drives the transition from pro-family to prosocial behavior, and (ii) the developmental requirements of the technology shape the smoothness of this transition, ranging from abrupt to gradual. These results emphasize the significance of considering the interplay between the technological level, the nature of the technology, and cultural influences when examining settlement patterns and the dynamics of pro-family and prosocial behaviors in human societies.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"46 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505703","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 : 2024-06-19DOI: 10.1088/2632-072x/ad5635
Christian Bick, Tobias Böhle and Oleh E Omel’chenko
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott–Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is π apart) as well as twisted states with a different winding number.
{"title":"Hopf bifurcations of twisted states in phase oscillators rings with nonpairwise higher-order interactions","authors":"Christian Bick, Tobias Böhle and Oleh E Omel’chenko","doi":"10.1088/2632-072x/ad5635","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5635","url":null,"abstract":"Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott–Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is π apart) as well as twisted states with a different winding number.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"36 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505704","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 : 2024-06-16DOI: 10.1088/2632-072x/ad5263
Marina Carpineti, Valerio Lupo Sepe, Antonella Senese, Giacomo Traversa, Guglielmina A Diolaiuti and Alberto Vailati
The investigation of the evolution of glaciers largely relies on the characterisation of extensive quantities like their mass, area, and perimeter. In this work we use fractal and multifractal analysis to investigate the non-extensive structural properties of the perimeters of glaciers in the Svalbard Archipelago. We show that the perimeters of the glaciers exhibit a fractal structure with a fractal dimension , independently from the area of the glaciers. The investigation of the multifractal properties of the perimeters shows that small glaciers exhibit a more pronounced multifractal structure, as witnessed by the larger range of generalized dimensions Dq needed to characterise them. The range ΔDq of generalised dimensions required to characterise the multifractal perimeter of a glacier exhibits a power-law dependence with exponent −1.2 from the area, and represents a non-extensive parameter able to grab effectively the dependence of the multifractal structure of the perimeters on the size of glaciers. The comparison with similar results obtained in a previous study performed on glaciers in the Lombardy region of the Italian Alps confirms the robustness of the analysis performed, which does not appear to be affected by the morphology of the substrate or by climate conditions.
{"title":"Multifractal analysis of the perimeters of glaciers in the Svalbard Archipelago","authors":"Marina Carpineti, Valerio Lupo Sepe, Antonella Senese, Giacomo Traversa, Guglielmina A Diolaiuti and Alberto Vailati","doi":"10.1088/2632-072x/ad5263","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5263","url":null,"abstract":"The investigation of the evolution of glaciers largely relies on the characterisation of extensive quantities like their mass, area, and perimeter. In this work we use fractal and multifractal analysis to investigate the non-extensive structural properties of the perimeters of glaciers in the Svalbard Archipelago. We show that the perimeters of the glaciers exhibit a fractal structure with a fractal dimension , independently from the area of the glaciers. The investigation of the multifractal properties of the perimeters shows that small glaciers exhibit a more pronounced multifractal structure, as witnessed by the larger range of generalized dimensions Dq needed to characterise them. The range ΔDq of generalised dimensions required to characterise the multifractal perimeter of a glacier exhibits a power-law dependence with exponent −1.2 from the area, and represents a non-extensive parameter able to grab effectively the dependence of the multifractal structure of the perimeters on the size of glaciers. The comparison with similar results obtained in a previous study performed on glaciers in the Lombardy region of the Italian Alps confirms the robustness of the analysis performed, which does not appear to be affected by the morphology of the substrate or by climate conditions.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"20 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505759","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 : 2024-06-16DOI: 10.1088/2632-072x/ad5264
Miki U Kobayashi, Kengo Nakai and Yoshitaka Saiki
We computed the Lyapunov spectrum and finite-time Lyapunov exponents of a data-driven model constructed using reservoir computing. This analysis was performed for two dynamics that exhibit a highly dimensionally unstable structure. We focused on the reconstruction of heterochaotic dynamics, which are characterized by the coexistence of different numbers of unstable dimensions. This was achieved by computing fluctuations in the number of positive finite-time Lyapunov exponents.
{"title":"Lyapunov analysis of data-driven models of high dimensional dynamics using reservoir computing: Lorenz-96 system and fluid flow","authors":"Miki U Kobayashi, Kengo Nakai and Yoshitaka Saiki","doi":"10.1088/2632-072x/ad5264","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5264","url":null,"abstract":"We computed the Lyapunov spectrum and finite-time Lyapunov exponents of a data-driven model constructed using reservoir computing. This analysis was performed for two dynamics that exhibit a highly dimensionally unstable structure. We focused on the reconstruction of heterochaotic dynamics, which are characterized by the coexistence of different numbers of unstable dimensions. This was achieved by computing fluctuations in the number of positive finite-time Lyapunov exponents.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"61 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529269","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 : 2024-06-16DOI: 10.1088/2632-072x/ad4f3d
Bernardo Caldarola, Dario Mazzilli, Lorenzo Napolitano, Aurelio Patelli and Angelica Sbardella
Economic Complexity (EC) methods have gained increasing popularity across fields and disciplines. In particular, the EC toolbox has proved particularly promising in the study of complex and interrelated phenomena, such as the transition towards a more sustainable economy. Using the EC approach, scholars have been investigating the relationship between EC and sustainability, and identifying the distinguishing characteristics of green activities and to assess the readiness of productive and technological structures for the sustainability transition. This article proposes to review and summarize the data, methods, and empirical literature that are relevant to the study of the sustainability transition from an EC perspective. We review three distinct but connected blocks of literature on EC and environmental sustainability. First, we survey the evidence linking measures of EC to indicators related to environmental sustainability. Second, we review articles that strive to assess the green competitiveness of productive systems. Third, we examine evidence on green technological development and its connection to non-green knowledge bases. Finally, we summarize the findings for each block, while identifying criticalities and avenues for further research in this recent and growing body of empirical literature.
{"title":"Economic complexity and the sustainability transition: a review of data, methods, and literature","authors":"Bernardo Caldarola, Dario Mazzilli, Lorenzo Napolitano, Aurelio Patelli and Angelica Sbardella","doi":"10.1088/2632-072x/ad4f3d","DOIUrl":"https://doi.org/10.1088/2632-072x/ad4f3d","url":null,"abstract":"Economic Complexity (EC) methods have gained increasing popularity across fields and disciplines. In particular, the EC toolbox has proved particularly promising in the study of complex and interrelated phenomena, such as the transition towards a more sustainable economy. Using the EC approach, scholars have been investigating the relationship between EC and sustainability, and identifying the distinguishing characteristics of green activities and to assess the readiness of productive and technological structures for the sustainability transition. This article proposes to review and summarize the data, methods, and empirical literature that are relevant to the study of the sustainability transition from an EC perspective. We review three distinct but connected blocks of literature on EC and environmental sustainability. First, we survey the evidence linking measures of EC to indicators related to environmental sustainability. Second, we review articles that strive to assess the green competitiveness of productive systems. Third, we examine evidence on green technological development and its connection to non-green knowledge bases. Finally, we summarize the findings for each block, while identifying criticalities and avenues for further research in this recent and growing body of empirical literature.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"13 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505761","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 : 2024-06-13DOI: 10.1088/2632-072x/ad5247
Marc Harper and Joshua Safyan
We combine momentum from machine learning with evolutionary dynamics, where momentum can be viewed as a simple mechanism of intergenerational memory similar to epigenetic mechanisms. Using information divergences as Lyapunov functions, we show that momentum accelerates the convergence of evolutionary dynamics including the continuous and discrete replicator equations and Euclidean gradient descent on populations. When evolutionarily stable states are present, these methods prove convergence for small learning rates or small momentum, and yield an analytic determination of the relative decrease in time to converge that agrees well with computations. The main results apply even when the evolutionary dynamic is not a gradient flow. We also show that momentum can alter the convergence properties of these dynamics, for example by breaking the cycling associated to the rock–paper–scissors landscape, leading to either convergence to the ordinarily non-absorbing equilibrium, or divergence, depending on the value and mechanism of momentum.
{"title":"Momentum accelerates evolutionary dynamics","authors":"Marc Harper and Joshua Safyan","doi":"10.1088/2632-072x/ad5247","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5247","url":null,"abstract":"We combine momentum from machine learning with evolutionary dynamics, where momentum can be viewed as a simple mechanism of intergenerational memory similar to epigenetic mechanisms. Using information divergences as Lyapunov functions, we show that momentum accelerates the convergence of evolutionary dynamics including the continuous and discrete replicator equations and Euclidean gradient descent on populations. When evolutionarily stable states are present, these methods prove convergence for small learning rates or small momentum, and yield an analytic determination of the relative decrease in time to converge that agrees well with computations. The main results apply even when the evolutionary dynamic is not a gradient flow. We also show that momentum can alter the convergence properties of these dynamics, for example by breaking the cycling associated to the rock–paper–scissors landscape, leading to either convergence to the ordinarily non-absorbing equilibrium, or divergence, depending on the value and mechanism of momentum.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"17 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141518211","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 : 2024-06-04DOI: 10.1088/2632-072x/ad4dfb
Federico Corberi and Claudio Castellano
The voter model is an extremely simple yet nontrivial prototypical model of ordering dynamics, which has been studied in great detail. Recently, a great deal of activity has focused on long-range statistical physics models, where interactions take place among faraway sites, with a probability slowly decaying with distance. In this paper, we study analytically the one-dimensional long-range voter model, where an agent takes the opinion of another at distance r with probability . The model displays rich and diverse features as α is changed. For α > 3 the behavior is similar to the one of the nearest-neighbor version, with the formation of ordered domains whose typical size grows as until consensus (a fully ordered configuration) is reached. The correlation function between two agents at distance r obeys dynamical scaling with sizeable corrections at large distances , slowly fading away in time. For violations of scaling appear, due to the simultaneous presence of two lengh-scales, the size of domains growing as , and the distance over which correlations extend. For the system reaches a partially ordered stationary state, characterised by an algebraic correlator, whose lifetime diverges in the thermodynamic limit of infinitely many agents, so that consensus is not reached. For a finite system escape towards the fully ordered configuration is finally promoted by development of large distance correlations. In a system of N sites, global consensus is achieved after a time for α > 3, for , and for .
投票者模型是一个极其简单但又非简单的有序动力学原型模型，人们对它进行了深入细致的研究。最近，大量研究都集中在远距离统计物理模型上，在这种模型中，相互作用发生在遥远的地点之间，概率随距离缓慢衰减。在本文中，我们分析研究了一维远距离选民模型，其中一个代理人以概率 。随着 α 的变化，该模型显示出丰富多样的特征。当 α > 3 时，该模型的行为类似于近邻模型，会形成有序域，其典型大小随着共识（完全有序配置）的达成而增长。距离 r 的两个代理之间的相关函数服从动态缩放，在距离较大时有相当大的修正，并随着时间的推移慢慢消失。由于同时存在两个长度尺度，即域的大小随着距离的增大而增大，以及相关性延伸的距离。系统会达到部分有序的静止状态，其特征是代数相关器，其寿命在无限多代理的热力学极限下发散，因此无法达成共识。对于有限系统来说，大距离相关性的发展最终会促进系统向完全有序的构型逃逸。在一个由 N 个位点组成的系统中，当 α > 3、 、 和 时，会在一段时间后达成全局共识。
{"title":"Kinetics of the one-dimensional voter model with long-range interactions","authors":"Federico Corberi and Claudio Castellano","doi":"10.1088/2632-072x/ad4dfb","DOIUrl":"https://doi.org/10.1088/2632-072x/ad4dfb","url":null,"abstract":"The voter model is an extremely simple yet nontrivial prototypical model of ordering dynamics, which has been studied in great detail. Recently, a great deal of activity has focused on long-range statistical physics models, where interactions take place among faraway sites, with a probability slowly decaying with distance. In this paper, we study analytically the one-dimensional long-range voter model, where an agent takes the opinion of another at distance r with probability . The model displays rich and diverse features as α is changed. For α > 3 the behavior is similar to the one of the nearest-neighbor version, with the formation of ordered domains whose typical size grows as until consensus (a fully ordered configuration) is reached. The correlation function between two agents at distance r obeys dynamical scaling with sizeable corrections at large distances , slowly fading away in time. For violations of scaling appear, due to the simultaneous presence of two lengh-scales, the size of domains growing as , and the distance over which correlations extend. For the system reaches a partially ordered stationary state, characterised by an algebraic correlator, whose lifetime diverges in the thermodynamic limit of infinitely many agents, so that consensus is not reached. For a finite system escape towards the fully ordered configuration is finally promoted by development of large distance correlations. In a system of N sites, global consensus is achieved after a time for α > 3, for , and for .","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"42 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252986","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 : 2024-05-27DOI: 10.1088/2632-072x/ad4c45
Benjamin Krawciw, Lincoln D Carr and Cecilia Diniz Behn
Complex network theory has focused on properties of networks with real-valued edge weights. However, in signal transfer networks, such as those representing the transfer of light across an interferometer, complex-valued edge weights are needed to represent the manipulation of the signal in both magnitude and phase. These complex-valued edge weights introduce interference into the signal transfer, but it is unknown how such interference affects network properties such as small-worldness. To address this gap, we have introduced a small-world interferometer network model with complex-valued edge weights and generalized existing network measures to define the interferometric clustering coefficient, the apparent path length, and the interferometric small-world coefficient. Using high-performance computing resources, we generated a large set of small-world interferometers over a wide range of parameters in system size, nearest-neighbor count, and edge-weight phase and computed their interferometric network measures. We found that the interferometric small-world coefficient depends significantly on the amount of phase on complex-valued edge weights: for small edge-weight phases, constructive interference led to a higher interferometric small-world coefficient; while larger edge-weight phases induced destructive interference which led to a lower interferometric small-world coefficient. Thus, for the small-world interferometer model, interferometric measures are necessary to capture the effect of interference on signal transfer. This model is an example of the type of problem that necessitates interferometric measures, and applies to any wave-based network including quantum networks.
{"title":"The small-world effect for interferometer networks","authors":"Benjamin Krawciw, Lincoln D Carr and Cecilia Diniz Behn","doi":"10.1088/2632-072x/ad4c45","DOIUrl":"https://doi.org/10.1088/2632-072x/ad4c45","url":null,"abstract":"Complex network theory has focused on properties of networks with real-valued edge weights. However, in signal transfer networks, such as those representing the transfer of light across an interferometer, complex-valued edge weights are needed to represent the manipulation of the signal in both magnitude and phase. These complex-valued edge weights introduce interference into the signal transfer, but it is unknown how such interference affects network properties such as small-worldness. To address this gap, we have introduced a small-world interferometer network model with complex-valued edge weights and generalized existing network measures to define the interferometric clustering coefficient, the apparent path length, and the interferometric small-world coefficient. Using high-performance computing resources, we generated a large set of small-world interferometers over a wide range of parameters in system size, nearest-neighbor count, and edge-weight phase and computed their interferometric network measures. We found that the interferometric small-world coefficient depends significantly on the amount of phase on complex-valued edge weights: for small edge-weight phases, constructive interference led to a higher interferometric small-world coefficient; while larger edge-weight phases induced destructive interference which led to a lower interferometric small-world coefficient. Thus, for the small-world interferometer model, interferometric measures are necessary to capture the effect of interference on signal transfer. This model is an example of the type of problem that necessitates interferometric measures, and applies to any wave-based network including quantum networks.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"97 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170809","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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