Semantic Information Theory (SIT) offers a new approach to evaluating the information architecture of complex systems. In this study we describe the steps required to {it operationalize} SIT via its application to dynamical problems. Our road map has four steps: (1) separating the dynamical system into agent-environment sub-systems; (2) choosing an appropriate coarse graining and quantifying correlations; (3) identifying a measure of viability; (4) implementing a scrambling protocol and measuring the semantic content. We apply the road map to a model inspired by the neural dynamics of epileptic seizures whereby an agent (a control process) attempts to maintain an environment (a base process) in a desynchronized state. The synchronization dynamics is studied through the well-known Kuramoto model of phase synchronization. Our application of SIT to this problem reveals new features of both semantic information and the Kuramoto model. For the latter we find articulating the correlational structure for agent and environment(the oscillators), allows us to cast the model in in a novel computational (information theoretic) perspective, where the agent-environment dynamics can be thought of as analyzing a communication channel. For the former we find that all the information in our system is semantic. This is in contrast to previous SIT studies of foragers in which semantic thresholds where seen above which no further semantic content was obtained.
语义信息论（SIT）为评估复杂系统的信息架构提供了一种新方法。在本研究中，我们描述了将 SIT 应用于动态问题所需的步骤。通过将SIT应用于动态问题所需的步骤。我们的路线图有四个步骤：(1)将动态系统分离为人-环境子系统；(2)选择适当的粗粒度并量化相关性；(3)确定可行性度量；(4)实施扰码协议并测量语义内容。我们将路线图应用到一个受癫痫发作神经动力学启发的模型中，在该模型中，代理（控制过程）试图将环境（基础过程）维持在非同步状态。同步动力学通过著名的仓本相位同步模型进行研究。我们将 SIT 应用于这一问题，揭示了语义信息和仓本模型的新特征。对于后者，我们发现将代理和环境（振荡器）的相关结构衔接起来，可以将模型置于一个新颖的计算（信息论）视角中，代理-环境动力学可以被视为对通信通道的分析。对于前者，我们发现我们系统中的所有信息都是语义信息。这与之前对觅食者进行的 SIT 研究形成了鲜明对比，在之前的研究中，我们看到了语义阈值，超过这个阈值就无法获得更多语义内容。
{"title":"Semantic Information Theory in a feedback-control Kuramoto Model","authors":"Damian R Sowinski, Adam Frank, Gourab Ghoshal","doi":"arxiv-2404.02221","DOIUrl":"https://doi.org/arxiv-2404.02221","url":null,"abstract":"Semantic Information Theory (SIT) offers a new approach to evaluating the\u0000information architecture of complex systems. In this study we describe the\u0000steps required to {it operationalize} SIT via its application to dynamical\u0000problems. Our road map has four steps: (1) separating the dynamical system into\u0000agent-environment sub-systems; (2) choosing an appropriate coarse graining and\u0000quantifying correlations; (3) identifying a measure of viability; (4)\u0000implementing a scrambling protocol and measuring the semantic content. We apply\u0000the road map to a model inspired by the neural dynamics of epileptic seizures\u0000whereby an agent (a control process) attempts to maintain an environment (a\u0000base process) in a desynchronized state. The synchronization dynamics is\u0000studied through the well-known Kuramoto model of phase synchronization. Our\u0000application of SIT to this problem reveals new features of both semantic\u0000information and the Kuramoto model. For the latter we find articulating the\u0000correlational structure for agent and environment(the oscillators), allows us\u0000to cast the model in in a novel computational (information theoretic)\u0000perspective, where the agent-environment dynamics can be thought of as\u0000analyzing a communication channel. For the former we find that all the\u0000information in our system is semantic. This is in contrast to previous SIT\u0000studies of foragers in which semantic thresholds where seen above which no\u0000further semantic content was obtained.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598310","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}
Many natural, living and engineered systems display oscillations that are characterized by multiple timescales. Typically, such systems are described as slow-fast systems, where the slow dynamics result from a hyperbolic slow manifold that guides the movement of the system trajectories. Recently, we have provided an alternative description in which the slow dynamics result from a non-hyperbolic and Lyapunov-unstable attracting sets from connected dynamical ghosts that form a closed orbit (termed ghost cycles). Here we investigate the response properties of both type of systems to external forcing. Using the classical Van-der-Pol oscillator and two modified versions of this model that correspond to a 1-ghost and a 2-ghost cycle, respectively, we find that ghost cycles are characterized by significant increase especially in the 1:1 entrainment regions as demonstrated by the corresponding Arnold tongues and exhibit richer dynamics (bursting, chaos) in contrast to the classical slow-fast system. Phase plane analysis reveals that these features result from the continuous remodeling of the attractor landscape of the ghost cycles models characteristic for non-autonomous systems, whereas the attractor landscape of the corresponding slow-fast system remains qualitatively unaltered. We propose that systems containing ghost cycles display increased flexibility and responsiveness to continuous environmental changes.
{"title":"Ghost cycles exhibit increased entrainment and richer dynamics in response to external forcing compared to slow-fast systems","authors":"Daniel Koch, Aneta Koseska","doi":"arxiv-2403.19624","DOIUrl":"https://doi.org/arxiv-2403.19624","url":null,"abstract":"Many natural, living and engineered systems display oscillations that are\u0000characterized by multiple timescales. Typically, such systems are described as\u0000slow-fast systems, where the slow dynamics result from a hyperbolic slow\u0000manifold that guides the movement of the system trajectories. Recently, we have\u0000provided an alternative description in which the slow dynamics result from a\u0000non-hyperbolic and Lyapunov-unstable attracting sets from connected dynamical\u0000ghosts that form a closed orbit (termed ghost cycles). Here we investigate the\u0000response properties of both type of systems to external forcing. Using the\u0000classical Van-der-Pol oscillator and two modified versions of this model that\u0000correspond to a 1-ghost and a 2-ghost cycle, respectively, we find that ghost\u0000cycles are characterized by significant increase especially in the 1:1\u0000entrainment regions as demonstrated by the corresponding Arnold tongues and\u0000exhibit richer dynamics (bursting, chaos) in contrast to the classical\u0000slow-fast system. Phase plane analysis reveals that these features result from\u0000the continuous remodeling of the attractor landscape of the ghost cycles models\u0000characteristic for non-autonomous systems, whereas the attractor landscape of\u0000the corresponding slow-fast system remains qualitatively unaltered. We propose\u0000that systems containing ghost cycles display increased flexibility and\u0000responsiveness to continuous environmental changes.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323904","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}
Sayantan Nag Chowdhury, Md Sayeed Anwar, Dibakar Ghosh
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological processes. The current literature has investigated cluster synchronization by focusing mostly on the case of attractive coupling among the oscillators. However, the case of two coexisting competing interactions is of practical interest due to their relevance in diverse natural settings, including neuronal networks consisting of excitatory and inhibitory neurons, the coevolving social model with voters of opposite opinions, ecological plant communities with both facilitation and competition, to name a few. In the present article, we investigate the impact of repulsive spanning trees on cluster formation within a connected network of attractively coupled limit cycle oscillators. We successfully predict which nodes belong to each cluster and the emergent frustration of the connected networks independent of the particular local dynamics at the network nodes. We also determine local asymptotic stability of the cluster states using an approach based on the formulation of a master stability function. We additionally validate the emergence of solitary states and antisynchronization for some specific choices of spanning trees and networks.
{"title":"Cluster formation due to repulsive spanning trees in attractively coupled networks","authors":"Sayantan Nag Chowdhury, Md Sayeed Anwar, Dibakar Ghosh","doi":"arxiv-2403.19240","DOIUrl":"https://doi.org/arxiv-2403.19240","url":null,"abstract":"Ensembles of coupled nonlinear oscillators are a popular paradigm and an\u0000ideal benchmark for analyzing complex collective behaviors. The onset of\u0000cluster synchronization is found to be at the core of various technological and\u0000biological processes. The current literature has investigated cluster\u0000synchronization by focusing mostly on the case of attractive coupling among the\u0000oscillators. However, the case of two coexisting competing interactions is of\u0000practical interest due to their relevance in diverse natural settings,\u0000including neuronal networks consisting of excitatory and inhibitory neurons,\u0000the coevolving social model with voters of opposite opinions, ecological plant\u0000communities with both facilitation and competition, to name a few. In the\u0000present article, we investigate the impact of repulsive spanning trees on\u0000cluster formation within a connected network of attractively coupled limit\u0000cycle oscillators. We successfully predict which nodes belong to each cluster\u0000and the emergent frustration of the connected networks independent of the\u0000particular local dynamics at the network nodes. We also determine local\u0000asymptotic stability of the cluster states using an approach based on the\u0000formulation of a master stability function. We additionally validate the\u0000emergence of solitary states and antisynchronization for some specific choices\u0000of spanning trees and networks.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323691","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}
Bosiljka Tadic, Alexander Shapoval, Mikhail Shnirman
Recognising changes in collective dynamics in complex systems is essential for predicting potential events and their development. Possessing intrinsic attractors with laws associated with scale invariance, self-organised critical dynamics represent a suitable example for quantitatively studying changes in collective behaviour. We consider two prototypal models of self-organised criticality, the sandpile automata with deterministic (Bak-Tang-Wiesenfeld) and probabilistic (Manna model) dynamical rules, focusing on the nature of stress fluctuations induced by driving - adding grains during the avalanche propagation, and dissipation through avalanches that hit the system boundary. Our analysis of stress evolution time series reveals robust cycles modulated by collective fluctuations with dissipative avalanches. These modulated cycles are multifractal within a broad range of time scales. Features of the associated singularity spectra capture the differences in the dynamic rules behind the self-organised critical states and their response to the increased driving rate, altering the process stochasticity and causing a loss of avalanche scaling. In the related sequences of outflow current, the first return distributions are found to follow modified laws that describe different pathways to the gradual loss of cooperative behaviour in these two models. The spontaneous appearance of cycles is another characteristic of self-organised criticality. It can also help identify the prominence of self-organisational phenomenology in an empirical time series when underlying interactions and driving modes remain hidden.
{"title":"Self-organised dynamics beyond scaling of avalanches: Cyclic stress fluctuations in critical sandpiles","authors":"Bosiljka Tadic, Alexander Shapoval, Mikhail Shnirman","doi":"arxiv-2403.15859","DOIUrl":"https://doi.org/arxiv-2403.15859","url":null,"abstract":"Recognising changes in collective dynamics in complex systems is essential\u0000for predicting potential events and their development. Possessing intrinsic\u0000attractors with laws associated with scale invariance, self-organised critical\u0000dynamics represent a suitable example for quantitatively studying changes in\u0000collective behaviour. We consider two prototypal models of self-organised\u0000criticality, the sandpile automata with deterministic (Bak-Tang-Wiesenfeld) and\u0000probabilistic (Manna model) dynamical rules, focusing on the nature of stress\u0000fluctuations induced by driving - adding grains during the avalanche\u0000propagation, and dissipation through avalanches that hit the system boundary.\u0000Our analysis of stress evolution time series reveals robust cycles modulated by\u0000collective fluctuations with dissipative avalanches. These modulated cycles are\u0000multifractal within a broad range of time scales. Features of the associated\u0000singularity spectra capture the differences in the dynamic rules behind the\u0000self-organised critical states and their response to the increased driving\u0000rate, altering the process stochasticity and causing a loss of avalanche\u0000scaling. In the related sequences of outflow current, the first return\u0000distributions are found to follow modified laws that describe different\u0000pathways to the gradual loss of cooperative behaviour in these two models. The\u0000spontaneous appearance of cycles is another characteristic of self-organised\u0000criticality. It can also help identify the prominence of self-organisational\u0000phenomenology in an empirical time series when underlying interactions and\u0000driving modes remain hidden.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"515 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299028","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}
Yawer H. Shah, Luigi Palatella, Korosh Mahmoodi, Orazio S. Santonocito, Mariangela Morelli, Gianmarco Ferri, Chiara M. Mazzanti, Paolo Grigolini, Bruce J. West
The analysis of glioblastoma (GB) cell locomotion and its modeling inspired by Levy random walks is presented herein. We study such walks occurring on a two-dimensional plane where the walk is similar to the motion of a bird flying with a constant velocity, but with random changes of direction in time. The intelligence of the bird is signaled by the instantaneous changes of flying direction, which become invisible in the time series obtained by projecting the 2D walk either on the x axis or the y axis. We establish that the projected 1D time series share the statistical complexity of time series frequently used to monitor physiological processes, shedding light on the role of crucial events (CE-s) in pathophysiology. Such CE-s are signified by abrupt changes of flying direction which are invisible in the 1D physiological time series. We establish a connection between the complex scaling index delta generated by the CE-s through mu_{R} = 2 - delta , where mu_{R} is the inverse power law index of the probability density function of the time interval between consecutive failures of the process of interest. We argue that the identification of empirical indices along with their theoretical relations afford important measures to control cancer.
本文受列维随机漫步的启发，分析了胶质母细胞瘤（GB）细胞的运动及其建模。我们研究的是发生在二维平面上的随机行走，这种行走类似于鸟类的匀速直线飞行，但在飞行过程中会随机改变方向。鸟的智能通过飞行方向的瞬时变化来体现，而这种变化在将二维行走投影到 x 轴或 y 轴后得到的时间序列中是不可见的。我们发现，投影的一维时间序列与常用来监测生理过程的时间序列具有相同的统计复杂性，从而揭示了关键事件（CE-s）在病理生理学中的作用。这种关键事件的标志是飞行方向的突然改变，而这种改变在一维生理时间序列中是不可见的。我们通过 mu_{R} = 2 - delta 建立了由 CE-sthrough 生成的复缩放指数 delta 之间的联系，其中 mu_{R} 是相关过程连续失败之间时间间隔的概率密度函数的反幂律指数。我们认为，经验指数的确定及其理论关系为控制癌症提供了重要措施。
{"title":"Cell Motility in Cancer, Crucial Events, Criticality, and Lévy Walks","authors":"Yawer H. Shah, Luigi Palatella, Korosh Mahmoodi, Orazio S. Santonocito, Mariangela Morelli, Gianmarco Ferri, Chiara M. Mazzanti, Paolo Grigolini, Bruce J. West","doi":"arxiv-2403.14842","DOIUrl":"https://doi.org/arxiv-2403.14842","url":null,"abstract":"The analysis of glioblastoma (GB) cell locomotion and its modeling inspired\u0000by Levy random walks is presented herein. We study such walks occurring on a\u0000two-dimensional plane where the walk is similar to the motion of a bird flying\u0000with a constant velocity, but with random changes of direction in time. The\u0000intelligence of the bird is signaled by the instantaneous changes of flying\u0000direction, which become invisible in the time series obtained by projecting the\u00002D walk either on the x axis or the y axis. We establish that the projected 1D\u0000time series share the statistical complexity of time series frequently used to\u0000monitor physiological processes, shedding light on the role of crucial events\u0000(CE-s) in pathophysiology. Such CE-s are signified by abrupt changes of flying\u0000direction which are invisible in the 1D physiological time series. We establish\u0000a connection between the complex scaling index delta generated by the CE-s\u0000through mu_{R} = 2 - delta , where mu_{R} is the inverse power law index of\u0000the probability density function of the time interval between consecutive\u0000failures of the process of interest. We argue that the identification of\u0000empirical indices along with their theoretical relations afford important\u0000measures to control cancer.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303406","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}
Emmanouil Giannakakis, Sina Khajehabdollahi, Anna Levina
Developing reliable mechanisms for continuous local learning is a central challenge faced by biological and artificial systems. Yet, how the environmental factors and structural constraints on the learning network influence the optimal plasticity mechanisms remains obscure even for simple settings. To elucidate these dependencies, we study meta-learning via evolutionary optimization of simple reward-modulated plasticity rules in embodied agents solving a foraging task. We show that unconstrained meta-learning leads to the emergence of diverse plasticity rules. However, regularization and bottlenecks to the model help reduce this variability, resulting in interpretable rules. Our findings indicate that the meta-learning of plasticity rules is very sensitive to various parameters, with this sensitivity possibly reflected in the learning rules found in biological networks. When included in models, these dependencies can be used to discover potential objective functions and details of biological learning via comparisons with experimental observations.
{"title":"Network bottlenecks and task structure control the evolution of interpretable learning rules in a foraging agent","authors":"Emmanouil Giannakakis, Sina Khajehabdollahi, Anna Levina","doi":"arxiv-2403.13649","DOIUrl":"https://doi.org/arxiv-2403.13649","url":null,"abstract":"Developing reliable mechanisms for continuous local learning is a central\u0000challenge faced by biological and artificial systems. Yet, how the\u0000environmental factors and structural constraints on the learning network\u0000influence the optimal plasticity mechanisms remains obscure even for simple\u0000settings. To elucidate these dependencies, we study meta-learning via\u0000evolutionary optimization of simple reward-modulated plasticity rules in\u0000embodied agents solving a foraging task. We show that unconstrained\u0000meta-learning leads to the emergence of diverse plasticity rules. However,\u0000regularization and bottlenecks to the model help reduce this variability,\u0000resulting in interpretable rules. Our findings indicate that the meta-learning\u0000of plasticity rules is very sensitive to various parameters, with this\u0000sensitivity possibly reflected in the learning rules found in biological\u0000networks. When included in models, these dependencies can be used to discover\u0000potential objective functions and details of biological learning via\u0000comparisons with experimental observations.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140202968","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}
Patrick Lawton, Ashkaan K. Fahimipour, Kurt E. Anderson
Decisions to disperse from a habitat stand out among organismal behaviors as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting in widespread behaviors like tracking resources or avoiding consumers in space. Despite this, metacommunity models often treat dispersal as a function of intraspecific density alone. We show, focusing initially on three-species network motifs, that interspecific dispersal rules generally drive a transition in metacommunities from homogeneous steady states to self-organized heterogeneous spatial patterns. However, when ecologically realistic constraints reflecting adaptive behaviors are imposed -- prey tracking and predator avoidance -- a pronounced homogenizing effect emerges where spatial pattern formation is suppressed. We demonstrate this effect for each motif by computing master stability functions that separate the contributions of local and spatial interactions to pattern formation. We extend this result to species rich food webs using a random matrix approach, where we find that eventually webs become large enough to override the homogenizing effect of adaptive dispersal behaviors, leading once again to predominately pattern forming dynamics. Our results emphasize the critical role of interspecific dispersal rules in shaping spatial patterns across landscapes, highlighting the need to incorporate adaptive behavioral constraints in efforts to link local species interactions and metacommunity structure.
{"title":"Interspecific dispersal constraints suppress pattern formation in metacommunities","authors":"Patrick Lawton, Ashkaan K. Fahimipour, Kurt E. Anderson","doi":"arxiv-2403.13098","DOIUrl":"https://doi.org/arxiv-2403.13098","url":null,"abstract":"Decisions to disperse from a habitat stand out among organismal behaviors as\u0000pivotal drivers of ecosystem dynamics across scales. Encounters with other\u0000species are an important component of adaptive decision-making in dispersal,\u0000resulting in widespread behaviors like tracking resources or avoiding consumers\u0000in space. Despite this, metacommunity models often treat dispersal as a\u0000function of intraspecific density alone. We show, focusing initially on\u0000three-species network motifs, that interspecific dispersal rules generally\u0000drive a transition in metacommunities from homogeneous steady states to\u0000self-organized heterogeneous spatial patterns. However, when ecologically\u0000realistic constraints reflecting adaptive behaviors are imposed -- prey\u0000tracking and predator avoidance -- a pronounced homogenizing effect emerges\u0000where spatial pattern formation is suppressed. We demonstrate this effect for\u0000each motif by computing master stability functions that separate the\u0000contributions of local and spatial interactions to pattern formation. We extend\u0000this result to species rich food webs using a random matrix approach, where we\u0000find that eventually webs become large enough to override the homogenizing\u0000effect of adaptive dispersal behaviors, leading once again to predominately\u0000pattern forming dynamics. Our results emphasize the critical role of\u0000interspecific dispersal rules in shaping spatial patterns across landscapes,\u0000highlighting the need to incorporate adaptive behavioral constraints in efforts\u0000to link local species interactions and metacommunity structure.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203151","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}
Predicting and understanding the chaotic dynamics in complex systems is essential in various applications. However, conventional approaches, whether full-scale simulations or small-scale omissions, fail to offer a comprehensive solution. This instigates exploration into whether modeling or omitting small-scale dynamics could benefit from the well-captured large-scale dynamics. In this paper, we introduce a novel methodology called Neural Downscaling (ND), which integrates neural operator techniques with the principles of inertial manifold and nonlinear Galerkin theory. ND effectively infers small-scale dynamics within a complementary subspace from corresponding large-scale dynamics well-represented in a low-dimensional space. The effectiveness and generalization of the method are demonstrated on the complex systems governed by the Kuramoto-Sivashinsky and Navier-Stokes equations. As the first comprehensive deterministic model targeting small-scale dynamics, ND sheds light on the intricate spatiotemporal nonlinear dynamics of complex systems, revealing how small-scale dynamics are intricately linked with and influenced by large-scale dynamics.
{"title":"Neural Downscaling for Complex Systems: from Large-scale to Small-scale by Neural Operator","authors":"Pengyu Lai, Jing Wang, Rui Wang, Dewu Yang, Haoqi Fei, Hui Xu","doi":"arxiv-2403.13016","DOIUrl":"https://doi.org/arxiv-2403.13016","url":null,"abstract":"Predicting and understanding the chaotic dynamics in complex systems is\u0000essential in various applications. However, conventional approaches, whether\u0000full-scale simulations or small-scale omissions, fail to offer a comprehensive\u0000solution. This instigates exploration into whether modeling or omitting\u0000small-scale dynamics could benefit from the well-captured large-scale dynamics.\u0000In this paper, we introduce a novel methodology called Neural Downscaling (ND),\u0000which integrates neural operator techniques with the principles of inertial\u0000manifold and nonlinear Galerkin theory. ND effectively infers small-scale\u0000dynamics within a complementary subspace from corresponding large-scale\u0000dynamics well-represented in a low-dimensional space. The effectiveness and\u0000generalization of the method are demonstrated on the complex systems governed\u0000by the Kuramoto-Sivashinsky and Navier-Stokes equations. As the first\u0000comprehensive deterministic model targeting small-scale dynamics, ND sheds\u0000light on the intricate spatiotemporal nonlinear dynamics of complex systems,\u0000revealing how small-scale dynamics are intricately linked with and influenced\u0000by large-scale dynamics.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203058","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}
We present experimental results on the single file motion of a group of robots interacting with each other through position sensors. We successfully replicate the fundamental diagram typical of these systems, with a transition from free flow to congested traffic as the density of the system increases. In the latter scenario we also observe the characteristic stop-and-go waves. The unique advantages of this novel system, such as experimental stability and repeatability, allow for extended experimental runs, facilitating a comprehensive statistical analysis of the global dynamics. Above a certain density, we observe a divergence of the average jam duration and the average number of robots involved in it. This discovery enables us to precisely identify another transition: from congested intermittent flow (for intermediate densities) to a totally congested scenario for high densities. Beyond this finding, the present work demonstrates the suitability of robot swarms to model complex behaviors in many particle systems.
{"title":"Single file motion of robot swarms","authors":"Laciel Alonso-Llanes, Angel Garcimartín, Iker Zuriguel","doi":"arxiv-2403.08683","DOIUrl":"https://doi.org/arxiv-2403.08683","url":null,"abstract":"We present experimental results on the single file motion of a group of\u0000robots interacting with each other through position sensors. We successfully\u0000replicate the fundamental diagram typical of these systems, with a transition\u0000from free flow to congested traffic as the density of the system increases. In\u0000the latter scenario we also observe the characteristic stop-and-go waves. The\u0000unique advantages of this novel system, such as experimental stability and\u0000repeatability, allow for extended experimental runs, facilitating a\u0000comprehensive statistical analysis of the global dynamics. Above a certain\u0000density, we observe a divergence of the average jam duration and the average\u0000number of robots involved in it. This discovery enables us to precisely\u0000identify another transition: from congested intermittent flow (for intermediate\u0000densities) to a totally congested scenario for high densities. Beyond this\u0000finding, the present work demonstrates the suitability of robot swarms to model\u0000complex behaviors in many particle systems.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126326","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}
Seungjae Lee, Lucas Braun, Frieder Bönisch, Malte Schröder, Moritz Thümler, Marc Timme
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost five decades of research, many questions remain open, in particular for finite-size systems. Here, we generalize recent work [Phys. Rev. Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state variables analytically continued to the complex domain and also complexify its system parameters. Intriguingly, systems of two units with purely imaginary coupling do not actively synchronize even for arbitrarily large magnitudes of the coupling strengths, $|K| rightarrow infty$, but exhibit conservative dynamics with asynchronous rotations or librations for all $|K|$. For generic complex coupling, both, traditional phase-locked states and asynchronous states generalize to complex locked states, fixed points off the real subspace that exist even for arbitrarily weak coupling. We analyze a new collective mode of rotations exhibiting finite, yet arbitrarily large winding numbers. Numerical simulations for large networks indicate a novel form of discontinuous phase transition. We close by pointing to a range of exciting questions for future research.
{"title":"Complexified Synchrony","authors":"Seungjae Lee, Lucas Braun, Frieder Bönisch, Malte Schröder, Moritz Thümler, Marc Timme","doi":"arxiv-2403.02006","DOIUrl":"https://doi.org/arxiv-2403.02006","url":null,"abstract":"The Kuramoto model and its generalizations have been broadly employed to\u0000characterize and mechanistically understand various collective dynamical\u0000phenomena, especially the emergence of synchrony among coupled oscillators.\u0000Despite almost five decades of research, many questions remain open, in\u0000particular for finite-size systems. Here, we generalize recent work [Phys. Rev.\u0000Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state\u0000variables analytically continued to the complex domain and also complexify its\u0000system parameters. Intriguingly, systems of two units with purely imaginary\u0000coupling do not actively synchronize even for arbitrarily large magnitudes of\u0000the coupling strengths, $|K| rightarrow infty$, but exhibit conservative\u0000dynamics with asynchronous rotations or librations for all $|K|$. For generic\u0000complex coupling, both, traditional phase-locked states and asynchronous states\u0000generalize to complex locked states, fixed points off the real subspace that\u0000exist even for arbitrarily weak coupling. We analyze a new collective mode of\u0000rotations exhibiting finite, yet arbitrarily large winding numbers. Numerical\u0000simulations for large networks indicate a novel form of discontinuous phase\u0000transition. We close by pointing to a range of exciting questions for future\u0000research.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"129 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036583","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：