Inverse stochastic resonance (ISR) is a phenomenon where noise reduces rather than increases the firing rate of a neuron, sometimes leading to complete quiescence. ISR was first experimentally verified with cerebellar Purkinje neurons. These experiments showed that ISR enables optimal information transfer between the input and output spike train of neurons. Subsequent studies demonstrated the efficiency of information processing and transfer in neural networks with small-world topology. We conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bistable regime with a stable fixed point and a limit cycle -- a prerequisite for ISR. Our results show that the degree of ISR is highly dependent on the FHN model's timescale separation parameter $epsilon$. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter $P$, or homeostatic structural plasticity (HSP) with rewiring frequency $F$. We demonstrate that both STDP and HSP amplify ISR when $epsilon$ lies within the bistability region of FHN neurons. Specifically, at larger values of $epsilon$ within the bistability regime, higher rewiring frequencies $F$ enhance ISR at intermediate (weak) synaptic noise intensities, while values of $P$ consistent with depression-domination (potentiation-domination) enhance (deteriorate) ISR. Moreover, although STDP and HSP parameters may jointly enhance ISR, $P$ has a greater impact on ISR compared to $F$. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize information transfer between input and output spike trains in neuromorphic systems, and prompt venues for experiments in neural networks.
{"title":"Inverse stochastic resonance in adaptive small-world neural networks","authors":"Marius E. Yamakou, Jinjie Zhu, Erik A. Martens","doi":"arxiv-2407.03151","DOIUrl":"https://doi.org/arxiv-2407.03151","url":null,"abstract":"Inverse stochastic resonance (ISR) is a phenomenon where noise reduces rather\u0000than increases the firing rate of a neuron, sometimes leading to complete\u0000quiescence. ISR was first experimentally verified with cerebellar Purkinje\u0000neurons. These experiments showed that ISR enables optimal information transfer\u0000between the input and output spike train of neurons. Subsequent studies\u0000demonstrated the efficiency of information processing and transfer in neural\u0000networks with small-world topology. We conducted a numerical investigation into\u0000the impact of adaptivity on ISR in a small-world network of noisy\u0000FitzHugh-Nagumo (FHN) neurons, operating in a bistable regime with a stable\u0000fixed point and a limit cycle -- a prerequisite for ISR. Our results show that\u0000the degree of ISR is highly dependent on the FHN model's timescale separation\u0000parameter $epsilon$. The network structure undergoes dynamic adaptation via\u0000mechanisms of either spike-time-dependent plasticity (STDP) with\u0000potentiation-/depression-domination parameter $P$, or homeostatic structural\u0000plasticity (HSP) with rewiring frequency $F$. We demonstrate that both STDP and\u0000HSP amplify ISR when $epsilon$ lies within the bistability region of FHN\u0000neurons. Specifically, at larger values of $epsilon$ within the bistability\u0000regime, higher rewiring frequencies $F$ enhance ISR at intermediate (weak)\u0000synaptic noise intensities, while values of $P$ consistent with\u0000depression-domination (potentiation-domination) enhance (deteriorate) ISR.\u0000Moreover, although STDP and HSP parameters may jointly enhance ISR, $P$ has a\u0000greater impact on ISR compared to $F$. Our findings inform future ISR\u0000enhancement strategies in noisy artificial neural circuits, aiming to optimize\u0000information transfer between input and output spike trains in neuromorphic\u0000systems, and prompt venues for experiments in neural networks.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547943","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}
Soumen Majhi, Biswambhar Rakshit, Amit Sharma, Jürgen Kurths, Dibakar Ghosh
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems. Complex networks have proven efficient in elucidating the topological structures of both natural and artificial systems and describing diverse processes occurring within them. Recent advancements have significantly enhanced our understanding of emergent dynamics in complex networks. Among various processes, a substantial body of work explores the dynamical robustness of complex networks, their ability to withstand degradation in network constituents while maintaining collective oscillatory dynamics. Many physical and biological systems experience a decline in dynamic activities due to natural or environmental factors. The impact of such damages on network performance can be significant, and the system's robustness indicates its capability to maintain functionality despite dynamic changes, often termed aging. This review provides a comprehensive overview of notable research examining how networks sustain global oscillation despite increasing inactive dynamical units. We present contemporary research dedicated to the theoretical understanding and enhancement mechanisms of dynamical robustness in complex networks. Our focus includes various network structures and coupling functions, elucidating the persistence of networked systems. We cover system characteristics from heterogeneity in network connectivity to heterogeneity in dynamical units. Finally, we discuss challenges in this field and open areas for future studies.
{"title":"Dynamical robustness of network of oscillators","authors":"Soumen Majhi, Biswambhar Rakshit, Amit Sharma, Jürgen Kurths, Dibakar Ghosh","doi":"arxiv-2407.02260","DOIUrl":"https://doi.org/arxiv-2407.02260","url":null,"abstract":"Most complex systems are nonlinear, relying on emergent behavior from\u0000interacting subsystems, often characterized by oscillatory dynamics. Collective\u0000oscillatory behavior is essential for the proper functioning of many real world\u0000systems. Complex networks have proven efficient in elucidating the topological\u0000structures of both natural and artificial systems and describing diverse\u0000processes occurring within them. Recent advancements have significantly\u0000enhanced our understanding of emergent dynamics in complex networks. Among\u0000various processes, a substantial body of work explores the dynamical robustness\u0000of complex networks, their ability to withstand degradation in network\u0000constituents while maintaining collective oscillatory dynamics. Many physical\u0000and biological systems experience a decline in dynamic activities due to\u0000natural or environmental factors. The impact of such damages on network\u0000performance can be significant, and the system's robustness indicates its\u0000capability to maintain functionality despite dynamic changes, often termed\u0000aging. This review provides a comprehensive overview of notable research\u0000examining how networks sustain global oscillation despite increasing inactive\u0000dynamical units. We present contemporary research dedicated to the theoretical\u0000understanding and enhancement mechanisms of dynamical robustness in complex\u0000networks. Our focus includes various network structures and coupling functions,\u0000elucidating the persistence of networked systems. We cover system\u0000characteristics from heterogeneity in network connectivity to heterogeneity in\u0000dynamical units. Finally, we discuss challenges in this field and open areas\u0000for future studies.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"158 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512044","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}
Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is crucial for deciphering a range of phenomena from brain activity to power grid stability. Recent interest in co-evolutionary networks has highlighted the intricate interplay between dynamics on and of the network with mixed time scales. Here, we explore the collective behavior of excitable oscillators in a simple networks of two Theta neurons with adaptive coupling without self-interaction. Through a combination of bifurcation analysis and numerical simulations, we seek to understand how the level of adaptivity in the coupling strength, $a$, influences the dynamics. We first investigate the dynamics possible in the non-adaptive limit; our bifurcation analysis reveals stability regions of quiescence and spiking behaviors, where the spiking frequencies mode-lock in a variety of configurations. Second, as we increase the adaptivity $a$, we observe a widening of the associated Arnol'd tongues, which may overlap and give room for multi-stable configurations. For larger adaptivity, the mode-locked regions may further undergo a period-doubling cascade into chaos. Our findings contribute to the mathematical theory of adaptive networks and offer insights into the potential mechanisms underlying neuronal communication and synchronization.
{"title":"Co-evolutionary dynamics for two adaptively coupled Theta neurons","authors":"Felix Augustsson, Erik Andreas Martens","doi":"arxiv-2407.01089","DOIUrl":"https://doi.org/arxiv-2407.01089","url":null,"abstract":"Natural and technological networks exhibit dynamics that can lead to complex\u0000cooperative behaviors, such as synchronization in coupled oscillators and\u0000rhythmic activity in neuronal networks. Understanding these collective dynamics\u0000is crucial for deciphering a range of phenomena from brain activity to power\u0000grid stability. Recent interest in co-evolutionary networks has highlighted the\u0000intricate interplay between dynamics on and of the network with mixed time\u0000scales. Here, we explore the collective behavior of excitable oscillators in a\u0000simple networks of two Theta neurons with adaptive coupling without\u0000self-interaction. Through a combination of bifurcation analysis and numerical\u0000simulations, we seek to understand how the level of adaptivity in the coupling\u0000strength, $a$, influences the dynamics. We first investigate the dynamics\u0000possible in the non-adaptive limit; our bifurcation analysis reveals stability\u0000regions of quiescence and spiking behaviors, where the spiking frequencies\u0000mode-lock in a variety of configurations. Second, as we increase the adaptivity\u0000$a$, we observe a widening of the associated Arnol'd tongues, which may overlap\u0000and give room for multi-stable configurations. For larger adaptivity, the\u0000mode-locked regions may further undergo a period-doubling cascade into chaos.\u0000Our findings contribute to the mathematical theory of adaptive networks and\u0000offer insights into the potential mechanisms underlying neuronal communication\u0000and synchronization.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"349 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512092","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}
Karan Singh, V. K. Chandrasekar, D. V. Senthilkumar
Cascading failures represent a fundamental threat to the integrity of complex systems, often precipitating a comprehensive collapse across diverse infrastructures and financial networks. This research articulates a robust and pragmatic approach designed to attenuate the risk of such failures within complex networks, emphasizing the pivotal role of local network topology. The core of our strategy is an innovative algorithm that systematically identifies a subset of critical nodes within the network, a subset whose relative size is substantial in the context of the network's entirety. Enhancing this algorithm, we employ a graph coloring heuristic to precisely isolate nodes of paramount importance, thereby minimizing the subset size while maximizing strategic value. Securing these nodes significantly bolsters network resilience against cascading failures. The method proposed to identify critical nodes and experimental results show that the proposed technique outperforms other typical techniques in identifying critical nodes. We substantiate the superiority of our approach through comparative analyses with existing mitigation strategies and evaluate its performance across various network configurations and failure scenarios. Empirical validation is provided via the application of our method to real-world networks, confirming its potential as a strategic tool in enhancing network robustness.
{"title":"Streamlined approach to mitigation of cascading failure in complex networks","authors":"Karan Singh, V. K. Chandrasekar, D. V. Senthilkumar","doi":"arxiv-2406.18949","DOIUrl":"https://doi.org/arxiv-2406.18949","url":null,"abstract":"Cascading failures represent a fundamental threat to the integrity of complex\u0000systems, often precipitating a comprehensive collapse across diverse\u0000infrastructures and financial networks. This research articulates a robust and\u0000pragmatic approach designed to attenuate the risk of such failures within\u0000complex networks, emphasizing the pivotal role of local network topology. The\u0000core of our strategy is an innovative algorithm that systematically identifies\u0000a subset of critical nodes within the network, a subset whose relative size is\u0000substantial in the context of the network's entirety. Enhancing this algorithm,\u0000we employ a graph coloring heuristic to precisely isolate nodes of paramount\u0000importance, thereby minimizing the subset size while maximizing strategic\u0000value. Securing these nodes significantly bolsters network resilience against\u0000cascading failures. The method proposed to identify critical nodes and\u0000experimental results show that the proposed technique outperforms other typical\u0000techniques in identifying critical nodes. We substantiate the superiority of\u0000our approach through comparative analyses with existing mitigation strategies\u0000and evaluate its performance across various network configurations and failure\u0000scenarios. Empirical validation is provided via the application of our method\u0000to real-world networks, confirming its potential as a strategic tool in\u0000enhancing network robustness.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"146 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530319","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}
Leonardo Reyes, Kilver Campos, Douglas Avendaño, Lenin González-Paz, Alejandro Vivas, Ysaías J. Alvarado, Saúl Flores
We have analyzed phenology data and jumps in protein configurations with the non-linear forecasting method proposed by May and Sugihara cite{MS90}. Full plots of prediction quality as a function of dimensionality and forecasting time give fast and valuable information about Complex Systems dynamics.
{"title":"Seasonal footprints on ecological time series and jumps in dynamic states of protein configurations from a non-linear forecasting method characterization","authors":"Leonardo Reyes, Kilver Campos, Douglas Avendaño, Lenin González-Paz, Alejandro Vivas, Ysaías J. Alvarado, Saúl Flores","doi":"arxiv-2406.13811","DOIUrl":"https://doi.org/arxiv-2406.13811","url":null,"abstract":"We have analyzed phenology data and jumps in protein configurations with the\u0000non-linear forecasting method proposed by May and Sugihara cite{MS90}. Full\u0000plots of prediction quality as a function of dimensionality and forecasting\u0000time give fast and valuable information about Complex Systems dynamics.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512093","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}
Michael Crosscombe, Ilya Horiguchi, Norihiro Maruyama, Shigeto Dobata, Takashi Ikegami
We introduce a simulation environment to facilitate research into emergent collective behaviour, with a focus on replicating the dynamics of ant colonies. By leveraging real-world data, the environment simulates a target ant trail that a controllable agent must learn to replicate, using sensory data observed by the target ant. This work aims to contribute to the neuroevolution of models for collective behaviour, focusing on evolving neural architectures that encode domain-specific behaviours in the network topology. By evolving models that can be modified and studied in a controlled environment, we can uncover the necessary conditions required for collective behaviours to emerge. We hope this environment will be useful to those studying the role of interactions in emergent behaviour within collective systems.
{"title":"A Simulation Environment for the Neuroevolution of Ant Colony Dynamics","authors":"Michael Crosscombe, Ilya Horiguchi, Norihiro Maruyama, Shigeto Dobata, Takashi Ikegami","doi":"arxiv-2406.13147","DOIUrl":"https://doi.org/arxiv-2406.13147","url":null,"abstract":"We introduce a simulation environment to facilitate research into emergent\u0000collective behaviour, with a focus on replicating the dynamics of ant colonies.\u0000By leveraging real-world data, the environment simulates a target ant trail\u0000that a controllable agent must learn to replicate, using sensory data observed\u0000by the target ant. This work aims to contribute to the neuroevolution of models\u0000for collective behaviour, focusing on evolving neural architectures that encode\u0000domain-specific behaviours in the network topology. By evolving models that can\u0000be modified and studied in a controlled environment, we can uncover the\u0000necessary conditions required for collective behaviours to emerge. We hope this\u0000environment will be useful to those studying the role of interactions in\u0000emergent behaviour within collective systems.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512039","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}
Jonathan D. Shaw, Juan G. Restrepo, Nancy Rodríguez
Motivated by the need to understand the factors driving gentrification, we introduce and analyze two simple dynamical systems that model the interplay between three potential drivers of the phenomenon. The constructed systems are based on the assumption that three canonical drivers exist: a subpopulation that increases the desirability of a neighborhood, the desirability of a neighborhood, and the average price of real estate in a neighborhood. The second model modifies the first and implements a simple rent control scheme. For both models, we investigate the linear stability of equilibria and numerically determine the characteristics of oscillatory solutions as a function of system parameters. Introducing a rent control scheme stabilizes the system, in the sense that the parameter regime under which solutions approach equilibrium is expanded. However, oscillatory time series generated by the rent control model are generally more disorganized than those generated by the non-rent control model; in fact, long-term transient chaos was observed under certain conditions in the rent control case. Our results illustrate that even simple models of urban gentrification can lead to complex temporal behavior.
{"title":"A dynamical system model of gentrification: Exploring a simple rent control strategy","authors":"Jonathan D. Shaw, Juan G. Restrepo, Nancy Rodríguez","doi":"arxiv-2406.12092","DOIUrl":"https://doi.org/arxiv-2406.12092","url":null,"abstract":"Motivated by the need to understand the factors driving gentrification, we\u0000introduce and analyze two simple dynamical systems that model the interplay\u0000between three potential drivers of the phenomenon. The constructed systems are\u0000based on the assumption that three canonical drivers exist: a subpopulation\u0000that increases the desirability of a neighborhood, the desirability of a\u0000neighborhood, and the average price of real estate in a neighborhood. The\u0000second model modifies the first and implements a simple rent control scheme.\u0000For both models, we investigate the linear stability of equilibria and\u0000numerically determine the characteristics of oscillatory solutions as a\u0000function of system parameters. Introducing a rent control scheme stabilizes the\u0000system, in the sense that the parameter regime under which solutions approach\u0000equilibrium is expanded. However, oscillatory time series generated by the rent\u0000control model are generally more disorganized than those generated by the\u0000non-rent control model; in fact, long-term transient chaos was observed under\u0000certain conditions in the rent control case. Our results illustrate that even\u0000simple models of urban gentrification can lead to complex temporal behavior.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512040","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}
Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks have often been limited to specific models, such as the Kuramoto model, or have focused solely on higher-order interactions within individual layers. Here, we present a comprehensive framework for investigating synchronization, particularly global synchronization, in multilayer networks with higher-order interactions. Our framework considers interactions beyond pairwise connections, both within and across layers. We demonstrate the existence of a stable global synchronous state, with a condition resembling the master stability function, contingent on the choice of coupling functions. Our theoretical findings are supported by simulations using Hindmarsh-Rose neuronal and R"{o}ssler oscillators. These simulations illustrate how synchronization is facilitated by higher-order interactions, both within and across layers, highlighting the advantages over scenarios involving interactions within single layers.
{"title":"Global synchronization in generalized multilayer higher-order networks","authors":"Palash Kumar Pal, Md Sayeed Anwar, Matjaz Perc, Dibakar Ghosh","doi":"arxiv-2406.03771","DOIUrl":"https://doi.org/arxiv-2406.03771","url":null,"abstract":"Networks incorporating higher-order interactions are increasingly recognized\u0000for their ability to introduce novel dynamics into various processes, including\u0000synchronization. Previous studies on synchronization within multilayer networks\u0000have often been limited to specific models, such as the Kuramoto model, or have\u0000focused solely on higher-order interactions within individual layers. Here, we\u0000present a comprehensive framework for investigating synchronization,\u0000particularly global synchronization, in multilayer networks with higher-order\u0000interactions. Our framework considers interactions beyond pairwise connections,\u0000both within and across layers. We demonstrate the existence of a stable global\u0000synchronous state, with a condition resembling the master stability function,\u0000contingent on the choice of coupling functions. Our theoretical findings are\u0000supported by simulations using Hindmarsh-Rose neuronal and R\"{o}ssler\u0000oscillators. These simulations illustrate how synchronization is facilitated by\u0000higher-order interactions, both within and across layers, highlighting the\u0000advantages over scenarios involving interactions within single layers.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547941","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}
Guido Caldarelli, Andrea Gabrielli, Tommaso Gili, Pablo Villegas
The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of universality classes. RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate interplay of correlations on multiple scales. Existing approaches have relied on hypotheses involving hidden geometries and based on embedding complex networks into hidden metric spaces. Here, we present a practical overview of the recently introduced Laplacian Renormalization Group for heterogeneous networks. First, we present a brief overview that justifies the use of the Laplacian as a natural extension for well-known field theories to analyze spatial disorder. We then draw an analogy to traditional real-space renormalization group procedures, explaining how the LRG generalizes the concept of "Kadanoff supernodes" as block nodes that span multiple scales. These supernodes help mitigate the effects of cross-scale correlations due to small-world properties. Additionally, we rigorously define the LRG procedure in momentum space in the spirit of Wilson RG. Finally, we show different analyses for the evolution of network properties along the LRG flow following structural changes when the network is properly reduced.
{"title":"Laplacian Renormalization Group: An introduction to heterogeneous coarse-graining","authors":"Guido Caldarelli, Andrea Gabrielli, Tommaso Gili, Pablo Villegas","doi":"arxiv-2406.02337","DOIUrl":"https://doi.org/arxiv-2406.02337","url":null,"abstract":"The renormalization group (RG) constitutes a fundamental framework in modern\u0000theoretical physics. It allows the study of many systems showing states with\u0000large-scale correlations and their classification in a relatively small set of\u0000universality classes. RG is the most powerful tool for investigating\u0000organizational scales within dynamic systems. However, the application of RG\u0000techniques to complex networks has presented significant challenges, primarily\u0000due to the intricate interplay of correlations on multiple scales. Existing\u0000approaches have relied on hypotheses involving hidden geometries and based on\u0000embedding complex networks into hidden metric spaces. Here, we present a\u0000practical overview of the recently introduced Laplacian Renormalization Group\u0000for heterogeneous networks. First, we present a brief overview that justifies\u0000the use of the Laplacian as a natural extension for well-known field theories\u0000to analyze spatial disorder. We then draw an analogy to traditional real-space\u0000renormalization group procedures, explaining how the LRG generalizes the\u0000concept of \"Kadanoff supernodes\" as block nodes that span multiple scales.\u0000These supernodes help mitigate the effects of cross-scale correlations due to\u0000small-world properties. Additionally, we rigorously define the LRG procedure in\u0000momentum space in the spirit of Wilson RG. Finally, we show different analyses\u0000for the evolution of network properties along the LRG flow following structural\u0000changes when the network is properly reduced.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254640","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}
Artificial neural networks (ANNs), which are inspired by the brain, are a central pillar in the ongoing breakthrough in artificial intelligence. In recent years, researchers have examined mechanical implementations of ANNs, denoted as Physical Neural Networks (PNNs). PNNs offer the opportunity to view common materials and physical phenomena as networks, and to associate computational power with them. In this work, we incorporated mechanical bistability into PNNs, enabling memory and a direct link between computation and physical action. To achieve this, we consider an interconnected network of bistable liquid-filled chambers. We first map all possible equilibrium configurations or steady states, and then examine their stability. Building on these maps, both global and local algorithms for training multistable PNNs are implemented. These algorithms enable us to systematically examine the network's capability to achieve stable output states and thus the network's ability to perform computational tasks. By incorporating PNNs and multistability, we can design structures that mechanically perform tasks typically associated with electronic neural networks, while directly obtaining physical actuation. The insights gained from our study pave the way for the implementation of intelligent structures in smart tech, metamaterials, medical devices, soft robotics, and other fields.
{"title":"Multistable Physical Neural Networks","authors":"Eran Ben-Haim, Sefi Givli, Yizhar Or, Amir Gat","doi":"arxiv-2406.00082","DOIUrl":"https://doi.org/arxiv-2406.00082","url":null,"abstract":"Artificial neural networks (ANNs), which are inspired by the brain, are a\u0000central pillar in the ongoing breakthrough in artificial intelligence. In\u0000recent years, researchers have examined mechanical implementations of ANNs,\u0000denoted as Physical Neural Networks (PNNs). PNNs offer the opportunity to view\u0000common materials and physical phenomena as networks, and to associate\u0000computational power with them. In this work, we incorporated mechanical\u0000bistability into PNNs, enabling memory and a direct link between computation\u0000and physical action. To achieve this, we consider an interconnected network of\u0000bistable liquid-filled chambers. We first map all possible equilibrium\u0000configurations or steady states, and then examine their stability. Building on\u0000these maps, both global and local algorithms for training multistable PNNs are\u0000implemented. These algorithms enable us to systematically examine the network's\u0000capability to achieve stable output states and thus the network's ability to\u0000perform computational tasks. By incorporating PNNs and multistability, we can\u0000design structures that mechanically perform tasks typically associated with\u0000electronic neural networks, while directly obtaining physical actuation. The\u0000insights gained from our study pave the way for the implementation of\u0000intelligent structures in smart tech, metamaterials, medical devices, soft\u0000robotics, and other fields.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254447","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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