IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0211692

Guillaume Pourcel, Mirko Goldmann, Ingo Fischer, Miguel C Soriano

{"title":"Adaptive control of recurrent neural networks using conceptors.","authors":"Guillaume Pourcel, Mirko Goldmann, Ingo Fischer, Miguel C Soriano","doi":"10.1063/5.0211692","DOIUrl":"https://doi.org/10.1063/5.0211692","url":null,"abstract":"Recurrent neural networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a machine learning setting, the network's parameters are adapted during a training phase to match the requirements of a given task/problem increasing its computational capabilities. After the training, the network parameters are kept fixed to exploit the learned computations. The static parameters, therefore, render the network unadaptive to changing conditions, such as an external or internal perturbation. In this paper, we demonstrate how keeping parts of the network adaptive even after the training enhances its functionality and robustness. Here, we utilize the conceptor framework and conceptualize an adaptive control loop analyzing the network's behavior continuously and adjusting its time-varying internal representation to follow a desired target. We demonstrate how the added adaptivity of the network supports the computational functionality in three distinct tasks: interpolation of temporal patterns, stabilization against partial network degradation, and robustness against input distortion. Our results highlight the potential of adaptive networks in machine learning beyond training, enabling them to not only learn complex patterns but also dynamically adjust to changing environments, ultimately broadening their applicability.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142459294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A novel and effective method for characterizing time series correlations based on martingale difference correlation. 基于马氏差分相关性的表征时间序列相关性的新型有效方法。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0237801

Ang Li, Du Shang, Pengjian Shang

{"title":"A novel and effective method for characterizing time series correlations based on martingale difference correlation.","authors":"Ang Li, Du Shang, Pengjian Shang","doi":"10.1063/5.0237801","DOIUrl":"https://doi.org/10.1063/5.0237801","url":null,"abstract":"Analysis of correlation between time series is an essential step for complex system studies and dynamical characteristics extractions. Martingale difference correlation (MDC) theory is mainly concerned with the correlation of conditional mean values between response variables and predictor variables. It is the generalization and deepening of the Pearson correlation coefficient, Spearman correlation coefficient, Kendall correlation coefficient, and other statistics. In this paper, on the basis of phase space reconstruction, the generalized dependence index (GDI) is proposed by using MDC and martingale difference divergence matrix theories, which can measure the degree of dependence between time series more effectively. Moreover, motivated by the theoretical framework of the refined distance correlation method, the corresponding dependence measure (DE) is employed in this paper to construct the DE-GDI plane, so as to comprehensively and intuitively distinguish different types of data and deeply explore the operating mechanism behind the relevant time series and complex systems. According to the performances tested by the different simulated and real-world data, our proposed method performs relatively reasonably and reliably in dependence measuring and data distinguishing. The proposal of this complex data clustering method can not only recognize the features of complex systems but also distinguish them effectively so as to acquire more relevant detailed information.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142459293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic entrainment: A deep learning and data-driven process approach for synchronization in the Hodgkin-Huxley model. 动态诱导：霍奇金-赫胥黎模型中同步的深度学习和数据驱动过程方法。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0219848

Soheil Saghafi, Pejman Sanaei

引用次数: 0

Rigorously proven chaos in chemical kinetics. 经过严格验证的化学动力学混沌。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0206749

M Susits, J Tóth

引用次数: 0

Shortest path counting in complex networks based on powers of the adjacency matrix. 基于邻接矩阵幂的复杂网络最短路径计数。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0226144

Dingrong Tan, Ye Deng, Yu Xiao, Jun Wu

{"title":"Shortest path counting in complex networks based on powers of the adjacency matrix.","authors":"Dingrong Tan, Ye Deng, Yu Xiao, Jun Wu","doi":"10.1063/5.0226144","DOIUrl":"https://doi.org/10.1063/5.0226144","url":null,"abstract":"Complex networks describe a broad range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a crucial role in network science, where the computation of shortest path lengths and numbers has garnered substantial focus. It is well known that powers of the adjacency matrix can calculate the number of walks, specifying their corresponding lengths. However, developing methodologies to quantify both the number and length of shortest paths through the adjacency matrix remains a challenge. Here, we extend powers of the adjacency matrix from walks to shortest paths. We address the all-pairs shortest path count problem and propose a fast algorithm based on powers of the adjacency matrix that counts both the number and the length of all shortest paths. Numerous experiments on synthetic and real-world networks demonstrate that our algorithm is significantly faster than the classical algorithms across various network types and sizes. Moreover, we verified that the time complexity of our proposed algorithm significantly surpasses that of the current state-of-the-art algorithms. The superior property of the algorithm allows for rapid calculation of all shortest paths within large-scale networks, offering significant potential applications in traffic flow optimization and social network analysis.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142459306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Targeting attack activity-driven networks. 以攻击活动驱动的网络为目标。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0234562

Dandan Zhao, Li Wang, Bo Zhang, Cheng Qian, Ming Zhong, Shenghong Li, Jianmin Han, Hao Peng, Wei Wang

{"title":"Targeting attack activity-driven networks.","authors":"Dandan Zhao, Li Wang, Bo Zhang, Cheng Qian, Ming Zhong, Shenghong Li, Jianmin Han, Hao Peng, Wei Wang","doi":"10.1063/5.0234562","DOIUrl":"https://doi.org/10.1063/5.0234562","url":null,"abstract":"Real-world complex systems demonstrated temporal features, i.e., the network topology varies with time and should be described as temporal networks since the traditional static networks cannot accurately characterize. To describe the deliberate attack events in the temporal networks, we propose an activity-based targeted attack on the activity-driven network to investigate temporal networks' temporal percolation properties and resilience. Based on the node activity and network mapping framework, the giant component and temporal percolation threshold are solved according to percolation theory and generating function. The theoretical results coincide with the simulation results near the thresholds. We find that targeted attacks can affect the temporal network, while random attacks cannot. As the probability of a highly active node being deleted increases, the temporal percolation threshold increases, and the giant component increases, thus enhancing robustness. When the network's activity distribution is extremely heterogeneous, network robustness decreases consequently. These findings help us to analyze and understand real-world temporal networks.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142496088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tapping strength variability in sensorimotor experiments on rhythmic tapping. 关于有节奏敲击的感觉运动实验中的敲击力度变化。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0211078

C Nelias, B Schulz, G Datseris, T Geisel

引用次数: 0

Spiking activities in small neural networks induced by external forcing. 外力作用下小型神经网络的尖峰活动

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0226896

E Rybalova, N Semenova

引用次数: 0

Optimal synchronization to a limit cycle. 与极限周期的最佳同步