IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0276348

Dawen Wu, Ludovic Chamoin

{"title":"Approximations of the cumulative distribution function using transport maps learning.","authors":"Dawen Wu, Ludovic Chamoin","doi":"10.1063/5.0276348","DOIUrl":"https://doi.org/10.1063/5.0276348","url":null,"abstract":"This paper considers approximating the cumulative distribution function (CDF). For many important probability distributions, such as the normal distribution, their CDFs lack closed-form expressions representable by elementary functions. Although approximation methods exist, common techniques such as the empirical CDF typically rely on large amounts of sample data to construct sufficiently accurate approximations. The aim of this paper is to provide accurate and data-efficient closed-form approximations for CDFs. Our methodology is inspired by the theory of transport maps. We leverage the fundamental property that in the specific one-dimensional case, the transport map transforming a target random variable to the standard uniform distribution U(0,1) is identical to the target variable's CDF. Building upon this key insight, we propose Transport Map Learning (TML). We utilize TML to train a neural network whose output is subsequently processed by a sigmoid function. This composite architecture serves as our closed-form CDF approximation, inherently constraining the output to the [0,1] range appropriate for a CDF. The effectiveness of the proposed method is validated on three benchmark probability distributions: the standard normal distribution, the beta distribution, and the gamma distribution. The results demonstrate that, given the same amount of training data, the proposed TML method generates highly accurate closed-form approximations for the CDFs. These approximations achieve superior accuracy compared to established methods based on the empirical CDF combined with various interpolation strategies.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145085358","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

Scaling of the rotation number for perturbations of rational rotations. 有理旋转扰动下旋转数的缩放。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0290311

Paul Glendinning

引用次数: 0

Collapse of multi-headed chimera states in biologically based neuronal networks. 基于生物学的神经网络中多头嵌合体状态的崩溃。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0282696

Lucas E Bentivoglio, Diogo L M Souza, Enrique C Gabrick, Paulo R Protachevicz, Gustavo A Sousa, Iberê L Caldas, Ricardo L Viana, Kelly C Iarosz, Antonio M Batista, Fernando S Borges

引用次数: 0

Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors. 水库计算机中的虚构动力学：用未经训练的吸引子填补空白。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0283285

Jack O'Hagan, Andrew Keane, Andrew Flynn

{"title":"Confabulation dynamics in a reservoir computer: Filling in the gaps with untrained attractors.","authors":"Jack O'Hagan, Andrew Keane, Andrew Flynn","doi":"10.1063/5.0283285","DOIUrl":"https://doi.org/10.1063/5.0283285","url":null,"abstract":"Artificial intelligence has advanced significantly in recent years, thanks to innovations in the design and training of artificial neural networks (ANNs). Despite these advancements, we still understand relatively little about how elementary forms of ANNs learn, fail to learn, and generate false information without the intent to deceive, a phenomenon known as \"confabulation.\" To provide some foundational insight, in this paper, we analyze how confabulation occurs in reservoir computers (RCs): a dynamical system in the form of an ANN. RCs are particularly useful to study as they are known to confabulate in a well-defined way: when RCs are trained to reconstruct the dynamics of a given attractor, they sometimes construct an attractor that they were not trained to construct, a so-called \"untrained attractor\" (UA). This paper sheds light on the role played by UAs when reconstruction fails and their influence when modeling transitions between reconstructed attractors. Based on our results, we conclude that UAs are an intrinsic feature of learning systems whose state spaces are bounded and that this means of confabulation may be present in systems beyond RCs.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145032883","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

Strategy dominance in mixed games under weak selection. 弱选择下混合博弈中的策略优势。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0290642

Yu Chen, Bin-Quan Li

引用次数: 0

Noise-induced transitions in random Pomeau-Manneville maps. 随机Pomeau-Manneville地图中的噪声诱导转换。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0247727

Tetsu Endo, Yuzuru Sato, Hiroki Takahasi, Eli Barkai, Takuma Akimoto

{"title":"Noise-induced transitions in random Pomeau-Manneville maps.","authors":"Tetsu Endo, Yuzuru Sato, Hiroki Takahasi, Eli Barkai, Takuma Akimoto","doi":"10.1063/5.0247727","DOIUrl":"https://doi.org/10.1063/5.0247727","url":null,"abstract":"We introduce randomness to Pomeau-Manneville (PM) maps by incorporating dichotomous multiplicative noise that alternates between dynamics with an attracting and a repelling fixed point. We characterize the dynamical behavior by measuring the separation of two nearby orbits. Controlling the probability of selecting the repelling PM map, we find two noise-induced transitions. When the repelling map is selected with probability less than 1/2, orbits converge to the origin, which is an indifferent fixed point shared by both maps. When the selection probability exceeds 1/2, nearby orbits contract. When the noise-averaged PM map exhibits weak chaos, this leads to weak synchronization, where the distance between orbits asymptotically approaches zero at a subexponential rate. Further increases in the selection probability lead to the second transition to chaotic or weakly chaotic behavior, depending on whether the noise-averaged PM map exhibits chaos or weak chaos, respectively. Additionally, we show that a power-law exponent of 3/2 in the sojourn-time distribution near the indifferent fixed point is universally observed at the first transition point. These results provide insights into how introducing multiplicative noise to chaotic or weakly chaotic systems can lead to rich dynamical behaviors, shedding light on the effects of noise in intermittent dynamical systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144991626","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

Unwrapping photonic reservoirs: Enhanced expressivity via random Fourier encoding over stretched domains. 展开光子储层：通过在拉伸域上的随机傅立叶编码增强表达性。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0283442

Gerard McCaul, Girish Tripathy, Giulia Marcucci, Juan Sebastian Totero Gongora

{"title":"Unwrapping photonic reservoirs: Enhanced expressivity via random Fourier encoding over stretched domains.","authors":"Gerard McCaul, Girish Tripathy, Giulia Marcucci, Juan Sebastian Totero Gongora","doi":"10.1063/5.0283442","DOIUrl":"https://doi.org/10.1063/5.0283442","url":null,"abstract":"Photonic Reservoir Computing (RC) systems leverage the complex propagation and nonlinear interaction of optical waves to perform information processing tasks. These systems employ a combination of optical data encoding (in the field amplitude and/or phase), random scattering, and nonlinear detection to generate nonlinear features that can be processed via a linear readout layer. In this work, we propose a novel scattering-assisted photonic reservoir encoding scheme where the input phase is deliberately wrapped multiple times beyond the natural period of the optical waves [0,2π). We demonstrate that, rather than hindering nonlinear separability through loss of bijectivity, wrapping significantly improves the reservoir's prediction performance across regression and classification tasks that are unattainable within the canonical 2π period. We demonstrate that this counterintuitive effect stems from the nonlinear interference between sets of random synthetic frequencies introduced by the encoding, which generates a rich feature space spanning both the feature and sample dimensions of the data. Our results highlight the potential of engineered phase wrapping as a computational resource in RC systems based on phase encoding, paving the way for novel approaches to designing and optimizing physical computing platforms based on topological and geometric stretching.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145029042","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

An improved non-smooth coordinate transformation for analyzing bilateral vibro-impact systems with stochastic excitations. 一种改进的非光滑坐标变换用于分析具有随机激励的双边振动碰撞系统。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0266439

Meng Su, Wenting Zhang, Li Liu, Wei Xu

{"title":"An improved non-smooth coordinate transformation for analyzing bilateral vibro-impact systems with stochastic excitations.","authors":"Meng Su, Wenting Zhang, Li Liu, Wei Xu","doi":"10.1063/5.0266439","DOIUrl":"https://doi.org/10.1063/5.0266439","url":null,"abstract":"Vibro-impact systems exhibit non-smooth characteristics and pose significant challenges for analysis. Non-smooth coordinate transformations are widely recognized for their ability to convert vibro-impact systems into systems with continuous trajectories, thereby enabling the application of some classical methods. This paper introduces an improved non-smooth coordinate transformation method [Su et al., Chaos 32, 043118 (2022)], developed from the Zhuravlev and Ivanov transformations, and extends it to the analysis of bilateral vibro-impact systems with stochastic excitations. We provide a detailed derivation of the transformation, which allows the conversion of the original non-smooth system into a form with continuous and periodic trajectories. According to two typical examples, the effectiveness of the proposed method is validated by solving the corresponding Fokker-Planck equation and comparing the stationary probability density functions obtained from this approach with results from Monte-Carlo simulations. The good agreement demonstrates that the improved transformation method, which can be directly applied to vibro-impact systems with asymmetric bilateral barriers accompanied with distinct restitution coefficients or a unilateral barrier, offers an effective tool for studying stochastic responses and bifurcations of such complex systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022966","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

Weak signal amplification induced by oscillator diversity in a globally coupled bistable system. 全局耦合双稳系统中由振荡器分集引起的弱信号放大。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0266165

Shanshan Cheng, Yage Zheng, Yashi Zhang, Xiaoqian Liu, Ming Yi, Lulu Lu

{"title":"Weak signal amplification induced by oscillator diversity in a globally coupled bistable system.","authors":"Shanshan Cheng, Yage Zheng, Yashi Zhang, Xiaoqian Liu, Ming Yi, Lulu Lu","doi":"10.1063/5.0266165","DOIUrl":"https://doi.org/10.1063/5.0266165","url":null,"abstract":"Neuron diversity in the brain can effectively process and amplify the signal, and enhance the response of biological systems to weak signals. Weak signal amplification in a globally coupled network of the FitzHugh-Nagumo (FHN) oscillators is investigated, where parameter diversity is introduced via Gaussian-distributed excitability with standard deviation. In addition, the proportion of negative oscillators is introduced to independently investigate how the balance between positive and negative oscillators affects signal amplification. Both the simulation results and theoretical predictions indicate that (i) there exists an optimal interval of negative oscillator proportion in the globally coupled system that makes the weak signal propagation the strongest, within which all oscillators exhibit large-amplitude oscillations, and (ii) a critical level of oscillator diversity is reached at which the propagation of weak signals is observed to transition from failure to success. This transition is associated with a change in the system's potential from a W-shaped to a U-shaped profile. Below the threshold, the oscillators are confined within a single well due to a high potential barrier, and signal amplification is suppressed. Once the threshold is exceeded, the barrier is reduced, allowing inter-well transitions through which the system's response to weak signals is enhanced. Our qualitative analysis of the oscillator diversity provides a theoretical basis for the study of signal amplification in the neural system.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145063661","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

Data-driven modeling of traffic flow in macroscopic network systems. 宏观网络系统中交通流的数据驱动建模。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0285930

Toprak Firat, Deniz Eroglu

{"title":"Data-driven modeling of traffic flow in macroscopic network systems.","authors":"Toprak Firat, Deniz Eroglu","doi":"10.1063/5.0285930","DOIUrl":"10.1063/5.0285930","url":null,"abstract":"Urban traffic modeling is essential for understanding and mitigating congestion, yet existing approaches face a trade-off between realism and scalability. Microscopic agent-based simulators capture individual vehicle behavior but are computationally intensive and hard to calibrate at scale. Macroscopic models, while more efficient, often rely on strong assumptions, such as fixed origin-destination flows, or oversimplify network dynamics. In this work, we propose a data-driven macroscopic model that simulates traffic as a discrete-time load-exchange process over flow networks. The model captures key phenomena such as bottlenecks, spillbacks, and adaptive load redistribution using only road-type attributes, network structure, and observed traffic density. Parameter learning is performed via evolutionary optimization, allowing the model to adapt to both synthetic and real-world conditions without assuming latent travel demand. We evaluate the framework on synthetic grid-like networks and on real traffic data from London, Istanbul, and New York. The resulting framework provides a scalable and interpretable alternative for urban traffic forecasting, balancing predictive accuracy with computational efficiency across diverse network conditions.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145069116","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

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