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On Weakly Contracting Dynamics for Convex Optimization

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arXiv 2024年

作者： Centorrino, Veronica Davydov, Alexander Gokhale, Anand Russo, Giovanni Bullo, Francesco Scuola Superiore Meridionale Italy The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States The Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

We analyze the convergence behavior of globally weakly and locally strongly contracting dynamics. Such dynamics naturally arise in the context of convex optimization problems with a unique minimizer. We show that convergence to the equilibrium is linear-exponential, in the sense that the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. As we show, the linear-exponential dependency arises naturally in certain dynamics with saturations. Additionally, we provide a sufficient condition for local input-to-state stability. Finally, we illustrate our results on, and propose a conjecture for, continuous-time dynamical systems solving linear programs. Copyright © 2024, The Authors. All rights reserved.

关键词： Dynamics

Forecasting Slow-Wave Sleep Deficiency Through Stress-Related Markers in Forehead EEG

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Forecasting Slow-Wave Sleep Deficiency Through Stress-Relate...

2024 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2024

作者： Su, Cheng-Hua Ko, Li-Wei Jung, Tzyy-Ping Onton, Julie Tzou, Shey-Cherng Juang, Jia-Chi Hsu, Chung-Yao Institute of Bioinformatics and Systems Biology National Yang Ming Chiao Tung University Hsinchu300 Taiwan Institute of Electrical and Control Engineering National Yang Ming Chiao Tung University Hsinchu300 Taiwan Kaohsiung Medical University Drug Development and Value Creation Research Center Department of Biomedical Science and Environmental Biology Kaohsiung807 Taiwan Institute for Neural Computation Institute of Engineering in Medicine University of California San Diego La Jolla CA92093 United States College of Electrical Engineering National Yang Ming Chiao Tung University Hsinchu300 Taiwan Institute for Neural Computation University of California San Diego La Jolla CA92093 United States Kaohsiung Medical University Hospital Sleep Disorders Center Department of Neurology Kaohsiung807 Taiwan College of Medicine Kaohsiung Medical University Department of Neurology Kaohsiung807 Taiwan

ISBN: (纸本)9781665410205

Sleep quality is critical for human well-being. Lack of sleep and poor sleep quality impair daily cognitive functions and health. While stress has been recognized as a detrimental factor on sleep quality, the relationship between pre-sleep stress level, resting EEG and subsequent sleep structure remains to be explored. This study presents a novel approach that evaluates pre-sleep stress levels using a 2-channel EEG to predict slow-wave sleep (SWS) deficiency. We recorded forehead EEG immediately before sleep onset, then utilized power spectra and entropy analysis to extract stress-related neurological features, including beta/delta correlation, alpha asymmetry, fuzzy entropy (FuzzEn), and spectral entropy (SpEn). We found that individuals with SWS deficiency exhibited signs of stress, such as a robust beta/delta correlation, higher alpha asymmetry, and increased FuzzEn. Conversely, individuals with ample SWS displayed weak beta/delta correlation and reduced FuzzEn in EEG recordings. Finally, we tested the robustness of the selected neuro markers with two supervised learning models and found that the selected markers predict SWS deficiency with an accuracy above 70%. Our study demonstrated that stress-related neurological markers derived from pre-sleep EEG can effectively predict SWS deficiency. The proposed method can be integrated with a portable EEG device and sleep-improving interventions to develop a personalized sleep-improvement solution. © 2024 IEEE.

关键词： Sleep research

Extracting Stress-Related EEG Patterns from Pre-Sleep EEG for Forecasting Slow-Wave Sleep Deficiency

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IEEE Transactions on Neural Systems and Rehabilitation engineering 2024年 32卷 1817-1827页

作者： Su, Cheng-Hua Ko, Li-Wei Jung, Tzyy-Ping Onton, Julie Tzou, Shey-Cherng Juang, Jia-Chi Hsu, Chung-Yao Institute of Bioinformatics and Systems Biology National Yang Ming Chiao Tung University Hsinchu300 Taiwan Institute of Electrical and Control Engineering National Yang Ming Chiao Tung University Hsinchu300 Taiwan Kaohsiung Medical University Drug Development and Value Creation Research Center Department of Biomedical Science and Environmental Biology Kaohsiung807 Taiwan University of California San Diego Swartz Center for Computational Neuroscience La Jolla CA92093 United States National Yang Ming Chiao Tung University Department of Computer Science Hsinchu300 Taiwan University of California San Diego Institute for Neural Computation La Jolla CA92093 United States National Yang Ming Chiao Tung University Department of Biological Science and Technology Hsinchu300 Taiwan Kaohsiung Medical University Hospital Sleep Disorders Center Department of Neurology Kaohsiung807 Taiwan Kaohsiung Medical University College of Medicine Department of Neurology Kaohsiung807 Taiwan

Sleep is vital to our daily activity. Lack of proper sleep can impair functionality and overall health. While stress is known for its detrimental impact on sleep quality, the precise effect of pre-sleep stress on subsequent sleep structure remains unknown. This study introduced a novel approach to study the pre-sleep stress effect on sleep structure, specifically slow-wave sleep (SWS) deficiency. To achieve this, we selected forehead resting EEG immediately before and upon sleep onset to extract stress-related neurological markers through power spectra and entropy analysis. These markers include beta/delta correlation, alpha asymmetry, fuzzy entropy (FuzzEn) and spectral entropy (SpEn). Fifteen subjects were included in this study. Our results showed that subjects lacking SWS often exhibited signs of stress in EEG, such as an increased beta/delta correlation, higher alpha asymmetry, and increased FuzzEn in frontal EEG. Conversely, individuals with ample SWS displayed a weak beta/delta correlation and reduced FuzzEn. Finally, we employed several supervised learning models and found that the selected neurological markers can predict subsequent SWS deficiency. Our investigation demonstrated that the classifiers could effectively predict varying levels of slow-wave sleep (SWS) from pre-sleep EEG segments, achieving a mean balanced accuracy surpassing 0.75. The SMOTE-Tomek resampling method could improve the performance to 0.77. This study suggests that stress-related neurological markers derived from pre-sleep EEG can effectively predict SWS deficiency. Such information can be integrated with existing sleep-improving techniques to provide a personalized sleep forecasting and improvement solution. © 2001-2011 IEEE.

关键词： Entropy

HOW SOCIAL INFLUENCE AFFECTS THE WISDOM OF CROWDS IN INFLUENCE NETWORKS

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arXiv 2022年

作者： Tian, Ye Wang, Long Bullo, Francesco Center for Systems and Control College of Engineering Peking University Beijing100871 China Mechanical Engineering Department The Center of Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States

A long-standing debate is whether social influence improves the collective wisdom of a crowd or undermines it. This paper addresses the question based on a naïve learning setting in influence systems theory: in our models individuals evolve their estimates of an unknown truth according to the weighted-average opinion dynamics. A formal mathematization is provided with rigorous theoretical analysis. We obtain various conditions for improving, optimizing and undermining the crowd accuracy, respectively. We prove that if the wisdom of a finite-size group is improved, then the collective estimate converges to the truth as the group size increases. We show that whether social influence improves or undermines the wisdom is determined by the social power allocations in the influence system: if the influence system allocates relatively larger social power to relatively more accurate individuals, it improves the wisdom;on the contrary, if the influence system assigns less social power to more accurate individuals, it undermines the wisdom. At a population level, individuals' susceptibilities to interpersonal influence and network centralities are both crucial. To improve the wisdom, more accurate individuals should be less susceptible and have larger network centralities. Particularly, in democratic influence networks, if relatively more accurate individuals are relatively less susceptible, the wisdom is improved;if more accurate individuals are more susceptible, the wisdom is undermined, which is consistent with the reported empirical evidence. Our investigation provides a theoretical framework for understanding the role social influence plays in the emergence of collective wisdom. Copyright © 2022, The Authors. All rights reserved.

关键词： Economic and social effects

Positive Competitive Networks for Sparse Reconstruction

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arXiv 2023年

作者： Centorrino, Veronica Gokhale, Anand Davydov, Alexander Russo, Giovanni Bullo, Francesco Scuola Superiore Meridionale Italy The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States The Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with non-negativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including for example neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then, we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence: (i) only depends on a property of the dictionary;(ii) is linear-exponential, in the sense that initially the convergence rate is at worst linear and then, after a transient, it becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without non-negativity constraints. Finally, we validate the effectiveness of our approach via a numerical example. Copyright © 2023, The Authors. All rights reserved.

关键词： Signal processing

Convergence of the Heterogeneous Deffuant-Weisbuch Model: A Complete Proof and Some Extensions

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arXiv 2024年

作者： Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco The Academy of Mathematics and Systems Science Chinese Academy of Sciences China The School of Mathematics and Statistics Beijing Jiaotong University China The Department of Mechanics and Engineering Science Peking University China The Center of Control Dynamical-Systems and Computation University of California Santa Barbara United States

The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over 20 years, its convergence proof is open. Our previous paper [1] solves the problem for the case of uniform weighting factors greater than or equal to 1/2, but the general case remains unresolved. This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions. © 2024, CC0.

关键词： Multi agent systems

THE YAKUBOVICH S-LEMMA REVISITED: STABILITY AND CONTRACTIVITY IN NON-EUCLIDEAN NORMS

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arXiv 2022年

作者： Proskurnikov, Anton V. Davydov, Alexander Bullo, Francesco Department of Electronics and Telecommunications Politecnico di Torino Turin Italy Department of Mechanical Engineering The Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic Lyapunov function in the Lur'e problem of absolute stability. A quadratic Lyapunov function is, however, nothing else than a squared Euclidean norm on the state space (that is, a norm induced by an inner product). A natural question arises as to whether squared non-Euclidean norms V (x) = ǁxǁ2 may serve as Lyapunov functions in stability problems. This paper presents a novel non-polynomial S-Lemma that leads to constructive criteria for the existence of such functions defined by weighted p norms. Our generalized S-Lemma leads to new absolute stability and absolute contractivity criteria for Lur'e-type systems, including, for example, a new simple proof of the Aizerman and Kalman conjectures for positive Lur'e *** Codes 34H05, 93C15 Copyright © 2022, The Authors. All rights reserved.

关键词： Lyapunov functions

Time-Varying Convex Optimization: A Contraction and Equilibrium Tracking Approach

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arXiv 2023年

作者： Davydov, Alexander Centorrino, Veronica Gokhale, Anand Russo, Giovanni Bullo, Francesco Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States Scuola Superiore Meridionale Naples Italy Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is asymptotically proportional to the rate of change of the parameter and that the proportionality constant is upper bounded by Lipschitz constant in which the parameter appears divided by the contraction rate of the dynamics squared. We additionally establish that augmenting any parameter-dependent contracting dynamics with a feedforward prediction term ensures that the tracking error vanishes exponentially quickly. To apply these results to time-varying convex optimization, we establish the strong infinitesimal contractivity of dynamics solving three canonical problems: monotone inclusions, linear equality-constrained problems, and composite minimization problems. For each case, we derive the sharpest-known contraction rates and provide explicit bounds on the tracking error between solution trajectories and minimizing trajectories. We validate our theoretical results on two numerical examples and on an application to control barrier function-based controller design that involves real hardware. Copyright © 2023, The Authors. All rights reserved.

关键词： Continuous time systems

Multidimensional Opinion Dynamics with Heterogeneous Bounded Confidences and Random Interactions

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arXiv 2024年

作者： Cheng, Jiangjiang Chen, Ge Mei, Wenjun Bullo, Francesco School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mechanics and Engineering Science Peking University Beijing100871 China Department of Mechanical Engineering The Center of Control Dynamical-Systems and Computation University of California Santa BarbaraCA93106-5070 United States

This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other’s opinions with a specific probability. This revised model is motivated by the observation that the standard Hegselmann-Krause (HK) dynamics requires unrealistic all-to-all interactions at certain configurations. For this randomized BC opinion dynamics, regardless of initial opinions and positive confidence bounds, we show that the agents’ states converge to fixed final opinions in finite time almost surely and that the convergence rate follows a negative exponential distribution in mean square. Furthermore, we establish sufficient conditions for the heterogeneous BC opinion dynamics with random interactions to achieve consensus in finite time. Copyright © 2024, The Authors. All rights reserved.

关键词： Random processes