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arXiv 2022年

作者： Centorrino, Veronica Bullo, Francesco Russo, Giovanni Scuola Superiore Meridionale Naples Italy The Department of Mechanical Engineering The Center for Control Dynamical Systems and Computation University of California Santa Barbara United States The Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian learning rules. To capture the synaptic sparsity of neural circuits we propose a low dimensional formulation. We then characterize certain key dynamical properties. First, we give biologically-inspired forward invariance results. Then, we give sufficient conditions for the non-Euclidean contractivity of the models. Our contraction analysis leads to stability and robustness of time-varying trajectories - for networks with both excitatory and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. For each model, we propose a contractivity test based upon biologically meaningful quantities, e.g., neural and synaptic decay rate, maximum in-degree, and the maximum synaptic strength. Then, we show that the models satisfy Dale's Principle. Finally, we illustrate the effectiveness of our results via a numerical example. Copyright © 2022, The Authors. All rights reserved.

关键词： Hopfield neural networks

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The missing base molecules in atmospheric acid-base nucleation

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National Science Review 2022年第10期9卷 196-208页

作者： Runlong Cai Rujing Yin Chao Yan Dongsen Yang Chenjuan Deng Lubna Dada Juha Kangasluoma Jenni Kontkanen Roope Halonen Yan Ma Xiuhui Zhang Pauli Paasonen Tuukka Pet?j? Veli-Matti Kerminen Yongchun Liu Federico Bianchi Jun Zheng Lin Wang Jiming Hao James N.Smith Neil M. Donahue Markku Kulmala Douglas R.Worsnop Jingkun Jiang State Key Joint Laboratory of Environment Simulation and Pollution Control School of Environment Tsinghua University Institute for Atmospheric and Earth System Research/Physics Faculty of Science University of Helsinki Aerosol and Haze Laboratory Beijing Advanced Innovation Center for Soft Matter Science and Engineering Beijing University of Chemical Technology Collaborative Innovation Center of Atmospheric Environment and Equipment Technology Nanjing University of Information Science and Technology Laboratory of Atmospheric Chemistry Paul Scherrer Institute Center for Joint Quantum Studies and Department of Physics School of Science Tianjin University Key Laboratory of Cluster Science Ministry of Education of China School of Chemistry and Chemical Engineering Beijing Institute of Technology Shanghai Key Laboratory of Atmospheric Particle Pollution and Prevention (LAP3) Department of Environmental Science and Engineering Fudan University Chemistry Department University of California Center for Atmospheric Particle Studies Carnegie Mellon University Department of Chemistry Carnegie Mellon University Aerodyne Research Inc.

Transformation of low-volatility gaseous precursors to new particles affects aerosol number concentration,cloud formation and hence the *** clustering of acid and base molecules is a major mechanism driving fast nucleation and initial growth of new particles in the ***,the acid-base cluster composition,measured using state-of-the-art mass spectrometers,cannot explain the measured high formation rate of new *** we present strong evidence for the existence of base molecules such as amines in the smallest atmospheric sulfuric acid clusters prior to their detection by mass *** demonstrate that forming（H2SO4）1（amine）1is the rate-limiting step in atmospheric H2SO4-amine nucleation and the uptake of（H2SO4）1（amine）1is a major pathway for the initial growth of *** proposed mechanism is very consistent with measured new particle formation in urban Beijing,in which dimethylamine is the key base for H2SO4nucleation while other bases such as ammonia may contribute to the growth of larger *** findings further underline the fact that strong amines,even at low concentrations and when undetected in the smallest clusters,can be crucial to particle formation in the planetary boundary layer.

关键词： new particle formation acid-base nucleation aerosol polluted urban environment

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From Contraction Theory to Fixed Point Algorithms on Riemannian and Non-Euclidean Spaces

From Contraction Theory to Fixed Point Algorithms on Riemann...

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IEEE Conference on Decision and control

作者： Francesco Bullo Pedro Cisneros-Velarde Alexander Davydov Saber Jafarpour Center of Control Dynamical Systems and Computation University of California Santa Barbara USA

ISBN: (纸本)9781665436601

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the relationship between Demidovich conditions, one-sided Lipschitz conditions, and contractivity theorems. We review the standard contraction theory on Euclidean spaces as well as little-known results for Riemannian manifolds. Special emphasis is placed on the setting of non-Euclidean norms and the recently introduced weak pairings for the ℓ 1 and ℓ ∞ norms. We highlight recent results on explicit and implicit fixed point schemes for non-Euclidean contracting systems.

关键词： Manifolds Heart Machine learning algorithms Conferences Tutorials Machine learning Aerospace electronics

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Pursuit-Evasion on a Sphere and When It Can Be Considered Flat 63

Pursuit-Evasion on a Sphere and When It Can Be Considered Fl...

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63rd IEEE Conference on Decision and control, CDC 2024

作者： Milutinovic, Dejan Moll, Alexander Von Manyam, Satyanarayana G. Casbeer, David W. Weintraub, Isaac E. Pachter, Meir Electrical and Computer Engineering Dept. University of California Santa Cruz Santa CruzCA United States Control Science Center Aerospace Systems Directorate Air Force Research Laboratory DaytonOH45435 United States Dcs Corporation DaytonOH United States Air Force Institute of Technology Wright-Patterson Afb Dept. of Electrical Engineering OH United States

ISBN: (纸本)9798350316339

In planar pursuit-evasion differential games considering a faster pursuer and slower evader, the interception points resulting from equilibrium strategies lie on the Apollonius circle. This property is instrumental for leveraging geometric approaches for solving multiple pursuit-evasion scenarios in the plane. Here, we study a pursuit-evasion differential game on a sphere and generalize the planar Apollonius set to the spherical domain. We find that the interception point from the equilibrium strategies can leave the Apollonius set boundary and present a condition to keep the intercept point on the boundary. This condition allows for generalizing planar pursuitevasion strategies to the sphere. © 2024 IEEE.

关键词： Spheres

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Contraction Analysis of Hopfield Neural Networks with Hebbian Learning

Contraction Analysis of Hopfield Neural Networks with Hebbia...

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IEEE Conference on Decision and control

作者： Veronica Centorrino Francesco Bullo Giovanni Russo Scuola Superiore Meridionale University of Naples Federico II Italy Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa Barbara USA Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Motivated by advances in neuroscience and machine learning, this paper is concerned with the modeling and analysis of Hopfield neural networks with dynamic recurrent connections undergoing Hebbian learning. To capture the synaptic sparsity of neural circuits, we propose a low dimensional formulation for the model and then characterize its key dynamical properties. First, we give a biologically-inspired forward invariance result. Then, we give sufficient conditions for the non-Euclidean contractivity of the model. Our contraction analysis leads to stability and robustness of time-varying trajectories – for networks with both excitatory and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. Our proposed contractivity test is based upon biologically meaningful quantities, e.g., neural and synaptic decay rate, maximum out-degree, and the maximum synaptic strength. Finally, we show that the model satisfies Dale’s principle. The effectiveness of our results is illustrated via a numerical example.

关键词： Sufficient conditions Biological system modeling Hopfield neural networks Stability analysis Robustness Trajectory Integrated circuit modeling

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An Exploration of Optimal Parameters for Efficient Blind Source Separation of EEG Recordings Using AMICA

An Exploration of Optimal Parameters for Efficient Blind Sou...

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IEEE Symposium on Bioinformatics and Bioengineering (BIBE)

作者： Gwenevere Frank Seyed Yahya Shirazi Jason Palmer Gert Cauwenberghs Scott Makeig Arnaud Delorme Electrical and Computer Engineering University of California San Diego La Jolla USA Swartz Center for Computational Neuroscience Institute for Neural Computation University of California San Diego La Jolla USA Statistics West Virginia University Morgantown USA Institute for Neural Computation University of California San Diego La Jolla USA Centre de recherche Cerveau et Cognition Paul Sabatier University Toulouse France

EEG continues to find a multitude of uses in both neuroscience research and medical practice, and independent component analysis (ICA) continues to be an important tool for analyzing EEG. A multitude of ICA algorithms for EEG decomposition exist, and in the past, their relative effectiveness has been studied. AMICA is considered the benchmark against which to compare the performance of other ICA algorithms for EEG decomposition. AMICA exposes many parameters to the user to allow for precise control of the decomposition. However, several of the parameters currently tend to be set according to “rules of thumb” shared in the EEG community. Here, 70-channel AMICA decompositions are run on data from a collection of participants while varying certain key parameters. The running time and quality of decompositions are analyzed based on two metrics, Pairwise Mutual Information (PMI) and Mutual Information Reduction (MIR), and derived recommendations for selecting parameter values are presented.

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Biologically plausible robust control with Neural Network weight reset for unmanned aircraft systems under impulsive disturbances

Biologically plausible robust control with Neural Network we...

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American control Conference (ACC)

作者： Ignacio Rubio Scola Luis Rodolfo Garcia Carrillo Andrew T. Sornborger João P. Hespanha Department of Industrial Products Engineering INTI CONICET and UNR Rosario Argentina Klipsch School of Electrical and Computer Engineering New Mexico State University Las Cruces NM USA Los Alamos National Laboratory Los Alamos NM USA Center for Control Dynamical Systems and Computation University of California Santa Barbara USA

Self-learning control techniques mimicking the functionality of the limbic system in the mammalian brain have shown advantages in terms of superior learning ability and low computational cost. However, accompanying stability analyses and mathematical proofs rely on unrealistic assumptions which limit not only the performance, but also the implementation of such controllers in real-world scenarios. In this work the limbic system inspired control (LISIC) framework is revisited, introducing three contributions that facilitate the implementation of this type of controller in real-time. First, an extension enabling the implementation of LISIC to the domain of SISO affine systems is proposed. Second, a strategy for resetting the controller’s Neural Network (NN) weights is developed, in such a way that now it is possible to deal with piece-wise smooth references and impulsive perturbations. And third, for the case when a nominal model of the system is available, a technique is proposed to compute a set of optimal NN reset weight values by solving a convex constrained optimization problem. Numerical simulations addressing the stabilization of an unmanned aircraft system via the robust LISIC demonstrate the advantages obtained when adopting the extension to SISO systems and the two NN weight reset strategies.

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Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks

Non-Euclidean Monotone Operator Theory with Applications to ...

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IEEE Conference on Decision and control

作者： Alexander Davydov Saber Jafarpour Anton V. Proskurnikov Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara USA School of Electrical and Computer Engineering Georgia Institute of Technology Department of Electronics and Telecommunications Politecnico di Torino Turin Italy

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces ℓ 1 and ℓ ∞ . We first establish properties of mappings which are monotone with respect to the non-Euclidean norms ℓ 1 or ℓ ∞ . In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates.

关键词： Casting Analytical models Recurrent neural networks Machine learning Aerospace electronics control systems Robustness

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Extending dynamic mode decomposition to data from multiple outputs

arXiv

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arXiv 2021年

作者： Boddupalli, Nibodh Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA United States

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system. Estimation of these spectral objects has become widely accessible with the numerous algorithms developed in recent years. We show how one such algorithm – extended dynamic mode decomposition – can be used on data from multiple outputs of a system. These outputs that are functions of state are called observables in the literature and could be known outputs like the state itself or unknown outputs like data from sensors used in systems of biological interest. To this end, we approximate the desired observables and their iterates in time using minimizers of regularized least-squares problems which have analytic solutions with heuristic provisions for expected estimates. © 2021, CC BY-SA.

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Dubins Vehicle Intercept of a Brownian Target on a Sphere

Dubins Vehicle Intercept of a Brownian Target on a Sphere

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IEEE Conference on Decision and control

作者： Dejan Milutinović David W. Casbeer Department of Electrical and Computer Engineering University of California Santa Cruz CA USA Control Science Center Air Force Research Laboratory Wright-Patterson AFB OH USA

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

This paper focuses on a navigation of a Dubins vehicle (DV) to intercept a moving target on a sphere. The uncertainty in the target motion is described by a Brownian motion model. An Itô-type stochastic differential equation for the relative motion between DV and the Brownian moving target is derived. This stochastic differential equation is used to formulate an intercept controller as a minimum time optimal controller. The properties of the controller are incorporated into the numerical computations of the controller, which by its construction can intercept a Brownian target. Our numerical simulation results show that the computed controller can intercept both stationary and moving targets on the sphere.

关键词： Space vehicles Uncertainty Planets Space debris Stochastic processes Optimal control Differential equations Satellite navigation systems Numerical simulation Numerical models

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