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arXiv 2024年

作者： Betteti, Simone Baggio, Giacomo Bullo, Francesco Zampieri, Sandro Department of Information Engineering Università degli Studi di Padova Padova35131 Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States

The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and retrieval dynamics, capacity estimates, and sequential transitions among memories. Notably, the role and impact of external inputs has been largely underexplored, from their effects on neural dynamics to how they facilitate effective memory retrieval. To bridge this gap, we propose a novel dynamical system framework in which the external input directly influences the neural synapses and shapes the energy landscape of the Hopfield model. This plasticity-based mechanism provides a clear energetic interpretation of the memory retrieval process and proves effective at correctly classifying highly mixed inputs. Furthermore, we integrate this model within the framework of modern Hopfield architectures, using this connection to elucidate how current and past information are combined during the retrieval process. Finally, we embed both the classic and the new model in an environment disrupted by noise and compare their robustness during memory *** Codes 37N25 (Primary) 37C75, 34D45 (Secondary) © 2024, CC BY.

关键词： Associative storage

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computation of Hopf Bifurcation Points in the Magnetic Levitation System 4th

Computation of Hopf Bifurcation Points in the Magnetic Levit...

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4th International Conference on Information and Communication Technology for Intelligent Systems, ICTIS 2020

作者： Valluru, Sudarshan K. Gupta, Anshul Verma, Aditya Center for Control of Dynamical Systems and Computation Department of Electrical Engineering Delhi Technological University Delhi110042 India

ISBN: (纸本)9789811570773

This research brief aims to study the bifurcation analysis of an electromagnetic levitation (maglev) system. The bifurcation analysis involves first performing the numerical analysis, and then the simulations using MATLAB are analyzed to verify the results. The study requires derivation of a mathematical model for the maglev system, which can be used for the bifurcation analysis. The bifurcation analysis involves a numerical comparison of the system equations with the predefined constraints. The input voltage is being used as the bifurcation parameter, which is by ball’s position, ball’s velocity, and the current flowing through the circuit. The analysis allows us to compute a combination of values of parameters, when simulations are performed to check system characteristics, periodic oscillations at these values are obtained. Hence, it proves the existence of Hopf bifurcation at the computed value of system parameters. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Hopf bifurcation

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A Framework to Evaluate Independent Component Analysis applied to EEG signal: testing on the Picard algorithm

A Framework to Evaluate Independent Component Analysis appli...

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2022 IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2022

作者： Frank, Gwenevere Makeig, Scott Delorme, Arnaud University of California San Diego Electrical and Computer Engineering La Jolla United States Institute for Neural Computation University of California San Diego La Jolla United States Swartz Center for Computational Neuroscience Institute for Neural Computation University of California San Diego La Jolla United States Paul Sabatier University Centre de Recherche Cerveau et Cognition Toulouse France

ISBN: (纸本)9781665468190

Independent component analysis (ICA), is a blind source separation method that is becoming increasingly used to separate brain and non-brain related activities in electroencephalographic (EEG) and other electrophysiological recordings. It can be used to extract effective brain source activities and estimate their cortical source areas, and is commonly used in machine learning applications to classify EEG artifacts. Previously, we compared results of decomposing 1371-channel scalp EEG datasets using 22 ICA and other blind source separation (BSS) algorithms. We are now making this framework available to the scientific community and, in the process of its release are testing a recent ICA algorithm (Picard) not included in the previous assay. Our test framework uses three main metrics to assess BSS performance: Pairwise Mutual Information (PMI) between scalp channel pairs;PMI remaining between component pairs after decomposition;and, the complete (not pairwise) Mutual Information Reduction (MIR) produced by each algorithm. We also measure the 'dipolarity' of the scalp projection maps for the decomposed component, defined by the number of components whose scalp projection maps nearly match the projection of a single equivalent dipole located in the volume of a template boundary element method (BEM) electrical forward problem head model. Within this framework, Picard performed similarly to Infomax ICA. This is not surprising since Picard is a type of Infomax algorithm that uses the LBFGS method for faster convergence, in contrast to Infomax and Extended Infomax (runica) which use gradient descent. Our results show that Picard performs similarly to Infomax and, likewise, better than other BSS algorithms, excepting the more computationally complex AMICA. Further research might determine if partial Picard decomposition, followed by AMICA, might produce unequaled performance without a large time penalty. We have released the source code of our framework and the test data thro

关键词： Independent component analysis

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Stabilizing two-qubit entanglement with dynamically decoupled active feedback

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Physical Review Applied 2024年第2期21卷 024022-024022页

作者： Sacha Greenfield Leigh Martin Felix Motzoi K. Birgitta Whaley Justin Dressel Eli M. Levenson-Falk Department of Physics and Astronomy University of Southern California Los Angeles California 90089 USA Center for Quantum Information Science and Technology University of Southern California Los Angeles California 90089 USA Institute for Quantum Studies Chapman University Orange California 92866 USA Berkeley Center for Quantum Information and Computation Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA Department of Chemistry University of California Berkeley California 94720 USA Peter Grünberg Institute of Quantum Control (PGI-8) Forschungszentrum Jülich GmbH Wilhelm-Johnen-Straße Jülich 52428 Germany Schmid College of Science and Technology Chapman University Orange California 92866 USA Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles California 90089 USA

We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/f-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.

关键词： Measurement back action Optoelectronics Quantum control Quantum feedback Quantum information with solid state qubits Quantum measurements Superconducting qubits Microwave techniques

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Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks

Comparative Analysis of Interval Reachability for Robust Imp...

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IEEE Conference on Decision and control

作者： Alexander Davydov Saber Jafarpour Matthew Abate Francesco Bullo Samuel Coogan Center for Control Dynamical Systems and Computation University of California Santa Barbara School of Electrical and Computer Engineering Georgia Institute of Technology

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Implicit neural networks (INNs) are a class of learning models that use implicit algebraic equations as layers and have been shown to exhibit several notable benefits over traditional feedforward neural networks (FFNNs). In this paper, we use interval reachability analysis to study robustness of INNs and compare them with FFNNs. We first introduce the notion of tight inclusion function and use it to provide the tightest rectangular over-approximation of the neural network’s input-output map. We also show that tight inclusion functions lead to sharper robustness guarantees than the well-studied robustness measures of Lipschitz constants. Like exact Lipschitz constants, tight inclusions functions are computationally challenging to obtain, and thus we develop a framework based upon mixed monotonicity and contraction theory to estimate the tight inclusion functions for INNs. We show that our approach performs at least as well as, and generally better than, state-ofthe-art interval-bound propagation methods for INNs. Finally, we design a novel optimization problem for training robust INNs and we provide empirical evidence that suitably-trained INNs can be more robust than comparably-trained FFNNs.

关键词： Training Robustness Mathematical models Feedforward neural networks computational efficiency Reachability analysis Optimization

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A Comparative Analysis of Deep Neural Network Models using Transfer Learning for Electrocardiogram Signal Classification 6

A Comparative Analysis of Deep Neural Network Models using T...

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6th International Conference on Recent Trends on Electronics, Information, Communication and Technology, RTEICT 2021

作者： Rahuja, Nitin Valluru, Sudarshan K. Center for Control of Dynamical Systems and Computation Delhi Technological University Dept. of Electrical Engineering Delhi110042 India

ISBN: (纸本)9781665435598

With the development of computational resources in the past decade, the adoption of deep learning methodologies has taken a steep rise. Particularly, the use of various Convolutional Neural Network (CNN) based architectures for various computer vision and image classification problems in healthcare research can be witnessed. In this scope, performance evaluation and comparison of three different CNN architectures for multi-class classification of Electrocardiogram (ECG) signals is presented in this paper. Three distinct classes of ECG signal i.e. Normal Sinus Rhythm (NSR), Arrhythmia (ARR), and Congestive Heart failure (CHF) are utilized in this work, which is representative of an individual's heart conditions. The classification methodology adopted makes use of Continuous Wavelet Transform (CWT) which provides a 2-dimensional time-frequency representation of available samples of ECG signals. ECG dataset was collected from different PhysioBank databases, which provides openly-accessible medical research data. Images with time-frequency representation of ECG signals were applied as input to three CNN architectures namely, AlexNet, GoogLeNet, and SqueezeNet. Using transfer learning approach and modification in certain output layers of three architectures, ECG classification was performed and the performance of three CNN architectures was studied. The results revealed classification accuracy of 97.80%, 97.78% and 97.22% by AlexNet, GoogLeNet and SqueezeNet respectively. AlexNet outperformed GoogLeNet and SqueezeNet models in terms of accuracy as well as training time. © 2021 IEEE.

关键词： Electrocardiograms

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A Deep Neural Network Approach to Automatic Multi-Class Classification of Electrocardiogram Signals

A Deep Neural Network Approach to Automatic Multi-Class Clas...

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2021 International Conference on Intelligent Technologies, CONIT 2021

作者： Rahuja, Nitin Valluru, Sudarshan K. Delhi Technological University Center for Control of Dynamical Systems and Computation Dept. of Electrical Engineering Delhi110042 India

ISBN: (纸本)9781728185835

Classification of electrocardiogram (ECG) signals is essential for accurate clinical diagnosis of coronary illness. Deep Neural Network (DNN) has emerged as a promising tool for feature identification in ECG signals with advancements in signal processing techniques and artificial intelligence. Particularly, Convolutional Neural Network (CNN) has enabled intricate feature identification and classification of images. In this scope, an efficient classification methodology utilizing wavelet transform and AlexNet CNN is presented in this paper to classify the ECG signals into three different categories, namely: Arrythmia (ARR), Congestive Heart failure (CHF) and Normal Sinus Rhythm (NSR). Physionet research dataset is utilized in this work. Firstly, all ECG signals are converted to a corresponding scalogram using Continuous Wavelet Transform (CWT). Then, these scalograms are applied as input to AlexNet, which is a pretrained CNN. Finally, transfer learning and fine-tuning are done, and the performance of modified AlexNet is evaluated. The study revealed a good accuracy of 97.3%. © 2021 IEEE.

关键词： Electrocardiograms

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The Parametrized Complexity of Quantum Verification 17

The Parametrized Complexity of Quantum Verification

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17th Conference on the Theory of Quantum computation, Communication and Cryptography, TQC 2022

作者： Arunachalam, Srinivasan Bravyi, Sergey Nirkhe, Chinmay O'Gorman, Bryan IBM Quantum Thomas J Watson Research Center Yorktown Heights NY United States Electrical Engineering and Computer Sciences University of California BerkeleyCA United States Challenge Institute for Quantum Computation University of California BerkeleyCA United States

ISBN: (纸本)9783959772372

We initiate the study of parameterized complexity of QMA problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists a classical algorithm solving the problem with a runtime scaling exponentially in the number of non-Clifford gates but only polynomially with the system size. This result follows from our main result, that for any Clifford + t T-gate quantum circuit satisfiability problem, the search space of optimal witnesses can be reduced to a stabilizer subspace isomorphic to at most t qubits (independent of the system size). Furthermore, we derive new lower bounds on the T-count of circuit satisfiability instances and the T-count of the W-state assuming the classical exponential time hypothesis (ETH). Lastly, we explore the parameterized complexity of the quantum non-identity check problem. © Srinivasan Arunachalam, Sergey Bravyi, Chinmay Nirkhe, and Bryan O'Gorman;licensed under Creative Commons License CC-BY 4.0

关键词： Parameterization

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Semicontraction and Synchronization of Kuramoto-Sakaguchi Oscillator Networks

arXiv

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arXiv 2023年

作者： Delabays, Robin Bullo, Francesco The Institute of Sustainable Energy School of Engineering University of Applied Sciences and Arts of Western Switzerland The Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States

This paper studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets of the n-torus called winding cells. Second, we analyze the semicontractivity of the model, i.e., the property that the distance between trajectories decreases when measured according to a seminorm. This paper establishes the local semicontractivity of the Kuramoto-Sakaguchi model, which is equivalent to the local contractivity for the reduced model. The reduced model is defined modulo the rotational symmetry. The domains where the system is semicontracting are convex phase-cohesive subsets of winding cells. Our sufficient conditions and estimates of the semicontracting domains are less conservative and more explicit than in previous works. Based on semicontraction on phase-cohesive subsets, we establish the at most uniqueness of synchronous states within these domains, thereby characterizing the multistability of this model. © 2023, CC BY.

关键词： Winding

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

arXiv

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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

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