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When smoothness is not enough: Toward exact quantification and optimization of the price-of-anarchy

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arXiv 2019年

作者： Chandan, Rahul Paccagnan, Dario Marden, Jason R. Department of Electrical and Computer Engineering Center of Control Dynamical Systems and Computation UC Santa Barbara United States Department of Mechanical Engineering Center of Control Dynamical Systems and Computation UC Santa Barbara United States

Today's multiagent systems have grown too complex to rely on centralized controllers, prompting increasing interest in the design of distributed algorithms. In this respect, game theory has emerged as a valuable tool to complement more traditional techniques. The fundamental idea behind this approach is the assignment of agents' local cost functions, such that their selfish minimization attains, or is provably close to, the global objective. Any algorithm capable of computing an equilibrium of the corresponding game inherits an approximation ratio that is, in the worst case, equal to its price-of-anarchy. Therefore, a successful application of the game design approach hinges on the possibility to quantify and optimize the equilibrium performance. Toward this end, we introduce the notion of generalized smoothness, and show that the resulting efficiency bounds are significantly tighter compared to those obtained using the traditional smoothness approach. Leveraging this newly-introduced notion, we quantify the equilibrium performance for the class of local resource allocation games. Finally, we show how the agents' local decision rules can be designed in order to optimize the efficiency of the corresponding equilibria, by means of a tractable linear program. Copyright © 2019, The Authors. All rights reserved.

关键词： Linear programming

Prediction of fitness in bacteria with causal jump dynamic mode decomposition

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Prediction of fitness in bacteria with causal jump dynamic m...

American control Conference

作者： Shara Balakrishnan Aqib Hasnain Nibodh Boddupalli Dennis M. Joshy Robert G. Egbert Enoch Yeung Department of Electrical and Computer Engineering University of California Santa Barbara Department of Mechanical Engineering University of California Santa Barbara Environmental and Biological Sciences Directorate Pacific Northwest National Laboratory Richland WA Mechanical Engineering Center for Control Dynamical Systems and Computation and Biomolecular Science and Engineering University of California Santa Barbara

ISBN: (数字)9781538682661

ISBN: (纸本)9781538682678

In this paper, we consider the problem of learning a predictive model for population cell growth dynamics as a function of the media conditions. We first introduce a generic data-driven framework for training operator-theoretic models to predict cell growth rate. We then introduce the experimental design and data generated in this study, namely growth curves of Pseudomonas putida as a function of casein and glucose concentrations. We use a data driven approach for model identification, specifically the nonlinear autoregressive (NAR) model to represent the dynamics. We show theoretically that Hankel DMD can be used to obtain a solution of the NAR model. We show that it identifies a constrained NAR model and to obtain a more general solution, we define a causal state space system using 1-step, 2-step,..., τ-step predictors of the NAR model and identify a Koopman operator for this model using extended dynamic mode decomposition. The hybrid scheme we call causal-jump dynamic mode decomposition, which we illustrate on a growth profile or fitness prediction challenge as a function of different input growth conditions. We show that our model is able to recapitulate training growth curve data with 96.6% accuracy and predict test growth curve data with 91% accuracy.

关键词： health Growth curves SOLUTIONS(GENERAL) model identification bacteria data driven Pseudomonas putida

Correction: PDMATLAB2D: A Peridynamics MATLAB Two-dimensional Code

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Journal of Peridynamics and Nonlocal Modeling 2024年第3期6卷 530-530页

作者： Seleson, Pablo Pasetto, Marco John, Yohan Trageser, Jeremy Reeve, Samuel Temple Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge USA Department of Mechanical and Aerospace Engineering University of California San Diego La Jolla USA George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta USA Center for Control Dynamical Systems and Computation University of California at Santa Barbara Harold Frank Hall Room 5119 Santa Barbara USA Engineering Sciences Center Sandia National Laboratories Albuquerque USA Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak Ridge USA

Stable and Efficient Structures in Multigroup Network Formation

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arXiv 2020年

作者： Mohagheghi, Shadi Ma, Jingying Bullo, Francesco Department of Electrical and Computer Engineering Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106-9560 United States School of Mathematics and Statistics Ningxia University Yinchuan750021 China

In this work we present a strategic network formation model predicting the emergence of multigroup structures. Individuals decide to form or remove links based on the benefits and costs those connections carry;we focus on bilateral consent for link formation. An exogenous system specifies the frequency of coordination issues arising among the groups. We are interested in structures that arise to resolve coordination issues and, specifically, structures in which groups are linked through bridging, redundant, and co-membership interconnections. We characterize the conditions under which certain structures are stable and study their efficiency as well as the convergence of formation dynamics. Copyright © 2020, The Authors. All rights reserved.

关键词： Game theory

Fault-Tolerant Quantum computation with Static Linear Optics

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PRX Quantum 2021年第4期2卷 040353-040353页

作者： Ilan Tzitrin Takaya Matsuura Rafael N. Alexander Guillaume Dauphinais J. Eli Bourassa Krishna K. Sabapathy Nicolas C. Menicucci Ish Dhand Xanadu Toronto Ontario M5G 2C8 Canada Department of Physics University of Toronto Toronto Ontario M5S 1A7 Canada Department of Applied Physics Graduate School of Engineering The University of Tokyo 7–3–1 Hongo Bunkyo-ku Tokyo 113–8656 Japan Centre for Quantum Computation and Communication Technology School of Science RMIT University Melbourne VIC 3000 Australia Center for Quantum Information and Control University of New Mexico Albuquerque New Mexico 87131 USA

The scalability of photonic implementations of fault-tolerant quantum computing based on Gottesman-Kitaev-Preskill (GKP) qubits is injured by the requirements of inline squeezing and reconfigurability of the linear optical network. In this work we propose a topologically error-corrected architecture that does away with these elements at no cost—in fact, at an advantage—to state preparation overheads. Our computer consists of three modules: a two-dimensional (2D) array of probabilistic sources of GKP states; a depth-four circuit of static beam splitters, phase shifters, and short delay lines; and a 2D array of homodyne detectors. The symmetry of our proposed circuit allows us to combine the effects of finite squeezing and uniform photon loss within the noise model, resulting in more comprehensive threshold estimates. These jumps over both architectural and analytical hurdles considerably expedite the construction of a photonic quantum computer.

关键词： Measurement-based quantum computing Optical quantum information processing Quantum computation Quantum information architectures & platforms Quantum information processing with continuous variables Topological quantum computing

Prediction of fitness in bacteria with causal jump dynamic mode decomposition

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arXiv 2020年

作者： Balakrishnan, Shara Hasnain, Aqib Boddupalli, Nibodh Joshy, Dennis M. Egbert, Robert G. Yeung, Enoch Department of Electrical and Computer Engineering University of California Santa Barbara United States Department of Mechanical Engineering University of California Santa Barbara United States Environmental and Biological Sciences Directorate Pacific Northwest National Laboratory RichlandWA United States Department of Mechanical Engineering Center for Control Dynamical Systems and Computation Biomolecular Science and Engineering University of California Santa Barbara United States

— In this paper, we consider the problem of learning a predictive model for population cell growth dynamics as a function of the media conditions. We first introduce a generic data-driven framework for training operator-theoretic models to predict cell growth rate. We then introduce the experimental design and data generated in this study, namely growth curves of Pseudomonas putida as a function of casein and glucose concentrations. We use a data driven approach for model identification, specifically the nonlinear autoregressive (NAR) model to represent the dynamics. We show theoretically that Hankel DMD can be used to obtain a solution of the NAR model. We show that it identifies a constrained NAR model and to obtain a more general solution, we define a causal state space system using 1-step, 2-step,..., τ-step predictors of the NAR model and identify a Koopman operator for this model using extended dynamic mode decomposition. The hybrid scheme we call causal-jump dynamic mode decomposition, which we illustrate on a growth profile or fitness prediction challenge as a function of different input growth conditions. We show that our model is able to recapitulate training growth curve data with 96.6% accuracy and predict test growth curve data with 91% accuracy. Copyright © 2020, The Authors. All rights reserved.

关键词： Bacteria

Social power evolution in influence networks with stubborn individuals

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arXiv 2019年

作者： Tian, Ye Jia, Peng Mirtabatabaei, Anahita Wang, Long Friedkin, Noah E. Bullo, Francesco Center for Complex Systems School of Mechanoelectronic Engineering Xidian University Xi’an710071 China Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106 United States Mechanical Engineering Department Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106 United States Center for Systems and Control College of Engineering Peking University Beijing100871 China Department of Sociology Center for Control Dynamical Systems and Computation UC Santa BarbaraCA93106 United States

—This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the reflected appraisal mechanism, two models are proposed over issue sequences and over a single issue, respectively. These models generalize the original DeGroot-Friedkin (DF) model by including stubbornness. To the best of our knowledge, this paper is the first attempt to investigate the social power evolution of stubborn individuals basing on the reflected appraisal mechanism. Properties of equilibria and convergence are provided. We show that the models have same equilibrium social power and convergence property, where the equilibrium social power depends only upon interpersonal influence and individuals’ stubbornness. Roughly speaking, more stubborn individual has more equilibrium social power. Moreover, unlike the DF model without stubbornness, we prove that for the models with stubbornness, autocracy can never be achieved, while democracy can be achieved under any network topology. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamical systems

Fundamental issues regarding uncertainties in artificial neural networks

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arXiv 2020年

作者： Thacker, N.A. Twining, C.J. Tar, P.D. Notley, S. Ramesh, V. Division of Informatics Imaging & Data Sciences University of Manchester United Kingdom Department of Computer Science University of Manchester United Kingdom Department of Automatic Control and Systems Engineering University of Sheffield United Kingdom Center for Cognition and Computation Goethe-Universität Frankfurt am Main Germany

Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted, and in order to support safety critical systems, we require such systems to give an indication of the training sample related uncertainty associated with their output. Some readers may think that this is a well known issue which is already covered by the basic principles of pattern recognition. We will explain below how this is not the case and how the conventional (Likelihood estimate of) conditional probability of classification does not correctly assess this uncertainty. We provide a discussion of the standard interpretations of this problem and show how a quantitative approach based upon long standing methods can be practically applied. The methods are illustrated on the task of early diagnosis of dementing diseases using Magnetic Resonance Imaging. Copyright © 2020, The Authors. All rights reserved.

关键词： Extrapolation

Search strategy in a complex and dynamic environment: The MH370 case

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arXiv 2020年

作者： Ivić, Stefan Crnković, Bojan Arbabi, Hassan Loire, Sophie Clary, Patrick Mezić, Igor Faculty of Engineering University of Rijeka Rijeka Croatia Department of Mathematics University of Rijeka Rijeka Croatia Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge United States Bruker Nano Surfaces Santa Barbara United States Oregon State University Corvallis United States Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

Search and detection of objects on the ocean surface is a challenging task due to the complexity of the drift dynamics and lack of known optimal solutions for the path of the search agents. This challenge was highlighted by the unsuccessful search for Malaysian Flight 370 (MH370) which disappeared on March 8, 2014. In this paper, we propose an improvement of a search algorithm rooted in the ergodic theory of dynamical systems which can accommodate complex geometries and uncertainties of the drifting search areas on the ocean surface. We illustrate the effectiveness of this algorithm in a computational replication of the conducted search for MH370. In comparison to conventional search methods, the proposed algorithm leads to an order of magnitude improvement in success rate over the time period of the actual search operation. Simulations of the proposed search control also indicate that the initial success rate of finding debris increases in the event of delayed search commencement. This is due to the existence of convergence zones in the search area which leads to local aggregation of debris in those zones and hence reduction of the effective size of the area to be searched. Copyright © 2020, The Authors. All rights reserved.

关键词： Debris