Local parameter identifiability of large-scale nonlinear models based on the output sensitivity covariance matrix

Abstract Recently, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which could probe the ionization history, using simulated observations of 15 frequency CMB polarization maps of future generation Cosmic Origin Explorer (COrE) satellite mission. We find that the clean power spectra, from the usual ILC, are strongly biased due to non zero CMB-foregrounds chance correlations. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E mode reconstruction by incorporating prior information of theoretical E mode angular power spectrum while estimating the weights for linear combination of input maps (Sudevan & Saha 2018b). Using the E mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E mode map and its angular power spectrum. We compare the performance of the usual ILC and the new method over large angular scales and show that the later produces significantly statistically improved results than the former. The new E mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutlipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

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Enhancing the competitive swarm optimizer with covariance matrix adaptation for large scale optimization

Applied Intelligence ◽

10.1007/s10489-020-02078-4 ◽

2021 ◽

Author(s):

Wei Li ◽

Zhou Lei ◽

Junqing Yuan ◽

Haonan Luo ◽

Qingzheng Xu

Keyword(s):

Covariance Matrix ◽

Large Scale ◽

Large Scale Optimization ◽

Covariance Matrix Adaptation ◽

Scale Optimization

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Stepwise covariance matrix decomposition for efficient simulation of multivariate large-scale three-dimensional random fields

Applied Mathematical Modelling ◽

10.1016/j.apm.2018.11.011 ◽

2019 ◽

Vol 68 ◽

pp. 169-181 ◽

Cited By ~ 8

Author(s):

Dian-Qing Li ◽

Te Xiao ◽

Li-Min Zhang ◽

Zi-Jun Cao

Keyword(s):

Covariance Matrix ◽

Random Fields ◽

Large Scale ◽

Three Dimensional ◽

Matrix Decomposition ◽

Efficient Simulation ◽

Covariance Matrix Decomposition

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Damage Detection Using Large-Scale Covariance Matrix

Structural Health Monitoring, Volume 5 - Conference Proceedings of the Society for Experimental Mechanics Series ◽

10.1007/978-3-319-04570-2_10 ◽

2014 ◽

pp. 89-97 ◽

Cited By ~ 3

Author(s):

Luciana Balsamo ◽

Raimondo Betti ◽

Homayoon Beigi

Keyword(s):

Damage Detection ◽

Covariance Matrix ◽

Large Scale ◽

Scale Covariance

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Conclusion

Stability and Control of Large-Scale Dynamical Systems ◽

10.23943/princeton/9780691153469.003.0014 ◽

2011 ◽

Author(s):

Wassim M. Haddad ◽

Sergey G. Nersesov

Keyword(s):

Dynamical Systems ◽

Large Scale ◽

Multiple Equilibria ◽

Nonlinear Models ◽

Dynamical Behavior ◽

Transportation Systems ◽

Network Systems ◽

Grid Systems ◽

Feedback Interconnections ◽

And Control

This book has described a general stability analysis and control design framework for large-scale dynamical systems, with an emphasis on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. The large-scale dynamical systems are composed of interconnected subsystems whose relationships are often circular, giving rise to feedback interconnections. This leads to nonlinear models that can exhibit rich dynamical behavior, such as multiple equilibria, limit cycles, bifurcations, jump resonance phenomena, and chaos. The book concludes by discussing the potential for applying and extending the results across disciplines, such as economic systems, network systems, computer networks, telecommunication systems, power grid systems, and road, rail, air, and space transportation systems.

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Parameter identifiability analysis and visualization in large-scale kinetic models of biosystems

BMC Systems Biology ◽

10.1186/s12918-017-0428-y ◽

2017 ◽

Vol 11 (1) ◽

Cited By ~ 40

Author(s):

Attila Gábor ◽

Alejandro F. Villaverde ◽

Julio R. Banga

Keyword(s):

Kinetic Models ◽

Large Scale ◽

Identifiability Analysis ◽

Parameter Identifiability

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Modeling of an Electromagnetic Vibration Energy Harvester With Motion Magnification

Volume 7: Dynamic Systems and Control; Mechatronics and Intelligent Machines, Parts A and B ◽

10.1115/imece2011-65613 ◽

2011 ◽

Cited By ~ 20

Author(s):

Zhongjie Li ◽

Zachary Brindak ◽

Lei Zuo

Keyword(s):

Large Scale ◽

Nonlinear Models ◽

Vibration Energy ◽

Vibration Energy Harvesting ◽

Vibration Energy Harvester ◽

Modeling And Analysis ◽

Vehicle Suspensions ◽

Shock Absorbers ◽

Potential Applications ◽

Motion Magnification

This paper presents the modeling and analysis of an electromagnetic harvester for potential applications in large-scale vibration energy harvesting such as from vehicle suspensions or civil structures. The kinematics and dynamics of a motion mechanism and generator are considered, including backlash and friction. In this study, a dynamic model for a rack-pinion type regenerative shock absorber has been derived and analyzed based on differential equations. To understand the influence of the friction and backlash on the system, nonlinear models have been created. Simulations are carried out to study the features of the design. The validation of the models is demonstrated by comparing the simulation results with experimental measurements. Guidelines are given for the design of this type of regenerative shock absorbers.

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DC Large-Scale Simulation of Nonlinear Circuits on Parallel Processors

International Journal of Electronics and Telecommunications ◽

10.2478/v10177-012-0040-4 ◽

2012 ◽

Vol 58 (3) ◽

pp. 285-295

Author(s):

Diego Ernesto Cortés Udave ◽

Jan Ogrodzki ◽

Miguel Angel Gutiérrez De Anda

Keyword(s):

Large Scale ◽

Complexity Analysis ◽

Sparse Matrix ◽

Nonlinear Models ◽

Nonlinear Circuits ◽

Departure Point ◽

Parallel Solution ◽

Matrix Operations ◽

Time Required ◽

Numerical Complexity

Abstract Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries is managed through concurrent processes. In this paper it is shown how the numerical complexity of this problem (and thus its solution time) can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the Bordered-Block Diagonal (BBD) matrix structure. This BBD-parallel approach may give a considerable profit though it is strongly dependent on the system topology. This paper presents a theoretical foundation of the algorithm, its implementation, and numerical complexity analysis in virtue of practical measurements of matrix operations.

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