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Ma L, Kong Q. Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics. Entropy (Basel) 2023; 25:e25050719. [PMID: 37238474 DOI: 10.3390/e25050719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 04/03/2023] [Accepted: 04/08/2023] [Indexed: 05/28/2023]
Abstract
We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way. For classical control, we used the relative displacement between the ball and the trolley as the controller to study the anharmonic effect of the cartpole. Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range.
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Affiliation(s)
- Lanlan Ma
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist), Department of Physics, Shanghai University, Shanghai 200444, China
| | - Qian Kong
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist), Department of Physics, Shanghai University, Shanghai 200444, China
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Celi S, Gasparotti E, Capellini K, Bardi F, Scarpolini MA, Cavaliere C, Cademartiri F, Vignali E. An image-based approach for the estimation of arterial local stiffness in vivo. Front Bioeng Biotechnol 2023; 11:1096196. [PMID: 36793441 PMCID: PMC9923115 DOI: 10.3389/fbioe.2023.1096196] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2022] [Accepted: 01/19/2023] [Indexed: 01/31/2023] Open
Abstract
The analysis of mechanobiology of arterial tissues remains an important topic of research for cardiovascular pathologies evaluation. In the current state of the art, the gold standard to characterize the tissue mechanical behavior is represented by experimental tests, requiring the harvesting of ex-vivo specimens. In recent years though, image-based techniques for the in vivo estimation of arterial tissue stiffness were presented. The aim of this study is to define a new approach to provide local distribution of arterial stiffness, estimated as the linearized Young's Modulus, based on the knowledge of in vivo patient-specific imaging data. In particular, the strain and stress are estimated with sectional contour length ratios and a Laplace hypothesis/inverse engineering approach, respectively, and then used to calculate the Young's Modulus. After describing the method, this was validated by using a set of Finite Element simulations as input. In particular, idealized cylinder and elbow shapes plus a single patient-specific geometry were simulated. Different stiffness distributions were tested for the simulated patient-specific case. After the validation from Finite Element data, the method was then applied to patient-specific ECG-gated Computed Tomography data by also introducing a mesh morphing approach to map the aortic surface along the cardiac phases. The validation process revealed satisfactory results. In the simulated patient-specific case, root mean square percentage errors below 10% for the homogeneous distribution and below 20% for proximal/distal distribution of stiffness. The method was then successfully used on the three ECG-gated patient-specific cases. The resulting distributions of stiffness exhibited significant heterogeneity, nevertheless the resulting Young's moduli were always contained within the 1-3 MPa range, which is in line with literature.
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Affiliation(s)
- Simona Celi
- BioCardioLab, UOC Bioingegneria, Fondazione Toscana G Monasterio, Massa, Italy,*Correspondence: Simona Celi,
| | - Emanuele Gasparotti
- BioCardioLab, UOC Bioingegneria, Fondazione Toscana G Monasterio, Massa, Italy
| | - Katia Capellini
- BioCardioLab, UOC Bioingegneria, Fondazione Toscana G Monasterio, Massa, Italy
| | - Francesco Bardi
- BioCardioLab, UOC Bioingegneria, Fondazione Toscana G Monasterio, Massa, Italy,Mines Saint-Etienne, Universit’e de Lyon, INSERM, SaInBioSE U1059, Lyon, France
| | - Martino Andrea Scarpolini
- BioCardioLab, UOC Bioingegneria, Fondazione Toscana G Monasterio, Massa, Italy,Dipartimento di Ingegneria Industriale, Università “Tor Vergata”, Roma, Italy
| | | | | | - Emanuele Vignali
- BioCardioLab, UOC Bioingegneria, Fondazione Toscana G Monasterio, Massa, Italy
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Takahashi K. Dynamical invariant formalism of shortcuts to adiabaticity. Philos Trans A Math Phys Eng Sci 2022; 380:20220301. [PMID: 36335952 DOI: 10.1098/rsta.2022.0301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to mimic adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone and flow equation. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
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Affiliation(s)
- Kazutaka Takahashi
- Department of Physics Engineering, Faculty of Engineering, Mie University, Mie 514-8507, Japan
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Abstract
Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies (Weckwerth, 2011; Sun and Weckwerth, 2012; Nägele et al., 2014) by a differential Jacobian approach. The Jacobian is solved from an overdetermined system of equations as JC + CJT = −2D, called Lyapunov Equation in its generic form,1 where J is the Jacobian, C is the covariance matrix of metabolomics data, and D is the fluctuation matrix. Lyapunov Equation can be further simplified as the linear form Ax = b. Frequently, this linear equation system is ill-conditioned, i.e., a small variation in the right side b results in a big change in the solution x, thus making the solution unstable and error-prone. At the same time, inaccurate estimation of covariance matrix and uncertainties in the fluctuation matrix bring biases to the solution x. Here, we first reviewed common approaches to circumvent the ill-conditioned problems, including total least squares, Tikhonov regularization, and truncated singular value decomposition. Then, we benchmarked these methods on several in silico kinetic models with small to large perturbations on the covariance and fluctuation matrices. The results identified that the accuracy of the reverse Jacobian is mainly dependent on the condition number of A, the perturbation amplitude of C, and the stiffness of the kinetic models. Our research contributes a systematical comparison of methods to inversely solve Jacobian from metabolomics data.
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Affiliation(s)
- Xiaoliang Sun
- Department of Ecogenomics and Systems Biology, University of Vienna , Vienna , Austria ; Institute of Integrative Biology, University of Liverpool , Liverpool , United Kingdom
| | - Bettina Länger
- Department of Ecogenomics and Systems Biology, University of Vienna , Vienna , Austria
| | - Wolfram Weckwerth
- Department of Ecogenomics and Systems Biology, University of Vienna , Vienna , Austria ; Vienna Metabolomics Center (VIME), University of Vienna , Vienna , Austria
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