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ORCIDTryphon T. Georgiou
Tryphon Thomas Georgiou
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- affiliation: University of Minnesota, USA
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2020 – today
- 2024
[j98]Rui Fu, Olga Movilla Miangolarra, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Stochastic thermodynamic engines under time-varying temperature profile. Autom. 159: 111361 (2024)- [j97]Anqi Dong
, Arthur Stéphanovitch, Tryphon T. Georgiou:
Monge-Kantorovich optimal transport through constrictions and flow-rate constraints. Autom. 160: 111448 (2024) - [j96]Asmaa Eldesoukey, Olga Movilla Miangolarra, Tryphon T. Georgiou:
An Excursion Onto Schrödinger's Bridges: Stochastic Flows With Spatio-Temporal Marginals. IEEE Control. Syst. Lett. 8: 1138-1143 (2024) - [c68]Wuwei Wu, Shiqi Zhang, Zhongkui Li, Jie Chen, Tryphon T. Georgiou:
On Decomposition and Convergence of Distributed Optimization Algorithms. ACC 2024: 3391-3396 - [i73]Anqi Dong, Can Chen, Tryphon T. Georgiou:
Network Learning with Directional Sign Patterns. CoRR abs/2403.14915 (2024) - [i72]Asmaa Eldesoukey, Olga Movilla Miangolarra, Tryphon T. Georgiou:
Schr\"odinger's bridges with stopping: Steering of stochastic flows towards spatio-temporal marginals. CoRR abs/2404.07402 (2024) - [i71]Mahmoud Abdelgalil, Tryphon T. Georgiou:
Sub-Riemannian Geometry, Mixing, and the Holonomy of Optimal Mass Transport. CoRR abs/2408.14707 (2024) - [i70]Wuwei Wu, Jie Chen, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Tannenbaum's gain-margin optimization meets Polyak's heavy-ball algorithm. CoRR abs/2409.19882 (2024) - 2023
- [j95]Qi Mao, Yong Xu, Jie Chen, Tryphon T. Georgiou:
Implementation-oriented filtered PID control: Optimization of robustness margins. Autom. 152: 110974 (2023) - [j94]Olga Movilla Miangolarra, Amirhossein Taghvaei, Tryphon T. Georgiou:
A Matching Principle for Power Transfer in Stochastic Thermodynamics. IEEE Control. Syst. Lett. 7: 2107-2112 (2023) - [j93]Daniel Grange, Mohammad Al-Jarrah, Ricardo Baptista, Amirhossein Taghvaei, Tryphon T. Georgiou, Sean Phillips, Allen R. Tannenbaum:
Computational Optimal Transport and Filtering on Riemannian Manifolds. IEEE Control. Syst. Lett. 7: 3495-3500 (2023) - [c67]Olga Movilla Miangolarra, Amirhossein Taghvaei, Tryphon T. Georgiou:
Minimal entropy production in anisotropic temperature fields. ACC 2023: 616-621 - [i69]Olga Movilla Miangolarra, Amirhossein Taghvaei, Tryphon T. Georgiou:
Minimal entropy production in the presence of anisotropic fluctuations. CoRR abs/2302.04401 (2023) - [i68]Olga Movilla Miangolarra, Amirhossein Taghvaei, Tryphon T. Georgiou:
A matching principle for power transfer in Stochastic Thermodynamics. CoRR abs/2303.10161 (2023) - [i67]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Control and estimation of multi-commodity network flow under aggregation. CoRR abs/2307.05103 (2023) - [i66]Anqi Dong, Tryphon T. Georgiou, Allen R. Tannenbaum:
Negative probabilities in Gene Regulatory Networks. CoRR abs/2307.07738 (2023) - [i65]Anqi Dong, Tryphon T. Georgiou, Allen R. Tannenbaum:
Data Assimilation for Sign-indefinite Priors: A generalization of Sinkhorn's algorithm. CoRR abs/2308.11791 (2023) - [i64]Qi Mao, Yong Xu, Jianqi Chen, Jie Chen, Tryphon T. Georgiou:
Classical Stability Margins by PID Control. CoRR abs/2311.11460 (2023) - [i63]Asmaa Eldesoukey, Tryphon T. Georgiou:
Schrödinger's control and estimation paradigm with spatio-temporal distributions on graphs. CoRR abs/2312.05679 (2023) - [i62]Ralph Sabbagh, Olga Movilla Miangolarra, Tryphon T. Georgiou:
Wasserstein speed limits for Langevin systems. CoRR abs/2312.07788 (2023) - 2022
- [j92]Amirhossein Taghvaei, Olga Movilla Miangolarra, Rui Fu, Yongxin Chen, Tryphon T. Georgiou:
On the Relation Between Information and Power in Stochastic Thermodynamic Engines. IEEE Control. Syst. Lett. 6: 434-439 (2022) - [j91]Olga Movilla Miangolarra, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Geometry of Finite-Time Thermodynamic Cycles With Anisotropic Thermal Fluctuations. IEEE Control. Syst. Lett. 6: 3409-3414 (2022) - [j90]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
The Most Likely Evolution of Diffusing and Vanishing Particles: Schrödinger Bridges with Unbalanced Marginals. SIAM J. Control. Optim. 60(4): 2016-2039 (2022) - [j89]Fariba Ariaei, Zahra Askarzadeh, Yongxin Chen, Tryphon T. Georgiou:
Macroscopic Network Circulation for Planar Graphs. IEEE Trans. Control. Netw. Syst. 9(4): 1840-1850 (2022) - [c66]Qi Mao, Yong Xu, Jie Chen, Tryphon T. Georgiou:
Implementation-Oriented Filtered PID Control: Robustness Margins. CDC 2022: 5511-5516 - [i61]Olga Movilla Miangolarra, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Thermodynamic engine powered by anisotropic fluctuations. CoRR abs/2203.07573 (2022) - [i60]Olga Movilla Miangolarra, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Geometry of finite-time thermodynamic cycles with anisotropic thermal fluctuations. CoRR abs/2203.12483 (2022) - [i59]Arthur Stéphanovitch, Anqi Dong, Tryphon T. Georgiou:
Optimal transport through a toll. CoRR abs/2208.03587 (2022) - [i58]Olga Movilla Miangolarra, Amirhossein Taghvaei, Tryphon T. Georgiou:
Minimal entropy production in anisotropic temperature fields. CoRR abs/2210.01062 (2022) - [i57]Anqi Dong, Arthur Stéphanovitch, Tryphon T. Georgiou:
Monge-Kantorovich Optimal Transport Through Constrictions and Flow-rate Constraints. CoRR abs/2212.14509 (2022) - 2021
- [j88]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal Transport in Systems and Control. Annu. Rev. Control. Robotics Auton. Syst. 4: 89-113 (2021) - [j87]Rui Fu, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Maximal power output of a stochastic thermodynamic engine. Autom. 123: 109366 (2021) - [j86]Tryphon T. Georgiou, Anders Lindquist:
On a Fejér-Riesz factorization of generalized trigonometric polynomials. Commun. Inf. Syst. 21(3): 371-384 (2021) - [j85]Amir-Hossein Karimi, Luigia Ripani, Tryphon T. Georgiou:
Statistical Learning in Wasserstein Space. IEEE Control. Syst. Lett. 5(3): 899-904 (2021) - [j84]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge. SIAM Rev. 63(2): 249-313 (2021) - [j83]Valentina Ciccone, Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Regularized Transport Between Singular Covariance Matrices. IEEE Trans. Autom. Control. 66(7): 3339-3346 (2021) - [c65]Qi Mao, Yong Xu, Jianqi Chen, Jie Chen, Tryphon T. Georgiou:
Maximal Gain and Phase Margins Attainable by PID Control. CDC 2021: 1820-1825 - [c64]Amir-Hossein Karimi, Tryphon T. Georgiou:
The Challenge of Small Data: Dynamic Mode Decomposition, Redux. CDC 2021: 2276-2281 - [c63]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Fast and Asymptotic Steering to a Steady State for Networks Flows. GSI 2021: 860-868 - [i56]Rui Fu, Olga Movilla Miangolarra, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Harvesting energy from a periodic heat bath. CoRR abs/2101.02239 (2021) - [i55]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal steering to invariant distributions for networks flows. CoRR abs/2102.12628 (2021) - [i54]Amirhossein Taghvaei, Olga Movilla Miangolarra, Rui Fu, Yongxin Chen, Tryphon T. Georgiou:
On the relation between information and power in stochastic thermodynamic engines. CoRR abs/2103.03986 (2021) - [i53]Amir-Hossein Karimi, Tryphon T. Georgiou:
The Challenge of Small Data: Dynamic Mode Decomposition, Redux. CoRR abs/2104.04005 (2021) - [i52]Amir-Hossein Karimi, Tryphon T. Georgiou:
Regression analysis of distributional data through Multi-Marginal Optimal transport. CoRR abs/2106.15031 (2021) - [i51]Olga Movilla Miangolarra, Amirhossein Taghvaei, Rui Fu, Yongxin Chen, Tryphon T. Georgiou:
Energy harvesting from anisotropic fluctuations. CoRR abs/2108.00334 (2021) - [i50]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
The most likely evolution of diffusing and vanishing particles: Schrodinger Bridges with unbalanced marginals. CoRR abs/2108.02879 (2021) - 2020
- [j82]Armin Zare, Tryphon T. Georgiou, Mihailo R. Jovanovic:
Stochastic Dynamical Modeling of Turbulent Flows. Annu. Rev. Control. Robotics Auton. Syst. 3: 195-219 (2020) - [j81]Tryphon T. Georgiou, Faryar Jabbari, Malcolm C. Smith:
Principles of Lossless Adjustable One-Ports. IEEE Trans. Autom. Control. 65(1): 252-262 (2020) - [j80]Zahra Askarzadeh, Rui Fu, Abhishek Halder, Yongxin Chen, Tryphon T. Georgiou:
Stability Theory of Stochastic Models in Opinion Dynamics. IEEE Trans. Autom. Control. 65(2): 522-533 (2020) - [j79]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Stochastic Control and Nonequilibrium Thermodynamics: Fundamental Limits. IEEE Trans. Autom. Control. 65(7): 2979-2991 (2020) - [j78]Armin Zare, Hesameddin Mohammadi, Neil K. Dhingra, Tryphon T. Georgiou, Mihailo R. Jovanovic:
Proximal Algorithms for Large-Scale Statistical Modeling and Sensor/Actuator Selection. IEEE Trans. Autom. Control. 65(8): 3441-3456 (2020) - [j77]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon, Allen R. Tannenbaum:
Relaxed Schrödinger Bridges and Robust Network Routing. IEEE Trans. Control. Netw. Syst. 7(2): 923-931 (2020) - [c62]Anqi Dong, Amirhossein Taghvaei, Tryphon T. Georgiou:
Lasso formulation of the shortest path problem. CDC 2020: 402-407 - [c61]Rui Fu, Olga Movilla Miangolarra, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Harvesting energy from a periodic heat bath. CDC 2020: 3034-3039 - [i49]Rui Fu, Amirhossein Taghvaei, Yongxin Chen, Tryphon T. Georgiou:
Maximal power output of a stochastic thermodynamic engine. CoRR abs/2001.00979 (2020) - [i48]Fariba Ariaei, Zahra Askarzadeh, Yongxin Chen, Tryphon T. Georgiou:
Macroscopic network circulation for planar graphs. CoRR abs/2004.02053 (2020) - [i47]Clément Guilloteau, Antonios Mamalakis, Lawrence Vulis, Tryphon T. Georgiou, Efi Foufoula-Georgiou:
Rotated spectral principal component analysis (rsPCA) for identifying dynamical modes of variability in climate systems. CoRR abs/2004.11411 (2020) - [i46]Anqi Dong, Amirhossein Taghvaei, Tryphon T. Georgiou:
Lasso formulation of the shortest path problem. CoRR abs/2005.09152 (2020) - [i45]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Stochastic control liasons: Richard Sinkhorn meets Gaspard Monge on a Schroedinger bridge. CoRR abs/2005.10963 (2020) - [i44]Tryphon T. Georgiou, Anders Lindquist:
On a Fejer-Riesz factorization of generalized trigonometric polynomials. CoRR abs/2005.11920 (2020) - [i43]Valentina Ciccone, Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Regularized transport between singular covariance matrices. CoRR abs/2006.10000 (2020) - [i42]Amirhossein Taghvaei, Prashant G. Mehta, Tryphon T. Georgiou:
Optimality vs Stability Trade-off in Ensemble Kalman Filters. CoRR abs/2010.09920 (2020) - [i41]Amir-Hossein Karimi, Tryphon T. Georgiou:
Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric. CoRR abs/2011.00759 (2020)
2010 – 2019
- 2019
- [j76]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Optimal Transport for Gaussian Mixture Models. IEEE Access 7: 6269-6278 (2019) - [j75]Tryphon T. Georgiou, Anders Lindquist:
Dynamic Relations in Sampled Processes. IEEE Control. Syst. Lett. 3(1): 144-149 (2019) - [c60]Zahra Askarzadeh, Rui Fu, Abhishek Halder, Yongxin Chen, Tryphon T. Georgiou:
Opinion Dynamics over Influence Networks. ACC 2019: 1873-1878 - [c59]Abhishek Halder, Tryphon T. Georgiou:
Proximal Recursion for the Wonham Filter. CDC 2019: 660-665 - [c58]Daniele Alpago, Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
On optimal steering of a non-Markovian Gaussian process. CDC 2019: 2556-2561 - [c57]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Covariance steering in zero-sum linear-quadratic two-player differential games. CDC 2019: 8204-8209 - [c56]Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou, Luigia Ripani:
Multi-marginal Schrödinger Bridges. GSI 2019: 725-732 - [i40]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Probabilistic Kernel Support Vector Machines. CoRR abs/1904.06762 (2019) - [i39]Tryphon T. Georgiou, Faryar Jabbari, Malcolm C. Smith:
Principles of lossless adjustable one-ports. CoRR abs/1905.06504 (2019) - [i38]Armin Zare, Tryphon T. Georgiou, Mihailo R. Jovanovic:
Stochastic dynamical modeling of turbulent flows. CoRR abs/1908.09487 (2019) - [i37]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Covariance steering in zero-sum linear-quadratic two-player differential games. CoRR abs/1909.05468 (2019) - [i36]Abhishek Halder, Tryphon T. Georgiou:
Proximal Recursion for the Wonham Filter. CoRR abs/1909.05827 (2019) - [i35]Shreyas Fadnavis, Hamza Farooq, Maryam Afzali, Christophe Lenglet, Tryphon T. Georgiou, Hu Cheng, Sharlene D. Newman, Shahnawaz Ahmed, Rafael Neto Henriques, Eric Peterson, Serge Koudoro, Ariel Rokem, Eleftherios Garyfallidis:
Fitting IVIM with Variable Projection and Simplicial Optimization. CoRR abs/1910.00095 (2019) - 2018
- [j74]Tryphon T. Georgiou:
Rudolf E. Kalman's quest for algebraic characterizations of positivity. Annu. Rev. Control. 45: 205-206 (2018) - [j73]Yongxin Chen, Johan Karlsson, Tryphon T. Georgiou:
The Role of the Time-Arrow in Mean-Square Estimation of Stochastic Processes. IEEE Control. Syst. Lett. 2(1): 85-90 (2018) - [j72]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Steering the Distribution of Agents in Mean-Field Games System. J. Optim. Theory Appl. 179(1): 332-357 (2018) - [j71]Yongxin Chen, Eldad Haber, Kaoru Yamamoto, Tryphon T. Georgiou, Allen R. Tannenbaum:
An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport. J. Sci. Comput. 77(1): 79-100 (2018) - [j70]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Vector-Valued Optimal Mass Transport. SIAM J. Appl. Math. 78(3): 1682-1696 (2018) - [j69]Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou:
Measure-Valued Spline Curves: An Optimal Transport Viewpoint. SIAM J. Math. Anal. 50(6): 5947-5968 (2018) - [j68]Kaoru Yamamoto, Yongxin Chen, Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum:
Regularization and Interpolation of Positive Matrices. IEEE Trans. Autom. Control. 63(4): 1208-1212 (2018) - [j67]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon, Allen R. Tannenbaum:
Efficient Robust Routing for Single Commodity Network Flows. IEEE Trans. Autom. Control. 63(7): 2287-2294 (2018) - [j66]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Matrix Optimal Mass Transport: A Quantum Mechanical Approach. IEEE Trans. Autom. Control. 63(8): 2612-2619 (2018) - [j65]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal Steering of a Linear Stochastic System to a Final Probability Distribution - Part III. IEEE Trans. Autom. Control. 63(9): 3112-3118 (2018) - [c55]Abhishek Halder, Tryphon T. Georgiou:
Gradient Flows in Filtering and Fisher-Rao Geometry. ACC 2018: 4281-4286 - [c54]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Steering the Distribution of Agents in Mean-Field Games. CDC 2018: 4403-4408 - [i34]Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou:
Measure-valued spline curves: an optimal transport viewpoint. CoRR abs/1801.03186 (2018) - [i33]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Stochastic control and non-equilibrium thermodynamics: fundamental limits. CoRR abs/1802.01271 (2018) - [i32]Tryphon T. Georgiou, Anders Lindquist:
Dynamic relations in sampled processes. CoRR abs/1805.02078 (2018) - [i31]Armin Zare, Neil K. Dhingra, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Proximal algorithms for large-scale statistical modeling and optimal sensor/actuator selection. CoRR abs/1807.01739 (2018) - 2017
- [j64]Yongxin Chen, Tryphon T. Georgiou, Lipeng Ning, Allen R. Tannenbaum:
Matricial Wasserstein-1 Distance. IEEE Control. Syst. Lett. 1(1): 14-19 (2017) - [j63]Armin Zare, Yongxin Chen, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Low-Complexity Modeling of Partially Available Second-Order Statistics: Theory and an Efficient Matrix Completion Algorithm. IEEE Trans. Autom. Control. 62(3): 1368-1383 (2017) - [j62]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal Transport Over a Linear Dynamical System. IEEE Trans. Autom. Control. 62(5): 2137-2152 (2017) - [j61]Tryphon T. Georgiou, Anders Lindquist:
Likelihood Analysis of Power Spectra and Generalized Moment Problems. IEEE Trans. Autom. Control. 62(9): 4580-4592 (2017) - [j60]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon, Allen R. Tannenbaum:
Robust Transport Over Networks. IEEE Trans. Autom. Control. 62(9): 4675-4682 (2017) - [j59]Tryphon T. Georgiou, Anders Lindquist:
Optimal Estimation With Missing Observations via Balanced Time-Symmetric Stochastic Models. IEEE Trans. Autom. Control. 62(11): 5590-5603 (2017) - [c53]Abhishek Halder, Tryphon T. Georgiou:
Gradient flows in uncertainty propagation and filtering of linear Gaussian systems. CDC 2017: 3081-3088 - [c52]Armin Zare, Neil K. Dhingra, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Structured covariance completion via proximal algorithms. CDC 2017: 3775-3780 - [i30]Abhishek Halder, Tryphon T. Georgiou:
Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systems. CoRR abs/1704.00102 (2017) - [i29]Zahra Askarzadeh, Rui Fu, Abhishek Halder, Yongxin Chen, Tryphon T. Georgiou:
Stability Theory in $\ell_1$ for Nonlinear Markov Chains and Stochastic Models for Opinion Dynamics over Influence Networks. CoRR abs/1706.03158 (2017) - [i28]Yongxin Chen, Eldad Haber, Kaoru Yamamoto, Tryphon T. Georgiou, Allen R. Tannenbaum:
An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport. CoRR abs/1706.08841 (2017) - [i27]Abhishek Halder, Tryphon T. Georgiou:
Gradient Flows in Filtering and Fisher-Rao Geometry. CoRR abs/1710.00064 (2017) - [i26]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Optimal transport for Gaussian mixture models. CoRR abs/1710.07876 (2017) - [i25]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Steering the distribution of agents in mean-field and cooperative games. CoRR abs/1712.03578 (2017) - 2016
- [j58]Athanasios C. Antoulas, Tryphon T. Georgiou, Pramod P. Khargonekar, A. Bülent Özgüler, Eduardo D. Sontag, Yutaka Yamamoto:
Obituary for Professor Rudolf Emil Kalman. Autom. 74: 370-371 (2016) - [j57]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint. J. Optim. Theory Appl. 169(2): 671-691 (2016) - [j56]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Entropic and Displacement Interpolation: A Computational Approach Using the Hilbert Metric. SIAM J. Appl. Math. 76(6): 2375-2396 (2016) - [j55]Yongxin Chen, Tryphon T. Georgiou:
Stochastic Bridges of Linear Systems. IEEE Trans. Autom. Control. 61(2): 526-531 (2016) - [j54]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal Steering of a Linear Stochastic System to a Final Probability Distribution, Part I. IEEE Trans. Autom. Control. 61(5): 1158-1169 (2016) - [j53]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal Steering of a Linear Stochastic System to a Final Probability Distribution, Part II. IEEE Trans. Autom. Control. 61(5): 1170-1180 (2016) - [c51]Yongxin Chen, Sei Zhen Khong, Tryphon T. Georgiou:
On the definiteness of graph Laplacians with negative weights: Geometrical and passivity-based approaches. ACC 2016: 2488-2493 - [c50]Romeil Sandhu, Sarah Tannenbaum, Tryphon T. Georgiou, Allen R. Tannenbaum:
Geometry of correlation networks for studying the biology of cancer. CDC 2016: 2501-2506 - [c49]Hamza Farooq, Yongxin Chen, Tryphon T. Georgiou, Christophe Lenglet:
Some geometric ideas for feature enhancement of diffusion tensor fields. CDC 2016: 3856-3861 - [c48]Armin Zare, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Perturbation of system dynamics and the covariance completion problem. CDC 2016: 7036-7041 - [c47]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon, Allen R. Tannenbaum:
A new approach to robust transportation over networks. CDC 2016: 7623-7628 - [i24]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon, Allen R. Tannenbaum:
Robust transport over networks. CoRR abs/1603.08129 (2016) - [i23]Tryphon T. Georgiou, Anders Lindquist:
Likelihood Analysis of Power Spectra and Generalized Moment Problems. CoRR abs/1605.03652 (2016) - [i22]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal steering of a linear stochastic system to a final probability distribution, Part III. CoRR abs/1608.03622 (2016) - [i21]Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum:
Transport Distance on Graphs and Vector-Valued Optimal Mass Transport. CoRR abs/1611.09946 (2016) - 2015
- [j52]Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum, Stephen P. Boyd:
Linear Models Based on Noisy Data and the Frisch Scheme. SIAM Rev. 57(2): 167-197 (2015) - [j51]Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum:
On Matrix-Valued Monge-Kantorovich Optimal Mass Transport. IEEE Trans. Autom. Control. 60(2): 373-382 (2015) - [c46]Armin Zare, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Alternating direction optimization algorithms for covariance completion problems. ACC 2015: 515-520 - [c45]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal steering of inertial particles diffusing anisotropically with losses. ACC 2015: 1252-1257 - [c44]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Steering state statistics with output feedback. CDC 2015: 6502-6507 - [c43]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal control of the state statistics for a linear stochastic system. CDC 2015: 6508-6515 - [c42]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal Mass Transport over Bridges. GSI 2015: 77-84 - [i20]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal transport over a linear dynamical system. CoRR abs/1502.01265 (2015) - [i19]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal mass transport over bridges. CoRR abs/1503.00215 (2015) - [i18]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal control of the state statistics for a linear stochastic system. CoRR abs/1503.04885 (2015) - [i17]Tryphon T. Georgiou, Anders Lindquist:
Optimal estimation with missing observations via balanced time-symmetric stochastic models. CoRR abs/1503.06014 (2015) - [i16]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Steering state statistics with output feedback. CoRR abs/1504.00874 (2015) - [i15]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Entropic and displacement interpolation: a computational approach using the Hilbert metric. CoRR abs/1506.04255 (2015) - 2014
- [c41]Armin Zare, Mihailo R. Jovanovic, Tryphon T. Georgiou:
Completion of partially known turbulent flow statistics. ACC 2014: 1674-1679 - [c40]Lipeng Ning, Tryphon T. Georgiou:
Metrics for Matrix-valued Measures via Test Functions. CDC 2014: 2642-2647 - [c39]Yongxin Chen, Tryphon T. Georgiou:
The flatness of power spectral zeros and their significance in quadratic estimation. CDC 2014: 4166-4171 - [i14]Yongxin Chen, Tryphon T. Georgiou:
Stochastic bridges of linear systems. CoRR abs/1407.3421 (2014) - [i13]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal steering of a linear stochastic system to a final probability distribution. CoRR abs/1408.2222 (2014) - [i12]Lipeng Ning, Tryphon T. Georgiou:
Metrics for matrix-valued measures via test functions. CoRR abs/1409.4097 (2014) - [i11]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Optimal steering of a linear stochastic system to a final probability distribution, part II. CoRR abs/1410.3447 (2014) - [i10]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
Fast cooling for a system of stochastic oscillators. CoRR abs/1411.1323 (2014) - [i9]Yongxin Chen, Tryphon T. Georgiou, Michele Pavon:
On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint. CoRR abs/1412.4430 (2014) - 2013
- [j50]Lipeng Ning, Xianhua Jiang, Tryphon T. Georgiou:
On the Geometry of Covariance Matrices. IEEE Signal Process. Lett. 20(8): 787-790 (2013) - [j49]Johan Karlsson, Tryphon T. Georgiou:
Uncertainty Bounds for Spectral Estimation. IEEE Trans. Autom. Control. 58(7): 1659-1673 (2013) - [j48]Tryphon T. Georgiou, Anders Lindquist:
The Separation Principle in Stochastic Control, Redux. IEEE Trans. Autom. Control. 58(10): 2481-2494 (2013) - [c38]Fu Lin, Mihailo R. Jovanovic, Tryphon T. Georgiou:
An ADMM algorithm for matrix completion of partially known state covariances. CDC 2013: 1684-1689 - [c37]Yongxin Chen, Mihailo R. Jovanovic, Tryphon T. Georgiou:
State covariances and the matrix completion problem. CDC 2013: 1702-1707 - [c36]Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum:
Matrix-valued Monge-Kantorovich optimal mass transport. CDC 2013: 3906-3911 - [c35]Lipeng Ning, Tryphon T. Georgiou:
The Wasserstein metric in Factor Analysis. SIAM Conf. on Control and its Applications 2013: 8-12 - [i8]Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum, Stephen P. Boyd:
Linear models based on noisy data and the Frisch scheme. CoRR abs/1304.3877 (2013) - [i7]Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum:
Matrix-valued Monge-Kantorovich Optimal Mass Transport. CoRR abs/1304.3931 (2013) - [i6]Francesca P. Carli, Lipeng Ning, Tryphon T. Georgiou:
Approximation in the Wasserstein distance with application to clustering. CoRR abs/1307.5459 (2013) - [i5]Tryphon T. Georgiou, Anders Lindquist:
On time-reversibility of linear stochastic models. CoRR abs/1309.0165 (2013) - 2012
- [j47]Xianhua Jiang, Lipeng Ning, Tryphon T. Georgiou:
Distances and Riemannian Metrics for Multivariate Spectral Densities. IEEE Trans. Autom. Control. 57(7): 1723-1735 (2012) - [j46]Xianhua Jiang, Zhi-Quan Luo, Tryphon T. Georgiou:
Geometric Methods for Spectral Analysis. IEEE Trans. Signal Process. 60(3): 1064-1074 (2012) - [c34]Lipeng Ning, Xianhua Jiang, Tryphon T. Georgiou:
Geometric methods for structured covariance estimation. ACC 2012: 1877-1882 - [c33]Tryphon T. Georgiou, Anders Lindquist:
Revisiting the separation principle in stochastic control. CDC 2012: 1459-1465 - [c32]Lipeng Ning, Xianhua Jiang, Tryphon T. Georgiou:
Metrics for multivariate power spectra. CDC 2012: 4727-4732 - [i4]Johan Karlsson, Tryphon T. Georgiou:
Uncertainty Bounds for Spectral Estimation. CoRR abs/1201.4469 (2012) - 2011
- [j45]Francesca P. Carli, Tryphon T. Georgiou:
On the Covariance Completion Problem Under a Circulant Structure. IEEE Trans. Autom. Control. 56(4): 918-922 (2011) - [c31]Lipeng Ning, Tryphon T. Georgiou:
Sparse factor analysis via likelihood and ℓ1-regularization. CDC/ECC 2011: 5188-5192 - [i3]Tryphon T. Georgiou, Anders Lindquist:
The Separation Principle in Stochastic Control, Redux. CoRR abs/1103.3005 (2011) - [i2]Xianhua Jiang, Lipeng Ning, Tryphon T. Georgiou:
Distances and Riemannian metrics for multivariate spectral densities. CoRR abs/1107.1345 (2011) - [i1]Lipeng Ning, Xianhua Jiang, Tryphon T. Georgiou:
Geometric methods for estimation of structured covariances. CoRR abs/1110.3695 (2011) - 2010
- [j44]Tryphon T. Georgiou, Malcolm C. Smith:
Feedback control and the arrow of time. Int. J. Control 83(7): 1325-1338 (2010) - [j43]Johan Karlsson, Tryphon T. Georgiou, Anders Lindquist:
The Inverse Problem of Analytic Interpolation With Degree Constraint and Weight Selection for Control Synthesis. IEEE Trans. Autom. Control. 55(2): 405-418 (2010) - [j42]Mir Shahrouz Takyar, Tryphon T. Georgiou:
Analytic Interpolation With a Degree Constraint for Matrix-Valued Functions. IEEE Trans. Autom. Control. 55(5): 1075-1088 (2010) - [c30]Dapeng Li, Naira Hovakimyan, Tryphon T. Georgiou:
Robustness of L1 adaptive controllers in the gap metric. ACC 2010: 3247-3252 - [c29]Lipeng Ning, Tryphon T. Georgiou, Allen R. Tannenbaum:
Separation of system dynamics and line spectra via sparse representation. CDC 2010: 473-478 - [c28]Emmanuel Tannenbaum, Tryphon T. Georgiou, Allen R. Tannenbaum:
Signals and control aspects of optimal mass transport and the Boltzmann entropy. CDC 2010: 1885-1890 - [c27]Dapeng Li, Naira Hovakimyan, Tryphon T. Georgiou:
Robustness of ℒ1 adaptive controllers in the gap metric in the presence of nonzero initialization. CDC 2010: 2723-2728
2000 – 2009
- 2009
- [j41]Tryphon T. Georgiou, Johan Karlsson, Mir Shahrouz Takyar:
Metrics for Power Spectra: An Axiomatic Approach. IEEE Trans. Signal Process. 57(3): 859-867 (2009) - [c26]Katerina Georgiou, Tryphon T. Georgiou:
Graceful switching in hybrid models. CDC 2009: 3882-3884 - 2008
- [j40]Subbarao Varigonda, Tryphon T. Georgiou, Ronald A. Siegel, Prodromos Daoutidis:
Optimal periodic control of a drug delivery system. Comput. Chem. Eng. 32(10): 2256-2262 (2008) - [j39]Tryphon T. Georgiou, Anders Lindquist:
A Convex Optimization Approach to ARMA Modeling. IEEE Trans. Autom. Control. 53(5): 1108-1119 (2008) - [j38]Mir Shahrouz Takyar, Ali Nasiri Amini, Tryphon T. Georgiou:
Weight Selection in Feedback Design With Degree Constraints. IEEE Trans. Autom. Control. 53(8): 1951-1955 (2008) - [c25]Johan Karlsson, Mir Shahrouz Takyar, Tryphon T. Georgiou:
Transport metrics for power spectra. CDC 2008: 143-148 - [c24]Mir Shahrouz Takyar, Tryphon T. Georgiou:
On the Jordan structure of the spectral-zero dynamics in multivariable analytic interpolation. CDC 2008: 971-976 - [c23]Xianhua Jiang, Zhi-Quan Luo, Tryphon T. Georgiou:
Power spectral geodesics and tracking. CDC 2008: 1315-1319 - [c22]Tryphon T. Georgiou, Malcolm C. Smith:
Feedback control and the arrow of time. CDC 2008: 2214-2219 - [c21]Johan Karlsson, Tryphon T. Georgiou, Anders Lindquist:
Weight selection for gap robustness with degree-constrained controllers. CDC 2008: 4127-4134 - [c20]Romeil Sandhu, Tryphon T. Georgiou, Allen R. Tannenbaum:
A new distribution metric for image segmentation. Image Processing 2008: 691404 - [p1]Xianhua Jiang, Mir Shahrouz Takyar, Tryphon T. Georgiou:
Metrics and Morphing of Power Spectra. Recent Advances in Learning and Control 2008: 125-135 - 2007
- [j37]Tryphon T. Georgiou:
An Intrinsic Metric for Power Spectral Density Functions. IEEE Signal Process. Lett. 14(8): 561-563 (2007) - [j36]Tryphon T. Georgiou:
The Carathéodory-Fejér-Pisarenko Decomposition and Its Multivariable Counterpart. IEEE Trans. Autom. Control. 52(2): 212-228 (2007) - [j35]Tryphon T. Georgiou:
The Maximum Entropy Principle in the Absence of a Time-Arrow: Fractional-Pole Models. IEEE Trans. Inf. Theory 53(8): 2841-2851 (2007) - [j34]Tryphon T. Georgiou:
Distances and Riemannian Metrics for Spectral Density Functions. IEEE Trans. Signal Process. 55(8): 3995-4003 (2007) - [c19]Mir Shahrouz Takyar, Tryphon T. Georgiou:
Analytic interpolation with degree constraints: the multivariable case. ACC 2007: 5182-5187 - [c18]Mir Shahrouz Takyar, Tryphon T. Georgiou:
The fractional integrator as a control design element. CDC 2007: 239-244 - 2006
- [j33]Tryphon T. Georgiou:
Decomposition of Toeplitz Matrices via Convex Optimization. IEEE Signal Process. Lett. 13(9): 537-540 (2006) - [j32]Tryphon T. Georgiou, Anders Lindquist:
Remarks on control design with degree constraint. IEEE Trans. Autom. Control. 51(7): 1150-1156 (2006) - [j31]Tryphon T. Georgiou:
Relative entropy and the multivariable multidimensional moment problem. IEEE Trans. Inf. Theory 52(3): 1052-1066 (2006) - [j30]Ali Nasiri Amini, Tryphon T. Georgiou:
Tunable line spectral estimators based on state-covariance subspace analysis. IEEE Trans. Signal Process. 54(7): 2662-2671 (2006) - [c17]Tryphon T. Georgiou:
Singular decompositions of state-covariances. ACC 2006: 1-6 - [c16]Mir Shahrouz Takyar, Ali Nasiri Amini, Tryphon T. Georgiou:
Sensitivity shaping with degree constraint via convex optimization. ACC 2006: 1-4 - [c15]Johan Karlsson, Tryphon T. Georgiou, Anders Lindquist:
The Inverse Problem of Analytic Interpolation with Degree Constraint. CDC 2006: 559-564 - [c14]Tryphon T. Georgiou:
The error variance of the optimal linear smoother and maximum-variance fractional pole models. CDC 2006: 1685-1691 - [c13]Mir Shahrouz Takyar, Ali Nasiri Amini, Tryphon T. Georgiou:
Weight Selection in Interpolation with a Dimensionality Constraint. CDC 2006: 3536-3541 - [c12]Ali Nasiri Amini, Mir Shahrouz Takyar, Tryphon T. Georgiou:
A Homotopy Approach for Multirate Spectrum Estimation. ICASSP (3) 2006: 532-535 - 2005
- [j29]Ali Nasiri Amini, Tryphon T. Georgiou:
Avoiding ambiguity in beamspace processing. IEEE Signal Process. Lett. 12(5): 372-375 (2005) - [j28]Tryphon T. Georgiou:
Solution of the general moment problem via a one-parameter imbedding. IEEE Trans. Autom. Control. 50(6): 811-826 (2005) - [j27]Ali Nasiri Amini, Emad S. Ebbini, Tryphon T. Georgiou:
Noninvasive estimation of tissue temperature via high-resolution spectral analysis techniques. IEEE Trans. Biomed. Eng. 52(2): 221-228 (2005) - [c11]Tryphon T. Georgiou:
Relative Entropy and Moment Problems. CDC/ECC 2005: 4397-4403 - [c10]Johan Karlsson, Tryphon T. Georgiou:
Signal analysis, moment problems & uncertainty measures. CDC/ECC 2005: 5710-5715 - 2004
- [j26]Subbarao Varigonda, Tryphon T. Georgiou, Prodromos Daoutidis:
Numerical solution of the optimal periodic control problem using differential flatness. IEEE Trans. Autom. Control. 49(2): 271-275 (2004) - 2003
- [j25]Tryphon T. Georgiou, Anders Lindquist:
Kullback-Leibler approximation of spectral density functions. IEEE Trans. Inf. Theory 49(11): 2910-2917 (2003) - [c9]Tryphon T. Georgiou, Anders Lindquist:
Kullback-Leibler approximation of spectral density functions. CDC 2003: 4237-4242 - 2002
- [j24]Tryphon T. Georgiou:
The structure of state covariances and its relation to the power spectrum of the input. IEEE Trans. Autom. Control. 47(7): 1056-1066 (2002) - [j23]Tryphon T. Georgiou:
Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parametrization. IEEE Trans. Autom. Control. 47(11): 1811-1823 (2002) - [c8]Ali Nasiri Amini, Tryphon T. Georgiou:
Statistical analysis of state-covariance subspace-estimation methods. CDC 2002: 2633-2638 - 2001
- [j22]Tryphon T. Georgiou:
Spectral estimation via selective harmonic amplification. IEEE Trans. Autom. Control. 46(1): 29-42 (2001) - [j21]Subbarao Varigonda, Tryphon T. Georgiou:
Dynamics of relay relaxation oscillators. IEEE Trans. Autom. Control. 46(1): 65-77 (2001) - [j20]Tryphon T. Georgiou, Malcolm C. Smith:
Remarks on "Robustness analysis of nonlinear feedback systems: an input-output approach". IEEE Trans. Autom. Control. 46(1): 171-172 (2001) - [j19]Hans U. Walther, Tryphon T. Georgiou, Allen R. Tannenbaum:
On the computation of switching surfaces in optimal control: a Grobner basis approach. IEEE Trans. Autom. Control. 46(4): 534-540 (2001) - [j18]Christopher I. Byrnes, Tryphon T. Georgiou, Anders Lindquist:
A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint. IEEE Trans. Autom. Control. 46(6): 822-839 (2001) - [c7]Subbarao Varigonda, Tryphon T. Georgiou, Prodromos Daoutidis:
A flatness based algorithm for optimal periodic control problems. ACC 2001: 831-836 - [c6]Tryphon T. Georgiou:
Spectral analysis and analytic interpolation. CDC 2001: 4800-4805 - 2000
- [j17]Tryphon T. Georgiou:
Signal estimation via selective harmonic amplification: MUSIC, Redux. IEEE Trans. Signal Process. 48(3): 780-790 (2000) - [j16]Christopher I. Byrnes, Tryphon T. Georgiou, Anders Lindquist:
A new approach to spectral estimation: a tunable high-resolution spectral estimator. IEEE Trans. Signal Process. 48(11): 3189-3205 (2000) - [c5]Tryphon T. Georgiou, Malcolm C. Smith:
Robustness of a relaxation oscillator. CDC 2000: 246-250 - [c4]Subbarao Varigonda, Tryphon T. Georgiou:
Global stability of periodic orbits in relay feedback systems. CDC 2000: 3843-3847 - [c3]Tryphon T. Georgiou, Allen R. Tannenbaum:
High resolution sensing and anisotropic segmentation for SAR imagery. CDC 2000: 4324-4326 - [c2]Tryphon T. Georgiou:
Subspace analysis of state covariances. ICASSP 2000: 269-272
1990 – 1999
- 1999
- [j15]Tryphon T. Georgiou:
The interpolation problem with a degree constraint. IEEE Trans. Autom. Control. 44(3): 631-635 (1999) - [j14]Ian Fialho, Tryphon T. Georgiou:
Worst case analysis of nonlinear systems. IEEE Trans. Autom. Control. 44(6): 1180-1196 (1999) - 1997
- [j13]Tryphon T. Georgiou, Malcolm C. Smith:
Robustness analysis of nonlinear feedback systems: an input-output approach. IEEE Trans. Autom. Control. 42(9): 1200-1221 (1997) - [j12]Ian Fialho, Tryphon T. Georgiou:
l2 state-feedback control with a prescribed rate of exponential convergence. IEEE Trans. Autom. Control. 42(10): 1476-1481 (1997) - 1995
- [j11]Tryphon T. Georgiou, Malcolm C. Smith:
Intrinsic difficulties in using the doubly-infinite time axis for input-output control theory. IEEE Trans. Autom. Control. 40(3): 516-518 (1995) - [j10]Harry Dym, Tryphon T. Georgiou, Malcolm C. Smith:
Explicit formulas for optimally robust controllers for delay systems. IEEE Trans. Autom. Control. 40(4): 656-669 (1995) - [j9]Ian Fialho, Tryphon T. Georgiou:
On the 𝓛1 norm of uncertain linear systems. IEEE Trans. Autom. Control. 40(6): 1142-1147 (1995) - 1994
- [j8]Ian Fialho, Tryphon T. Georgiou:
On stability and performance of sampled-data systems subject to wordlength constraint. IEEE Trans. Autom. Control. 39(12): 2476-2481 (1994) - [j7]Craig R. Shankwitz, Tryphon T. Georgiou:
The envelope of spectral power for stochastic processes. IEEE Trans. Inf. Theory 40(2): 584-588 (1994) - 1993
- [j6]Tryphon T. Georgiou, Malcolm C. Smith:
Graphs, causality, and stabilizability: Linear, shift-invariant systems on ℒ2[0, ∞). Math. Control. Signals Syst. 6(3): 195-223 (1993) - [j5]Tryphon T. Georgiou:
Differential stability and robust control of nonlinear systems. Math. Control. Signals Syst. 6(4): 289-306 (1993) - [j4]Tryphon T. Georgiou, Malcolm C. Smith:
Upper and lower bounds for approximation in the gap metric. IEEE Trans. Autom. Control. 38(6): 946-951 (1993) - 1990
- [j3]Craig R. Shankwitz, Tryphon T. Georgiou:
On the maximum entropy method for interval covariance sequences. IEEE Trans. Acoust. Speech Signal Process. 38(10): 1815-1817 (1990)
1980 – 1989
- 1987
- [j2]Tryphon T. Georgiou, António Manuel Santos Pascoal, Pramod P. Khargonekar:
On the robust stabilizability of uncertain linear time-invariant plants using nonlinear time-varying controllers. Autom. 23(5): 617-624 (1987) - [j1]Tryphon T. Georgiou:
Realization of power spectra from partial covariance sequences. IEEE Trans. Acoust. Speech Signal Process. 35(4): 438-449 (1987) - 1984
- [c1]Tryphon T. Georgiou:
Topological aspects of the caratheodory problem. ICASSP 1984: 220-223
Coauthor Index
[j98] [i67] [j92] [j91] [j90] [j89] [i61] [i60] [j88] [j87] [j84] [j83] [c63] [i56] [i55] [i54] [i51] [i50] [j80] [j79] [j77] [c61] [i49] [i48] [i45] [i43] [j76] [c60] [c58] [c57] [c56] [i40] [i37] [j73] [j72] [j71] [j70] [j69] [j68] [j67] [j66] [j65] [c54] [i34] [i33] [j64] [j63] [j62] [j60] [i29] [i28] [i26] [i25] [j57] [j56] [j55] [j54] [j53] [c51] [c49] [c47] [i24] [i22] [i21] [c45] [c44] [c43] [c42] [i20] [i19] [i18] [i16] [i15] [c39] [i14] [i13] [i11] [i10] [i9] [c37]
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