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Avila B, Augusto P, Zimmer M, Serafino M, Makse HA. Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome. ARXIV 2024:arXiv:2305.19367v2. [PMID: 37396607 PMCID: PMC10312817] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 07/04/2023]
Abstract
Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.
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Affiliation(s)
- Bryant Avila
- Levich Institute, Physics Department, City College of New York, New York, NY, USA
| | - Pedro Augusto
- Vienna Biocenter PhD Program, Doctoral School of the University of Vienna and Medical University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Manuel Zimmer
- Research Institute of Molecular Pathology (IMP), Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Matteo Serafino
- Levich Institute, Physics Department, City College of New York, New York, NY, USA
| | - Hernán A. Makse
- Levich Institute, Physics Department, City College of New York, New York, NY, USA
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Avila B, Serafino M, Augusto P, Zimmer M, Makse HA. Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome. PLoS One 2024; 19:e0297669. [PMID: 38598455 PMCID: PMC11006206 DOI: 10.1371/journal.pone.0297669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 01/11/2024] [Indexed: 04/12/2024] Open
Abstract
Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.
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Affiliation(s)
- Bryant Avila
- Physics Department, Levich Institute, City College of New York, New York, NY, United Stated of America
| | - Matteo Serafino
- Physics Department, Levich Institute, City College of New York, New York, NY, United Stated of America
| | - Pedro Augusto
- Vienna Biocenter PhD Program, Doctoral School of the University of Vienna and Medical University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Manuel Zimmer
- Research Institute of Molecular Pathology (IMP), Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Hernán A. Makse
- Physics Department, Levich Institute, City College of New York, New York, NY, United Stated of America
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Khanra P, Ghosh S, Aleja D, Alfaro-Bittner K, Contreras-Aso G, Criado R, Romance M, Boccaletti S, Pal P, Hens C. Endowing networks with desired symmetries and modular behavior. Phys Rev E 2023; 108:054309. [PMID: 38115459 DOI: 10.1103/physreve.108.054309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 10/18/2023] [Indexed: 12/21/2023]
Abstract
Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of designing a desired set of clusters and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.
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Affiliation(s)
- P Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo 14260, USA
| | - S Ghosh
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - D Aleja
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
- Department of Internal Medicine, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - K Alfaro-Bittner
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - G Contreras-Aso
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - R Criado
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - M Romance
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - S Boccaletti
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
- CNR - Institute of Complex Systems, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141701, Russian Federation
- Complex Systems Lab, Department of Physics, Indian Institute of Technology, Indore - Simrol, Indore 453552, India
| | - P Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - C Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
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Nazerian A, Nathe C, Hart JD, Sorrentino F. Synchronizing chaos using reservoir computing. CHAOS (WOODBURY, N.Y.) 2023; 33:103121. [PMID: 37832520 PMCID: PMC10576628 DOI: 10.1063/5.0161076] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 09/14/2023] [Indexed: 10/15/2023]
Abstract
We attempt to achieve complete synchronization between a drive system unidirectionally coupled with a response system, under the assumption that limited knowledge on the states of the drive is available at the response. Machine-learning techniques have been previously implemented to estimate the states of a dynamical system from limited measurements. We consider situations in which knowledge of the non-measurable states of the drive system is needed in order for the response system to synchronize with the drive. We use a reservoir computer to estimate the non-measurable states of the drive system from its measured states and then employ these measured states to achieve complete synchronization of the response system with the drive.
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Affiliation(s)
- Amirhossein Nazerian
- Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Chad Nathe
- Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | | | - Francesco Sorrentino
- Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Zhang M, Yang Y, Yang J. Hierarchy of partially synchronous states in a ring of coupled identical oscillators. Phys Rev E 2023; 108:034202. [PMID: 37849175 DOI: 10.1103/physreve.108.034202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 08/25/2023] [Indexed: 10/19/2023]
Abstract
In coupled identical oscillators, complete synchronization has been well formulated; however, partial synchronization still calls for a general theory. In this work, we study the partial synchronization in a ring of N locally coupled identical oscillators. We first establish the correspondence between partially synchronous states and conjugacy classes of subgroups of the dihedral group D_{N}. Then we present a systematic method to identify all partially synchronous dynamics on their synchronous manifolds by reducing a ring of oscillators to short chains with various boundary conditions. We find that partially synchronous states are organized into a hierarchical structure and, along a directed path in the structure, upstream partially synchronous states are less synchronous than downstream ones.
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Affiliation(s)
- Mei Zhang
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Yuhe Yang
- School of Mathematics, Peking University, Beijing 100871, People's Republic of China
| | - Junzhong Yang
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China
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Nazerian A, Vides F, Sorrentino F. Algebraic Decomposition of Model Predictive Control Problems. IEEE CONTROL SYSTEMS LETTERS 2023; 7:1441-1446. [PMID: 37841505 PMCID: PMC10569442 DOI: 10.1109/lcsys.2023.3252162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
This paper is concerned with the application of model predictive control (MPC) to large-scale linear dynamical systems with linear inequality constraints. A decomposition is proposed of such problems into sets of independent MPCs of lower dimensions that preserves all information about the system, cost function, and constraints. Different from previous work, the constraints are incorporated in the decomposition procedure, which is attained by generalizing a previously developed technique to simultaneously block diagonalize a set of matrices. This approach is applied to practical examples involving large-scale systems with inequality constraints. It is shown that the computational complexity and the CPU time required to solve the transformed MPC problems are lower than those required by the solution of the original MPC problem.
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Affiliation(s)
- Amirhossein Nazerian
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, 87131 USA
| | - Fredy Vides
- Scientific Computing Innovation Center, UNAH, Tegucigalpa, Honduras, and with National Commission of Banks and Insurance Companies, Tegucigalpa, Honduras
| | - Francesco Sorrentino
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, 87131 USA
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Nazerian A, Bhatta K, Sorrentino F. Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices. IEEE OPEN JOURNAL OF CONTROL SYSTEMS 2023; 2:24-35. [PMID: 36845944 PMCID: PMC9956949 DOI: 10.1109/ojcsys.2022.3231553] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is 'exact' in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.
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Affiliation(s)
- Amirhossein Nazerian
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131 USA
| | - Kshitij Bhatta
- Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903 USA
| | - Francesco Sorrentino
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131 USA
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