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Chen L, Hamarash II, Jafari S, Rajagopal K, Hussain I. Various bifurcations in the development of stem cells. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2021; 231:1015-1021. [PMID: 34804377 PMCID: PMC8590129 DOI: 10.1140/epjs/s11734-021-00322-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/02/2021] [Accepted: 10/30/2021] [Indexed: 06/13/2023]
Abstract
Cell development from an undifferentiated stem cell to a differentiated one is essential in forming an organism. In this paper, various bifurcations of a stem cell during this process are studied using a model based on Furusawa and Kaneko's hypothesis. Furusawa and Kaneko's hypothesis tells that the gene expression of stem cells is chaotic. By developing to a differentiated cell, the gene expression in more order, which is the cause of losing pluripotency. In this model, the chaotic dynamics of gene expression in the stem cells become ordered during the developments. Various patterns and bifurcation points can be seen during development. The bifurcation points and their predictions during the process of cell development are studied in this paper. Some well-known critical slowing down indicators are used to show the variations of slowness during the cell's development and predict the bifurcation points. It is vital since the unexpected changes of the state can cause a disaster. All of the indicators have a proper trend by approaching the bifurcation points and faring away.
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Affiliation(s)
- Lianyu Chen
- School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou, 213001 China
| | - Ibrahim Ismael Hamarash
- Electrical Engineering Department, Salahaddin University-Erbil, Kirkuk Rd., Erbil, Kurdistan Iraq
- School of Computer Science and Engineering, University of Kurdistan Hewler, 40m St., Erbil, Kurdistan Iraq
| | - Sajad Jafari
- Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413 Iran
- Health Technology Research Institute, Amirkabir University of Technology, No.350, Hafez Ave, Valiasr Square, Tehran, 159163-4311 Iran
| | | | - Iqtadar Hussain
- Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713 Qatar
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Ebrahimi A, Nowzari-Dalini A, Jalili M, Masoudi-Nejad A. Appropriate time to apply control input to complex dynamical systems. Sci Rep 2020; 10:22035. [PMID: 33328499 PMCID: PMC7744535 DOI: 10.1038/s41598-020-78909-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 11/12/2020] [Indexed: 12/13/2022] Open
Abstract
Controlling a network structure has many potential applications many fields. In order to have an effective network control, not only finding good driver nodes is important, but also finding the optimal time to apply the external control signals to network nodes has a critical role. If applied in an appropriate time, one might be to control a network with a smaller control signals, and thus less energy. In this manuscript, we show that there is a relationship between the strength of the internal fluxes and the effectiveness of the external control signal. To be more effective, external control signals should be applied when the strength of the internal states is the smallest. We validate this claim on synthetic networks as well as a number of real networks. Our results may have important implications in systems medicine, in order to find the most appropriate time to inject drugs as a signal to control diseases.
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Affiliation(s)
- Ali Ebrahimi
- Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran
| | | | - Mahdi Jalili
- School of Engineering, RMIT University, Melbourne, Australia
| | - Ali Masoudi-Nejad
- Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran.
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Lilienkamp T, Parlitz U. Terminating transient chaos in spatially extended systems. CHAOS (WOODBURY, N.Y.) 2020; 30:051108. [PMID: 32491910 DOI: 10.1063/5.0011506] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
In many real-life systems, transient chaotic dynamics plays a major role. For instance, the chaotic spiral or scroll wave dynamics of electrical excitation waves during life-threatening cardiac arrhythmias can terminate by itself. Epileptic seizures have recently been related to the collapse of transient chimera states. Controlling chaotic transients, either by maintaining the chaotic dynamics or by terminating it as quickly as possible, is often desired and sometimes even vital (as in the case of cardiac arrhythmias). We discuss in this study that the difference of the underlying structures in state space between a chaotic attractor (persistent chaos) and a chaotic saddle (transient chaos) may have significant implications for efficient control strategies in real life systems. In particular, we demonstrate that in the latter case, chaotic dynamics in spatially extended systems can be terminated via a relatively low number of (spatially and temporally) localized perturbations. We demonstrate as a proof of principle that control and targeting of high-dimensional systems exhibiting transient chaos can be achieved with exceptionally small interactions with the system. This insight may impact future control strategies in real-life systems like cardiac arrhythmias.
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Affiliation(s)
- Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
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Vashishtha S, Verma S. Restoring chaos using deep reinforcement learning. CHAOS (WOODBURY, N.Y.) 2020; 30:031102. [PMID: 32237764 DOI: 10.1063/5.0002047] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 03/04/2020] [Indexed: 06/11/2023]
Abstract
A catastrophic bifurcation in non-linear dynamical systems, called crisis, often leads to their convergence to an undesirable non-chaotic state after some initial chaotic transients. Preventing such behavior has been quite challenging. We demonstrate that deep Reinforcement Learning (RL) is able to restore chaos in a transiently chaotic regime of the Lorenz system of equations. Without requiring any a priori knowledge of the underlying dynamics of the governing equations, the RL agent discovers an effective strategy for perturbing the parameters of the Lorenz system such that the chaotic trajectory is sustained. We analyze the agent's autonomous control-decisions and identify and implement a simple control-law that successfully restores chaos in the Lorenz system. Our results demonstrate the utility of using deep RL for controlling the occurrence of catastrophes in non-linear dynamical systems.
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Affiliation(s)
- Sumit Vashishtha
- Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431, USA
| | - Siddhartha Verma
- Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431, USA
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Sellitto MA, Balugani E, Lolli F. Spare Parts Replacement Policy Based on Chaotic Models. ACTA ACUST UNITED AC 2018. [DOI: 10.1016/j.ifacol.2018.08.486] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Levi A, Sabuco J, A. F. Sanjuán M. When the firm prevents the crash: Avoiding market collapse with partial control. PLoS One 2017; 12:e0181925. [PMID: 28832608 PMCID: PMC5568173 DOI: 10.1371/journal.pone.0181925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Accepted: 06/28/2017] [Indexed: 11/18/2022] Open
Abstract
Market collapse is one of the most dramatic events in economics. Such a catastrophic event can emerge from the nonlinear interactions between the economic agents at the micro level of the economy. Transient chaos might be a good description of how a collapsing market behaves. In this work, we apply a new control method, the partial control method, with the goal of avoiding this disastrous event. Contrary to common control methods that try to influence the system from the outside, here the market is controlled from the bottom up by one of the most basic components of the market—the firm. This is the first time that the partial control method is applied on a strictly economical system in which we also introduce external disturbances. We show how the firm is capable of controlling the system avoiding the collapse by only adjusting the selling price of the product or the quantity of production in accordance to the market circumstances. Additionally, we demonstrate how a firm with a large market share is capable of influencing the demand achieving price stability across the retail and wholesale markets. Furthermore, we prove that the control applied in both cases is much smaller than the external disturbances.
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Affiliation(s)
- Asaf Levi
- Nonlinear Dynamics, Chaos and Complex Systems Group. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Juan Sabuco
- Nonlinear Dynamics, Chaos and Complex Systems Group. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Miguel A. F. Sanjuán
- Nonlinear Dynamics, Chaos and Complex Systems Group. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States of America
- * E-mail:
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Fradkov AL. Horizons of cybernetical physics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160223. [PMID: 28115620 PMCID: PMC5311442 DOI: 10.1098/rsta.2016.0223] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/02/2016] [Indexed: 05/30/2023]
Abstract
The subject and main areas of a new research field-cybernetical physics-are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control.This article is part of the themed issue 'Horizons of cybernetical physics'.
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Affiliation(s)
- Alexander L Fradkov
- Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia
- Department of Control of Complex Systems, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, 197101 Saint Petersburg, Russia
- Department of Theoretical Cybernetics, Saint Petersburg State University, 199034 Saint Petersburg, Russia
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