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Lin ZH, Feng M, Tang M, Liu Z, Xu C, Hui PM, Lai YC. Non-Markovian recovery makes complex networks more resilient against large-scale failures. Nat Commun 2020; 11:2490. [PMID: 32427821 PMCID: PMC7237476 DOI: 10.1038/s41467-020-15860-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2019] [Accepted: 03/26/2020] [Indexed: 11/10/2022] Open
Abstract
Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. How does the non-Markovian characteristic affect failure propagation in complex networks? We consider failures due to internal causes at the nodal level and external failures due to an adverse environment, and develop a pair approximation analysis taking into account the two-node correlation. In general, a high failure stationary state can arise, corresponding to large-scale failures that can significantly compromise the functioning of the network. We uncover a striking phenomenon: memory associated with nodal recovery can counter-intuitively make the network more resilient against large-scale failures. In natural systems, the intrinsic non-Markovian characteristic of nodal recovery may thus be one reason for their resilience. In engineering design, incorporating certain non-Markovian features into the network may be beneficial to equipping it with a strong resilient capability to resist catastrophic failures.
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Affiliation(s)
- Zhao-Hua Lin
- State Key Laboratory of Precision Spectroscopy and School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China
| | - Mi Feng
- Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai, 200241, China
| | - Ming Tang
- State Key Laboratory of Precision Spectroscopy and School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China. .,Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai, 200241, China.
| | - Zonghua Liu
- State Key Laboratory of Precision Spectroscopy and School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China.
| | - Chen Xu
- School of Physical Science and Technology, Soochow University, Suzhou, 215006, China
| | - Pak Ming Hui
- Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, 85287, USA
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Majhi S, Ghosh D, Kurths J. Emergence of synchronization in multiplex networks of mobile Rössler oscillators. Phys Rev E 2019; 99:012308. [PMID: 30780214 DOI: 10.1103/physreve.99.012308] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Indexed: 12/11/2022]
Abstract
Different aspects of synchronization emerging in networks of coupled oscillators have been examined prominently in the last decades. Nevertheless, little attention has been paid on the emergence of this imperative collective phenomenon in networks displaying temporal changes in the connectivity patterns. However, there are numerous practical examples where interactions are present only at certain points of time owing to physical proximity. In this work, we concentrate on exploring the emergence of interlayer and intralayer synchronization states in a multiplex dynamical network comprising of layers having mobile nodes performing two-dimensional lattice random walk. We thoroughly illustrate the impacts of the network parameters, in particular, the vision range ϕ and the step size u together with the inter- and intralayer coupling strengths ε and k on these synchronous states arising in coupled Rössler systems. The presented numerical results are very well validated by analytically derived necessary conditions for the emergence and stability of the synchronous states. Furthermore, the robustness of the states of synchrony is studied under both structural and dynamical perturbations. We find interesting results on interlayer synchronization for a continuous removal of the interlayer links as well as for progressively created static nodes. We demonstrate that the mobility parameters responsible for intralayer movement of the nodes can retrieve interlayer synchrony under such structural perturbations. For further analysis of survivability of interlayer synchrony against dynamical perturbations, we proceed through the investigation of single-node basin stability, where again the intralayer mobility properties have noticeable impacts. We also discuss the scenarios related mainly to effects of the mobility parameters in cases of varying lattice size and percolation of the whole network.
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Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany.,Saratov State University, Saratov, Russia
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Majhi S, Perc M, Ghosh D. Chimera states in a multilayer network of coupled and uncoupled neurons. CHAOS (WOODBURY, N.Y.) 2017; 27:073109. [PMID: 28764400 DOI: 10.1063/1.4993836] [Citation(s) in RCA: 67] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We study the emergence of chimera states in a multilayer neuronal network, where one layer is composed of coupled and the other layer of uncoupled neurons. Through the multilayer structure, the layer with coupled neurons acts as the medium by means of which neurons in the uncoupled layer share information in spite of the absence of physical connections among them. Neurons in the coupled layer are connected with electrical synapses, while across the two layers, neurons are connected through chemical synapses. In both layers, the dynamics of each neuron is described by the Hindmarsh-Rose square wave bursting dynamics. We show that the presence of two different types of connecting synapses within and between the two layers, together with the multilayer network structure, plays a key role in the emergence of between-layer synchronous chimera states and patterns of synchronous clusters. In particular, we find that these chimera states can emerge in the coupled layer regardless of the range of electrical synapses. Even in all-to-all and nearest-neighbor coupling within the coupled layer, we observe qualitatively identical between-layer chimera states. Moreover, we show that the role of information transmission delay between the two layers must not be neglected, and we obtain precise parameter bounds at which chimera states can be observed. The expansion of the chimera region and annihilation of cluster and fully coherent states in the parameter plane for increasing values of inter-layer chemical synaptic time delay are illustrated using effective range measurements. These results are discussed in the light of neuronal evolution, where the coexistence of coherent and incoherent dynamics during the developmental stage is particularly likely.
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Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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4
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Majhi S, Perc M, Ghosh D. Chimera states in uncoupled neurons induced by a multilayer structure. Sci Rep 2016; 6:39033. [PMID: 27958355 PMCID: PMC5153648 DOI: 10.1038/srep39033] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2016] [Accepted: 11/16/2016] [Indexed: 01/23/2023] Open
Abstract
Spatial coexistence of coherent and incoherent dynamics in network of coupled oscillators is called a chimera state. We study such chimera states in a network of neurons without any direct interactions but connected through another medium of neurons, forming a multilayer structure. The upper layer is thus made up of uncoupled neurons and the lower layer plays the role of a medium through which the neurons in the upper layer share information among each other. Hindmarsh-Rose neurons with square wave bursting dynamics are considered as nodes in both layers. In addition, we also discuss the existence of chimera states in presence of inter layer heterogeneity. The neurons in the bottom layer are globally connected through electrical synapses, while across the two layers chemical synapses are formed. According to our research, the competing effects of these two types of synapses can lead to chimera states in the upper layer of uncoupled neurons. Remarkably, we find a density-dependent threshold for the emergence of chimera states in uncoupled neurons, similar to the quorum sensing transition to a synchronized state. Finally, we examine the impact of both homogeneous and heterogeneous inter-layer information transmission delays on the observed chimera states over a wide parameter space.
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Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India
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Podobnik B, Horvatic D, Lipic T, Perc M, Buldú JM, Stanley HE. The cost of attack in competing networks. J R Soc Interface 2016; 12:rsif.2015.0770. [PMID: 26490628 DOI: 10.1098/rsif.2015.0770] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Real-world attacks can be interpreted as the result of competitive interactions between networks, ranging from predator-prey networks to networks of countries under economic sanctions. Although the purpose of an attack is to damage a target network, it also curtails the ability of the attacker, which must choose the duration and magnitude of an attack to avoid negative impacts on its own functioning. Nevertheless, despite the large number of studies on interconnected networks, the consequences of initiating an attack have never been studied. Here, we address this issue by introducing a model of network competition where a resilient network is willing to partially weaken its own resilience in order to more severely damage a less resilient competitor. The attacking network can take over the competitor's nodes after their long inactivity. However, owing to a feedback mechanism the takeovers weaken the resilience of the attacking network. We define a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks. Within this formalism, we determine the cost and optimal duration of an attack, allowing a network to evaluate the risk of initiating hostilities.
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Affiliation(s)
- B Podobnik
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia Zagreb School of Economics and Management, 10000 Zagreb, Croatia
| | - D Horvatic
- Faculty of Natural Sciences, University of Zagreb, 10000 Zagreb, Croatia
| | - T Lipic
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA Rudjer Boskovic Institute, Centre for Informatics and Computing, 10000 Zagreb, Croatia
| | - M Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia Department of Physics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
| | - J M Buldú
- Center for Biomedical Technology (UPM), 28223 Pozuelo de Alarcón, Madrid, Spain Complex Systems Group, Rey Juan Carlos University, 28933 Móstoles, Madrid, Spain
| | - H E Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
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Localized recovery of complex networks against failure. Sci Rep 2016; 6:30521. [PMID: 27456202 PMCID: PMC4960604 DOI: 10.1038/srep30521] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2016] [Accepted: 07/04/2016] [Indexed: 11/08/2022] Open
Abstract
Resilience of complex networks to failure has been an important issue in network research for decades, and recent studies have begun to focus on the inverse recovery of network functionality through strategically healing missing nodes or edges. However, the effect of network recovery is far from fully understood, and a general theory is still missing. Here we propose and study a general model of localized recovery, where a group of neighboring nodes are restored in an invasive way from a seed node. We develop a theoretical framework to compare the effect of random recovery (RR) and localized recovery (LR) in complex networks including Erdős-Rényi networks, random regular networks, and scale-free networks. We find detailed phase diagrams for the subnetwork of occupied nodes and the "complement network" of failed nodes under RR and LR. By identifying the two competitive forces behind LR, we present an analytical and numerical approach to guide us in choosing the appropriate recovery strategy and provide estimation on its effect by using the degree distribution of the original network as the only input. Our work therefore provides insight for quantitatively understanding recovery process and its implications in infrastructure protection in various complex systems.
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Majdandzic A, Braunstein LA, Curme C, Vodenska I, Levy-Carciente S, Eugene Stanley H, Havlin S. Multiple tipping points and optimal repairing in interacting networks. Nat Commun 2016; 7:10850. [PMID: 26926803 PMCID: PMC4773515 DOI: 10.1038/ncomms10850] [Citation(s) in RCA: 64] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2015] [Accepted: 01/26/2016] [Indexed: 11/09/2022] Open
Abstract
Systems composed of many interacting dynamical networks-such as the human body with its biological networks or the global economic network consisting of regional clusters-often exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread and recovery. Here we develop a model for such systems and find a very rich phase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of two interacting networks we find two critical points, four triple points, ten allowed transitions and two 'forbidden' transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyse an example of real interacting financial networks and find evidence of rapid dynamical transitions between well-defined states, in agreement with the predictions of our model.
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Affiliation(s)
- Antonio Majdandzic
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Lidia A. Braunstein
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Physics Department, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, 7600 Mar del Plata, Argentina
| | - Chester Curme
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Irena Vodenska
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Administrative Sciences Department, Metropolitan College, Boston University, Boston, Massachusetts 02215 USA
| | - Sary Levy-Carciente
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Economics and Social Sciences Faculty, Central University of Venezuela, 1040 Caracas, Venezuela
| | - H. Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Shlomo Havlin
- Center for Polymer Studies and Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
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Does the Wage Gap between Private and Public Sectors Encourage Political Corruption? PLoS One 2015; 10:e0141211. [PMID: 26495847 PMCID: PMC4619698 DOI: 10.1371/journal.pone.0141211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 10/05/2015] [Indexed: 11/19/2022] Open
Abstract
We present a dynamic network model of corrupt and noncorrupt employees representing two states in the public and private sector. Corrupt employees are more connected to one another and are less willing to change their attitudes regarding corruption than noncorrupt employees. This behavior enables them to prevail and become the majority in the workforce through a first-order phase transition even though they initially represented a minority. In the model, democracy—understood as the principle of majority rule—does not create corruption, but it serves as a mechanism that preserves corruption in the long run. The motivation for our network model is a paradox that exists on the labor market. Although economic theory indicates that higher risk investments should lead to larger rewards, in many developed and developing countries workers in lower-risk public sector jobs are paid more than workers in higher-risk private sector jobs. To determine the long-run sustainability of this economic paradox, we study data from 28 EU countries and find that the public sector wage premium increases with the level of corruption.
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Jusup M, Iwami S, Podobnik B, Stanley HE. Dynamically rich, yet parameter-sparse models for spatial epidemiology: Comment on "Coupled disease-behavior dynamics on complex networks: A review" by Z. Wang et al. Phys Life Rev 2015; 15:43-6. [PMID: 26454709 DOI: 10.1016/j.plrev.2015.09.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2015] [Accepted: 09/30/2015] [Indexed: 10/22/2022]
Affiliation(s)
- Marko Jusup
- Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan.
| | - Shingo Iwami
- Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan; PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
| | - Boris Podobnik
- Center for Polymer Studies, Boston University, Boston, MA 02215, United States; Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia; Zagreb School of Economics and Management, 10000 Zagreb, Croatia
| | - H Eugene Stanley
- Center for Polymer Studies, Boston University, Boston, MA 02215, United States
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Predicting the Lifetime of Dynamic Networks Experiencing Persistent Random Attacks. Sci Rep 2015; 5:14286. [PMID: 26387609 PMCID: PMC4585692 DOI: 10.1038/srep14286] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Accepted: 08/11/2015] [Indexed: 11/13/2022] Open
Abstract
Estimating the critical points at which complex systems abruptly flip from one state to another is one of the remaining challenges in network science. Due to lack of knowledge about the underlying stochastic processes controlling critical transitions, it is widely considered difficult to determine the location of critical points for real-world networks, and it is even more difficult to predict the time at which these potentially catastrophic failures occur. We analyse a class of decaying dynamic networks experiencing persistent failures in which the magnitude of the overall failure is quantified by the probability that a potentially permanent internal failure will occur. When the fraction of active neighbours is reduced to a critical threshold, cascading failures can trigger a total network failure. For this class of network we find that the time to network failure, which is equivalent to network lifetime, is inversely dependent upon the magnitude of the failure and logarithmically dependent on the threshold. We analyse how permanent failures affect network robustness using network lifetime as a measure. These findings provide new methodological insight into system dynamics and, in particular, of the dynamic processes of networks. We illustrate the network model by selected examples from biology, and social science.
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Lee JH, Jusup M, Podobnik B, Iwasa Y. Agent-based mapping of credit risk for sustainable microfinance. PLoS One 2015; 10:e0126447. [PMID: 25945790 PMCID: PMC4422753 DOI: 10.1371/journal.pone.0126447] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2015] [Accepted: 04/02/2015] [Indexed: 11/17/2022] Open
Abstract
By drawing analogies with independent research areas, we propose an unorthodox framework for mapping microfinance credit risk---a major obstacle to the sustainability of lenders outreaching to the poor. Specifically, using the elements of network theory, we constructed an agent-based model that obeys the stylized rules of microfinance industry. We found that in a deteriorating economic environment confounded with adverse selection, a form of latent moral hazard may cause a regime shift from a high to a low loan payment probability. An after-the-fact recovery, when possible, required the economic environment to improve beyond that which led to the shift in the first place. These findings suggest a small set of measurable quantities for mapping microfinance credit risk and, consequently, for balancing the requirements to reasonably price loans and to operate on a fully self-financed basis. We illustrate how the proposed mapping works using a 10-year monthly data set from one of the best-known microfinance representatives, Grameen Bank in Bangladesh. Finally, we discuss an entirely new perspective for managing microfinance credit risk based on enticing spontaneous cooperation by building social capital.
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Affiliation(s)
- Joung-Hun Lee
- Faculty of Sciences, Kyushu University, Fukuoka, Japan
| | - Marko Jusup
- Faculty of Sciences, Kyushu University, Fukuoka, Japan
| | - Boris Podobnik
- Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia; Faculty of Economics, University of Ljubljana, Ljubljana, Slovenia; Zagreb School of Economics and Management, Zagreb, Croatia
| | - Yoh Iwasa
- Faculty of Sciences, Kyushu University, Fukuoka, Japan
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Abstract
Time series forecasting is of fundamental importance for a variety of domains including the prediction of earthquakes, financial market prediction, and the prediction of epileptic seizures. We present an original approach that brings a novel perspective to the field of long-term time series forecasting. Nonlinear properties of a time series are evaluated and used for long-term predictions. We used financial time series, medical time series and climate time series to evaluate our method. The results we obtained show that the long-term prediction of complex nonlinear time series is no longer unrealistic. The new method has the ability to predict the long-term evolutionary trend of stock market time series, and it attained an accuracy level with 100% sensitivity and specificity for the prediction of epileptic seizures up to 17 minutes in advance based on data from 21 epileptic patients. Our new method also predicted the trend of increasing global temperature in the last 30 years with a high level of accuracy. Thus, our method for making long-term time series predictions is vastly superior to existing methods. We therefore believe that our proposed method has the potential to be applied to many other domains to generate accurate and useful long-term predictions.
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