Special Issue "Markov-Chain Modelling and Applications"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 28 February 2022.

Special Issue Editors

Prof. Dr. José Álvarez-García
E-Mail Website
Guest Editor
Financial Economy and Accounting Department, Faculty of Business, Finance and Tourism, University of Extremadura, 10071 Cáceres, Spain
Interests: business and tourism; resource and service management; water resources management; water governance; sustainable rural development; financial economics; accounting and management; sustainability; entrepreneurship; innovation; quality and environmental management systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Oscar V. De la Torre-Torres
E-Mail Website
Guest Editor
Faculty of Accounting and Management, Saint Nicholas and Hidalgo Michoacán State University (UMSNH), Morelia 58030, Mexico
Interests: portfolio management; financial econometrics; sustainable investment; pension funds; algorithmic trading
Prof. Dr. María de la Cruz del Río-Rama
E-Mail Website1 Website2
Guest Editor
Business Management and Marketing Department, Faculty of Business Sciences and Tourism, University of Vigo, 32004 Ourense, Spain
Interests: business and tourism; resource and service management; water resources management; water governance; sustainable rural development; sustainability; entrepreneurship; innovation; quality and environmental management systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Markov chain, also known as the Markov model or Markov process, is defined as a special type of discrete stochastic process in which the probability of an event occurring depends only on the immediately preceding event. In this regard, if the present state of an event is known, additional information from the past will be useful to make the best prediction about its future. Its applications are very diverse in multiple fields of science, including meteorology, genetic and epidemiological processes, financial and economic modelling, music generation, cyber security, and the development of artificial intelligence. Currently, Markov chains as statistical tools allow us to explain the natural and social reality in which we live, and are used to support decision-making.

In this framework, this Special Issue aims to compile novel research papers in which the Markov chain is applied in numerous areas of knowledge.

The relevant topics are:

  1. Markov processes in the calculation of probabilities.
  2. Application of the Markov chain in finance, economics, and actuarial science.
  3. Application of Markov processes in logistics, optimization, and operations management.
  4. Application of the Markov chain in study techniques in biology, human or veterinary medicine, genetics, epidemiology, or related medical sciences.
  5. Development of models and technological applications in computer security, internet and search criteria, big data, data mining, and artificial intelligence with Markov processes.
  6. Application of the Markov chain in Earth sciences such as geology, volcanology, seismology, meteorology, etc.
  7. Use of the Markov chain in physics, astronomy, or cosmology.
  8. Theoretical developments related to Markov processes and probability calculation.

Other interesting and related topics.

Prof. Dr. José Álvarez-García
Prof. Dr. Oscar V. De la Torre-Torres
Prof. Dr. María de la Cruz del Río-Rama
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Markov chains
  • Markov model
  • Stochastic processes
  • Analysis of behavior
  • Probability theory

Published Papers (12 papers)

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Research

Article
Currency Hedging Strategies Using Histogram-Valued Data: Bivariate Markov Switching GARCH Models
Mathematics 2021, 9(21), 2773; https://doi.org/10.3390/math9212773 - 01 Nov 2021
Viewed by 220
Abstract
Previous studies aimed at determining hedging strategies commonly used daily closing spot and futures prices for the analysis and strategy building. However, the daily closing price might not be the appropriate for price in some or all trading days. This is because the [...] Read more.
Previous studies aimed at determining hedging strategies commonly used daily closing spot and futures prices for the analysis and strategy building. However, the daily closing price might not be the appropriate for price in some or all trading days. This is because the intraday data at various minute intervals, in our view, are likely to better reflect the information about the concrete behavior of the market returns and reactions of the market participants. Therefore, in this study, we propose using high-frequency data along with daily data in an attempt to determine hedging strategies, using five major international currencies against the American dollar. Specifically, in our study we used the 5-min, 30-min, 60-min, and daily closing prices of the USD/CAD (Canadian Dollar), USD/CNY (Chinese Yuan), USD/EUR (Euro), USD/GBP (British Pound), and USD/JPY (Japanese Yen) pairs over the 2018–2019 period. Using data at 5-min, 30-min, and 60-min intervals or high-frequency data, however, means the use of a relatively large number of observations for information extractions in general and econometric model estimations, making data processing and analysis a rather time-consuming and complicated task. To deal with such drawbacks, this study collected the high-frequency data in the form of a histogram and selected the representative daily price, which does not have to be the daily closing value. Then, these histogram-valued data are used for investigating the linear and nonlinear relationships and the volatility of the interested variables by various single- and two-regime bivariate GARCH models. Our results indicate that the Markov Switching Dynamic Copula-Generalized autoregressive conditional heteroskedasticity (GARCH) model performs the best with the lowest BIC and gives the highest overall value of hedging effectiveness (HE) compared with the other models considered in the present endeavor. Consequently, we can conclude that the foreign exchange market for both spot and futures trading has a nonlinear structure. Furthermore, based on the HE results, the best derivatives instrument is CAD using one-day frequency data, while GBP using 30-min frequency data is the best considering the highest hedge ratio. We note that the derivative with the highest hedging effectiveness might not be the one with the highest hedge ratio. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Asymptotic Analysis for Systems with Deferred Abandonment
Mathematics 2021, 9(18), 2187; https://doi.org/10.3390/math9182187 - 07 Sep 2021
Viewed by 399
Abstract
This short paper concerns the analysis of the M/M/k queueing system with customer abandonment. In this system, service managers provide a finite buffer space, which is a waiting area that prevents customers from abandoning the system. Abandonment of the system can occur from [...] Read more.
This short paper concerns the analysis of the M/M/k queueing system with customer abandonment. In this system, service managers provide a finite buffer space, which is a waiting area that prevents customers from abandoning the system. Abandonment of the system can occur from reneging (exiting from the queue while waiting), and/or balking (leaving the system without waiting). We derive an analytical expression to represent the impact of the buffer space capacity on the delay probability and the abandonment probability for a system with deferred abandonment. The result indicates the provision of the buffer space in a large system could only increase the delay probability while the abandonment probability remains unchanged. Despite the benevolent intentions of service managers, providing a buffer space may exacerbate the performance of larger systems. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Development of a Shipment Policy for Collection Centers
Mathematics 2021, 9(12), 1385; https://doi.org/10.3390/math9121385 - 15 Jun 2021
Viewed by 474
Abstract
Natural disasters represent a latent threat for every country in the world. Due to climate change and other factors, statistics show that they continue to be on the rise. This situation presents a challenge for the communities and the humanitarian organizations to be [...] Read more.
Natural disasters represent a latent threat for every country in the world. Due to climate change and other factors, statistics show that they continue to be on the rise. This situation presents a challenge for the communities and the humanitarian organizations to be better prepared and react faster to natural disasters. In some countries, in-kind donations represent a high percentage of the supply for the operations, which presents additional challenges. This research proposes a Markov Decision Process (MDP) model to resemble operations in collection centers, where in-kind donations are received, sorted, packed, and sent to the affected areas. The decision addressed is when to send a shipment considering the uncertainty of the donations’ supply and the demand, as well as the logistics costs and the penalty of unsatisfied demand. As a result of the MDP a Monotone Optimal Non-Decreasing Policy (MONDP) is proposed, which provides valuable insights for decision-makers within this field. Moreover, the necessary conditions to prove the existence of such MONDP are presented. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Markov Chain K-Means Cluster Models and Their Use for Companies’ Credit Quality and Default Probability Estimation
Mathematics 2021, 9(8), 879; https://doi.org/10.3390/math9080879 - 16 Apr 2021
Cited by 1 | Viewed by 726
Abstract
This research aims to determine the existence of inflection points when companies’ credit risk goes from being minimal (Hedge) to being high (Ponzi). We propose an analysis methodology that determines the probability of hedge credits to migrate to speculative and then to Ponzi, [...] Read more.
This research aims to determine the existence of inflection points when companies’ credit risk goes from being minimal (Hedge) to being high (Ponzi). We propose an analysis methodology that determines the probability of hedge credits to migrate to speculative and then to Ponzi, through simulations with homogeneous Markov chains and the k-means clustering method to determine thresholds and migration among clusters. To prove this, we used quarterly financial data from a sample of 35 public enterprises over the period between 1 July 2006 and 28 March 2020 (companies listed on the USA, Mexico, Brazil, and Chile stock markets). For simplicity, we make the assumption of no revolving credits for the companies and that they face their next payment only with their operating cash flow. We found that Ponzi companies (1) have a 0.79 probability average of default, while speculative ones had (0) 0.28, and hedge companies (−1) 0.009, which are the inflections point we were looking for. Our work’s main limitation lies in not considering the entities’ behavior when granting credits in altered states (credit relaxation due to credit supply excess). Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
The Markovian Pattern of Social Deprivation for Mexicans with Diabetes
Mathematics 2021, 9(7), 780; https://doi.org/10.3390/math9070780 - 03 Apr 2021
Viewed by 653
Abstract
This paper aims to determine the Markovian pattern of the factors influencing social deprivation in Mexicans with Type 2 diabetes mellitus (DM2). To this end, we develop a methodology to meet the theoretical and practical considerations involved in applying a Hidden Markov Model [...] Read more.
This paper aims to determine the Markovian pattern of the factors influencing social deprivation in Mexicans with Type 2 diabetes mellitus (DM2). To this end, we develop a methodology to meet the theoretical and practical considerations involved in applying a Hidden Markov Model that uses non-panel data. After estimating the latent states and ergodic vectors for diabetic and non-diabetic populations, we find that the long-term state-dependent probabilities for people with DM2 show a darker perspective of impoverishment than the rest of the Mexican population. In the absence of extreme events that modify the present probability structure, the Markovian pattern confirms that people with DM2 will most likely become the poorest of Mexico’s poor. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Regime Switching in High-Tech ETFs: Idiosyncratic Volatility and Return
Mathematics 2021, 9(7), 742; https://doi.org/10.3390/math9070742 - 31 Mar 2021
Cited by 1 | Viewed by 455
Abstract
The volatility of asset returns can be classified into market and firm-specific volatility, otherwise known as idiosyncratic volatility. Idiosyncratic volatility is increasing over time with some literature attributing this to the IT revolution. An understanding of the relationship between idiosyncratic risk and return [...] Read more.
The volatility of asset returns can be classified into market and firm-specific volatility, otherwise known as idiosyncratic volatility. Idiosyncratic volatility is increasing over time with some literature attributing this to the IT revolution. An understanding of the relationship between idiosyncratic risk and return is indeed relevant for idiosyncratic risk pricing and asset allocation, in a context of emerging technologies. The case of high-tech exchange traded funds (ETFs) is especially interesting, since ETFs introduce new noise to the market due to arbitrage activities and high frequency trading. This article examines the relevance of idiosyncratic risk in explaining the return of nine high-tech ETFs. The Markov regime-switching (MRS) methodology for heteroscedastic regimes has been applied. We found that high-tech ETF returns are negatively related to idiosyncratic risk during the high volatility regime and positively related to idiosyncratic risk during the low volatility regime. These results suggest that idiosyncratic volatility matters in high-tech ETF pricing, and that the effects are driven by volatility regimes, leading to changes across them. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Personalized Cotesting Policies for Cervical Cancer Screening: A POMDP Approach
Mathematics 2021, 9(6), 679; https://doi.org/10.3390/math9060679 - 22 Mar 2021
Viewed by 598
Abstract
Screening for cervical cancer is a critical policy that requires clinical and managerial vigilance because of its serious health consequences. Recently the practice of conducting simultaneous tests of cytology and Human Papillomavirus (HPV)-DNA testing (known as cotesting) has been included in the public [...] Read more.
Screening for cervical cancer is a critical policy that requires clinical and managerial vigilance because of its serious health consequences. Recently the practice of conducting simultaneous tests of cytology and Human Papillomavirus (HPV)-DNA testing (known as cotesting) has been included in the public health policies and guidelines with a fixed frequency. On the other hand, personalizing medical interventions by incorporating patient characteristics into the decision making process has gained considerable attention in recent years. We develop a personalized partially observable Markov decision process (POMDP) model for cervical cancer screening decisions by cotesting. In addition to the merits offered by the guidelines, by availing the possibility of including patient-specific risks and other attributes, our POMDP model provides a patient-tailored screening plan. Our results show that the policy generated by the POMDP model outperforms the static guidelines in terms of quality-adjusted life years (QALY) gain, while performing comparatively equal in lifetime risk reduction. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Analyzing the Influence of Transportations on Chinese Inbound Tourism: Markov Switching Penalized Regression Approaches
Mathematics 2021, 9(5), 515; https://doi.org/10.3390/math9050515 - 02 Mar 2021
Viewed by 499
Abstract
This study investigates the nonlinear impact of various modes of transportation (air, road, railway, and maritime) on the number of foreign visitors to China originating from major source countries. Our nonlinear tourism demand equations are determined through the Markov-switching regression (MSR) model, thereby, [...] Read more.
This study investigates the nonlinear impact of various modes of transportation (air, road, railway, and maritime) on the number of foreign visitors to China originating from major source countries. Our nonlinear tourism demand equations are determined through the Markov-switching regression (MSR) model, thereby, capturing the possible structural changes in Chinese tourism demand. Due to many variables and the limitations from the small number of observations confronted in this empirical study, we may face multicollinearity and endogeneity bias. Therefore, we introduce the two penalized maximum likelihoods, namely Ridge and Lasso, to estimate the high dimensional parameters in the MSR model. This investigation found the structural changes in all tourist arrival series with significant coefficient shifts in transportation variables. We observe that the coefficients are relatively more significant in regime 1 (low tourist arrival regime). The coefficients in regime 1 are all positive (except railway length in operation), while the estimated coefficients in regime 2 are positive in fewer numbers and weak. This study shows that, in the process of transportation, development and changing inbound tourism demand from ten countries, some variables with the originally strong positive effect will have a weak positive effect when tourist arrivals are classified in the high tourist arrival regime. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Modeling Precious Metal Returns through Fractional Jump-Diffusion Processes Combined with Markov Regime-Switching Stochastic Volatility
Mathematics 2021, 9(4), 407; https://doi.org/10.3390/math9040407 - 19 Feb 2021
Cited by 3 | Viewed by 674
Abstract
This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by [...] Read more.
This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by fractional Brownian motions, combined with Poisson processes and modulated by continuous-time homogeneous Markov chains. The calibration is carried out by estimating the Jump Generalized Autoregressive Conditional Heteroscedasticity (Jump-GARCH) and Markov regime-switching models of each precious metal, as well as computing their Hurst exponents. The novelty in this research is the use of non-linear, non-normal, multi-factor, time-varying risk stochastic models, useful for an investors’ decision-making process when they intend to include precious metals in their portfolios as safe-haven assets. The main empirical results are as follows: (1) all metals stay in low volatility most of the time and have long memories, which means that past returns have an effect on current and future returns; (2) silver and platinum have the largest jump sizes; (3) silver’s negative jumps have the highest intensity; and (4) silver reacts more than gold and platinum, and it is also the most volatile, having the highest probability of intensive jumps. Gold is the least volatile, as its percentage of jumps is the lowest and the intensity of its jumps is lower than that of the other two metals. Finally, a set of recommendations is provided for the decision-making process of an average investor looking to buy and sell precious metals. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Indistinguishability Operators via Yager t-norms and Their Applications to Swarm Multi-Agent Task Allocation
Mathematics 2021, 9(2), 190; https://doi.org/10.3390/math9020190 - 19 Jan 2021
Viewed by 820
Abstract
In this paper, we propose a family of indistinguishability operators, that we have called Yager Possibilitic Response Functions (YPRFs for short), as an appropriate tool for allocating tasks to a collective of agents. In order to select the best agent to carry out [...] Read more.
In this paper, we propose a family of indistinguishability operators, that we have called Yager Possibilitic Response Functions (YPRFs for short), as an appropriate tool for allocating tasks to a collective of agents. In order to select the best agent to carry out each task, we have used the so-called response threshold method, where each agent decides the next task to perform following a probabilistic Markov process and, in addition, involves a response function which models how appropriate the task is for the agent. In previous works, we developed a new response threshold method which incorporates the use of indistinguishability operators as response functions and possibility theory instead of probability, for task allocation from a very general perspective without taking into account the specific characteristics of the agents except their limitations to carry out a task. Such an allocation is modelled by means of possibilistic, instead of probabilisitic, Markov chains. We show that possibilistic Markov chains outperform its probabilistic counterparts for the aforementioned propose. All the indistinguishability operators considered in previous papers were not able to take into account the agents’ restrictions for moving from a task to another one, or equivalently to carry out a task instead of another one. In order to avoid this handicap, we introduce a new kind of response functions, YPRFs, which are modelled by means of indistinguishability operators obtained via Yager t-norms. This new type of response functions drops to zero when an agent, due to its limitations, is not able to execute a task and, therefore, is able to model a generic multi-agent system with restrictions. The performed simulation, under Matlab, allows us to compare the results obtained using the new YPRFs with those obtained applying celebrated response functions also generated via indistinguishability operators (that we call Original Possibilitic Response Functions, OPRFs for short). Moreover, the results confirm that the YPRFs are able to take into account agent’s restrictions while the OPRFs are not able. Finally, in the light of the experimental results, we can confirm that those systems modelled. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
Enhancing Portfolio Performance and VIX Futures Trading Timing with Markov-Switching GARCH Models
Mathematics 2021, 9(2), 185; https://doi.org/10.3390/math9020185 - 18 Jan 2021
Cited by 2 | Viewed by 781
Abstract
In the present paper, we test the use of Markov-Switching (MS) models with time-fixed or Generalized Autoregressive Conditional Heteroskedasticity (GARCH) variances. This, to enhance the performance of a U.S. dollar-based portfolio that invest in the S&P 500 (SP500) stock index, the 3-month U.S. [...] Read more.
In the present paper, we test the use of Markov-Switching (MS) models with time-fixed or Generalized Autoregressive Conditional Heteroskedasticity (GARCH) variances. This, to enhance the performance of a U.S. dollar-based portfolio that invest in the S&P 500 (SP500) stock index, the 3-month U.S. Treasury-bill (T-BILL) or the 1-month volatility index (VIX) futures. For the investment algorithm, we propose the use of two and three-regime, Gaussian and t-Student, MS and MS-GARCH models. This is done to forecast the probability of high volatility episodes in the SP500 and to determine the investment level in each asset. To test the algorithm, we simulated 8 portfolios that invested in these three assets, in a weekly basis from 23 December 2005 to 14 August 2020. Our results suggest that the use of MS and MS-GARCH models and VIX futures leads the simulated portfolio to outperform a buy and hold strategy in the SP500. Also, we found that this result holds only in high and extreme volatility periods. As a recommendation for practitioners, we found that our investment algorithm must be used only by institutional investors, given the impact of stock trading fees. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Article
A Predator–Prey Two-Sex Branching Process
Mathematics 2020, 8(9), 1408; https://doi.org/10.3390/math8091408 - 23 Aug 2020
Viewed by 2250
Abstract
In this paper, we present the first stochastic process to describe the interaction of predator and prey populations with sexual reproduction. Specifically, we introduce a two-type two-sex controlled branching model. This process is a two-type branching process, where the first type corresponds to [...] Read more.
In this paper, we present the first stochastic process to describe the interaction of predator and prey populations with sexual reproduction. Specifically, we introduce a two-type two-sex controlled branching model. This process is a two-type branching process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. In view of their potential for the conservation of species, we provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of them and the coexistence of both of them. Moreover, the description of the present predator–prey two-sex branching process on the fixation events can be performed in terms of the behaviour of a one-type two-sex branching process with a random control on the number of individuals, which is also introduced and analysed. Full article
(This article belongs to the Special Issue Markov-Chain Modelling and Applications)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: The Markovian pattern of social deprivation for Mexican people with diabetes
Authors: José Carlos Ramírez; Francisco Ortiz-Arango; Leovardo Mata
Affiliation: 1. Fellow-researcher at the Department of Economic Studies, El Colegio de la Frontera Norte, Tijuana, Mexico, [email protected] 2. Fellow-researcher at Universidad Panamericana, CDMX, Mexico, [email protected] 3. Fellow-researcher at Anahuac-Mexico-Norte University, [email protected]
Abstract: This paper aims to determine the Markovian pattern of the social factors influencing poverty in Mexicans with diabetes mellitus type 2 (DM2). Using a Hidden Markov Model, we estimate the latent states and ergodic vectors for diabetic and non-diabetic populations. The main finding is that the long-term state-dependent probabilities for people with diabetes show a darker perspective of impoverishment than the rest of the Mexicans. In the absence of radical economic improvements, people with diabetes will likely become the poorest of Mexico's poor.

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