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Entropy
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Modeling and Forecasting of Rare and Extreme Events
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Modeling and Forecasting of Rare and Extreme Events

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (15 December 2021) | Viewed by 15293

Special Issue Editors

Prof. Dr. José A. Tenreiro Machado

grade Website
Guest Editor
Department of Electrical Engineering, Institute of Engineering, Polytechnic Institute of Porto, 4249-015 Porto, Portugal
Interests: nonlinear dynamics; fractional calculus; modeling; control; evolutionary computing; genomics; robotics, complex systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dimitri Volchenkov

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Guest Editor
Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA
Interests: data analysis; stochastic nonlinear dynamics; urban studies; complexity and uncertainty in the real-world systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Rare or extreme events designate phenomena that occur with low frequency, but that have huge and dramatic impact. These types of events encompasses natural phenomena, problems produced by the human activities, or even a combination of both. The case of natural events is portraited by catastrophes such as earthquakes, tsunamis, tornadoes, volcanos, floods, asteroid impacts, solar flares. For the events produced by the human species, also called anthropogenic hazards, we have bloody conflicts, such as warfare and terrorism, large industrial accidents, financial and commodity market crashes, economic crisis, Internet security outbreaks, energy or communications blackouts, and others. Regarding calamities involving both natural and anthropogenic factors we can mention global warming, forest fires, migrations, epidemic diseases outbreaks, and many others.

These phenomena often occur in complex systems, characterized by scale-invariance, self-similarity, fractality and non-locality, with power law behavior and alpha–stable distributions characterized by heavy-tails, giving non-negligible probability to extreme events. We find scattered in the literature names such as "dragon kings", "black swans", and others, to mention special cases of apparently unpredictable catastrophic events.

The Coronavirus disease 2019 (COVID-19) outbreak, spreading across the world with dramatic consequences for social, healthcare and economic systems, is an example of an extreme event.

This Collection on Modeling and Forecasting of Rare and Extreme Events focuses on original and new research results in mathematical, computational, algorithmic, or data-driven studies.

Manuscripts on new methodologies, advanced forms of system modeling and event forecasting, nonlinearity and novel perspectives for information processing are solicited. We welcome submissions addressing such issues, as well as those on more specific topics, illustrating the broad impact of entropy- and information-based techniques on the understanding of these type of phenomena.

Given the present state of COVID19 emergency in the world, submissions on the topic are welcome.

Prof. José A. Tenreiro Machado
Prof. Dimitri Volchenkov 
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 submissions that pass pre-check are 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. Entropy is an international peer-reviewed open access monthly 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 2600 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

  • entropy
  • information
  • complexity
  • nonlinearity
  • catastrophes
  • hazards
  • earthquakes
  • tsunamis
  • tornadoes
  • volcanos
  • floods
  • asteroid impacts
  • solar flares
  • warfare
  • terrorism
  • large industrial accidents
  • market crashes
  • economic crises
  • Internet attacks
  • energy blackout
  • communications blackout
  • global warming
  • forest fires
  • migrations
  • extinctions
  • epidemics
  • pandemics.

Published Papers (6 papers)

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Research

19 pages, 4872 KiB  
Article
Complexity of COVID-19 Dynamics
by Bellie Sivakumar and Bhadran Deepthi
Entropy 2022, 24(1), 50; https://0-doi-org.brum.beds.ac.uk/10.3390/e24010050 - 27 Dec 2021
Cited by 10 | Viewed by 2797
Abstract
With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made [...] Read more.
With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Rare and Extreme Events)
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15 pages, 3396 KiB  
Article
Understanding the Impact of Walkability, Population Density, and Population Size on COVID-19 Spread: A Pilot Study of the Early Contagion in the United States
by Fernando T. Lima, Nathan C. Brown and José P. Duarte
Entropy 2021, 23(11), 1512; https://0-doi-org.brum.beds.ac.uk/10.3390/e23111512 - 14 Nov 2021
Cited by 12 | Viewed by 2490
Abstract
The novel coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global event that has been challenging governments, health systems, and communities worldwide. Available data from the first months indicated varying patterns of the spread of COVID-19 within American cities, when the spread was [...] Read more.
The novel coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global event that has been challenging governments, health systems, and communities worldwide. Available data from the first months indicated varying patterns of the spread of COVID-19 within American cities, when the spread was faster in high-density and walkable cities such as New York than in low-density and car-oriented cities such as Los Angeles. Subsequent containment efforts, underlying population characteristics, variants, and other factors likely affected the spread significantly. However, this work investigates the hypothesis that urban configuration and associated spatial use patterns directly impact how the disease spreads and infects a population. It follows work that has shown how the spatial configuration of urban spaces impacts the social behavior of people moving through those spaces. It addresses the first 60 days of contagion (before containment measures were widely adopted and had time to affect spread) in 93 urban counties in the United States, considering population size, population density, walkability, here evaluated through walkscore, an indicator that measures the density of amenities, and, therefore, opportunities for population mixing, and the number of confirmed cases and deaths. Our findings indicate correlations between walkability, population density, and COVID-19 spreading patterns but no clear correlation between population size and the number of cases or deaths per 100 k habitants. Although virus spread beyond these initial cases may provide additional data for analysis, this study is an initial step in understanding the relationship between COVID-19 and urban configuration. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Rare and Extreme Events)
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13 pages, 770 KiB  
Article
Inference on COVID-19 Epidemiological Parameters Using Bayesian Survival Analysis
by Chiara Bardelli
Entropy 2021, 23(10), 1262; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101262 - 28 Sep 2021
Cited by 1 | Viewed by 1365
Abstract
The need to provide accurate predictions in the evolution of the COVID-19 epidemic has motivated the development of different epidemiological models. These models require a careful calibration of their parameters to capture the dynamics of the phenomena and the uncertainty in the data. [...] Read more.
The need to provide accurate predictions in the evolution of the COVID-19 epidemic has motivated the development of different epidemiological models. These models require a careful calibration of their parameters to capture the dynamics of the phenomena and the uncertainty in the data. This work analyzes different parameters related to the personal evolution of COVID-19 (i.e., time of recovery, length of stay in hospital and delay in hospitalization). A Bayesian Survival Analysis is performed considering the age factor and period of the epidemic as fixed predictors to understand how these features influence the evolution of the epidemic. These results can be easily included in the epidemiological SIR model to make prediction results more stable. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Rare and Extreme Events)
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16 pages, 902 KiB  
Article
The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market
by Kyungwon Kim and Minhyuk Lee
Entropy 2021, 23(9), 1234; https://0-doi-org.brum.beds.ac.uk/10.3390/e23091234 - 20 Sep 2021
Cited by 12 | Viewed by 3436
Abstract
The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics [...] Read more.
The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Rare and Extreme Events)
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19 pages, 1273 KiB  
Article
Piecewise Modeling the Accumulated Daily Growth of COVID-19 Deaths: The Case of the State of São Paulo, Brazil
by Erlandson Ferreira Saraiva and Carlos Alberto de Bragança Pereira
Entropy 2021, 23(8), 1013; https://0-doi-org.brum.beds.ac.uk/10.3390/e23081013 - 04 Aug 2021
Viewed by 1651
Abstract
The pandemic scenery caused by the new coronavirus, called SARS-CoV-2, increased interest in statistical models capable of projecting the evolution of the number of cases (and associated deaths) due to COVID-19 in countries, states and/or cities. This interest is mainly due to the [...] Read more.
The pandemic scenery caused by the new coronavirus, called SARS-CoV-2, increased interest in statistical models capable of projecting the evolution of the number of cases (and associated deaths) due to COVID-19 in countries, states and/or cities. This interest is mainly due to the fact that the projections may help the government agencies in making decisions in relation to procedures of prevention of the disease. Since the growth of the number of cases (and deaths) of COVID-19, in general, has presented a heterogeneous evolution over time, it is important that the modeling procedure is capable of identifying periods with different growth rates and proposing an adequate model for each period. Here, we present a modeling procedure based on the fit of a piecewise growth model for the cumulative number of deaths. We opt to focus on the modeling of the cumulative number of deaths because, other than for the number of cases, these values do not depend on the number of diagnostic tests performed. In the proposed approach, the model is updated in the course of the pandemic, and whenever a “new” period of the pandemic is identified, it creates a new sub-dataset composed of the cumulative number of deaths registered from the change point and a new growth model is chosen for that period. Three growth models were fitted for each period: exponential, logistic and Gompertz models. The best model for the cumulative number of deaths recorded is the one with the smallest mean square error and the smallest Akaike information criterion (AIC) and Bayesian information criterion (BIC) values. This approach is illustrated in a case study, in which we model the number of deaths due to COVID-19 recorded in the State of São Paulo, Brazil. The results have shown that the fit of a piecewise model is very effective for explaining the different periods of the pandemic evolution. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Rare and Extreme Events)
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8 pages, 260 KiB  
Article
Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State
by Xuze Zhang, Saumyadipta Pyne and Benjamin Kedem
Entropy 2021, 23(6), 675; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060675 - 27 May 2021
Cited by 1 | Viewed by 2262
Abstract
In disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations [...] Read more.
In disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations from multiple sources to compute tail probabilities that could not be obtained otherwise due to a lack of lower or upper tail data. The estimation of multivariate lower and upper tail probabilities from a given small reference data set that lacks complete information about such tail data is addressed in terms of pertussis case count data. Fusion of data from multiple sources in conjunction with the density ratio model is used to give probability estimates that are non-obtainable from the empirical distribution. Based on a density ratio model with variable tilts, we first present a univariate fit and, subsequently, improve it with a multivariate extension. In the multivariate analysis, we selected the best model in terms of the Akaike Information Criterion (AIC). Regional prediction, in Washington state, of the number of pertussis cases is approached by providing joint probabilities using fused data from several relatively small samples following the selected density ratio model. The model is validated by a graphical goodness-of-fit plot comparing the estimated reference distribution obtained from the fused data with that of the empirical distribution obtained from the reference sample only. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Rare and Extreme Events)
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