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Topic Review Peer Reviewed
Pandemic Equation and COVID-19 Evolution
The Pandemic Equation describes multiple pandemic waves and has been applied to describe the COVID-19 pandemic. Using the generalized approaches of solid-state physics, we derive the Pandemic Equation, which accounts for the effects of pandemic mitigation measures and multiple pandemic waves. The Pandemic Equation uses slow and fast time scales for “curve flattening” and describing vaccination and mitigation measures and the Scaled Fermi–Dirac distribution functions for describing transitions between pandemic waves. The Pandemic Equation parameters extracted from the pandemic curves can be used for comparing different scenarios of the pandemic evolution and for extrapolating the pandemic evolution curves for the periods of time on the order of the instantaneous Pandemic Equation characteristic time constant. The parameter extraction for multiple locations could also allow for uncertainty quantification for such pandemic evolution predictions.
  • 182
  • 19 Apr 2024
Topic Review
Synthetic Datasets
With the consistent growth in the importance of machine learning and big data analysis, feature selection stands to be one of the most relevant techniques in the field. Extending into many disciplines, the use of feature selection in medical applications, cybersecurity, DNA micro-array data, and many more areas is witnessed. Machine learning models can significantly benefit from the accurate selection of feature subsets to increase the speed of learning and also to generalize the results. Feature selection can considerably simplify a dataset, such that the training models using the dataset can be “faster” and can reduce overfitting. Synthetic datasets were presented as a valuable benchmarking technique for the evaluation of feature selection algorithms.
  • 51
  • 20 Mar 2024
Biography
Delfim Fernando Marado Torres (Delfim F. M. Torres)
Professor Dr. Delfim F. M. Torres, D.Sc. (Habilitation) in Mathematics, Ph.D. in Mathematics, Web of Science Highly Cited Researcher (2015, 2016, 2017 and 2019). Full Professor of Mathematics (Professor Catedrático), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal. Director of the R&D unit CIDMA (http://cidma.ua.pt). Coordinator of the Systems and Control Group (http:
  • 176
  • 04 Mar 2024
Topic Review
Predictive Maintenance of Ball Bearing Systems
In the era of Industry 4.0 and beyond, ball bearings remain an important part of industrial systems. The failure of ball bearings can lead to plant downtime, inefficient operations, and significant maintenance expenses.
  • 67
  • 01 Feb 2024
Topic Review
Sound Source Localization and Detection Methods
Many acoustic detection and localization methods have been developed. However, all of the methods require capturing the audio signal. Therefore, any method’s essential element and requirement is using an acoustic sensor. In addition to converting sound waves into an electrical signal, they also perform other functions, such as: reducing ambient noise, or capturing sounds with frequencies beyond the hearing range of the human ear. Classic methods have stood the test of time and are still widely used due to their simplicity, reliability, and effectiveness. There are three main mathematical methods for determining the sound source. These include triangulation, trilateration, and multilateration
  • 122
  • 28 Dec 2023
Topic Review Video
K-Center Problem
This entry is adapted from the peer-reviewed paper 10.1109/ACCESS.2019.2933875 K-center problems are particular cases of the facility location problem, where a set of optimal centers are to be found given a set of constraints. In a nutshell, a k-center problem usually seeks a set of at most k centers that minimize the distance a client must travel to its nearest center. Namely, their objective function is often a minmax one. Naturally, these problems are well suited for modeling real location problems. Although many different problems fit within the description of a k-center problem, the most popular of these is the vertex k-center problem, where the input is a simple graph and an integer k, and the goal is to find at most k vertices whose distance to the remaining vertices is minimal.
  • 267
  • 30 Nov 2023
Topic Review
Fuzzy Time Series for Electricity Demand
A time series is a succession of data ordered chronologically in defined time intervals. The data may be evenly spaced, such as the record of daily solar generation from a photovoltaic plant, or it may be different, such as the number of annual earthquakes in a defined area. This type of representation offers many advantages because its analysis allows us to discover underlying relationships in the data, which can be from various time series or within the data itself. These can be used to extrapolate behavior in the past, during periods of data loss, and in the future.
  • 90
  • 22 Nov 2023
Topic Review
Role of Visual Tools in Understanding Mathematical Culture
The term mathematical culture’ cannot be naturally defined; we will understand it in the same way as ‘good mathematics’ is understood by, i.e., good ways of solving mathematical issues, good mathematical techniques, good mathematical applications and cultivating of mathematical insight, creativity and beauty of mathematics. Cultivation of a mathematical culture means teaching how to see the roots of mathematics in reality (in nature, in society, but also in mathematics itself), getting to know the world of mathematical concepts, understanding this world and being able to apply it in a cultivated and correct way when solving various problems.
  • 166
  • 25 Jul 2023
Topic Review
Facility Location and Vehicle-Routing Problem in Reverse Logistics
The concept of reverse logistics (RL) was put forward in 1992, whose essence was to transfer end-of-life (EOL) products from the consumer to the producer for processing.
  • 459
  • 13 Jan 2023
Biography
Mark Krasnosel'skii
Mark Alexandrovich Krasnosel'skii (Russian: Ма́рк Алекса́ндрович Красносе́льский) (April 27, 1920, Starokostiantyniv – February 13, 1997, Moscow) was a Soviet, Russia n and Ukraine mathematician renowned for his work on nonlinear functional analysis and its applications. Mark Krasnosel'skii was born in the town of Starokostiantyniv in Ukraine on the 27 Ap
  • 483
  • 03 Jan 2023
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