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Topic Review
Journal Axioms
Axioms (ISSN 2075-1680) is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published quarterly online by MDPI. It's now indexed within SCIE (Web of Science), Scopus, dblp, and other databases.
  • 1.0K
  • 26 Sep 2021
Topic Review
Mathematical Modeling to Estimate Photosynthesis
Photosynthesis is a process that indicates the productivity of crops. The estimation of this variable can be achieved through methods based on mathematical models.
  • 1.0K
  • 22 Jun 2022
Topic Review
Expenditures and Oscillation Analysis
The main purpose is to identify among variables that constitute water resources consumption at public schools, the link between consumption and expenditures oscillations. It was obtained a theoretical model of how oscillations patterns are originated and how time lengths have an important role over expenditures oscillations ergodicity and non-ergodicity.
  • 979
  • 01 Nov 2020
Topic Review
Multiple Traveling Salesperson Problems
Multiple traveling salesperson problems (mTSP) are a collection of problems that generalize the classical traveling salesperson problem (TSP). In a nutshell, an mTSP variant seeks a minimum-cost collection of m paths that visit all vertices of a given weighted complete graph. Conceptually, mTSP lies between TSP and vehicle routing problems (VRP).
  • 917
  • 20 Jul 2023
Topic Review
Conditional Frontier Analysis (DEA)
Conditional Frontier Analysis is part of the Nonparametric Robust Estimators proposed to overcome some drawbacks in the traditional Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH) measures for the technical efficiency. In special, this methodology extends the nonparametric input/output production technology to robustly account for extreme values or outliers in the data, and allow measuring the effect of external environmental variables on the efficiency of Decision Making Units (DMUs). 
  • 864
  • 01 May 2021
Topic Review
Convolutional Neural Network
Convolutional neural network (CNN)-based deep learning (DL) has a wide variety of applications in the geospatial and remote sensing (RS) sciences, and consequently has been a focus of many recent studies. 
  • 803
  • 29 Jan 2022
Topic Review
Efficiency of Industrial Based on Network DEA Method
There are two main methods to study the efficiency of industrial sectors. The first is parametric method represented by stochastic frontier method (SFA). The other is the more widely used non-parametric method represented by data envelopment analysis (DEA), which makes up for the shortcomings of the SFA method. It does not need to specify a certain functional relationship between input and output. The operation process of the Chinese provincial industrial system consists of four stages, namely the production (P) stage, wastewater treatment (WWT) stage, solid waste treatment (SWT) stage, and sulfur dioxide treatment (SDT) stage. Based on this structure, a four-stage data envelopment analysis (DEA) model is developed to evaluate the eco-efficiency, production efficiency, wastewater treatment efficiency, solid waste treatment efficiency, and sulfur dioxide treatment efficiency of provincial industrial systems in China, considering the undesirable output and variable returns to scale (VRS). 
  • 762
  • 24 May 2022
Topic Review
Random Number Generation
Ever since the antiquity, random number generation has played an important role both in common everyday life activities, such as leisure games, as well as in the advancement of science. Such means as dice and coins have been employed since the ancient times in order to generate random numbers that were used for gambling, dispute resolution, leisure games, and perhaps even fortune-telling. The theory behind the generation of random numbers, as well as the ability to potentially predict the outcome of this process, has been heavily studied and exploited by mathematics, in an attempt to either ensure the randomness of the process, to gain an advantage in correctly predicting its future outcomes, or to approximate the results of rather complicated computations. Especially in cryptography, random numbers are used due to the aforementioned properties, so that attackers have no other option but to guess the secret. This fact, in conjunction with the ongoing digitalisation of our world, has led to an interest in random number generation within the framework of computer science. In this context, random number generation systems are classified into two main categories: pseudorandom number generators and true random number generators, with the former generating sequences of numbers that appear to be random, but are in fact completely predictable when the initial value (being referred to as the seed) and conditions used for the number generation process are known, and with the latter generating truly random sequences of numbers that can only be predicted (correctly) with negligible probability, even if the initial value and conditions are known. 
  • 757
  • 24 Mar 2023
Topic Review
COVID-19 Pandemic Prediction
Several epidemiological models are being used around the world to project the number of infected individuals and the mortality rates of the COVID-19 outbreak. Advancing accurate prediction models is of utmost importance to take proper actions. Due to the lack of essential data and uncertainty, the epidemiological models have been challenged regarding the delivery of higher accuracy for long-term prediction. As an alternative to the susceptible-infected-resistant (SIR)-based models, this study proposes a hybrid machine learning approach to predict the COVID-19, and we exemplify its potential using data from Hungary. The hybrid machine learning methods of adaptive network-based fuzzy inference system (ANFIS) and multi-layered perceptron-imperialist competitive algorithm (MLP-ICA) are proposed to predict time series of infected individuals and mortality rate. The models predict that by late May, the outbreak and the total morality will drop substantially. The validation is performed for 9 days with promising results, which confirms the model accuracy. It is expected that the model maintains its accuracy as long as no significant interruption occurs. This paper provides an initial benchmarking to demonstrate the potential of machine learning for future research.
  • 734
  • 02 Feb 2021
Topic Review Video Peer Reviewed
Geometry-Based Deep Learning in the Natural Sciences
Nature is composed of elements at various spatial scales, ranging from the atomic to the astronomical level. In general, human sensory experience is limited to the mid-range of these spatial scales, in that the scales which represent the world of the very small or very large are generally apart from our sensory experiences. Furthermore, the complexities of Nature and its underlying elements are not tractable nor easily recognized by the traditional forms of human reasoning. Instead, the natural and mathematical sciences have emerged to model the complexities of Nature, leading to knowledge of the physical world. This level of predictiveness far exceeds any mere visual representations as naively formed in the Mind. In particular, geometry has served an outsized role in the mathematical representations of Nature, such as in the explanation of the movement of planets across the night sky. Geometry not only provides a framework for knowledge of the myriad of natural processes, but also as a mechanism for the theoretical understanding of those natural processes not yet observed, leading to visualization, abstraction, and models with insight and explanatory power. Without these tools, human experience would be limited to sensory feedback, which reflects a very small fraction of the properties of objects that exist in the natural world. As a consequence, as taught during the times of antiquity, geometry is essential for forming knowledge and differentiating opinion from true belief. It not only provides a framework for understanding astronomy, classical mechanics, and relativistic physics, but also the morphological evolution of living organisms, along with the complexities of the cognitive systems. Geometry also has a role in the information sciences, where it has explanatory power in visualizing the flow, structure, and organization of information in a system. This role further impacts the explanations of the internals of deep learning systems as developed in the fields of computer science and engineering.
  • 720
  • 21 Jun 2023
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