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The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates asymptomatic and super-spreader individuals in a single compartmental model. We highlight the advantages of utilizing incommensurate fractional order derivatives in ordinary differential equations, including increased flexibility in capturing disease dynamics and refined memory effects in the transmission process. We conduct a qualitative analysis of our proposed model, which involves determining the basic reproduction number and analysing the disease-free equilibrium's stability. By fitting the proposed model with real data from Portugal and comparing it with existing models, we demonstrate that the incorporation of supplementary population classes and fractional derivatives significantly improves the model's goodness of fit. Sensitivity analysis further provides valuable insights for designing effective strategies to mitigate the spread of the virus., Comment: This is a preprint version of the paper published open access in 'Mathematical Biosciences' at [https://doi.org/10.1016/j.mbs.2024.109373]

In this study, we present a reformulation of classical equilibrium thermodynamics by replacing the obscure and ambiguous concept of entropy with the clear and intuitive concept of information stored in a thermodynamic system. Specifically, we rewrite the laws of thermodynamics in the mathematical terminology borrowed from information theory with an emphasis on information instead of entropy and on binary logarithm instead of natural one. We also define a modified ideal gas constant denoted as $\mathcal{R}$ that quantifies the energy cost of storing or retrieving a mole of information. Moreover an application to the ideal gas is carried and new insight on the evolution of the system is acquired. This new formulation might serve as a basis to teaching thermodynamics, where one deals with the concept of energy and information both stored in a thermodynamic system and avoids the lack of cognitive representations inherent in the concept of entropy., Comment: 12 pages, 1 figure

The main purpose of this paper is to introduce and study minimal and maximal ideals defined on ideal topological spaces. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of $2^X$, where $2^X$ is the power set of $X.$ We obtain some of their fundamental properties. In addition, several relationships among the above notions have been discussed. Moreover, we get a new topology, called sharp topology via the sharp operator defined in the scope of this study, finer than the old one. Furthermore, a decomposition of the notion of open set has been obtained. Finally, we conclude our work with some interesting applications.

Uncrewed aerial vehicles (UAVs) have attracted recent attention for sixth-generation (6G) networks due to their low cost and flexible deployment. In order to maximize the ever-increasing data rates, spectral efficiency, and wider coverage, technologies such as reconfigurable intelligent surface (RIS) and non-orthogonal multiple access (NOMA) are adapted with UAVs (UAV-RIS NOMA). However, the error performance of UAV-RIS NOMA has not been considered, yet. In this letter, we investigate the error probability of UAV-RIS NOMA systems. We also consider the practical constraints of hardware impairments (HWI) at the transceivers, inter-cell interference (ICI), and imperfect successive interference cancellation (SIC). The analytical derivations are validated by Monte-Carlo simulations. Our results demonstrate that our proposed system achieves higher performance gain (more than 5 dB with increasing the number of RIS elements) with less error probability compared to UAVs without RIS. Moreover, it is found that the HWI, ICI, and imperfect SIC have shown a negative impact on the system performance.

In order to bolster future wireless networks, there has been a great deal of interest in non-terrestrial networks, especially aerial platforms including high-altitude platform stations (HAPS) and uncrewed aerial vehicles (UAVs). These platforms can integrate advanced technologies such as reconfigurable intelligent surfaces (RIS) and non-orthogonal multiple access (NOMA). In this regard, this paper proposes a multi-layer network architecture consisting of HAPS and UAV, where the former acts as a HAPS super macro base station (HAPS-SMBS), while the latter serves as a relay node for the ground Internet of Things (IoT) devices. The UAV is equipped with active transmissive RIS, which is a novel technology with promising benefits. We also utilize multiple-input single-output (MISO) technology, i.e., multiple antennas at the HAPS-SMBS and a single antenna at the IoT devices. Additionally, we consider NOMA as the multiple access technology as well as the existence of hardware impairments as a practical limitation. We compare the proposed system model with various scenarios, all involving the HAPS-SMBS and RIS-equipped UAV relay combination, but with different types of RIS, antenna configurations, and access technologies. Sum rate and energy efficiency are used as performance metrics, and the findings demonstrate that, in comparison to all benchmarks, the proposed system yields significant performance gains. Moreover, the hardware impairment limits the system performance at high transmit power levels.

We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo fractional-orders derivatives. We establish continuity and differentiability of the state solutions with respect to perturbed trajectories. Then, we state and prove a Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems. Finally, we give an example, illustrating the applicability of our Pontryagin maximum principle., Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', at [https://doi.org/10.3390/math11194218]. Cite this paper as: F. Nda\"{\i}rou and D.F.M. Torres, Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems, Mathematics 11 (2023), no. 19, Art. 4218, 12 pp

This research presents an advanced fractional-order compartmental model designed to delve into the complexities of COVID-19 transmission dynamics, specifically accounting for the influence of environmental pathogens on disease spread. By enhancing the classical compartmental framework, our model distinctively incorporates the effects of order derivatives and environmental shedding mechanisms on the basic reproduction numbers, thus offering a holistic perspective on transmission dynamics. Leveraging fractional calculus, the model adeptly captures the memory effect associated with disease spread, providing an authentic depiction of the virus's real-world propagation patterns. A thorough mathematical analysis confirming the existence, uniqueness, and stability of the model's solutions emphasizes its robustness. Furthermore, the numerical simulations, meticulously calibrated with real COVID-19 case data, affirm the model's capacity to emulate observed transmission trends, demonstrating the pivotal role of environmental transmission vectors in shaping public health strategies. The study highlights the critical role of environmental sanitation and targeted interventions in controlling the pandemic's spread, suggesting new insights for research and policy-making in infectious disease management.

Probing the thermodynamic properties of the Hawking-Page phase transition of asymptotically-flat black holes in R\'enyi statistics. We reveal the evidence for the persisting of the dual universal formula associated with the Hawking-Page (HP) and minimum black hole thermodynamical transition points. Our study unveils the universal properties of the black holes in different statistics, in particular beyond the Gibbs-Boltzmann formalism, and motivates a further promising bridge between the nonextensivity R\'enyi parameter {\lambda} and the cosmological constant ? . Besides, we discover that universal ratios related to horizon radius, R\'enyi temperature, and entropy can be shown to appear in presence of such a transition., Comment: 10 pages, 3 figures

The purpose of this paper is to introduce a new structure `primal'. Primal is dual to grill. Like ideal, dual of filter, this new structure also generates a new topology named `primal topology'. We introduce a new operator using primal, which satisfies Kuratowski's closure axioms. Mainly, we prove that primal topology is finer than the topology of a primal topological space. We provide structure of base of primal topology and prove other fundamental results related to this new structure.

Non-orthogonal multiple access (NOMA) has been a strong candidate to support massive connectivity in future wireless networks. In this regard, its implementation into cooperative relaying, named cooperative-NOMA (CNOMA), has received tremendous attention by researchers. However, most of the existing CNOMA studies have failed to address practical constraints since they assume ideal conditions. Particularly, error performance of CNOMA schemes with imperfections has not been investigated, yet. In this letter, we provide an analytical framework for error performance of CNOMA schemes under practical assumptions where we take into account imperfect successive interference canceler (SIC), imperfect channel estimation (ICSI), and hardware impairments (HWI) at the transceivers. We derive bit error rate (BER) expressions in CNOMA schemes whether the direct links between source and users exist or not which is, to the best of the authors' knowledge, the first study in the open literature. For comparisons, we also provide BER expression for downlink NOMA with practical constraints which has also not been given in literature, yet. The theoretical BER expressions are validated with computer simulations where the perfect-match is observed. Finally, we discuss the effects of the system parameters (e.g., power allocation, HWI level) on the performance of CNOMA schemes to reveal fruitful insights for the society., Comment: submitted to IEEE

Cooperative non-orthogonal multiple access (CNOMA) has recently been adapted with energy harvesting (EH) to increase energy efficiency and extend the lifetime of energy-constrained wireless networks. This paper proposes a hybrid EH protocol-assisted CNOMA, which is a combination of the two main existing EH protocols (power splitting (PS) and time switching (TS)). The end-to-end bit error rate (BER) expressions of users in the proposed scheme are obtained over Nakagami-$m$ fading channels. The proposed hybrid EH (HEH) protocol is compared with the benchmark schemes (i.e., existing EH protocols and no EH). Based on the extensive simulations, we reveal that the analytical results match perfectly with simulations which proves the correctness of the derivations. Numerical results also show that the HEH-CNOMA outperforms the benchmarks significantly. In addition, we discuss the optimum value of EH factors to minimize the error probability in HEH-CNOMA and show that an optimum value can be obtained according to channel parameters., Comment: submitted to IEEE

In academia, plagiarism is certainly not an emerging concern, but it became of a greater magnitude with the popularisation of the Internet and the ease of access to a worldwide source of content, rendering human-only intervention insufficient. Despite that, plagiarism is far from being an unaddressed problem, as computer-assisted plagiarism detection is currently an active area of research that falls within the field of Information Retrieval (IR) and Natural Language Processing (NLP). Many software solutions emerged to help fulfil this task, and this paper presents an overview of plagiarism detection systems for use in Arabic, French, and English academic and educational settings. The comparison was held between eight systems and was performed with respect to their features, usability, technical aspects, as well as their performance in detecting three levels of obfuscation from different sources: verbatim, paraphrase, and cross-language plagiarism. An indepth examination of technical forms of plagiarism was also performed in the context of this study. In addition, a survey of plagiarism typologies and classifications proposed by different authors is provided., Comment: 26 pages, 2 figures, 19 tables

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed., Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', at [https://doi.org/10.3390/math9192355]. Cite this paper as: F. Nda\"{\i}rou and D.F.M. Torres, Optimal control problems involving combined fractional operators with general analytic kernels, Mathematics 9 (2021), no. 19, Art. 2355, 17 pp

We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability of solutions of control differential equations. This allow us to obtain a weak version of Pontryagin's maximum principle. Moreover, our approach also allow us to consider mixed problems with both integer and fractional order operators and derive necessary optimality conditions for isoperimetric variational problems and other problems of the calculus of variations., Comment: This is a preprint whose final form is published by Elsevier in the book 'Fractional Order Systems and Applications in Engineering'. Submitted 10/Sept/2020; Revised 22/Nov/2020 and 18/May/2021; Accepted 05/Sept/2021

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example., Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', available in [https://doi.org/10.3390/math9161883]. Please cite this article as: F. Nda\"irou and D. F. M. Torres, Pontryagin Maximum Principle for Distributed-Order Fractional Systems, Mathematics 9 (2021), no. 16, Art. 1883, 12 pp

In October 2019, the central 28 m telescope of the H.E.S.S. experiment has been upgraded with a new camera. The camera is based on the FlashCam design which has been developed in view of a possible future implementation in the Medium-Sized Telescopes of the Cherenkov Telescope Array (CTA), with emphasis on cost and performance optimization and on reliability. The fully digital design of the trigger and readout system makes it possible to operate the camera at high event rates and to precisely adjust and understand the trigger system. The novel design of the front-end electronics achieves a dynamic range of over 3,000 photoelectrons with only one electronics readout circuit per pixel. Here we report on the performance parameters of the camera obtained during the first year of operation in the field, including operational stability and optimization of calibration algorithms., Comment: Proceedings of the 37th International Cosmic Ray Conference (ICRC 2021)

We look at the fundamental use of complex numbers in Quantum Mechanics (QM). A review of some of the most popular reasons given in the literature to support the necessity of the complex formalism, We add some insight by invoking others. This short study is aimed at strengthening the delicate pedagogical endeavor of explaining Why Quantum mechanics needs complex numbers, Comment: 10 pages