This study introduces a new signal analysis method called SCSA, based on a semi-classical approach. The main idea in the SCSA is to interpret a pulse-shaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results obtained with this method on the analysis of arterial blood pressure waveforms.
Abstract. In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are spacevarying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.
Goal:
Coronavirus disease (COVID-19) is a contagious disease caused by a newly discovered coronavirus, initially identified in the mainland of China, late December 2019. COVID-19 has been confirmed as a higher infectious disease that can spread quickly in a community population depending on the number of susceptible and infected cases and also depending on their movement in the community. Since January 2020, COVID-19 has reached out to many countries worldwide, and the number of daily cases remains to increase rapidly.
Method:
Several mathematical and statistical models have been developed to understand, track, and forecast the trend of the virus spread.
Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP)
model is one of the most promising epidemiological models that has been suggested for estimating the transmissibility of the COVID-19. In the present study, we propose a fractional-order SEIQRDP model to analyze the COVID-19 pandemic. In the recent decade, it has proven that many aspects in many domains can be described very successfully using fractional order differential equations. Accordingly, the Fractional-order paradigm offers a flexible, appropriate, and reliable framework for pandemic growth characterization. In fact, due to its non-locality properties, a fractional-order operator takes into consideration the variables’ memory effect, and hence, it takes into account the sub-diffusion process of confirmed and recovered cases.
Results–
The validation of the studied fractional-order model using real COVID-19 data for different regions in China, Italy, and France show the potential of the proposed paradigm in predicting and understanding the pandemic dynamic.
Conclusions:
Fractional-order epidemiological models might play an important role in understanding and predicting the spread of the COVID-19, also providing relevant guidelines for controlling the pandemic.
This paper studies the problem of localization and tracking of a mobile target ship with an autonomous underwater vehicle (AUV). A hybrid acoustic-optical underwater communication solution is proposed, in which the acoustic link is used for the non-line-of-sight (NLoS) localization, and the optical link is for the line-of-sight (LoS) transmission. By coordinating these two complementary technologies, it is possible to overcome their respective weaknesses and achieve accurate localization, tracking, and high-rate underwater data transmission. The main challenge for reliable operation is to maintain the AUV over an optical link range while the target dynamics is unknown at all times. Hence, we design an error-based adaptive model predictive controller (MPC) and a proportional-derivative (PD) controller incorporating a real-time acoustic localization system to guide the AUV towards the sensor node mounted on the surface ship. We define a connectivity threshold cone with its apex coinciding with the sensor node such that when the underwater vehicle stays inside of this cone, a minimum bit rate is guaranteed. The localization, tracking control and optical communication scheme are validated through online simulations that integrate a realistic AUV model where the effectiveness of the proposed adaptive MPC and PD controller are demonstrated.
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