Through simulation, we show that the machine learning approach using the averaged PSD sequence as training data outperforms the other machine learning approach using the channel frequency response (CFR) sequence as training data and two other existing Doppler estimation approaches. We detail intermediate mathematical derivatives of the machine learning process, making it easy to graft the derived results into other wireless communication technologies. When preprocessing the channel state information (CSI) collected under the mixed-channel scenario, we propose averaged power spectral density (PSD) sequence as high-quality training data in machine learning for Doppler spread estimation. We present a carefully designed neural network architecture to achieve good performance in a mixed-channel scenario in which channel characteristic variables such as Rician K factor, azimuth angle of arrival (AOA) width, mean direction of azimuth AOA, and channel estimation errors are randomly generated. In this paper, we propose a Doppler spread estimation approach based on machine learning for an OFDM system. We proposed a Population Balance Equations (PBE)-based model and derived a conceptually new and computationally tractable numerical approach for its solution in order to provide a systematic tool for a morphology prediction in composite polymers.įinally, we designed a stochastic simulation framework for continuous measurements performed on quantum systems of theoretical and experimental interest, which helped us to re-examine the “fuzzy continuous measurements” theory by Audretsch and Mensky (1997) and expose some of its deficiencies, while making amendments where necessary.Īll developed modelling approaches are general enough to be applied to the broad range of physical applications and thus ultimately to contribute to the understanding and prediction of complex chemical and physical processes. The efficient stochastic simulation (SS) approach allowing for an accurate description of CRP has been formulated, theoretically grounded and tested using experimental data and the less advanced SS algorithms.Īn accurate prediction of a morphology development in multi-phase polymers is vital for synthesis of new materials but still not feasible due to its complexity. The question, “Why kinetic models cannot reproduce experimental observations in Controlled Radical Polymerization (CRP)?” has been answered by introducing in the kinetic model a delay and treating CRP as a non-Markovian process. In this study, we developed the mathematical tools for solving three long-standing problems in Polymer Science and Quantum Measurement theory. While probabilistic modelling has been widely used in the last decades, the quantitative prediction in stochastic modelling of real physical problems remains a great challenge and requires sophisticated mathematical models and advanced numerical algorithms. Finally, an argument is presented for the creation of a framework for a historical heuristics for mathematics education, possibly beyond the bounds of semiotics. Our example illustrates the semiotic deformations alluded by (Fried, 2008), and points out a possible explanation of how this may lead to unrealistic pedagogical expectations for student performance. In this exposition, an example related to an application of the history of the chain rule to the didactics of calculus is presented. The description in (Fried, 2008), is presented in the parlance of Sausserian Semiotics and identifies two semiotic “deformations” that arise when one fails to observe that the pairing between signs and meanings in a given synchronic “cross-section” associated with the development of mathematics need not hold for another synchronic cross section at a different time. 193) describes a pair of specific pitfalls that can arise in implementing such historical applications in mathematics education. Besides the widespread feeling that the introduction of didactic elements taken from the history of mathematics can detract the pedagogy of mathematics from the attainment of important goals, (Fried, 2008, p. According to (Fried, 2008), there is an intrinsic tension in trying to apply the history of mathematics to its didactics.
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