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Function approximation is a fundamental process in a variety of problems in computational mechanics, structural engineering, as well as other domains that require the precise approximation of a phenomenon with an analytic function. This work demonstrates a unified approach to these techniques, utilizing partial sums of the Taylor series in a high arithmetic precision. In particular, the proposed approach is capable of interpolation, extrapolation, numerical differentiation, numerical integration, solution of ordinary and partial differential equations, and system identification. The method employs Taylor polynomials and hundreds of digits in the computations to obtain precise results. Interestingly, some well-known problems are found to arise in the calculation accuracy and not methodological inefficiencies, as would be expected. In particular, the approximation errors are precisely predictable, the Runge phenomenon is eliminated, and the extrapolation extent may a priory be anticipated. The attained polynomials offer a precise representation of the unknown system as well as its radius of convergence, which provides a rigorous estimation of the prediction ability. The approximation errors are comprehensively analyzed for a variety of calculation digits and test problems and can be reproduced by the provided computer code. [ABSTRACT FROM AUTHOR]

Featured Application: The proposed optimization method is a general tool which can have numerous applications in various mathematical, engineering and technological fields. Due to its simplicity and straight-forward implementation, it can easily be applied by non-experts to obtain optimized results. A new, fast, elegant, and simple stochastic optimization search method is proposed, which exhibits surprisingly good performance and robustness considering its simplicity. We name the algorithm pure random orthogonal search (PROS). The method does not use any assumptions, does not have any parameters to adjust, and uses basic calculations to evolve a single candidate solution. The idea is that a single decision variable is randomly changed at every iteration and the candidate solution is updated only when an improvement is observed; therefore, moving orthogonally towards the optimal solution. Due to its simplicity, PROS can be easily implemented with basic programming skills and any non-expert in optimization can use it to solve problems and start exploring the fascinating optimization world. In the present work, PROS is explained in detail and is used to optimize 12 multi-dimensional test functions with various levels of complexity. The performance is compared with the pure random search strategy and other three well-established algorithms: genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE). The results indicate that, despite its simplicity, the proposed PROS method exhibits very good performance with fast convergence rates and quick execution time. The method can serve as a simple alternative to established and more complex optimizers. Additionally, it could also be used as a benchmark for other metaheuristic optimization algorithms as one of the simplest, yet powerful, optimizers. The algorithm is provided with its full source code in MATLAB for anybody interested to use, test or explore. [ABSTRACT FROM AUTHOR]

In this review paper, we computationally analyze a vast volume of published articles in the field of Adaptive Learning, as obtained by the Scopus Database. Particularly, we use a query with search terms targeting the area of Adaptive Learning Systems by utilizing a combination of specific keywords. Accordingly, we apply a multidimensional scaling algorithm to construct bibliometric maps for keywords, authors, and references. Subsequently, we present the computational results for the studied dataset, reveal significant patterns appearing in the field of adaptive learning and the inter-item associations, and interpret the findings based on the current state-of-the-art literature in the area. Furthermore, we demonstrate the time-series of the evolution of the research terms, their trends over time, as well as their prevalent statistical associations. [ABSTRACT FROM AUTHOR]

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes. [ABSTRACT FROM AUTHOR]

In this study, a climatology of two key boundary layer features, the Planetary Boundary Layer Height (PBLH) and the wind field over Greece is derived. The climatology is based on daily soundings collected in Athens, Thessaloniki and Heraklion and spanning a 32-year period. The PBLH is estimated using a method based on the gradient of potential temperature and a method based on the bulk Richardson number. The wind field is analyzed by calculating the wind shear and the turning angle of the wind vector between the surface and the top of the boundary layer. The PBLH of the daytime boundary layer over Athens and Thessaloniki is found to exhibit seasonal variability with summer maxima and winter minima and has annual median values in the range of 1.4–1.7 km estimated using the gradient method. The PBLH over Heraklion is found to exhibit weak seasonal variability with a lower median value of 1.2 km. The nighttime boundary layer over all three sites is found to be much shallower with PBLH values in the range of 150–200 m with no seasonal variations. In addition, the bulk Richardson number method is found to systematically underestimate the PBLH compared to the gradient method. The wind field in the daytime boundary layer at all three sites is found to have small shear of the order of 1 ms − 1 and wind turning angles that are lower than 15 degrees, while in the nocturnal boundary layer it has larger shear of the order of 5–10 ms − 1 with turning angles lower than 20 degrees. In addition, for both the daytime and the nighttime boundary layer there is no general preference for veering or backing. [ABSTRACT FROM AUTHOR]

A recent study of property valuation literature indicated that the vast majority of researchers and academics in the field of real estate are focusing on Mass Appraisals rather than on the further development of the existing valuation methods. Researchers are using a variety of mathematical models used within the field of Machine Learning, which are applied to real estate valuations with high accuracy. On the other hand, it appears that professional valuers do not use these sophisticated models during daily practice, rather they operate using the traditional five methods. The Department of Lands and Surveys in Cyprus recently published the property values (General Valuation) for taxation purposes which were calculated by applying a hybrid model based on the Cost approach with the use of regression analysis in order to quantify the specific parameters of each property. In this paper, the authors propose a number of algorithms based on Artificial Intelligence and Machine Learning approaches that improve the accuracy of these results significantly. The aim of this work is to investigate the capabilities of such models and how they can be used for the mass appraisal of properties, to highlight the importance of sensitivity analysis in such models and also to increase the transparency so that automated valuation models (AVM) can be used for the day-to-day work of the valuer. [ABSTRACT FROM AUTHOR]