Algorithmic Solution for Systems of Linear Equations, in O(mn)\mathcal{O}(mn) time

We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial, because, for each iteration, only one dimension of the given input matrix $\mathbf X$ is utilized. The execution time is very short compared with state-of-the-art methods, exhibiting $> \times 10^2$ speed-up and low memory allocation demands, especially for non-square Systems of Linear Equations, with ratio of equations versus features high (tall systems), or low (wide systems) accordingly. The accuracy is high and straightforwardly controlled, and the numerical results highlight the efficiency of the proposed algorithm, in terms of computation time, solution accuracy and memory demands. The paper also comprises a theoretical proof for the algorithmic convergence, and we extend the implementation of the proposed algorithmic rationale to feature selection tasks

An artificial intelligence algorithm analyzing 30 years of research in mass appraisals

The research papers issued in scientific journals, for a variety of thematic areas, are not only increasing, nonetheless exhibit an exponential growth over the last years. Accordingly, the researchers, struggle to retrieve information apropos of novel knowledge and get informed in their field, while the rigor and at the same time, the extensive composition of surveys, reviews, and overviews of research works, has become difficult or even impossible, as the number of the available research studies is enormous. However, such reviews, contain vital information regarding the evolution of a scientific subject, the trends of the literature, the most significant concepts, and the concealed associations among research papers, their references, as well as authors’ clusters. In this work, a scientometric study of the relevant to Mass Appraisals literature is for a first time accomplished, regarding the numerical models, computational procedures, and automated methods, utilized in the Mass Appraisals and Property Valuations literature. The study is based on an adequate pool of papers, constituted in Scopus database, utilizing a machine learning algorithm developed from one of the authors, for multidimensional scaling and clustering of the keywords found in the papers’ database, the authors and their cooperation and the co-occurrences of the references in the papers studied. The time-series of the most frequent keywords are also computed, demonstrating the evolution of the mass appraisals research and identifying future trends

A geometric interpretation of zonostrophic instability

The zonostrophic instability that leads to the emergence of zonal jets in barotropic beta-plane turbulence was analyzed through a geometric decomposition of the eddy stress tensor. The stress tensor is visualized by an eddy variance ellipse whose characteristics are related to eddy properties. The tilt of the ellipse principal axis is the tilt of the eddies with respect to the shear, the eccentricity of the ellipse is related to the eddy anisotropy, while its size is related to the eddy kinetic energy. Changes of these characteristics are directly related to the vorticity fluxes forcing the mean flow. The statistical state dynamics of the turbulent flow closed at second order was employed as it provides an analytic expression for both the zonostrophic instability and the stress tensor. For the linear phase of the instability, the stress tensor was analytically calculated at the stability boundary. For the non--linear equilibration of the instability the tensor was calculated in the limit of small supercriticality in which the amplitude of the jet velocity follows Ginzburg--Landau dynamics. It is found that dependent on the characteristics of the forcing, the jet is accelerated either because it primarily anisotropizes the eddies so as to produce upgradient fluxes or because it changes the eddy tilt. The instability equilibrates as these changes are partially reversed by the non--linear terms. Parameterizations of the ellipse characteristics are also discussed

Statistical state dynamics of weak jets in barotropic beta-plane turbulence

Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability') which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.Comment: 27 pages, 17 figure