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The purpose of this letter is to investigate the time complexity consequences of the truncated Taylor series, known as Taylor Polynomials \cite{bakas2019taylor,Katsoprinakis2011,Nestoridis2011}. In particular, it is demonstrated that the examination of the $\mathbf{P=NP}$ equality, is associated with the determination of whether the $n^{th}$ derivative of a particular solution is bounded or not. Accordingly, in some cases, this is not true, and hence in general.

We present a numerical scheme for computation of Artificial Neural Networks (ANN) weights, which stems from the Universal Approximation Theorem, avoiding laborious iterations. The proposed algorithm adheres to the underlying theory, is highly fast, and results in remarkably low errors when applied for regression and classification of complex data-sets, such as the Griewank function of multiple variables $\mathbf{x} \in \mathbb{R}^{100}$ with random noise addition, and MNIST database for handwritten digits recognition, with $7\times10^4$ images. The same mathematical formulation is found capable of approximating highly nonlinear functions in multiple dimensions, with low errors (e.g. $10^{-10}$) for the test-set of the unknown functions, their higher-order partial derivatives, as well as numerically solving Partial Differential Equations. The method is based on the calculation of the weights of each neuron in small neighborhoods of the data, such that the corresponding local approximation matrix is invertible. Accordingly, optimization of hyperparameters is not necessary, as the number of neurons stems directly from the dimensionality of the data, further improving the algorithmic speed. Under this setting, overfitting is inherently avoided, and the results are interpretable and reproducible. The complexity of the proposed algorithm is of class P with $\mathcal{O}(mn^2)+\mathcal{O}(\frac{m^3}{n^2})-\mathcal{O}(\log(n+1))$ computing time, with respect to the observations $m$ and features $n$, in contrast with the NP-Complete class of standard algorithms for ANN training. The performance of the method is high, irrespective of the size of the dataset, and the test-set errors are similar or smaller than the training errors, indicating the generalization efficiency of the algorithm.

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., RELAND: International Journal of Real Estate & Land Planning, Vol 2 (2019)

Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is demonstrated, by utilizing partial sums of Taylor series in high arithmetic precision. In particular, the proposed method is capable of interpolation, extrapolation, numerical differentiation, numerical integration, solution of ordinary and partial differential equations, and system identification. The method is based on the utilization of Taylor polynomials, by exploiting some hundreds of computer digits, resulting in highly accurate calculations. Interestingly, some well-known problems were found to reason by calculations accuracy, and not methodological inefficiencies, as supposed. 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 provide a rigor estimation of the prediction ability. The approximation errors have comprehensively been analyzed, for a variety of calculation digits and test problems.

Excluded articles. List of articles excluded with reasons for exclusion. (DOCX 54Â kb)

Planetary turbulence is observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models that retains the relevant dynamics of turbulent self-organization is a barotropic flow in a beta-plane channel with turbulence sustained by random stirring. Non-linear integrations of this model show that as the energy input rate of the forcing is increased, the homogeneity of the flow is first broken by the emergence of non-zonal, coherent, westward propagating structures and at larger energy input rates by the emergence of zonal jets. The emergence of both non-zonal coherent structures and zonal jets is studied using a statistical theory, Stochastic Structural Stability Theory (S3T). S3T directly models a second-order approximation to the statistical mean turbulent state and allows the identification of statistical turbulent equilibria and study of their stability. Using S3T, the bifurcation properties of the homogeneous state in barotropic beta-plane turbulence are determined. Analytic expressions for the zonal and non-zonal large-scale coherent flows that emerge as a result of structural instability are obtained and the equilibration of the incipient instabilities is studied through numerical integrations of the S3T dynamical system. The dynamics underlying the formation of zonal jets are also investigated. It is shown that zonal jets form from the upgradient momentum fluxes that result from the shearing of the eddies by the emerging infinitesimal large-scale flow. Finally, numerical simulations of the nonlinear equations confirm the characteristics (scale, amplitude and phase speed) of the structures predicted by S3T, even in highly non-linear parameter regimes such as the regime of zonostrophic turbulence., Comment: 17 pages, 14 figures, submitted to "Zonal jets" by Galperin B. and Read, P.L. (eds.). arXiv admin note: substantial text overlap with arXiv:1303.6435

Planetary and magnetohydrodynamic drift-wave turbulence is observed to self-organize into large scale structures such as zonal jets and coherent vortices. In this Letter we present a non-equilibrium statistical theory, the Stochastic Structural Stability theory (SSST), that can make predictions for the formation and finite amplitude equilibration of non-zonal and zonal structures (lattice and stripe patterns) in homogeneous turbulence. This theory reveals that the emergence of large scale structure is the result of an instability of the interaction between the coherent flow and the associated turbulent field. Comparison of the theory with nonlinear simulations of a barotropic flow in a beta-plane channel with turbulence sustained by isotropic random stirring, demonstrates that SSST predicts the threshold parameters at which the coherent structures emerge as well as the characteristics of the emerging structures (scale, amplitude, phase speed). It is shown that non-zonal structures (lattice states or zonons) emerge at lower energy input rates of the stirring compared to zonal flows (stripe states) and their emergence affects the dynamics of jet formation., 5 pages, 5 figures

281 σ., Στην παρούσα διατριβή, αξιολογήθηκε η επιρροή των μεγάλων εκκεντροτήτων των κέντρων ακαμψίας και αντοχής σε σχέση με το κέντρο μάζας όσον αφορά τη σεισμική απόκριση των κτηρίων. Οι διάφορες διατυπώσεις βέλτιστου σχεδιασμού αξιολογούνται ως προς την ελάχιστη στρεπτική απόκριση σε τρία επίπεδα επικινδυνότητας και ως προς το συνολικό κόστος κύκλου της ζωής. Έχει εφαρμοστεί ένας εξελικτικός αλγόριθμος βελτιστοποίησης για τη λύση των προβλημάτων βελτιστοποίησης. Η συμβολή καθώς και τα κύρια συμπεράσματα είναι: α) Ανάπτυξη μεθοδολογίας βέλτιστου σχεδιασμού γενικών τριδιάστατων κτηρίων με μεταβλητές τοπολογίας και μεγέθους. β) Ανάπτυξη λογισμικού εφαρμογής της μεθοδολογίας βέλτιστου σχεδιασμού συμπεριλαμβανομένων των κανονισμών και μη γραμμικής δυναμικής ανάλυσης με αντικειμενικές συναρτήσεις τα επιμέρους κριτήρια στρεπτικής συμπεριφοράς. και γ) Οι σχεδιασμοί με βάση το ROT (που προτείνεται μέσα από την παρούσα διατριβή), δίνουν καλύτερα αποτελέσματα σε γενικούς κτηριακούς φορείς τόσο στην ελαστική όσο και στην ανελαστική περιοχή με αξιολόγηση παραμορφώσεων και στρεπτικών ροπών βάσης κατά Chopra., In the present study, the influence of large eccentricity of the centers of stiffness and strength relative to the center of mass for the seismic response of buildings are investigated. The optimal design of various formulations evaluated for minimum torsional response at three hazard levels and to the total life cycle costs. It was verified for multi-storey buildings with irregularity in plan that the rigidity center eccentricity is important mainly when the structural system behaves linearly, while for nonlinear behavior the strength’s center eccentricity becomes more important. An evolutionary optimization algorithm to solve optimization problems has been used. The contribution and the main conclusions are: a) Developing an optimal design methodology for general three-dimensional buildings with topology and size variables. b) Software development of the optimal design methodology including regulations and nonlinear dynamic analysis with objective functions of the individual criteria torsional behavior. and c) designs based on ROT (proposed in the present study) gives better results in general building both in the elastic and inelastic stage in the assessment of deformations and torsional moments at base.

281 σ., Στην παρούσα διατριβή, αξιολογήθηκε η επιρροή των μεγάλων εκκεντροτήτων των κέντρων ακαμψίας και αντοχής σε σχέση με το κέντρο μάζας όσον αφορά τη σεισμική απόκριση των κτηρίων. Οι διάφορες διατυπώσεις βέλτιστου σχεδιασμού αξιολογούνται ως προς την ελάχιστη στρεπτική απόκριση σε τρία επίπεδα επικινδυνότητας και ως προς το συνολικό κόστος κύκλου της ζωής. Έχει εφαρμοστεί ένας εξελικτικός αλγόριθμος βελτιστοποίησης για τη λύση των προβλημάτων βελτιστοποίησης. Η συμβολή καθώς και τα κύρια συμπεράσματα είναι: α) Ανάπτυξη μεθοδολογίας βέλτιστου σχεδιασμού γενικών τριδιάστατων κτηρίων με μεταβλητές τοπολογίας και μεγέθους. β) Ανάπτυξη λογισμικού εφαρμογής της μεθοδολογίας βέλτιστου σχεδιασμού συμπεριλαμβανομένων των κανονισμών και μη γραμμικής δυναμικής ανάλυσης με αντικειμενικές συναρτήσεις τα επιμέρους κριτήρια στρεπτικής συμπεριφοράς. και γ) Οι σχεδιασμοί με βάση το ROT (που προτείνεται μέσα από την παρούσα διατριβή), δίνουν καλύτερα αποτελέσματα σε γενικούς κτηριακούς φορείς τόσο στην ελαστική όσο και στην ανελαστική περιοχή με αξιολόγηση παραμορφώσεων και στρεπτικών ροπών βάσης κατά Chopra., In the present study, the influence of large eccentricity of the centers of stiffness and strength relative to the center of mass for the seismic response of buildings are investigated. The optimal design of various formulations evaluated for minimum torsional response at three hazard levels and to the total life cycle costs. It was verified for multi-storey buildings with irregularity in plan that the rigidity center eccentricity is important mainly when the structural system behaves linearly, while for nonlinear behavior the strength’s center eccentricity becomes more important. An evolutionary optimization algorithm to solve optimization problems has been used. The contribution and the main conclusions are: a) Developing an optimal design methodology for general three-dimensional buildings with topology and size variables. b) Software development of the optimal design methodology including regulations and nonlinear dynamic analysis with objective functions of the individual criteria torsional behavior. and c) designs based on ROT (proposed in the present study) gives better results in general building both in the elastic and inelastic stage in the assessment of deformations and torsional moments at base., Νικόαλος Π. Μπάκας

The role of nonnormality in the overreflection of gravity waves is investigated. In the limit of weak stratification, wave packets having a critical level inside a shear layer of finite depth are reflected with amplified energy. This process, which exhibits the characteristics of stimulated emission, occurs in three stages: first, the incoming wave enters the shear layer and excites nonpropagating perturbations leaning with and against the shear. Subsequently, the energy of perturbations leaning against the shear grows in a manner similar to energy growth of perturbations in constant shear flows, indicating that the Orr mechanism that is slightly modified by stratification underlies the observed growth. Finally, the amplified perturbations excite propagating waves originating from the vicinity of the shear layer boundary. The role of nonnormality in this process is also investigated from the perspective of the associated nonorthogonality of the modes of the dynamical system. It is found that the incident wave packet projects on nonorthogonal analytic modes having the structure of a downward propagating wave in the far field below the shear layer and overreflection expressed by the interaction among these nonorthogonal modes.

Included articles. List of articles included in this study. (DOCX 61Â kb)

Systematic review definitions. Definitions of systematic reviews published in the literature. (DOCX 14Â kb)

Systematic review definitions. Definitions of systematic reviews published in the literature. (DOCX 14Â kb)

Included articles. List of articles included in this study. (DOCX 61Â kb)