Search results for "Linear Algebra."
showing 10 items of 552 documents
Discrete-mathematical approach to formal description of measurement procedure
1996
The discrete-mathematical model of measurement procedure is developed for facilitating the description of measurements in both quantitative and qualitative scales. On the basis of this model the Measurement Problem is formulated. It is shown that the problem can be considered, in the general case, as one of the discrete optimization problems. The suggested approach brings closer the concepts of a computing algorithm and measurement procedure so that it permits the application of similar tools for the analysis and development of both of them.
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
A Survey on Gaussian Processes for Earth-Observation Data Analysis: A Comprehensive Investigation
2016
Gaussian processes (GPs) have experienced tremendous success in biogeophysical parameter retrieval in the last few years. GPs constitute a solid Bayesian framework to consistently formulate many function approximation problems. This article reviews the main theoretical GP developments in the field, considering new algorithms that respect signal and noise characteristics, extract knowledge via automatic relevance kernels to yield feature rankings automatically, and allow applicability of associated uncertainty intervals to transport GP models in space and time that can be used to uncover causal relations between variables and can encode physically meaningful prior knowledge via radiative tra…
Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data
2020
Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we pro…
Weak versus strong dominance of shrinkage estimators
2021
We consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its eigenvalues. We prove that there are only two distinct eigenvalues and apply our findings to the James–Stein and the Thompson class of estimators. It turns out that the famous Stein paradox is no longer a paradox when we consider the whole mean squared error matrix rather than only its trace.
The measurement of rank mobility
2009
Abstract In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly represent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard (“global”) matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known “concordance” ordering. We then provide a characterization of an index of rank mobility based on partial matrices and show that, in the standard case of comparing global matrices, it is equi…
Optimization of a Sea Wave Energy Harvesting Electromagnetic Device
2008
This paper presents the optimization of a permanent magnet linear generator directly coupled to sea waves. In order to maximize energy extraction, the stochastic features of the energy source is included in the mathematical model of the system in order to satisfactorily tackle the problem. An optimization procedure which includes the stochastic features of the model is presented and a machine built on the basis of the results of this procedure is shown.
Computational modeling of isotropic electron paramagnetic resonance spectra of doublet state main group radicals
2007
The combined use of theoretical and mathematical methods in the analysis of electron paramagnetic resonance data has greatly increased the ability to interpret even the most complex spectra reported for doublet state inorganic main group radicals. This personal account summarizes the theoretical basis of such an approach and provides an in-depth discussion of some recent illustrative examples of the utilization of this methodology in practical applications. The emphasis is on displaying the enormous potential embodied within the approach. peerReviewed
Structural Health Monitoring Procedure for Composite Structures through the use of Artificial Neural Networks
2015
In this paper different architectures of Artificial Neural Networks (ANNs) for structural damage detection are studied. The main objective is to investigate an ANN able to detect and localize damage without any prior knowledge on its characteristics so as to serve as a real-time data processor for Structural Health Monitoring (SHM) systems. Two different architectures are studied: the standard feed-forward Multi Layer Perceptron (MLP) and the Radial Basis Function (RBF) ANNs. The training data are given, in terms of a Damage Index ℑD, properly defined using a piezoelectric sensor signal output to obtain suitable information on the damage position and dimensions. The electromechanical respon…
A semi-empirical multipurpose steady-state model of a fuel cell for household appliances
2013
In this paper, a multipurpose model of a proton exchange membrane fuel cell for household appliances is proposed. According to a conventional mathematical approach, the proposed model is derived from the physical and electro-chemical equations that rule the fuel cell behaviour. Differently from existing models, a parametric analysis is carried out and a few tunable parameters are accurately selected and identified. Furthermore, this paper proposes an innovative technique of unique model architecture which enables the designer to solve by himself the trade-off between complexity and accuracy on the basis of the specific applications. Three different choices could be performed by the designer…