Search results for "A priori and a posteriori"
showing 10 items of 119 documents
Guaranteed error bounds and local indicators for adaptive solvers using stabilised space–time IgA approximations to parabolic problems
2019
Abstract The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Further…
Neural networks with non-uniform embedding and explicit validation phase to assess Granger causality
2015
A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of assumptions in modeling the relevant features of the data. We tried to overcome those pitfalls using a neural network approach in which a model is built without any a priori assumptions. In this sense this method can be seen as a bridge between model-free and model-based approaches. The experiments perfo…
Artificial organisms as tools for the development of psychological theory: Tolman's lesson
2007
In the 1930s and 1940s, Edward Tolman developed a psychological theory of spatial orientation in rats and humans. He expressed his theory as an automaton (the ‘‘schematic sowbug’’) or what today we would call an ‘‘artificial organism.’’ With the technology of the day, he could not implement his model. Nonetheless, he used it to develop empirical predictions which tested with animals in the laboratory. This way of proceeding was in line with scientific practice dating back to Galileo. The way psychologists use artificial organisms in their work today breaks with this tradition. Modern ‘‘artificial organisms’’ are constructed a posteriori, working from experimental or ethological observations…
A Posteriori Error Bounds for Approximations of the Oseen Problem and Applications to the Uzawa Iteration Algorithm
2014
Abstract. We derive computable bounds of deviations from the exact solution of the stationary Oseen problem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an advanced form of the estimate, which takes into account approximation errors arising due to discretization of the boundary value problem, generated by the main step of the Uzawa method. Numerical tests confirm our theoretical results and show practical applicability of the estimates.
Perceptual adaptive insensitivity for support vector machine image coding.
2005
Support vector machine (SVM) learning has been recently proposed for image compression in the frequency domain using a constant epsilon-insensitivity zone by Robinson and Kecman. However, according to the statistical properties of natural images and the properties of human perception, a constant insensitivity makes sense in the spatial domain but it is certainly not a good option in a frequency domain. In fact, in their approach, they made a fixed low-pass assumption as the number of discrete cosine transform (DCT) coefficients to be used in the training was limited. This paper extends the work of Robinson and Kecman by proposing the use of adaptive insensitivity SVMs [2] for image coding u…
Mesh-adaptive methods for viscous flow problem with rotation
2007
In this paper, new functional type a posteriori error estimates for the viscous flow problem with rotating term are presented. The estimates give guaranteed upper bounds of the energy norm of the error and provide reliable error indication. We describe the implementation of the adaptive finite element methods (AFEM) in the framework of the functional type estimates proposed. Computational properties of the estimates are investigated on series of numerical examples.
Advances in the statistical methodology for the selection of image descriptors for visual pattern representation and classification
1995
Recent advances in the statistical methodology for selecting optimal subsets of features (image descriptors) for visual pattern representation and classification are presented. The paper attempts to provide a guideline about which approach to choose with respect to the a priori knowledge of the problem. Two basic approaches are reviewed and the conditions under which they should be used are specified. References to more detailed material about each one of the methods are given and experimental results supporting the main conclusions are briefly outlined.
Realistic Implementation of the Particle Model for the Visualization of Nanoparticle Precipitation and Growth
2019
An application for visualizing the aggregation of structureless atoms is presented. The application allows us to demonstrate on a qualitative basis, as well as by quantitatively monitoring the aggregate surface/volume ratio, that the enhanced reactivity of nanoparticles can be connected with their large specific surface. It is suggested that, along with the use of geometric analogies, this bottom-up approach can be effective in discussing the enhanced reactivity proprieties of nanoparticles. The application is based on a two-dimensional realistic dynamic model where atoms move because of their thermal and interaction potential energies, and the trajectories are determined by solving numeric…
Abstraction of covariations in incidental learning and covariation bias
1997
Experiment 1 was devised to distinguish, in a given set of features composing drawn robots, those whose variations were related a priori for participants from those whose variations were a priori independent. In Expt 2, correlations were experimentally induced between a priori-related features for one group of participants (pre-primed group), and between a priori-independent features for another group {arbitrary group), in incidental learning conditions. A subsequent transfer phase revealed that participants' performances were sensitive to experimentally induced correlations in both groups. However, only the performances of the pre-primed group accurately matched the predictions of a statis…
Guaranteed Error Bounds for Conforming Approximations of a Maxwell Type Problem
2009
This paper is concerned with computable error estimates for approximations to a boundary-value problem $$\mathrm{curl}\ {\mu }^{-1}\mathrm{curl}\ u + {\kappa }^{2}u = j\quad \textrm{ in }\Omega ,$$ where μ > 0 and κ are bounded functions. We derive a posteriori error estimates valid for any conforming approximations of the considered problems. For this purpose, we apply a new approach that is based on certain transformations of the basic integral identity. The consistency of the derived a posteriori error estimates is proved and the corresponding computational strategies are discussed.