Search results for "orthogonality"
showing 10 items of 31 documents
A taxonomy for wavelet neural networks applied to nonlinear modelling
2008
This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.
Umbilicity of surfaces with orthogonal asymptotic lines in R4
2002
We study some properties of surfaces in 4-space all whose points are umbilic with respect to some normal field. In particular, we show that this condition is equivalent to the orthogonality of the (globally defined) fields of asymptotic directions. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in 4-space. 2002 Elsevier Science B.V. All rights reserved.
Transparent boundary condition for acoustic propagation in lined guide with mean flow
2008
A finite element analysis of acoustic radiation in an infinite lined guide with mean flow is studied. In order to bound the domain, transparent boundary conditions are introduced by means of a Dirichlet to Neumann (DtN) operator based on a modal decomposition. This decomposition is easy to carry out in a hard‐walled guide. With absorbant lining, many difficulties occur even without mean flow. Since the eigenvalue problem is no longer selfadjoint, acoustic modes are not orthogonal with respect to the L2‐scalar product. However, an orthogonality relation exists which permits writing the modal decomposition. For a lined guide with uniform mean flow, modes are no longer orthogonal but a new sca…
Some analytical considerations on two-scale relations
1994
Scaling functions that generate a multiresolution analysis (MRA) satisfy, among other conditions, the so-called «two-scale relation» (TSR). In this paper we discuss a number of properties that follow from the TSR alone, independently of any MRA: position of zeros (mainly for continuous scaling functions), existence theorems (using fixed point and eigenvalue arguments) and orthogonality relation between integer translates. © 1994 Società Italiana di Fisica.
Novel T-Violation observable open to any pair of decay channels at meson factories
2013
Quantum entanglement between the two neutral mesons produced in meson factories has allowed the first indisputable direct observation of Time Reversal Violation in the time evolution of the neutral meson between the two decays. The exceptional meson transitions are directly connected to semileptonic and CP eigenstate decay channels. The possibility of extending the observable asymmetries to more decay channels confronts the problem of the “orthogonality condition”, which can be stated with this tongue-twister: Given a decay channel f , which is the decay channel f′f′ such that the meson state not decaying to f′f′ is orthogonal to the meson state not decaying to f? In this Letter we propose …
Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition with Spatial Sparsity Constraint
2022
Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI dat…
Left-star order structure of Rickart *-rings
2015
Janowitz proved in 1983 that the initial segments of a Rickart *-ring with the star order are orthomodular posets. In this paper, the same result is proved for the left-star order , which was introduced by Marovtet al., by finding an orthogonality which corresponds to in a certain way and then applying a result proved by Cīrulis which states that the initial segments of any quasi-orthomodular set are orthomodular.
<strong>New tool useful for drug discovery validated through benchmark datasets</strong>
2018
Atomic Weighted Vectors (AWVs) are vectors that contain the codified information of molecular structures, which can apply to a set of Aggregation Operators (AOs) to calculate total and local molecular descriptors (MDs). This article presents an exploratory study of a new tool useful for drug discovery using different datasets, such as DRAGON and Sutherland’s datasets, as well as their comparison with other well-known approaches. In order to evaluate the performance of the tool, several statistics and QSAR/QSPR experiments were performed. Variability analyses are used to quantify the information content of the AWVs obtained from the tool, by the way of an information theory-based algorithm. …
Multiple-Output Walsh Function Generation for Minimum Orthogonality Error
1978
A hazard-free multiple-output Walsh function generator is presented which requires a minimum amount of hardware and is as fast as the integrated logic family employed for the implementation. However, the main characteristic of the instrument is the optimum performance from the viewpoint of the orthogonality of the function generated, as it is shown by the experimental verifications reported.
Decoherence in a fermion environment: Non-Markovianity and Orthogonality Catastrophe
2013
We analyze the non-Markovian character of the dynamics of an open two-level atom interacting with a gas of ultra-cold fermions. In particular, we discuss the connection between the phenomena of orthogonality catastrophe and Fermi edge singularity occurring in such a kind of environment and the memory-keeping effects which are displayed in the time evolution of the open system.