Search results for "canonical"
showing 10 items of 221 documents
Fast nosological imaging using canonical correlation analysis of brain data obtained by two-dimensional turbo spectroscopic imaging.
2007
A new fast and accurate tissue typing technique has recently been successfully applied to prostate MR spectroscopic imaging (MRSI) data. This technique is based on canonical correlation analysis (CCA), a statistical method able to simultaneously exploit the spectral and spatial information characterizing the MRSI data. Here, the performance of CCA is further investigated by using brain data obtained by two-dimensional turbo spectroscopic imaging (2DTSI) from patients affected by glioblastoma. The purpose of this study is to investigate the applicability of CCA when typing tissues of heterogeneous tumors. The performance of CCA is also compared with that of ordinary correlation analysis on s…
The overlap algebra of regular opens
2010
Abstract Overlap algebras are complete lattices enriched with an extra primitive relation, called “overlap”. The new notion of overlap relation satisfies a set of axioms intended to capture, in a positive way, the properties which hold for two elements with non-zero infimum. For each set, its powerset is an example of overlap algebra where two subsets overlap each other when their intersection is inhabited. Moreover, atomic overlap algebras are naturally isomorphic to the powerset of the set of their atoms. Overlap algebras can be seen as particular open (or overt) locales and, from a classical point of view, they essentially coincide with complete Boolean algebras. Contrary to the latter, …
A decidable word problem without equivalent canonical term rewriting system
1989
We present a weak associative single-axiom system having the following property: the word problem is decidable with an efficient algorithm even though there does not exist any finite equivalent canonical term rewriting system.
Unitary Groups Acting on Grassmannians Associated with a Quadratic Extension of Fields
2006
Let (V, H) be an anisotropic Hermitian space of finite dimension over the algebraic closure of a real closed field K. We determine the orbits of the group of isometries of (V, H) in the set of K-subspaces of V . Throughout the paper K denotes a real closed field and K its algebraic closure. Then it is well known (see, for example, [4, Chapter 2], [23]; see also [8]) that K = K(i) with i = √−1. Also we let (V,H) be an anisotropic Hermitian space (with respect to the involution underlying the quadratic field extension K/K) of finite dimension n over K. In this context we consider the natural action of the unitary group U = U(V,H) of isometries of (V,H) on the set Xd of all ddimensional K-subs…
On Rough Sets in Topological Boolean Algebras
1994
We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.
The structure of the state representation of shift invariant controllable and observable group codes
2000
AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.
The Action of the Symplectic Group Associated with a Quadratic Extension of Fields
1999
Abstract Given a quadratic extension L/K of fields and a regular alternating space (V, f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group SpL(V, f) in the set of K-subspaces of V.
The cup product of Hilbert schemes for K3 surfaces
2003
To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.
The Hamilton–Jacobi Equation
2001
We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (q i , p i ) to 2N constant values (Q i , P i ), e.g., to the 2N initial values \((q_{i}^{0},p_{i}^{0})\) at time t = 0. Then the problem would be solved, q = q(q0, p0, t), p = p(q0, p0, t).
Online Detection and Removal of Eye Blink Artifacts from Electroencephalogram
2020
The most prominent type of artifact contaminating electroencephalogram (EEG)signals are the eyeblink (EB) artifacts, which could potentially lead tomisinterpretation of the EEG signal. Online detection and removal of eyeblink artifacts from EEG signals are essential in applications such a Brain-Computer Interfaces (BCI), neurofeedback and epilepsy diagnosis. In this thesis, algorithms that combine unsupervised eyeblink artifact detection (eADA) with enhanced Empirical Mode Decomposition (FastEMD) and Canonical Correlation Analysis (CCA) are proposed,i.e. FastEMD-CCA2 and FastCCA, to automatically identify eyeblink artifacts andremove them in an online setting. FastEMD-CCA2 and FastCCA have …