Search results for "Linear map"
showing 8 items of 68 documents
ERP denoising in multichannel EEG data using contrasts between signal and noise subspaces
2009
Abstract In this paper, a new method intended for ERP denoising in multichannel EEG data is discussed. The denoising is done by separating ERP/noise subspaces in multidimensional EEG data by a linear transformation and the following dimension reduction by ignoring noise components during inverse transformation. The separation matrix is found based on the assumption that ERP sources are deterministic for all repetitions of the same type of stimulus within the experiment, while the other noise sources do not obey the determinancy property. A detailed derivation of the technique is given together with the analysis of the results of its application to a real high-density EEG data set. The inter…
Some Non-linear Geometrical Properties of Banach Spaces
2014
In this survey we report on very recent results about some non-linear geometrical properties of many classes of real and complex Banach spaces and uniform algebras, including the ball algebra \(\fancyscript{A}_u(B_X)\) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space \(X\). These geometrical properties are: Polynomial numerical index, Polynomial Daugavet property and Bishop-Phelp-Bollobas property for multilinear mappings.
Multilinear Fourier multipliers related to time–frequency localization
2013
We consider multilinear multipliers associated in a natural way with localization operators. Boundedness and compactness results are obtained. In particular, we get a geometric condition on a subset A⊂R2d which guarantees that, for a fixed synthesis window ψ∈L2(Rd), the family of localization operators Lφ,ψA obtained when the analysis window φ varies on the unit ball of L2(Rd) is a relatively compact set of compact operators.
p-VARIATION OF VECTOR MEASURES WITH RESPECT TO BILINEAR MAPS
2008
AbstractWe introduce the spaces Vℬp(X) (respectively 𝒱ℬp(X)) of the vector measures ℱ:Σ→X of bounded (p,ℬ)-variation (respectively of bounded (p,ℬ)-semivariation) with respect to a bounded bilinear map ℬ:X×Y →Z and show that the spaces Lℬp(X) consisting of functions which are p-integrable with respect to ℬ, defined in by Blasco and Calabuig [‘Vector-valued functions integrable with respect to bilinear maps’, Taiwanese Math. J. to appear], are isometrically embedded in Vℬp(X). We characterize 𝒱ℬp(X) in terms of bilinear maps from Lp′×Y into Z and Vℬp(X) as a subspace of operators from Lp′(Z*) into Y*. Also we define the notion of cone absolutely summing bilinear maps in order to describe t…
QSPR with descriptors based on averages of vertex invariants. An artificial neural network study
2014
New type of indices, the mean molecular connectivity indices (MMCI), based on nine different concepts of mean are proposed to model, together with molecular connectivity indices (MCI), experimental parameters and random variables, eleven properties of organic solvents. Two model methodologies are used to test the different descriptors: the multilinear least-squares (MLS) methodology and the Artificial Neural Network (ANN) methodology. The top three quantitative structure–property relationships (QSPR) for each property are chosen with the MLS method. The indices of these three QSPRs were used to train the ANNs that selected the best training sets of indices to estimate the evaluation sets of…
On the algebraic types of the Bel–Robinson tensor
2008
The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov-Bel types and the additional ones are intrinsically characterized in terms of the sole Bel-Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.
Input-to-State Stability of Lur’e Hyperbolic Distributed Complex-Valued Parameter Control Systems: LOI Approach
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/364057 Open access In this work, input-to-state stability of Lur'e hyperbolic distributed complex-valued parameter control systems has been addressed. Using comparison principle, delay-dependent sufficient conditions for the input-to-state stability in complex Hilbert spaces are established in terms of linear operator inequalities. Finally, numerical computation illustrates our result.
Exploiting ongoing EEG with multilinear partial least squares during free-listening to music
2016
During real-world experiences, determining the stimulus-relevant brain activity is excitingly attractive and is very challenging, particularly in electroencephalography. Here, spectrograms of ongoing electroencephalogram (EEG) of one participant constructed a third-order tensor with three factors of time, frequency and space; and the stimulus data consisting of acoustical features derived from the naturalistic and continuous music formulated a matrix with two factors of time and the number of features. Thus, the multilinear partial least squares (PLS) conforming to the canonical polyadic (CP) model was performed on the tensor and the matrix for decomposing the ongoing EEG. Consequently, we …