Search results for "Linear Algebra"
showing 10 items of 552 documents
Trace Identities on Diagonal Matrix Algebras
2020
Let Dn be the algebra of n × n diagonal matrices. On such an algebra it is possible to define very many trace functions. The purpose of this paper is to present several results concerning trace identities satisfied by this kind of algebras.
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.
Possible extensions of the noncommutative integral
2011
In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.
Determinant Bundles over Grassmannians
1989
Denoting by H the Hilbert space of square-integrable Dirac spinor fields on a manifold M, transforming according to a unitary representation p of a gauge group G, we have a linear representation of the group g of gauge transformations in the space H. If ρ is faithful we can consider g as a subgroup of the general linear group GL(H). By constructing representations of GL(H) we automatically obtain representations of g. It turns out that in the case when the dimension d of M is odd, g is contained in a smaller group GLp ⊂ GL(H) which has the property that it perturbs the subspace H+ ⊂ H consisting of eigenvectors of a Dirac operator belonging to positive eigenvalues, by an operator A for whic…
Prediction of Highly Non-stationary Time Series Using Higher-Order Neural Units
2017
Adaptive predictive models can use conventional and nonconventional neural networks for highly non-stationary time series prediction. However, conventional neural networks present a series of known drawbacks. This paper presents a brief discussion about this concern as well as how the basis of higher-order neural units can overcome some of them; it also describes a sliding window technique alongside the batch optimization technique for capturing the dynamics of non-stationary time series over a Quadratic Neural Unit, a special case of higher-order neural units. Finally, an experimental analysis is presented to demonstrate the effectiveness of the proposed approach.
Why benchmark-quality computations are needed to reproduce 1-adamantyl cation NMR chemical shifts accurately.
2011
While the experimental (1)H NMR chemical shiftsof the 1-adamantyl cation can be computed within reasonably small error bounds, the usual Hartree-Fock and density functional quantum-chemical computations, as well as those based on rather elaborate second-order Møller-Plesset perturbation theory, fail to reproduce its experimental (13)C NMR chemical shifts satisfactorily. This also is true even if the NMR shielding calculations treat electron correlation adequately by the coupled-cluster singles and doubles model augmented by a perturbative correction for triple excitations (i.e., at the CCSD(T) level) with quadruple-ζ basis sets. We demonstrate that good agreement can be achieved if highly a…
A method for extracting subspace of deterministic sources from EEG data
2008
In this paper, an algorithm for separating linear subspaces of time-locked brain responses and other noise sources in multichannel electroencephalography data is proposed. The search criterion used by method discriminates time-locked brain components and noise components on the basis of the assumed deterministic behavior that the time-locked brain sources obey. The comprehensive derivation of the method is given together with the description and the analysis of the results of the method's application to simulated and real EEG data sets. The possibilities of improving the results are also discussed.
Artificial neural network applied to prediction of fluorquinolone antibacterial activity by topological methods.
2000
A new topological method that makes it possible to predict the properties of molecules on the basis of their chemical structures is applied in the present study to quinolone antimicrobial agents. This method uses neural networks in which training algorithms are used as well as different concepts and methods of artificial intelligence with a suitable set of topological descriptors. This makes it possible to determine the minimal inhibitory concentration (MIC) of quinolones. Analysis of the results shows that the experimental and calculated values are highly similar. It is possible to obtain a QSAR interpretation of the information contained in the network after the training has been carried …
Bond-extended stochastic and nonstochastic bilinear indices. I. QSPR/QSAR applications to the description of properties/activities of small-medium si…
2010
Bond-extended stochastic and nonstochastic bilinear indices are introduced in this article as novel bond-level molecular descriptors (MDs). These novel totals (whole-molecule) MDs are based on bilinear maps (forms) similar to use defined in linear algebra. The proposed nonstochastic indices try to match molecular structure provided by the molecular topology by using the kth Edge(Bond)-Adjacency Matrix (Ek, designed here as a nonstochastic E matrix). The stochastic parameters are computed by using the kth stochastic edge-adjacency matrix, ESk, as matrix operators of bilinear transformations. This new edge (bond)-adjacency relationship can be obtained directly from Ek and can be considered li…
Protein linear indices of the ‘macromolecular pseudograph α-carbon atom adjacency matrix’ in bioinformatics. Part 1: Prediction of protein stability …
2005
Abstract A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein’s total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on R n [ f k ( x m i ) : R n → R n ] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph α-carbon atom adjacency matrix. Total linear indices are linear functional on R n . That is, the kth total linear indices are linear maps from R n to the scalar R [ f k …