Search results for "Linear subspace"
showing 10 items of 65 documents
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.
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.
Governing Survival Probability to Distill Quantum States
2005
A quantum system interacting with a repeatedly measured one undergoes a nonunitary time evolution pushing it into some specific subspaces. We deeply investigate the origin of the relevant selection rule, bringing to the light its connection with the survival probability related with the two-system interaction. The possibility of inducing an effective dynamics in the distilled subspace just during the distillation process is demonstrated.
Extraction of ERP from EEG data
2007
In this article, a simple but novel technique for extracting a linear subspace related to event related potentials (ERPs) from ElectroEncephaloGraphy (EEG) data is introduced. The technique consists of a sequence of basic linear operations applied to multidimensional EEG data in a problem-specific manner. The derivation of the proposed technique is given and results with real data are described together with overall conclusions.
A characterization of the line set of an odd-dimensional Baer subspace
1990
Generalizing a theorem of Beutelspacher and Seeger, we consider line sets\(\mathcal{L}\) inP=PG(2t + 1,q),t ∈ IN, with the following properties: (1) any (t + 1)-dimensional subspace ofP contains at least one line of\(\mathcal{L}\), (2) if a pointx ofP is incident with at least two lines of\(\mathcal{L}\) then the points in the factor geometryP/x which are induced by the lines of\(\mathcal{L}\) throughx form a blocking set of type (t, 1) inP/x, (3) any line of\(\mathcal{L}\) is coplanar with at least one further line of\(\mathcal{L}\). We will show that the examples of minimal cardinality are exactly the line sets of Baer subspaces ofP.
Approximation of Feasible Parameter Set in worst case identification of block-oriented nonlinear models
2003
Abstract The estimation of the Feasible Parameter Set for block-oriented nonlinear models in a worst case setting is considered. A bounding procedure is determined both for polytopic and ellipsoidie sets, consisting in the projection of the FPS ⊂ R MN of the extended parameter vector onto suitable M or N-dimensional subspaces and in the solution of convex optimization problems which provide the extreme points of the Parameter Uncertainties Intervals of the model parameteres. Bounds obtained are tighter then in the previous approaches.
Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits
2017
In this paper we investigate the quantum dynamics of two spin-1 systems, $\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized $(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. We show that, due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two sub-dynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The …
Feature Selection for Ensembles of Simple Bayesian Classifiers
2002
A popular method for creating an accurate classifier from a set of training data is to train several classifiers, and then to combine their predictions. The ensembles of simple Bayesian classifiers have traditionally not been a focus of research. However, the simple Bayesian classifier has much broader applicability than previously thought. Besides its high classification accuracy, it also has advantages in terms of simplicity, learning speed, classification speed, storage space, and incrementality. One way to generate an ensemble of simple Bayesian classifiers is to use different feature subsets as in the random subspace method. In this paper we present a technique for building ensembles o…
Null Space Based Image Recognition Using Incremental Eigendecomposition
2011
An incremental approach to the discriminative common vector (DCV) method for image recognition is considered. Discriminative projections are tackled in the particular context in which new training data becomes available and learned subspaces may need continuous updating. Starting from incremental eigendecomposition of scatter matrices, an efficient updating rule based on projections and orthogonalization is given. The corresponding algorithm has been empirically assessed and compared to its batch counterpart. The same good properties and performance results of the original method are kept but with a dramatic decrease in the computation needed.
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…