Search results for "subspace"

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.

On almost Dugundji spaces and dyadic spaces

1994

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.

Diagrammatic approach to quantum search

2014

We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theory's effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with $N$.

The quantum trajectory approach to geometric phase for open systems

2005

The quantum jump method for the calculation of geometric phase is reviewed. This is an operational method to associate a geometric phase to the evolution of a quantum system subjected to decoherence in an open system. The method is general and can be applied to many different physical systems, within the Markovian approximation. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. It is shown that the geometric phase is to very large extent insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.

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.

Dynamic integration of classifiers in the space of principal components

2003

Recent research has shown the integration of multiple classifiers to be one of the most important directions in machine learning and data mining. It was shown that, for an ensemble to be successful, it should consist of accurate and diverse base classifiers. However, it is also important that the integration procedure in the ensemble should properly utilize the ensemble diversity. In this paper, we present an algorithm for the dynamic integration of classifiers in the space of extracted features (FEDIC). It is based on the technique of dynamic integration, in which local accuracy estimates are calculated for each base classifier of an ensemble, in the neighborhood of a new instance to be pr…

DECENTRALIZED SUBSPACE PROJECTION IN LARGE NETWORKS

2018

A great number of applications in wireless sensor networks involve projecting a vector of observations onto a subspace dictated by prior information. Accomplishing such a task in a centralized fashion entails great power consumption, congestion at certain nodes, and suffers from robustness issues. A sensible alternative is to compute such projections in a decentralized fashion. To this end, recent works proposed schemes based on graph filters, which compute projections exactly with a finite number of local exchanges among sensor nodes. However, existing methods to obtain these filters are confined to reduced families of projection matrices or small networks. This paper proposes a method tha…

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.