It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of L(R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA 85, 6582-6586], it follows that (if there is a supercompact cardinal) every set of reals in L(R) is deter...

The detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the subspace spanned by linear functions. Karhunen–Loeve expansion for the process is obtained, together with the explicit formula for the Laplace transform of the squared L 2 norm. Distribution identities are established in connection with the second order Brownian bridge dev...

A general framework for structure-preserving model reduction by Krylov subspace projection methods is developed. The goal is to preserve any substructures of importance in the matrices L, G, C, B that define the model prescribed by transfer function H(s) = L∗(G+sC)−1B. Many existing structure-preserving model-order reduction methods for linear and second-order dynamical systems can be derived u...

Compressed sensing is a novel signal sampling theory under the condition that the signal is sparse or compressible. The existing recovery algorithms based on the gradient projection can either need prior knowledge or recovery the signal poorly. In this paper, a new algorithm based on gradient projection is proposed, which is referred as Quasi Gradient Projection. The algorithm presented quasi g...

Presented to the Society, September 4, 1951 ; received by the editors December 10, 1951. 1 This work was supported by the Office of Naval Research. 1 We make the convention that the projection of an operator into a subspace is restricted to this subspace, so that the domain of ¿' is ©. 3 The formulation of the method in Hubert space as here presented was given for a special operator by Aronszaj...

In recent years, large high-dimensional data sets have become commonplace in a wide range of applications in science and commerce. Techniques for dimension reduction are of primary concern in statistical analysis. Projection methods play an important role. We investigate the use of projection algorithms that exploit properties of the α-stable distributions. We show that lα distances and quasi-d...

Let L be an Archimedean Riesz space with a weak order unit u. A sufficient condition under which Dedekind [σ-]completeness of the principal ideal Au can be lifted to L is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of C(X)-spaces. Similar results are obtained for the Riesz spaces Bn(T ), n = 1, 2, . . . , of all functions o...

Kalman information fusion filter is dealt with for WSNs (Wireless sensor networks), where multiplicative noises occur in the system model. There are l > 2 sub-systems, and for each sub-system, there are m > 2 observations that are sent through different wireless channel. Packet loss is inevitable for the wireless channel, and the optimal information fusion filter is given by the projection theo...

• The LWE error distribution Φαq is a continuous one-dimensional Gaussian, which is a projection of the spherical n-dimensional distribution Dαq onto its first coordinate. • The distribution Dαq is smooth in the following sense: If L is some lattice (or coset of a lattice) with λn(L) αq, then if we choose ~x← DL,r and ~y ← Ds such that r2 + s2 = (αq)2 then the induced distribution on ~x+ ~y is ...