Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient al...

The IEEE802.11b WLAN standard employs directsequence/spread-spectrum (DS/SS) modulation. With a fractional sampling RAKE receiver, it is possible to achieve diversity and reduce the BER in DS/SS communication. In order to realize the diversity through fractional sampling, the impulse response of the channel must be estimated. In this paper, a channel estimation scheme for a RAKE receiver with f...

In this paper, we extend previous results on average commute-times for undirected graphs to fully-connected directed graphs, corresponding to irreducible Markov chains. We introduce an unsymmetrized generalized Laplacian matrix and show how its pseudo-inverse directly yields the one-way first-transit times and round-trip commute times with formulas almost matching those for the undirected graph...

A new bound (Theorem 4.4) for the duration of the chip-firing game with N chips on a n-vertex graph is obtained, by a careful analysis of the pseudo-inverse of the discrete Laplacian matrix of the graph. This new bound is expressed in terms of the entries of the pseudo-inverse. It is shown (Section 5) to be always better than the classic bound due to Björner, Lovász and Shor. In some cases the ...

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient al...

The backpropagation algorithm, which had been originally introduced in the 1970s, is the workhorse of learning in neural networks. This backpropagation algorithm makes use of the famous machine learning algorithm known as Gradient Descent, which is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, ...

Understanding the grain size-dependent failure behavior of polycrystalline graphene is important for its applications both structurally and functionally. Here we perform molecular dynamics simulations to study the failure behavior of polycrystalline graphene by varying both grain size and distribution. We show that polycrystalline graphene fails in a brittle mode and grain boundary junctions se...

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study some matrix Using tool, characterize [Formula: see text], provided that text] is uniformly locally finite inverse semigroup. As an application, show Brandt semigroup pseudo-amenable if and only amenable finite. give examples to the differences between other classical notions amenability.

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this note we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. F...

In the presence of selection bias the traditional estimators for pseudo panel data models are inconsistent. This paper discusses a method to achieve consistency in static linear pseudo panels in the presence of selection bias and a testing procedure for sample selection bias. The authors’ approach uses a bias correction term proportional to the inverse Mills ratio with argument equal to the “no...