In this paper, we propose the block-diagonal matrix to approximate the Hessian matrix in the Levenberg Mar-quardt method in the training of neural networks. Two weight updating strategies, namely asynchronous and synchronous updating methods were investigated. Asyn-chronous method updates weights of one block at a time while synchronous method updates all weights at the same time. Variations of...

Cantor’s proof of this result [2, §2] makes use of nested intervals, but today a proof based on another ingenious idea of Cantor is more popular, namely the diagonal method, which he introduced in 1891 to prove the uncountability of 2 [3]. However, Cantor himself did not employ diagonalization directly in the proof of uncountability of R, but gave a rather intricate derivation of ∣ ∣2 ∣ ∣ = |R|...

We tested whether analogical training could help children learn a key principle of elementary engineering-namely, the use of a diagonal brace to stabilize a structure. The context for this learning was a construction activity at the Chicago Children's Museum, in which children and their families build a model skyscraper together. The results indicate that even a single brief analogical comparis...

Let T n denote the set of triangulations of a convex polygon K with n sides. We study the random walk on T n whose transitions are \\ips" of one of the n ? 3 internal diagonals of the current triangulation, the choice of diagonal being random. By bounding the conductance of this graph we show that the walk mixes rapidly, namely in time O(n). A direct argument is given for the fact that the mixi...

In this paper, we present a novel methodology to design block-diagonal stable decentralised controllers based on the KalmanYakubovich-Popov lemma. The approach yields closed-loop systems that are robust with respect to parameter uncertainty and structural perturbations. We demonstrate the methodology by designing controllers for the lateral and vertical subsystems of a vehicle emulator; namely,...

was introduced in [2, 3, 6] as a generalization of the coupled quantized harmonic oscillators [7], namely, themodel of light amplifier L−2 1 , and themodel of two-level optical atom L1, whose Hamiltonian model H = K0 +λ(K+ +K−), λ is the coupling parameter. The matrix representations of Lr of least degree satisfying the physical properties K2 =K† 1 († stands for Hermitian conjugation and K0 is ...

Let T be a linear opeartor and D be a matrix. So by its diagonal matrix, we get a lot of informations about T , namely we can almost answer any question about T . In this paper we introduce an efficient algorithm that characterizes whether a given matrix is diagonalizable in the field F or not (where F is the real field R or the complex field C). Mathematics Subject Classification: 11C08, 65F30...