In this paper, a new adjustment to the damping parameter of the Levenberg-Marquardt algorithm is proposed to save training time and to reduce error oscillations. The damping parameter of the Levenberg-Marquardt algorithm switches between a gradient descent method and the Gauss-Newton method. It also affects training speed and induces error oscillations when a decay rate is fixed. Therefore, our damping strategy decreases the damping parameter with the inner product between weight vectors to make the Levenberg-Marquardt algorithm behave more like the Gauss-Newton method, and it increases the damping parameter with a diagonally dominant matrix to make the Levenberg-Marquardt algorithm act like a gradient descent method. We tested two simple classifications and a handwritten digit recognition for this work. Simulations showed that our method improved training speed and error oscillations were fewer than those of other algorithms.
For an improved neuro-spike representation of auditory signals within cochlea models, a new digital ARMA-type low-pass filter structure is proposed. It is compared to more conventional AR-type counterpart on a classification of biosonar echoes, in which echoes from various tree species insonified with a bat-like chirp call are converted to biologically plausible feature vectors. Next, parametric and non-parametric models of the class-conditional densities are built from the echo feature vectors. The models are deployed in single-shot and sequential-decision classification algorithms. The results indicate that the proposed ARMA filter structure offers an improved single-echo classification performance, which leads to faster sequential-decision making than its AR-type counterpart.
$G(3,m,n)$ is the group presented by $\langle a,b\mid a^5=(ab)^2=b^{m+3}a^{-n}b^ma^{-n}=1\rangle $. In this paper, we study the structure of $G(3,m,n)$. We also give a new efficient presentation for the Projective Special Linear group $PSL(2,5)$ and in particular we prove that $PSL(2,5)$ is isomorphic to $G(3,m,n)$ under certain conditions.
Finite element methods with piecewise polynomial spaces in space for solving the nonstationary heat equation, as a model for parabolic equations are considered. The discretization in time is performed using the Crank-Nicolson method. A new a priori estimate is proved. Thanks to this new a priori estimate, a new error estimate in the discrete norm of W1,∞(L 2 ) is proved. An L∞(H1 )-error estimate is also shown. These error estimates are useful since they allow us to get second order time accurate approximations for not only the exact solution of the heat equation but also for its first derivatives (both spatial and temporal). Even the proof presented in this note is in some sense standard but the stated W1,∞(L 2 )- error estimate seems not to be present in the existing literature of the Crank-Nicolson finite element schemes for parabolic equations.
In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual lifetime moments, conditional moments and Rényi entropy. The parameters are estimated by the maximum likelihood method and the Fisher's information matrix is determined. Several special cases of this family are studied in some detail. An application to a real data set illustrates the performance of the family of distributions.
An n × n ray pattern A is called a spectrally arbitrary ray pattern if the complex matrices in Q(A) give rise to all possible complex polynomials of degree n. In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an n×n irreducible spectrally arbitrary ray pattern is 3n-1. In this paper, we introduce a new family of spectrally arbitrary ray patterns of order n with exactly 3n - 1 nonzeros., Yinzhen Mei, Yubin Gao, Yanling Shao, Peng Wang., and Obsahuje seznam literatury
In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that W3 - the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) - is the limit member of this family, showing how the mass of W3 is distributed on the plane x+y+z=2 of [0,1]3 in an easy manner, and providing the generalization of this result to n dimensions.