LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

A Modified Variational-Gradient Method for Quasilinear Equations

A modified variational-gradient method is proposed and substantiated for quasilinear operator equations in a Hilbert space.     

Best L1 Piecewise Monotonic Data Modelling

Let us consider n data measurements of a univariate process that have been altered by random errors. We assume that an underlying model function has a substantially smaller number of turning points than the observed ones. We propose algorithms that make least the sum of the moduli of the errors by requiring k monotonic sections, alternately increasing and decreasing, in the sequence of the smoothed values. The main difficulty in this calculation is that the optimal positions of the joins of the monotonic sections have to be found automatically among so many combinations that it is impossible to test each one separately. Moreover, the calculation seems to be very intractable to general optimization techniques because O(n^k) local minima can occur. It is shown that dynamic programming can be used for separating the data into optimal disjoint sections of adjacent data, where each section requires a single L₁ monotonic calculation. This procedure is highly efficient, requiring at most O(kn²) computer operations and O(n) best L₁ monotonic calculations to subranges of data for a global minimum.     

SPECTRAL DENSITY ESTIMATION FROM NONLINEARLY OBSERVED DATA

Abstract. The estimation of the spectral density function of a stationary Gaussian process at the input of an instantaneous nonlinearity is considered when the nonlinearity is known and a finite set of observations of the output process is given. A class of spectral estimates is considered and their quadratic-mean consistency is established; precise asymptotic expressions for their bias and covariance are derived and their asymptotic normality is obtained.     

Convergence of iterated boolean sums of simultaneous approximants

Explicit error estimates are given for the iterated Boolean sum of a sequence of simultaneous approximants; the rate of convergence is shown to be improved for smooth functions. The general results are applied in the case of the Bernstein, Durrmeyer and Stancu operators.     

关于Grünwald型多项式算子的线性组合

研究了Grünwald型多项式算子Hn(f;x,r)对f(x)∈Cj[-1,1],1≤j≤r的逼近阶,在连续状态下给出了点态的逼近阶.     

Micromechanical characterisation of fibre/matrix interfaces

Theoretical analyses for the single fibre pull-out and push-out models under monotonic loading are given which are based on a shear-lag analysis in a fracture mechanics approach considering non-constant friction at the debonded interface as a result of fibre Poisson contraction (or expansion). The solutions allow the determination of typical fibre/matrix interfacial properties such as the interfacial fracture toughness, G_ic, the coefficient of friction, μ, and the residual clamping stress, q₀. Under cyclic loading the interfacial properties are expected to degrade as a result of repetitive abrasion, and a power law function is assumed between μ and the number of elapsed cycles, N. However, G_ic is assumed to be unaffected and a fracture mechanics based debond criterion is derived for the relationship between the external applied stress, the debond length and the reduced friction coefficient for both fibre pull-out and fibre push-out. In addition, the relative displacements between the free fibre end and the matrix top are obtained for cyclic fatigue when the fibre is loaded and unloaded. A relationship obtained for the protrusion (or intrusion) length in fibre pull-out (or push-out) experiments allows the severity of the interface frictional degradation to be evaluated and characterised. Similarities and differences in the frictional degradation behaviour between fibre pull-out and push-out are also identified.     

高精细数字会聚校正系统

数字会聚校正使1%的会聚精度提高到0.1%以上。本文叙述了数字会聚校正系统的设计要求,工作原理以及设计计算,给出了在投影电视上的试验结果,最后,指出了今后发展的方向。     

Fixed point theorems on fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy convergent sequence, l-fuzzy weakly convergent sequence and l-fuzzy weakly compact set are given in a fuzzy normed linear space. The concepts of fuzzy normal structure, fuzzy non-expansive mapping, uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.