A high performance neural network for solving nonlinear programming problems with hybrid constraints

A continuous neural network is proposed in this Letter for solving optimization problems. It not only can solve nonlinear programming problems with the constraints of equality and inequality, but also has a higher performance. The main advantage of the network is that it is an extension of Newton's gradient method for constrained problems, the dynamic behavior of the network under special constraints and the convergence rate can be investigated. Furthermore, the proposed network is simpler than the existing networks even for solving positive definite quadratic programming problems. The network considered is constrained by a projection operator on a convex set. The advanced performance of the proposed network is demonstrated by means of simulation of several numerical examples.     

Image noise cancellation using linear matrix inequality and cellular neural network

In this paper, the technique of image noise cancellation is presented by employing cellular neural networks (CNN) and linear matrix inequality (LMI). The main objective is to obtain the templates of CNN by using a corrupted image and a corresponding desired image. A criterion for the uniqueness and global asymptotic stability of the equilibrium point of CNN is presented based on the Lyapunov stability theorem (i.e., the feedback template “A” of CNN is solved at this step), and the input template “B” of CNN is designed to achieve desirable output by using the property of saturation nonlinearity of CNN. It is shown that the problem of image noise cancellation can be characterized in terms of LMIs. The simulation results indicate that the proposed method is useful for practical application.     

An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

In this study,a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional.This paper presents the comprehensive discussion of the approach and also extensive applications.     

A contribution to the inequality and equality relations in structure analysis

On the basis of the non-negativity for electron density in a crystal (r), the existence of inequalities and equalities between the coefficients of the Fourier expansion of the function (r) (r+t) is shown, which limits the choice of phases of the structure factors.     

联合深度神经网络和凸优化的单通道语音增强算法

噪声估计的准确性直接影响语音增强算法的好坏,为提升当前语音增强算法的噪声抑制效果,有效求解无约束优化问题,提出一种联合深度神经网络(DNN)和凸优化的时频掩蔽优化算法进行单通道语音增强。首先,提取带噪语音的能量谱作为DNN的输入特征;接着,将噪声与带噪语音的频带内互相关系数(ICC Factor)作为DNN的训练目标;然后,利用DNN模型得到的互相关系数构造凸优化的目标函数;最后,联合DNN和凸优化,利用新混合共轭梯度法迭代处理初始掩蔽,通过新的掩蔽合成增强语音。仿真实验表明,在不同背景噪声的低信噪比下,相比改进前,新的掩蔽使增强语音获得了更好的对数谱距离(LSD)、主观语音质量(PESQ)、短时客观可懂度(STOI)和分段信噪比(segSNR)指标,提升了语音的整体质量并且可以有效抑制噪声。     

Blind image deconvolution subject to bandwidth and total variation constraints

We present a maximum likelihood (ML) deconvolution algorithm with bandwidth and total variation (TV) constraints for degraded image due to atmospheric turbulence. The bandwidth limit function is estimated in view of optical system parameters and Fourier optical theory. With the aid of bandwidth and TV minimization as compelling constraints, the algorithm can not only suppress noise effectively but also restrict the bandwidth of point-spread function (PSF) that may lead to trivial solution. Compared with the conventional ML method, the proposed algorithm is able to restore a noise-free image, and the detailed texture is better than that of ML.     

A hybrid neural network for image classification

Principles of the photorefractive perceptron learning algorithm are described. The influences of the finite response time and hologram erasure of the photorefractive gratings on the convergence property of the photorefractive perceptron learning are discussed. A novel neural network which could resolve these constraints is presented. It is a hybrid system which utilizes the photorefractive holographic gratings to implement the inner product between the input image and the interconnection matrix. A personal computer is used for storing the interconnection matrix and the updating procedure, and it also functions as a feedback means during the learning phase. After training the weight vectors are recorded in the volume hologram of an optical processor. This novel method combines the advantages of the massive parallelism of optical systems and the programmability of electronic computers. Experimental results of image classification are presented. It shows that the system could correctly classify the input patterns into one of the two groups after training on four examples in each group during successive iterations. The system has been extended to perform multi-category image classification.     

Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

The effects of vibrational anharmonic terms and of the g_K -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x ₁, x ₂, … depend on the anharmonic force constants. The functions F_i can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the F_i s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v ₂+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v ₂ including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v ₂=1 is now found to be 4g_K . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.     

A background elimination method based on linear programming for Raman spectra

In this paper, we consider a new background elimination method for Raman spectra. As a background is usually slowly varying with respect to wavelength, it could be approximated by a slowly varying curve. However, the usual curve‐fitting method cannot be applied because there is a constraint that the estimated background must be beneath a measured spectrum. To meet the requirement, we adopt a polynomial as an approximating function and show that background estimation could be converted to a linear programming problem which is a special case of constrained optimization. In addition, we present an order selection algorithm for automatic baseline elimination. According to the experimental results, it is shown that the proposed method could be successfully applied to experimental Raman spectra as well as synthetic spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

A maximum overlap neural network for pattern recognition

The problem of recognizing noisy patterns is trivially solved by identifying the key pattern which has the largest overlap with the input. We show that a procedure that does this can be implemented in a simple layered neural network. Recognition is free of spurious states, the network never reaches a state of total confusion. Processing time scales as log M, where M is the number of stored patterns.     

A duplication-free quantum neural network for universal approximation

Different from the concept of universal computation,the universality of a quantum neural network focuses on the ability to approximate arbitrary functions and is an important guarantee for effectiveness.However,conventional approaches of constructing a universal quantum neural network may result in a huge quantum register that is challenging to implement due to noise on a near-term device.To address this,we propose a simple design of a duplication-free quantum neural network whose universality c...     

Propagators for time-dependent linear and quadratic potentials and inverse Weierstrass transform

It is shown that the inversion of the Weierstrass transform allows obtaining the propagator without an explicit knowledge of an orthonormal complete system of solutions. The cases of the time-dependent linear and quadratic potentials are investigated in some detail.     

Propagator for the time-dependent charged oscillator via linear and quadratic invariants

The problem of a charged particle in the presence of a variable magnetic field is considered. Using the linear and the quadratic invariants as a tool, the wave functions in Fock state as well as in coherent state are obtained. The corresponding propagators which propagate the wave functions in the space-time are derived. Using numerical computations we have managed to draw some plots for the real, imaginary, and absolute values of the propagators. This has been used to analyze the properties of the propagators associated with both of the linear and the quadratic invariants. It has been shown that there is no essential difference between the behavior of the absolute value of the propagators in both of the linear and the quadratic invariants.     

Performance analysis of integer linear programming optical monitor placement for crosstalk attack detection in different network topologies

In this paper, an optimum optical power monitor placement is formulated in integer linear programming for crosstalk attack detection by exploiting monitoring information from test connections. The experimental results showed that equipping 6 out of 14, 8 out of 15 and 8 out of 16 nodes with optical power monitoring devices in NSF, MESH and GRID topologies are enough to detect the nodes that are traversed by the crosstalk attack in the networks.     

A neural network based model for urban noise prediction

Noise is a global problem. In 1972 the World Health Organization (WHO) classified noise as a pollutant. Since then, most industrialized countries have enacted laws and local regulations to prevent and reduce acoustic environmental pollution. A further aim is to alert people to the dangers of this type of pollution. In this context, urban planners need to have tools that allow them to evaluate the degree of acoustic pollution. Scientists in many countries have modeled urban noise, using a wide range of approaches, but their results have not been as good as expected. This paper describes a model developed for the prediction of environmental urban noise using Soft Computing techniques, namely Artificial Neural Networks (ANN). The model is based on the analysis of variables regarded as influential by experts in the field and was applied to data collected on different types of streets. The results were compared to those obtained with other models. The study found that the ANN system was able to predict urban noise with greater accuracy, and thus, was an improvement over those models. The principal component analysis (PCA) was also used to try to simplify the model. Although there was a slight decline in the accuracy of the results, the values obtained were also quite acceptable.     

Virasoro constraints and polynomial recursion for the linear Hodge integrals

The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.     

A delay-decomposition approach for stability of neural network with time-varying delay

This paper studies delay-dependent asymptotical stability problems for the neural system with time-varying delay. By dividing the whole interval into multiple segments such that each segment has a different Lyapunov matrix, some improved delay-dependent stability conditions are derived by employing an integral equality technique. A numerical example is given to demonstrate the effectiveness and less conservativeness of the proposed methods.