Performance Analysis of l_0 Norm Constraint Least Mean Square Algorithm

As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The performance of $l_0$-LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents all-around and throughout theoretical performance analysis of $l_0$-LMS for white Gaussian input data based on some reasonable assumptions. Expressions for steady-state mean square deviation (MSD) are derived and discussed with respect to algorithm parameters and system sparsity. The parameter selection rule is established for achieving the best performance. Approximated with Taylor series, the instantaneous behavior is also derived. In addition, the relationship between $l_0$-LMS and some previous arts and the sufficient conditions for $l_0$-LMS to accelerate convergence are set up. Finally, all of the theoretical results are compared with simulations and are shown to agree well in a large range of parameter setting.Comment: 31 pages, 8 figure

Skin Ageing and Cancer

Human matrix metalloproteinases (MMPs) belong to the M10 family of the MA clan of endopeptidases. They are ubiquitarian enzymes, structurally characterized by an active site where a Zn2+ atom, coordinated by three histidines, plays the catalytic role, assisted by a glutamic acid as a general base. Based on their structure and substrate specificity, they can be categorized into five main subgroups, namely (1) collagenases (MMP-1, MMP-8 and MMP-13); (2) gelatinases (MMP-2 and MMP-9); (3) stromelysins (MMP-3, MMP-10 and MMP-11); (4) matrilysins (MMP-7 and MMP-26) and (5) membrane-type (MT) MMPs (MMP-14, MMP-15, MMP-16, MMP-17, MMP-24 and MMP-25). MMPs can act on extracellular matrix (ECM) and non-ECM components affecting degradation and modulation of the ECM, growth-factor activation and cell-cell and cell-matrix signalling. In skin, MMPs are secreted by different cell types such as fibroblasts, keratinocytes, macrophages, endothelial cells, mast cells, and eosinophils. This chapter reviews the role of MMPs in maintaining skin homeostasis, skin ageing and skin cancer

Platinum: Reusing Constraint Solutions in Bounded Analysis of Relational Logic

Alloy is a light weight specification language based on relational logic, with an analysis engine that relies on SAT solvers to automate bounded verifica- tion of specifications. In spite of its strengths, the reliance of the Alloy Analyzer on computationally heavy solvers means that it can take a significant amount of time to verify software properties, even within limited bounds. This challenge is exacerbated by the ever-evolving nature of complex software systems. This paper presents PLATINUM, a technique for efficient analysis of evolving Alloy specifications, that recognizes opportunities for constraint reduction and reuse of previously identified constraint solutions. The insight behind PLATINUM is that formula constraints recur often during the analysis of a single specification and across its revisions, and constraint solutions can be reused over sequences of anal- yses performed on evolving specifications. Our empirical results show that PLAT- INUM substantially reduces (by 66.4% on average) the analysis time required on specifications extracted from real-world software systems

Optimization and Noise Analysis of the Quantum Algorithm for Solving One-Dimensional Poisson Equation

Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic or Hamiltonian simulation. In this letter, we further develop this algorithm to make it closer to the real application on the noisy intermediate-scale quantum (NISQ) devices. To this end, we first develop a new way of performing the sine transformation, and based on it the algorithm is optimized by reducing the depth of the circuit from n2 to n. Then, we analyze the effect of common noise existing in the real quantum devices on our algorithm using the IBM Qiskit toolkit. We find that the phase damping noise has little effect on our algorithm, while the bit flip noise has the greatest impact. In addition, threshold errors of the quantum gates are obtained to make the fidelity of the circuit output being greater than 90%. The results of noise analysis will provide a good guidance for the subsequent work of error mitigation and error correction for our algorithm. The noise-analysis method developed in this work can be used for other algorithms to be executed on the NISQ devices.Comment: 20 pages, 9 figure

Quantum-inspired Complex Convolutional Neural Networks

Quantum-inspired neural network is one of the interesting researches at the junction of the two fields of quantum computing and deep learning. Several models of quantum-inspired neurons with real parameters have been proposed, which are mainly used for three-layer feedforward neural networks. In this work, we improve the quantum-inspired neurons by exploiting the complex-valued weights which have richer representational capacity and better non-linearity. We then extend the method of implementing the quantum-inspired neurons to the convolutional operations, and naturally draw the models of quantum-inspired convolutional neural networks (QICNNs) capable of processing high-dimensional data. Five specific structures of QICNNs are discussed which are different in the way of implementing the convolutional and fully connected layers. The performance of classification accuracy of the five QICNNs are tested on the MNIST and CIFAR-10 datasets. The results show that the QICNNs can perform better in classification accuracy on MNIST dataset than the classical CNN. More learning tasks that our QICNN can outperform the classical counterparts will be found.Comment: 12pages, 6 figure

Black-Box Quantum State Preparation with Inverse Coefficients

Black-box quantum state preparation is a fundamental building block for many higher-level quantum algorithms, which is applied to transduce the data from computational basis into amplitude. Here we present a new algorithm for performing black-box state preparation with inverse coefficients based on the technique of inequality test. This algorithm can be used as a subroutine to perform the controlled rotation stage of the Harrow-Hassidim-Lloyd (HHL) algorithm and the associated matrix inversion algorithms with exceedingly low cost. Furthermore, we extend this approach to address the general black-box state preparation problem where the transduced coefficient is a general non-linear function. The present algorithm greatly relieves the need to do arithmetic and the error is only resulted from the truncated error of binary string. It is expected that our algorithm will find wide usage both in the NISQ and fault-tolerant quantum algorithms.Comment: 11 pages, 3 figure