In order to recover a signal from its compressive measurements, the compressed sensing theory seeks the sparsest signal that agrees with the measurements, which is actually an l;norm minimization problem. In this paper, we equivalently transform the l;norm minimization into a concave continuous piecewise linear programming,and propose an optimization algorithm based on a modified interior point method. Numerical experiments demonstrate that our algorithm improves the sufficient number of measurements, relaxes the restrictions of the sensing matrix to some extent, and performs robustly in the noisy scenarios.
This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear（CPWL） programming with generalization of hinging hyperplane objective and linear constraints. CPWL programming is popular since it can be equivalently transformed into difference of convex functions programming or concave optimization. Inspired by the concavity of the concave CPWL functions, we propose an Objective Variation Simplex Algorithm（OVSA）, which is able to find a local optimum in a reasonable time. Computational results are presented for further insights into the performance of the OVSA compared with two other algorithms on random test problems.
Recently, it has been demonstrated that memristors can be utilized as logic operations and memory elements. In this paper, we present a novel circuit design for complementary resistive switch（CRS）-based stateful logic operations. The proposed circuit can automatically write the destructive CRS cells back to the original states. In addition, the circuit can be used in massive passive crossbar arrays which can reduce sneak path current greatly. Moreover, the steps for CRS logic operations using our proposed circuit are reduced compared with previous circuit designs. We validate the effectiveness of our scheme through Hspice simulations on the logic circuits.
According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rssler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods.
The memristor, as the fourth basic circuit element, has drawn worldwide attention since its physical implementation was released by HP Labs in 2008. However, at the nano-scale, there are many difficulties for memristor physical realization. So a better understanding and analysis of a good model will help us to study the characteristics of a memristor. In this paper, we analyze a possible mechanism for the switching behavior of a memristor with a Pt/TiO2/Pt structure, and explain the changes of electronic barrier at the interface of Pt/TiO2. Then, a quantitative analysis about each parameter in the exponential model of memristor is conducted based on the calculation results. The analysis results are validated by simulation results. The efforts made in this paper will provide researchers with theoretical guidance on choosing appropriate values for(α, β, χ, γ) in this exponential model.
This paper works on a heuristic algorithm with determinacy for the global optimization of Continuous PieceWise Linear(CPWL) programming. The widely applied CPWL programming can be equivalently transformed into D.C. programming and concave optimization over a polyhedron. Considering that the super-level sets of concave piecewise linear functions are polyhedra, we propose the Hill Tunneling via Weighted Simplex Centroid(HTWSC) algorithm, which can escape a local optimum to reach the other side of its contour surface by cutting across the super-level set. The searching path for hill tunneling is established via the weighted centroid of a constructed simplex. In the numerical experiments, different weighting methods are studied first, and the best is chosen for the proposed HTWSC algorithm. Then, the HTWSC algorithm is compared with the hill detouring method and the software CPLEX for the equivalent mixed integer programming, with results indicating its superior performance in terms of numerical efficiency and the global search capability.
