Solving the large-scale problems with semidefinite programming (SDP) constraints is of great importance in modeling and model reduction of complex system, dynamical system, optimal control, computer vision, and machine learning. However, existing SDP solvers are of large complexities and thus unavailable to deal with large-scale problems. In this paper, we solve SDP using matrix generation, which is an extension of the classical column generation. The exponentiated gradient algorithm is also used
to solve the special structure subproblem of matrix generation. The numerical experiments show that our approach is efficient and scales very well with the problem dimension. Furthermore, the proposed algorithm is applied for a clustering problem. The experimental results on real datasets imply that the proposed approach outperforms the traditional interior-point SDP solvers in terms of efficiency and scalability.

Yongbin Zheng

Yuzhuang Yan

Sheng Liu

Xinsheng Huang

Wanying Xu

An Efficient Approach to Solve the Large-Scale Semidefinite Programming Problems

Cyber-physical networking systems (CPNSs) are made up of various physical systems that are heterogeneous in nature. Therefore, exploring universalities in CPNSs for either data or systems is desired in its fundamental theory. This paper is in the aspect of data, aiming at addressing that power laws may yet be a universality of data in CPNSs. The contributions of this paper are in triple folds. First, we provide a short tutorial about power laws. Then, we address the power laws related to some physical systems. Finally, we discuss that power-law-type data may be governed by stochastically differential equations of fractional order. As a side product, we present the point of view that the upper bound of data flow at large-time scaling and the small one also follows power laws.

Ming Li

Wei Zhao

Visiting Power Laws in Cyber-Physical Networking Systems

Motion trajectory contains plentiful motion information of moving objects, for example, human gestures and robot actions. Motion perception and recognition via trajectory are
useful for characterizing them and a flexible descriptor of motion trajectory plays important
role in motion analysis. However, in the existing tasks, trajectories were mostly used in raw
data and effective descriptor is lacking. In this paper, we present a mixed invariant signature
descriptor with global invariants for motion perception and recognition. The mixed signature
is viewpoint invariant for local and global features. A reliable approximation of the mixed
signature is proposed to reduce the noise in high-order derivatives. We use this descriptor for
motion trajectory description and explore the motion perception with DTW algorithm for
salient motion features. To achieve better accuracy, we modified the CDTW algorithm for
trajectory matching in motion recognition. Furthermore, a controllable weight parameter is
introduced to adjust the global features for tasks in different circumstances. The conducted
experiments validated the proposed method.

Jianyu Yang

Y. F. Li

Keyi Wang

Yuan Wu

Giuseppe Altieri

Massimo Scalia

Mixed Signature: An Invariant Descriptor for 3D Motion Trajectory Perception and Recognition

This paper works on hybrid force/position control in robotic manipulation
                              and proposes an improved radial basis functional (RBF) neural network,
                              which is a robust relying on the Hamilton Jacobi Issacs principle of
                              the force control loop. The method compensates uncertainties in a
                              robot system by using the property of RBF neural network. The error
                              approximation of neural network is regarded as an external
                              interference of the system, and it is eliminated by the robust control
                              method. Since the conventionally fixed structure of RBF network is not
                              optimal, resource allocating network (RAN) is proposed in this paper
                              to adjust the network structure in time and avoid the underfit.
                              Finally the advantage of system stability and transient performance is
                              demonstrated by the numerical simulations.

Shuhuan Wen

Junying Yuan

Jinghai Zhu

Radial Basis Functional Link Network and Hamilton Jacobi Issacs for Force/Position Control in Robotic Manipulation

This paper presents a novel region-based method for extracting useful information from microscopic images under complex conditions. It is especially used for blood cell segmentation and statistical analysis. The active model detects several inner and outer contours of an object from its background. The method incorporates a local binary fitting model into a maximum regional difference model. It utilizes both local and global intensity information as the driving forces of the contour model on the principle of the largest regional difference. The local and global fitting forces ensure that local dissimilarities can be captured and globally different areas can be segmented, respectively. By combining the advantages of local and global information, the motion of the contour is driven by the mixed fitting force, which is composed of the local and global fitting term in the energy function. Experiments are carried out in the laboratory, and results show that the novel model can yield good performances for microscopic image analysis.

Chunyan Yao

Jianwei Zhang

Min Chen

Qiu Guan

Incorporating a Local Binary Fitting Model into a Maximum Regional Difference Model for Extracting Microscopic Information under Complex Conditions

About this journal

Mathematical Problems in Engineering is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.

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Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.

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Mathematical Problems in Engineering - Table of contents 2012

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Mathematical Problems in Engineering