Hierarchical Laplacian-based compression of triangle meshes

In this paper, we present an algorithm for efficient encoding of triangle meshes. The algorithm preserves the local relations between vertices by encoding their Laplacian coordinates, while at the same time, it uses a hierarchy of additional vertex constraints that provides global rigidity and low absolute error, even for large meshes. Our scheme outperforms traversal based as well as Laplacian-based compression schemes in terms of both absolute and perceived distortion at a given data rate.     

A Bounded Real Lemma for Discrete‐Time Markovian Jump Singular Systems

This paper presents a bounded real lemma for discrete‐time Markovian jump singular systems. First, a new necessary and sufficient condition is proposed in terms of a strict linear matrix inequality, which guarantees the stochastic admissibility of the unforced Markovian jump singular systems. Then, a bounded real lemma for discrete‐time Markovian jump singular systems is derived. It is also proven that the bounded real lemma can be described by a strict matrix inequality. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory. The results are more tractable and reliable in numerical computations than existing conditions.     

高职学生数学学习中的习得性无助研究

数学作为高职学生一门必修的基础课程,对其后续学习有着至关重要的作用,本文研究了数学学习中习得性无助产生的原因,并提出相应的教学干预措施。     

Global Exponential Stability Analysis of Discrete‐Time Genetic Regulatory Networks with Time Delays

This paper focuses on the study of global robust exponential stability of discrete‐time genetic regulatory networks (GRNs) with time‐invariant/time‐varying delays and parameter uncertainties. Many existing results on this problem are based on the linear matrix inequality (LMI) approach, which needs to verify whether there exists a feasible solution of a set of LMIs. Along with the increase in the number of genes, dimensions of LMIs will increase accordingly, which will lead to a large amount of calculation. Based on M‐matrix theory, sufficient conditions ensuring the global robust exponential stability of a class of discrete‐time GRNs with time‐invariant/time‐varying delays and parameter uncertainties are presented. These given conditions are to check whether a constructed constant matrix is a nonsingular M‐matrix. Simulation results of several examples are given to demonstrate the validity of the proposed method.     

Geometric properties estimation from discrete curves using discrete derivatives

Accurate geometric properties estimation from discrete curves is an important problem in many application domains, such as computer vision, pattern recognition, image processing, and geometric modeling. In this paper, we propose a novel method for estimating the geometric properties from discrete curves based on derivative estimation. We develop derivative estimation by defining the derivative of a discrete function at a point, which will be called the discrete derivative. Similarly, the second and higher order discrete derivatives at that point are also defined, and their convergence is demonstrated by theory analysis. These definitions of the different order discrete derivatives provide a simple and reliable way to estimate the derivatives from discrete curves. Based on the discrete derivatives, classical differential geometry can be discretized, and the geometric properties are estimated from discrete curves by using differential geometry theory. The proposed method is independent of any analytic curve and estimates the geometric properties directly from discrete data points, which makes it robust to the geometric shapes of discrete curves. Another advantage of the proposed method is the robustness to noise because of the calculation characteristics of the discrete derivatives. The proposed method is evaluated and compared with other existing methods in the experiments with both synthetic and real discrete curves. The test results show that the proposed method has good performance, and is robust to noise and suitable for different curve shapes.     

Exact, scaled image rotations in finite Radon transform space

The Finite Radon Transform (FRT) is a discrete analogue of classical tomography. The FRT permits exact reconstruction of a discrete object from its discrete projections. The set of projection angles for the FRT is intrinsic to each image array size. It is shown here that the set of FRT angles is closed under a rotation by any of its members. A periodic re-ordering of the elements of the 1D FRT projections is then equivalent to an exact 2D image rotation. FRT-based rotations require minimal interpolation and preserve all of the original image pixel intensities. This approach has applications in image feature matching, multi-scale data representation and data encryption.     

Minimal non-convex words

Using a combinatorial characterization of digital convexity based on words, one defines the language of convex words. The complement of this language forms an ideal whose minimal elements, with respect to the factorial ordering, appear to have a particular combinatorial structure very close to the Christoffel words. In this paper, those words are completely characterized as those of the form uw^kv where k≥1, w=u⋅v and u,v,w are Christoffel words. Also, by considering the most balanced among the unbalanced words, we obtain a second characterization for a special class of minimal non-convex words that are of the form u²v² corresponding to the case k=1 in the previous form.     

Tabu Search with two approaches to parallel flowshop evaluation on CUDA platform

The introduction of NVidia’s powerful Tesla GPU hardware and Compute Unified Device Architecture (CUDA) platform enable many-core parallel programming. As a result, existing algorithms implemented on a GPU can run many times faster than on modern CPUs. Relatively little research has been done so far on GPU implementations of discrete optimisation algorithms. In this paper, two approaches to parallel GPU evaluation of the Permutation Flowshop Scheduling Problem, with makespan and total flowtime criteria, are proposed. These methods can be employed in most population-based algorithms, e.g. genetic algorithms, Ant Colony Optimisation, Particle Swarm Optimisation, and Tabu Search. Extensive computational experiments, on Tabu Search for Flowshop with both criteria, followed by statistical analysis, confirm great computational capabilities of GPU hardware. A GPU implementation of Tabu Search runs up to 89 times faster than its CPU counterpart.     

An improved model predictive control approach based on extended non-minimal state space formulation

This paper presents a new design method of model predictive control (MPC) based on extended non-minimal state space models, in which the measured input and output variables, their past values together with the defined output errors are chosen as the state variables. It shows that this approach does not need the design of an observer to access the state information any more and by augmenting the process model and its objective function to include the changes of the system state variables, the control performances are superior to those of the controller that does not bear this feature. Furthermore, closed-loop transfer function representation of the model predictive control system facilitates the use of frequency response analysis methods for the nominal control performances of the system.     

Identification of the unobservable behaviour of industrial automation systems by Petri nets

This paper addresses the problem of identifying the model of the unobservable behaviour of discrete event systems in the industrial automation sector. Assuming that the fault-free system structure and dynamics are known, the paper proposes an algorithm that monitors the system on-line, storing the occurred observable event sequence and the corresponding reached states. At each event observation, the algorithm checks whether some unobservable events have occurred on the basis of the knowledge of the Petri net (PN) modelling the nominal system behaviour and the knowledge of the current PN marking. By defining and solving some integer linear programming problems, the algorithm decides whether it is necessary to introduce some unobservable (silent) transitions in the PN model and provides a PN structure that is consistent with the observed event string. A case study describing an industrial automation system shows the efficiency and the applicability of the proposed algorithm.