ИНТЕЛЛЕКТУАЛЬНЫЙ числовым программным ДЛЯ MIMD-компьютер

For most scientific and engineering problems simulated on computers the solving of problems of the computational mathematics with approximately given initial data constitutes an intermediate or a final stage. Basic problems of the computational mathematics include the investigating and solving of linear algebraic systems, evaluating of eigenvalues and eigenvectors of matrices, the solving of systems of non-linear equations, numerical integration of initial- value problems for systems of ordinary differential equations.Для більшості наукових та інженерних задач моделювання на ЕОМ рішення задач обчислювальної математики з наближено заданими вихідними даними складає проміжний або остаточний етап. Основні проблеми обчислювальної математики відносяться дослідження і рішення лінійних алгебраїчних систем оцінки власних значень і власних векторів матриць, рішення систем нелінійних рівнянь, чисельного інтегрування початково задач для систем звичайних диференціальних рівнянь.Для большинства научных и инженерных задач моделирования на ЭВМ решение задач вычислительной математики с приближенно заданным исходным данным составляет промежуточный или окончательный этап. Основные проблемы вычислительной математики относятся исследования и решения линейных алгебраических систем оценки собственных значений и собственных векторов матриц, решение систем нелинейных уравнений, численного интегрирования начально задач для систем обыкновенных дифференциальных уравнений

Intelligent watermarking of long streams of document images

Digital watermarking has numerous applications in the imaging domain, including (but not limited to) fingerprinting, authentication, tampering detection. Because of the trade-off between watermark robustness and image quality, the heuristic parameters associated with digital watermarking systems need to be optimized. A common strategy to tackle this optimization problem formulation of digital watermarking, known as intelligent watermarking (IW), is to employ evolutionary computing (EC) to optimize these parameters for each image, with a computational cost that is infeasible for practical applications. However, in industrial applications involving streams of document images, one can expect instances of problems to reappear over time. Therefore, computational cost can be saved by preserving the knowledge of previous optimization problems in a separate archive (memory) and employing that memory to speedup or even replace optimization for future similar problems. That is the basic principle behind the research presented in this thesis. Although similarity in the image space can lead to similarity in the problem space, there is no guarantee of that and for this reason, knowledge about the image space should not be employed whatsoever. Therefore, in this research, strategies to appropriately represent, compare, store and sample from problem instances are investigated. The objective behind these strategies is to allow for a comprehensive representation of a stream of optimization problems in a way to avoid re-optimization whenever a previously seen problem provides solutions as good as those that would be obtained by reoptimization, but at a fraction of its cost. Another objective is to provide IW systems with a predictive capability which allows replacing costly fitness evaluations with cheaper regression models whenever re-optimization cannot be avoided. To this end, IW of streams of document images is first formulated as the problem of optimizing a stream of recurring problems and a Dynamic Particle Swarm Optimization (DPSO) technique is proposed to tackle this problem. This technique is based on a two-tiered memory of static solutions. Memory solutions are re-evaluated for every new image and then, the re-evaluated fitness distribution is compared with stored fitness distribution as a mean of measuring the similarity between both problem instances (change detection). In simulations involving homogeneous streams of bi-tonal document images, the proposed approach resulted in a decrease of 95% in computational burden with little impact in watermarking performace. Optimization cost was severely decreased by replacing re-optimizations with recall to previously seen solutions. After that, the problem of representing the stream of optimization problems in a compact manner is addressed. With that, new optimization concepts can be incorporated into previously learned concepts in an incremental fashion. The proposed strategy to tackle this problem is based on Gaussian Mixture Models (GMM) representation, trained with parameter and fitness data of all intermediate (candidate) solutions of a given problem instance. GMM sampling replaces selection of individual memory solutions during change detection. Simulation results demonstrate that such memory of GMMs is more adaptive and can thus, better tackle the optimization of embedding parameters for heterogeneous streams of document images when compared to the approach based on memory of static solutions. Finally, the knowledge provided by the memory of GMMs is employed as a manner of decreasing the computational cost of re-optimization. To this end, GMM is employed in regression mode during re-optimization, replacing part of the costly fitness evaluations in a strategy known as surrogate-based optimization. Optimization is split in two levels, where the first one relies primarily on regression while the second one relies primarily on exact fitness values and provide a safeguard to the whole system. Simulation results demonstrate that the use of surrogates allows for better adaptation in situations involving significant variations in problem representation as when the set of attacks employed in the fitness function changes. In general lines, the intelligent watermarking system proposed in this thesis is well adapted for the optimization of streams of recurring optimization problems. The quality of the resulting solutions for both, homogeneous and heterogeneous image streams is comparable to that obtained through full optimization but for a fraction of its computational cost. More specifically, the number of fitness evaluations is 97% smaller than that of full optimization for homogeneous streams and 95% for highly heterogeneous streams of document images. The proposed method is general and can be easily adapted to other applications involving streams of recurring problems

Quaternion Matrices : Statistical Properties and Applications to Signal Processing and Wavelets

Similarly to how complex numbers provide a possible framework for extending scalar signal processing techniques to 2-channel signals, the 4-dimensional hypercomplex algebra of quaternions can be used to represent signals with 3 or 4 components. For a quaternion random vector to be suited for quaternion linear processing, it must be (second-order) proper. We consider the likelihood ratio test (LRT) for propriety, and compute the exact distribution for statistics of Box type, which include this LRT. Various approximate distributions are compared. The Wishart distribution of a quaternion sample covariance matrix is derived from first principles. Quaternions are isomorphic to an algebra of structured 4x4 real matrices. This mapping is our main tool, and suggests considering more general real matrix problems as a way of investigating quaternion linear algorithms. A quaternion vector autoregressive (VAR) time-series model is equivalent to a structured real VAR model. We show that generalised least squares (and Gaussian maximum likelihood) estimation of the parameters reduces to ordinary least squares, but only if the innovations are proper. A LRT is suggested to simultaneously test for quaternion structure in the regression coefficients and innovation covariance. Matrix-valued wavelets (MVWs) are generalised (multi)wavelets for vector-valued signals. Quaternion wavelets are equivalent to structured MVWs. Taking into account orthogonal similarity, all MVWs can be constructed from non-trivial MVWs. We show that there are no non-scalar non-trivial MVWs with short support [0,3]. Through symbolic computation we construct the families of shortest non-trivial 2x2 Daubechies MVWs and quaternion Daubechies wavelets.Open Acces

Exploiting Spatio-Temporal Coherence for Video Object Detection in Robotics

This paper proposes a method to enhance video object detection for indoor environments in robotics. Concretely, it exploits knowledge about the camera motion between frames to propagate previously detected objects to successive frames. The proposal is rooted in the concepts of planar homography to propose regions of interest where to find objects, and recursive Bayesian filtering to integrate observations over time. The proposal is evaluated on six virtual, indoor environments, accounting for the detection of nine object classes over a total of ∼ 7k frames. Results show that our proposal improves the recall and the F1-score by a factor of 1.41 and 1.27, respectively, as well as it achieves a significant reduction of the object categorization entropy (58.8%) when compared to a two-stage video object detection method used as baseline, at the cost of small time overheads (120 ms) and precision loss (0.92).</p

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...