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This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ ( t ) ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.

Nowadays, determining if an image appeared somewhere on the web or in a magazine or is authentic or not has become crucial. Image forensics methods based on features have demonstrated so far to be very effective in detecting forgeries in which a portion of an image is cloned somewhere else onto the same image. Anyway such techniques cannot be adopted to deal with splicing attack, that is, when the image portion comes from another picture that then, usually, is not available anymore for an operation of feature match. In this paper, a procedure in which these techniques could also be employed will be shown to get rid of splicing attack by resorting to the use of some repositories of images available on the Internet like Google Images or TinEye Reverse Image Search. Experimental results are presented on some real case images retrieved on the Internet to demonstrate the capacity of the proposed procedure.

Nowadays, many disciplines have to deal with big datasets that additionally involve a high number of features. Feature selection methods aim at eliminating noisy, redundant, or irrelevant features that may deteriorate the classification performance. However, traditional methods lack enough scalability to cope with datasets of millions of instances and extract successful results in a delimited time. This paper presents a feature selection algorithm based on evolutionary computation that uses the MapReduce paradigm to obtain subsets of features from big datasets. The algorithm decomposes the original dataset in blocks of instances to learn from them in the map phase; then, the reduce phase merges the obtained partial results into a final vector of feature weights, which allows a flexible application of the feature selection procedure using a threshold to determine the selected subset of features. The feature selection method is evaluated by using three well-known classifiers (SVM, Logistic Regression, and Naive Bayes) implemented within the Spark framework to address big data problems. In the experiments, datasets up to 67 millions of instances and up to 2000 attributes have been managed, showing that this is a suitable framework to perform evolutionary feature selection, improving both the classification accuracy and its runtime when dealing with big data problems., This work is supported by the Research Projects TIN2014-57251-P, P10-TIC-6858, P11-TIC-7765, P12-TIC-2958, and TIN2013-47210-P. D. Peralta and S. Ramírez-Gallego hold two FPU scholarships from the Spanish Ministry of Education and Science (FPU12/04902, FPU13/00047). I. Triguero holds a BOF postdoctoral fellowship from the Ghent University.

Satisfying consistency requirements of pairwise comparison matrix (PCM) is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP) or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts asegment treeto gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs.