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Despite the superior performance in modeling complex patterns to address challenging problems, the black-box nature of Deep Learning (DL) methods impose limitations to their application in real-world critical domains. The lack of a smooth manner for enabling human reasoning about the black-box decisions hinder any preventive action to unexpected events, in which may lead to catastrophic consequences. To tackle the unclearness from black-box models, interpretability became a fundamental requirement in DL-based systems, leveraging trust and knowledge by providing ways to understand the model's behavior. Although a current hot topic, further advances are still needed to overcome the existing limitations of the current interpretability methods in unsupervised DL-based models for Anomaly Detection (AD). Autoencoders (AE) are the core of unsupervised DL-based for AD applications, achieving best-in-class performance. However, due to their hybrid aspect to obtain the results (by requiring additional calculations out of network), only agnostic interpretable methods can be applied to AE-based AD. These agnostic methods are computationally expensive to process a large number of parameters. In this paper we present the RXP (Residual eXPlainer), a new interpretability method to deal with the limitations for AE-based AD in large-scale systems. It stands out for its implementation simplicity, low computational cost and deterministic behavior, in which explanations are obtained through the deviation analysis of reconstructed input features. In an experiment using data from a real heavy-haul railway line, the proposed method achieved superior performance compared to SHAP, demonstrating its potential to support decision making in large scale critical systems., Comment: 8 pages

In this work we study the entanglement of pure fourpartite of qubit states. The analysis is realized through the comparison between two different entanglement measures: the Groverian entanglement measure and the residual entanglement measured with negativities. Furthemore, we discuss some applications of four-way entangled fourpartite states., Comment: 12 pages, 9 figure

Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical algorithm. It is possible to use Grover algorithm, taking profit of its ability to find a specific value in a unordered database, to find, for example, the zero of a logical function; the minimal or maximal value in a database or to recognize if an odd number is prime or not. Here we show quantum algorithms to solve those cited mathematical problems. The solution requires the use of a quantum bit string comparator being used as oracle. This quantum circuit compares two quantum states and identifies if they are equal or, otherwise, which of them is the largest. Moreover, we also show the quantum bit string comparator allow us to implement conditional statements in quantum computation, a fundamental structure for designing of algorithms., Comment: 9 pages, 6 figures