Tools that perform pattern recognition analysis of crimes, comprising at the same time forecasting, clustering, and recommendations on real data such as patrolling routes, are not fully integrated; modules are developed separately, and thus, a single

This paper aims at studying the relation between two rather relevant theoretic fields such as Graph Theory and Testor Theory, deepening in the unexploited relation between the concepts of Minimal Transversal and Irreducible Testor. First, the classic definitions of each concept are provided, and then the relation between them is shown and formalized. Some of the immediate consequences of this relation, in terms of the duality property of transversals and about the equivalence of the result of two specific algorithms, one from each field, are discussed. Finally, we also discuss several future research directions that arise from the relationship between the concepts of Minimal Transversal and Irreducible Testor, as well as the way in which those directions can potentially benefit the development of theory and algorithms for solving different practical problems in both areas.

Many endogenous and external components may affect the physiological, mental and behavioral states in humans. Monitoring tools are required to evaluate biomarkers, identify biological events, and predict their outcomes. Being one of the valuable indicators, brain biomarkers derived from temporal or spectral electroencephalography (EEG) signals processing, allow for the classification of mental disorders and mental tasks. An EEG signal has a nonstationary nature and individual frequency feature, hence it can be concluded that each subject has peculiar timing and data to extract unique features. In order to classify data, which are collected by performing four mental task (reciting the alphabet backwards, imagination of rotation of a cube, imagination of right hand movements (open/close) and performing mathematical operations), discriminative features were extracted using four competitive time-frequency techniques; Wavelet Packet Decomposition (WPD), Morlet Wavelet Transform (MWT), Short Time Fourier Transform (STFT) and Wavelet Filter Bank (WFB), respectively. The extracted features using both time and frequency domain information were then reduced using a principal component analysis for subset reduction. Finally, the reduced subsets were fed into a multi-layer perceptron neural network (MP-NN) trained with back propagation (BP) algorithm to generate a predictive model. This study mainly focuses on comparing the relative performance of time-frequency feature extraction methods that are used to classify mental tasks. The real-time (RT) conducted experimental results underlined that the WPD feature extraction method outperforms with 92% classification accuracy compared to three other aforementioned methods for four different mental tasks.