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Detecting spatio-temporal patterns as an interesting topic from different perspectives like detecting anomalies, unexpected and high-risk areas is a powerful means to manage future events by describing the current state and giving the possibility to predict the future. Criminology theories explain that the distribution of crime is not random. Although various specifications of crime are necessary for crime analysis, three types of most important information are location, time and environment data. Therefore, spatio-temporal crime patterns recognition plays an important role in crime analysis. This paper presents a new approach to detect the space and time areas which the crimes are most likely to happen. For this aim, a genetic-fuzzy system is developed to generate an interpretable fuzzy knowledge base that encompasses patterns for predicting future spatio-temporal crimes. It composed of three steps: fuzzy partitioning of the problem space, selecting meaningful features, and constructing the fuzzy knowledge base. We evaluate our proposed system using both a simulated dataset and a real-world dataset from Tehran, Iran. The results show that the proposed system is a suitable tool to find patterns and predict future crimes for environments with clustered crimes in space and time.

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing a subgroup of order 324 without inversions (see J. Math. Chem. 28(4) (2000) 377–388). In this work, a computational method is described, by means of which it is possible to calculate the symmetry group of molecules. We study the full non-rigid group (f-NRG) of Sponge and Pina molecules with C 2 and C i point groups, respectively. It proved that these are groups of order 162 and 13122 with 54 and 3240 conjugacy classes, respectively. The character tables of these groups are also computed.