The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines. The journal focuses on original high-quality research in the realm of computational science in parallel and distributed environments, encompassing the facilitating theoretical foundations and the applications of large-scale computations and massive data processing. It addresses researchers and practitioners in areas ranging from aerospace to biochemistry, from electronics to geosciences, from mathematics to software architecture, presenting verifiable computational methods, findings, and solutions and enabling industrial users to apply techniques of leading-edge, large-scale, high performance computational methods. The 13th issue of the Transactions on Computational Science journal consists of two parts. The six papers in Part I span the areas of computing collision probability, digital image contour extraction, multiplicatively weighted Voronoi diagrams, multi-phase segmentation, the rough-set approach to incomplete information systems, and fault-tolerant systolic arrays for matrix multiplications. The five papers in Part II focus on neural-network-based trajectory prediction, privacy in vehicular ad-hoc networks, augmented reality for museum display and the consumer garment try-on experience, and geospatial knowledge discovery for crime analysis.