In recent years, graph neural networks (GNNs) have become a promising method for analyzing data structured in graph format. By considering connections between entities in a graph, GNNs are able to extract valuable insights. One notable variation of GNN is the graph attention network (GAT), which employs the attention mechanism and has demonstrated promising performance in various applications. However, its ability to incorporate feature information from nodes beyond the immediate neighborhood is limited, leading to degraded performance on heterophilic data. To address this limitation, this thesis proposes a novel attention-based model, namely the Directional Graph Attention Network (DGAT). This model combines the feature-based attention with the global directional information extracted from the graph topology, as inspired by the Directional Graph Network (DGN). A new class of Laplacian matrices is proposed and an existing theoretical result on DGN is extended. This extension bridges a gap in the literature. The experimental results presented in the thesis, based on nine real-world benchmarks and ten synthetic data sets, demonstrate the superiority of the proposed DGAT model compared to the GAT baseline model. Particularly on heterophilic data sets, DGAT showed a notable average increase of approximately 35% in node classification tasks across all heterophilic real-world data sets. In addition, DGAT outperforms GAT by an average margin of around 51% in all ten synthetic data sets with various levels of heterophily

Diamond is a material with excellent performances which attracts the attention from researchers for decades. Pt (111), owing to its catalytic activity on diamond synthesis, is regarded to be a candidate for diamond hetero-epitaxity, which can enhance nucleation density. Molten surface at diamond growth temperature can also improve mobility and aggregation capability of primitive nuclei. Generally, (100)-oriented is welcomed for the achivement of high quality and large size diamond, since the formation of defects and twins are prevented. First-principle calculations and experimental researches were carried out for the study of transformation of orientation. The transformation from {111} to {100}-oriented diamond has been observed on Pt (111) substrate, which can be promoted by the increase of carbon source concentration and substrate temperature. The process is energetic favorable, which may provides a way towards large-scale (100) diamond films.

The investigation of plasma channels induced by focused ultra-short 1030-nm laser pulses in bulk of synthetic HPHT diamond revealed strong dependence of their size and shape on the used numerical aperture of the lens (NA=0.15-0.45). It was shown that at loose focusing conditions, it is possible to significantly increase the length of the plasma channel with a slight increase in pulse power, while tight focusing allows to obtain more compact structures in the same range of used powers. Such dependence paves the way to new possibilities in 3D processing of transparent dielectrics, allowing, for example, to vary the spatial parameters of modified regions without changing the setup, but only by controlling the lens aperture, which seems very promising for industrial applications.