A novel smart vaccination method is proposed in this paper to distribute a limited number of vaccines among the people of a large community, such as a country, consisting of smaller communities like cities or provinces. The proposed method is comprised of two phases; A vaccine allocation phase and a targeted vaccination phase. In the first phase, the available vaccines are allocated to the communities based on demoGraphics and the effectiveness of each type of vaccine. In the second phase, each community is modelled as a contact Graph, and the vaccines available to the community are administered to the individuals whose vaccination has the greatest impact on breaking the chain of transmission. As a result of utilizing the Node2Vec Graph Embedding algorithm, the complexity of the proposed method increases linearly with the number of people in the community, as opposed to common centrality based methods, the complexities of which increase with the square or cube of the number of individuals. Furthermore, the proposed method can distribute multiple types of vaccines with different probabilities of effectiveness. The performance of the proposed method is comparable to the common centrality based vaccination methods, while its complexity is lower. The results of the simulation show a 20% decrease in the peak number of infected individuals.

The economic downturn in recent years has had a significant negative impact on corporates performance. In the last two years, as in the last years of 2010s, many companies have been influenced by the economic conditions and some have gone bankrupt. This has led to an increase in companies' financial risk. One of the significant branches of financial risk is the emph{company's credit risk}. Lenders and investors attach great importance to determining a company's credit risk when granting a credit facility. Credit risk means the possibility of default on repayment of facilities received by a company. There are various models for assessing credit risk using statistical models or machine learning. In this paper, we will investigate the machine learning task of the binary classification of firms into bankrupt and healthy based on the emph{spectral Graph theory}. We first construct an emph{adjacency Graph} from a list of firms with their corresponding emph{feature vectors}. Next, we first embed this Graph into a one-dimensional Euclidean space and then into a two dimensional Euclidean space to obtain two lower-dimensional representations of the original data points. Finally, we apply the emph{support vector machine} and the emph{multi-layer perceptron} neural network techniques to proceed binary emph{node classification}. The results of the proposed method on the given dataset (selected firms of Tehran stock exchange market) show a comparative advantage over PCA method of emph{dimension reduction}. Finally, we conclude the paper with some discussions on further research directions.

Knowledge Graphs are widely used tools in the field of reasoning, where reasoning is facilitated through link prediction within the knowledge Graph. However, traditional methods have limitations, such as high complexity or an inability to effectively capture the structural features of the Graph. The main challenge lies in simultaneously handling both the structural and similarity features of the Graph. In this study, we employ a constraint satisfaction approach, where each proposed link must satisfy both structural and similarity constraints. For this purpose, each constraint is considered from a specific perspective, referred to as a view. Each view computes a probability score using a GRU-RNN, which satisfies its own predefined constraint. In the first constraint, the proposed node must have a probability of over 0.5 with frontier nodes. The second constraint computes the Bayesian Graph, and the proposed node must have a link in the Bayesian Graph. The last constraint requires that a proposed node must fall within an acceptable fault. This allows for N-N relationships to be accurately determined, while also addressing the limitations of Embedding. The results of the experiments showed that the proposed method improved performance on two standard datasets.

For a given measure space (X, B, m) we construct all measure spaces (Y, C, l) in which (X, B, m) is embeddable. The construction is modeled on the ultrafilter construction of the Stone-Cech compactification of a completely regular topological space.Under certain conditions the construction simplifies. Examples are given when this simplification occurs.

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a Graph Embedding problem. In this paper we compute the lower bound for dilation and congestion of Embedding onto wheel-like networks. Further, we compute the exact dilation of Embedding wheellike networks into hypertrees, proving that the lower bound obtained is sharp. Again, we compute the exact congestion of Embedding windmill Graphs into circulant Graphs, proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of Embedding wheels and fans into 1, 2-fault hamiltonian Graphs. Using this we estimate the exact wirelength of Embedding wheels and fans into circulant Graphs, generalized Petersen Graphs, augmented cubes, crossed cubes, Möbius cubes, twisted cubes, twisted n-cubes, locally twisted cubes, generalized twisted cubes, odd-dimensional cube connected cycle, hierarchical cubic networks, alternating group Graphs, arrangement Graphs, 3-regular planer hamiltonian Graphs, star Graphs, generalised matching networks, fully connected cubic networks, tori and 1-fault traceable Graphs.