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We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.
Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success…
Bispanning graphs are undirected graphs with an edge set that can be decomposed into two disjoint spanning trees. The operation of symmetrically swapping two edges between the trees, such that the result is a different pair of disjoint…
Signed link prediction in graphs is an important problem that has applications in diverse domains. It is a binary classification problem that predicts whether an edge between a pair of nodes is positive or negative. Existing approaches for…
Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…
A graph $G$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree and an interval $I$, such that each leaf of the tree is a vertex of the graph, and there is an edge $\{ x, y \}$ in $G$ if and only if the weight of…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…
Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose structural roles are identical. In contrast, unlabeled…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Reasoning about graphs evolving over time is a challenging concept in many domains, such as bioinformatics, physics, and social networks. We consider a common case in which edges can be short term interactions (e.g., messaging) or long term…
Evolution algebras are non-associative algebras inspired from biological phenomena, with applications to or connections with different mathematical fields. There are two natural ways to define an evolution algebra associated to a given…
The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This…
A real-world graph has a complex topological structure, which is often formed by the interaction of different latent factors. However, most existing methods lack consideration of the intrinsic differences in relations between nodes caused…
We consider graph labelings with an assignment of odd prime numbers to the vertices. Similarly to graceful graphs, a labeling is said to be elegant if the absolute differences between the labels of adjacent vertices describe exactly the…
Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level…
We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular,…
Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention…
A temporal graph can be represented by a graph with an edge labelling, such that an edge is present in the network if and only if the edge is assigned the corresponding time label. A journey is a labelled path in a temporal graph such that…
Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…