Related papers: Characterization of Word-Representable Graphs usin…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
We express the hairy graph complexes computing the rational homotopy groups of long embeddings (modulo immersion) of R^m in R^n as "decorated" graph complexes associated to certain representations of the outer automorphism groups of free…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
We model and compute the probability distribution of the letters in random generated words in a language by using the theory of set partitions, Young tableaux and graph theoretical representation methods. This has been of interest for…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
Visual Question Answering (VQA) is a challenging problem that requires to process multimodal input. Answer-Set Programming (ASP) has shown great potential in this regard to add interpretability and explainability to modular VQA…
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…
Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…
In this work, we define an orthogonal graph on the set of equivalence classes of $(2\nu + \delta)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $\nu$ are positive integers and $\delta = 0, 1$ or $2$. We classify our graph if it is strongly…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given…
Distributed word representations have been demonstrated to be effective in capturing semantic and syntactic regularities. Unsupervised representation learning from large unlabeled corpora can learn similar representations for those words…
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic…
A 1-11-representation of a graph $G(V,E)$ is a word over the alphabet $V$ such that two distinct vertices $x$ and $y$ are adjacent if and only if the restricted word $w{x,y}$ (obtained from $w$ by deleting all letters except $x$ and $y$)…
For any graph, we show that the graded permutation representation of the graph automorphism group given by matchings is strongly equivariantly log-concave. The proof gives a family of equivariant injections inspired by a combinatorial map…
Counting dominating sets in a graph $G$ is closely related to the neighborhood complex of $G$. We exploit this relation to prove that the number of dominating sets $d(G)$ of a graph is determined by the number of complete bipartite…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…