Related papers: Formalizing Mathematical Knowledge as a Biform The…
We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…
Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…
Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…
Noun phrases and relational phrases in Open Knowledge Bases are often not canonical, leading to redundant and ambiguous facts. In this work, we integrate structural information (from which tuple, which sentence) and semantic information…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
This paper revisits the bilinear attention networks in the visual question answering task from a graph perspective. The classical bilinear attention networks build a bilinear attention map to extract the joint representation of words in the…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…
Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them…
Connectedness and bipartiteness are basic properties of classical graphs, and the purpose of this paper is to investigate the case of quantum graphs. We introduce the notion of connectedness and bipartiteness of quantum graphs in terms of…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…