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It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately,…
The increased usage of the information technologies in everyday life and especially in education leads to demands for new forms of teaching, studying and appropriate examination and evaluation of acquired knowledge and skills of the…
Large language models (LLMs) have garnered significant attention for their superior performance in many knowledge-driven applications on the world wide web.These models are designed to train hundreds of millions or more parameters on large…
We demonstrate that thermodynamic knowledge acquired by humans can be transferred to computers so that the machine can use it to solve thermodynamic problems and produce explainable solutions with a guarantee of correctness. The actionable…
Despite improved digital access to scholarly literature in the last decades, the fundamental principles of scholarly communication remain unchanged and continue to be largely document-based. Scholarly knowledge remains locked in…
The ability of knowledge graphs to represent complex relationships at scale has led to their adoption for various needs including knowledge representation, question-answering, and recommendation systems. Knowledge graphs are often…
This paper describes a new kind of knowledge representation and mining system which we are calling the Semantic Knowledge Graph. At its heart, the Semantic Knowledge Graph leverages an inverted index, along with a complementary uninverted…
Knowledge graphs (KGs) contain rich information about world knowledge, entities and relations. Thus, they can be great supplements to existing pre-trained language models. However, it remains a challenge to efficiently integrate information…
In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of…
Knowledge graph embeddings are now a widely adopted approach to knowledge representation in which entities and relationships are embedded in vector spaces. In this chapter, we introduce the reader to the concept of knowledge graph…
Can one build a knowledge graph (KG) for all products in the world? Knowledge graphs have firmly established themselves as valuable sources of information for search and question answering, and it is natural to wonder if a KG can contain…
Context. In less than a year practitioners and researchers witnessed a rapid and wide implementation of Generative Artificial Intelligence. The daily availability of new models proposed by practitioners and researchers has enabled quick…
Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…
This paper presents an ecosystem for personal knowledge graphs (PKGs), commonly defined as resources of structured information about entities related to an individual, their attributes, and the relations between them. PKGs are a key enabler…
In this article we consider the basic ideas, approaches and results of developing of mathematical knowledge management technologies based on ontologies. These solutions form the basis of a specialized digital ecosystem OntoMath which…
Modeling real-world phenomena is a focus of many science and engineering efforts, such as ecological modeling and financial forecasting, to name a few. Building an accurate model for complex and dynamic systems improves understanding of…
MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database…
With a large number of software tools dedicated to the visualisation and/or demonstration of properties of geometric constructions and also with the emerging of repositories of geometric constructions, there is a strong need of linking…
NeuralKG is an open-source Python-based library for diverse representation learning of knowledge graphs. It implements three different series of Knowledge Graph Embedding (KGE) methods, including conventional KGEs, GNN-based KGEs, and…