Related papers: The Ramanujan Library -- Automated Discovery on th…
The zbMATH database contains more than 4 million bibliographic entries. We aim to provide easy access to these entries. Therefore, we maintain different index structures, including a formula index. To optimize the findability of the entries…
Mathematical symbols and descriptions appear in various forms across document section boundaries without explicit markup. In this paper, we present a new large-scale dataset that emphasizes extracting symbols and descriptions in scientific…
Semantic networks provide a useful tool to understand how related concepts are retrieved from memory. However, most current network approaches use pairwise links to represent memory recall patterns. Pairwise connections neglect higher-order…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
Search engines for equations now exist, which return results matching the query's mathematical meaning or structural presentation. Operating over scientific papers, online encyclopedias, and math discussion forums, their content includes…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Existing benchmarks like NLGraph and GraphQA evaluate LLMs on graphs by focusing mainly on pairwise relationships, overlooking the high-order correlations found in real-world data. Hypergraphs, which can model complex beyond-pairwise…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
We propose an approach that connects recurrent networks with different orders of hidden interaction with regular grammars of different levels of complexity. We argue that the correspondence between recurrent networks and formal…
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by showing that nondegenerate intersecting codes correspond to…
Large language models (LLMs) often need to incorporate external knowledge to solve theme-specific problems. Retrieval-augmented generation (RAG) has shown its high promise, empowering LLMs to generate more qualified responses with retrieved…
Finding unambiguous diagrammatic representations for first-order logical formulas and relational queries with arbitrarily nested disjunctions has been a surprisingly long-standing unsolved problem. We refer to this problem as the…
Entanglement is a crucial resource for quantum technologies ranging from quantum communication to quantum-enhanced measurements and computation. Finding experimental setups for these tasks is a conceptual challenge for human scientists due…
This paper introduces the first, open source software library for Constraint Consistent Learning (CCL). It implements a family of data-driven methods that are capable of (i) learning state-independent and -dependent constraints, (ii)…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a…
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…