Related papers: The polymake XML file format
One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human.…
This paper presents our experience on building RDF knowledge graphs for an industrial use case in the legal domain. The information contained in legal information systems are often accessed through simple keyword interfaces and presented as…
With the goal of bringing to reseachers of the ancient andean khipus with a tool to share and process electronically the current corpus of these ancient information devices, I present on this paper a proposal for a Quipu Description Format…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
Using worldsheet Hamiltonian methods we derive a charge algebra which generalizes the Courant bracket to include fluxes of general index type. This is achieved by coupling a bi-vector to the Hamiltonian of the Polyakov model. This bracket…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
Although they exist since more than ten years already, have attracted diverse implementations, and have been used successfully in a significant number of applications, declarative mapping languages for constructing knowledge graphs from…
Locating and distilling the valuable relevant information continued to be the major challenges of Information Retrieval (IR) Systems owing to the explosive growth of online web information. These challenges can be considered the XML…
The integration of tabular data from diverse sources is often hindered by inconsistencies in formatting and representation, posing significant challenges for data analysts and personal digital assistants. Existing methods for automating…
The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and…
We have developed the Model Master (MM) language for describing spreadsheets, and tools for converting MM programs to and from spreadsheets. The MM decompiler translates a spreadsheet into an MM program which gives a concise summary of its…
Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 3D logarithmic…
These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.
It is proposed a complex valued channel encoding for multidimensional data. The basic approach contains overlapping of complex nonlinear mappings. Its development leads to sparse representation of multi-channel data, increasing their…
Many important forms of data are stored digitally in XML format. Errors can occur in the textual content of the data in the fields of the XML. Fixing these errors manually is time-consuming and expensive, especially for large amounts of…
With XML becoming an ubiquitous language for data interoperability purposes in various domains, efficiently querying XML data is a critical issue. This has lead to the design of algebraic frameworks based on tree-shaped patterns akin to the…
The Outilex software platform, which will be made available to research, development and industry, comprises software components implementing all the fundamental operations of written text processing: processing without lexicons,…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional…
A survey of dictionary models and formats is presented as well as a presentation of corresponding recent standardisation activities.