Related papers: Confirmable Workflows in OSCAR
Computational experiments have become essential for scientific discovery, allowing researchers to test hypotheses, analyze complex datasets, and validate findings. However, as computational experiments grow in scale and complexity, ensuring…
In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of…
Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is…
Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic. Experiments with an implementation in OSCAR with various…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
We propose an approach for improved reproducibility that includes capturing and relating provenance characteristics and performance metrics, in a hybrid queriable system, the ProvEn server. The system capabilities are illustrated on two use…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
This work is devoted to the study of the problem of user-level capture and restoration of running computations in heterogeneous environments. Support for those operations has traditionally been offered through ready-made solutions for…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
The importance of computers is continually increasing in radiotherapy. Efficient algorithms, implementations and the ability to leverage advancements in computer science are crucial to improve cancer care even further and deliver the best…
Biclustering is a data mining technique which searches for local patterns in numeric tabular data with main application in bioinformatics. This technique has shown promise in multiple areas, including development of biomarkers for cancer,…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and then lift the modular results to the rationals. This method…
We propose a new type of self-aware systems inspired by ideas from higher-order theories of consciousness. First, we discussed the crucial distinction between introspection and reflexion. Then, we focus on computational reflexion as a…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
GPUs and other accelerators are popular devices for accelerating compute-intensive, parallelizable applications. However, programming these devices is a difficult task. Writing efficient device code is challenging, and is typically done in…
A conjecture for the dimension and the character of the homogenous components of the free Jordan algebras is proposed. As a support of the conjecture, some numerical evidences are generated by a computer and some new theoretical results are…
The point of this work is to explore axiomatisations of concurrent computation using the technology of proof theory and realizability. To deal with this problem, we redefine the Concurrent Realizability of Beffara using as realizers a…