Related papers: A framework to test interval arithmetic libraries …
We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software…
Testing is a vital part of software development, and spreadsheets are like any other software in this respect. This paper discusses the testing of spreadsheets in the light of one practitioner's experience. It considers the concept of…
In-context Learning (ICL) has achieved notable success in the applications of large language models (LLMs). By adding only a few input-output pairs that demonstrate a new task, the LLM can efficiently learn the task during inference without…
Quantum computing has emerged as a promising field with the potential to revolutionize various domains by harnessing the principles of quantum mechanics. As quantum hardware and algorithms continue to advance, developing high-quality…
Third-party libraries are crucial to the development of software projects. To get suitable libraries, developers need to search through millions of libraries by filtering, evaluating, and comparing. The vast number of libraries places a…
The Julia programming language continues to gain popularity both for its potential for programmer productivity and for its impressive performance on scientific code. It thus holds potential for large-scale HPC, but we have not yet seen this…
Many cluster similarity indices are used to evaluate clustering algorithms, and choosing the best one for a particular task remains an open problem. We demonstrate that this problem is crucial: there are many disagreements among the…
We propose a benchmarking strategy that is robust in the presence of timer error, OS jitter and other environmental fluctuations, and is insensitive to the highly nonideal statistics produced by timing measurements. We construct a model…
Attribute-based encryption (ABE) comprises a set of one-to-many encryption schemes that allow the encryption and decryption of data by associating it with access policies and attributes. Therefore, it is an asymmetric encryption scheme, and…
In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features…
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
Modern LLM agents increasingly create their own tools at runtime -- from Python functions to API clients -- yet existing benchmarks evaluate them almost exclusively by downstream task completion. This is analogous to judging a software…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
In the past years, analyzers have been introduced to detect classes of non-terminating queries for definite logic programs. Although these non-termination analyzers have shown to be rather precise, their applicability on real-life Prolog…
Testing is one of the most indispensable tasks in software engineering. The role of testing in software development has grown significantly because testing is able to reveal defects in the code in an early stage of development. Many unit…
Software intensively depends on external libraries whose relevance may change during its life cycle. As a consequence, software developers must periodically reconsider the libraries they depend on, and must think about \textit{library…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…