Related papers: Some Open Problems related to Creative Telescoping
Schubert calculus provides algebraic tools to solve enumerative problems. There have been several applied problems in systems theory, linear algebra and physics which were studied by means of Schubert calculus. The method is most powerful…
All sciences, including astronomy, are now entering the era of information abundance. The exponentially increasing volume and complexity of modern data sets promises to transform the scientific practice, but also poses a number of common…
The problems caused by the gap between system- and software-level architecting practices, especially in the context of Systems of Systems where the two disciplines inexorably meet, is a well known issue with a disappointingly low amount of…
With the advent of research-grade robotic telescopes (and professional archives) coupled with the wide availability of the Internet in schools, getting high-quality data in the classroom has become much easier than ever before. Robotic…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
We consider the problem of rescaling the lengths of a finite frame thereby transforming it into a tight one. Such frames are called scalable and have received a lot of attention in recent years. In this note we investigate the question in…
Interpretable machine learning tackles the important problem that humans cannot understand the behaviors of complex machine learning models and how these models arrive at a particular decision. Although many approaches have been proposed, a…
Recent machine learning techniques can be modified to produce creative results. Those results did not exist before; it is not a trivial combination of the data which was fed into the machine learning system. The obtained results come in…
The application of computer technology in the field of art has given rise to novel modes of artistic practice, including media art, and it is a necessity to find a commensurable conceptual fundament. Therefore, computer art starting from…
In spite of great progress over the last $\sim 10$ years, especially thanks to HST, a number of exciting open problem still puzzle astronomers working on globular clusters in our own and other galaxies. These problems range from determining…
Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
Most major discoveries in astronomy are unplanned, and result from surveying the Universe in a new way, rather than by testing a hypothesis or conducting an investigation with planned outcomes. For example, of the 10 greatest discoveries…
This note gives a short review of the statistical issues concerning upper limit calculation and claiming of discovery arising in the search for exotic physics with neutrino telescopes. Low sample sizes and significant instrumental…
We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
This paper provides a framework for evaluating creativity in co-creative systems: those that involve computer programs collaborating with human users on creative tasks. We situate co-creative systems within a broader context of…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…