Related papers: Some Open Problems related to Creative Telescoping
Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software…
A neural network mechanism that can compensate for poor optical quality was recently discovered in a biological context. We propose that this mechanism can and should be adopted for astronomical purposes. This would shift emphasis away from…
We describe the development of a system for an automated, iterative, real-time classification of transient events discovered in synoptic sky surveys. The system under development incorporates a number of Machine Learning techniques, mostly…
Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite…
In today's world of big data, computational analysis has become a key driver of biomedical research. Recent exponential growth in the volume of available omics data has reshaped the landscape of contemporary biology, creating demand for a…
A summation framework is developed that enhances Karr's difference field approach. It covers not only indefinite nested sums and products in terms of transcendental extensions, but it can treat, e.g., nested products defined over roots of…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
Recently, many artists and creative technologists created computer programming as a goal to create something expressive instead of something functional. In this paper, I analyzed 18 creative coding projects from the Google DevArt…
Active optics is defined as the control of the shape and the alignment of the components of an optical system at low temporal frequencies. For modern large telescopes with flexible monolithic or segmented primary mirrors and also flexible…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering and particularly in…
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
Developing students as well-rounded professionals is increasingly important for our modern society. Although there is a great consensus that technical and professional ("soft") skills should be developed and intertwined in the core of…
Quantitative assessment of the uncertainties tainting the results of computer simulations is nowadays a major topic of interest in both industrial and scientific communities. One of the key issues in such studies is to get information about…
Astronomy has entered the big data era and Machine Learning based methods have found widespread use in a large variety of astronomical applications. This is demonstrated by the recent huge increase in the number of publications making use…
We review some aspects of the current state of data-intensive astronomy, its methods, and some outstanding data analysis challenges. Astronomy is at the forefront of "big data" science, with exponentially growing data volumes and data…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
Abductive reasoning, reasoning for inferring explanations for observations, is often mentioned in scientific, design-related and artistic contexts, but its understanding varies across these domains. This paper reviews how abductive…
For centuries, the rich nocturnal environment of the starry sky could be modelled only by analogue tools such as paper planispheres, atlases, globes and numerical tables. The immersive sky simulator of the twentieth century, the…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…