Related papers: Tuning FORM with large calculations
While large language models (LLMs) are increasingly used to summarize long documents, this trend poses significant challenges in the legal domain, where the factual accuracy of deposition summaries is crucial. Nugget-based methods have been…
International standards for lexicon formats are in preparation. To a certain extent, the proposed formats converge with prior results of standardization projects. However, their adequacy for (i) lexicon management and (ii) lexicon-driven…
Big data is no more "all just hype" but widely applied in nearly all aspects of our business, governments, and organizations with the technology stack of AI. Its influences are far beyond a simple technique innovation but involves all rears…
This paper presents a family of rapidly convergent summation formulas for various finite sums of the form $\sum_{k=0}^{\lfloor x\rfloor}f(k)$, where $x$ is a positive real number.
Tables are a powerful and popular tool for organizing and manipulating data. A vast number of tables can be found on the Web, which represents a valuable knowledge resource. The objective of this survey is to synthesize and present two…
The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular application leads to the choice of a particular material…
Our number system is a magnificent tool. But it is far from perfect. Can it be improved? In this paper some possibilities are discussed, including the use of a different base or directed (negative as well as positive) numerals. We also put…
Multidimensional databases are a great asset for decision making. Their users express complex OLAP (On-Line Analytical Processing) queries, often returning huge volumes of facts, sometimes providing little or no information. Furthermore,…
Before we can get the whole potential of employing computers in the process of managing mathematical `knowledge', we have to convert informal knowledge into machine-oriented representations. How exactly to support this process so that it…
In many virus families, tens to thousands of proteins assemble spontaneously into a capsid (protein shell) while packaging the genomic nucleic acid. This review summarizes recent advances in computational modeling of these dynamical…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
Numerical methods play an ever more important role in astrophysics. This is especially true in theoretical works, but of course, even in purely observational projects, data analysis without massive use of computational methods has become…
Recent advancements in Large Language Models (LLMs) have markedly enhanced the interpretation and processing of tabular data, introducing previously unimaginable capabilities. Despite these achievements, LLMs still encounter significant…
Recently, increasingly large amounts of data are generated from a variety of sources. Existing data processing technologies are not suitable to cope with the huge amounts of generated data. Yet, many research works focus on Big Data, a…
We develop the calculus of superforms as a tool for convex geometry. The formalism is applied to valuations on convex bodies, the Alexandrov-Fenchel inequalities and Monge- Amp\`ere equations on the boundary of convex bodies.
We introduce and study expansions of real numbers with respect to two integer bases.
Advances in information technology and its widespread growth in several areas of business, engineering, medical and scientific studies are resulting in information/data explosion. Knowledge discovery and decision making from such rapidly…
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
Inspired by the exceptional general intelligence of Large Language Models (LLMs), researchers have begun to explore their application in pioneering the next generation of recommender systems - systems that are conversational, explainable,…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.