Related papers: A database of number fields
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
This paper addresses the problem of representing the set of repairs of a possibly inconsistent database by means of a disjunctive database. Specifically, the class of denial constraints is considered. We show that, given a database and a…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
Some recent additions to FORM are discussed. In particular large file support and the tablebases are presented.
Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including…
Knowledge bases are collections of domain-specific and commonsense facts. Recently, the sizes of KBs are rocketing due to automatic extraction for knowledge and facts. For example, the number of facts in WikiData is up to 974 million!…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
Large databases are often organized by hand-labeled metadata, or criteria, which are expensive to collect. We can use unsupervised learning to model database variation, but these models are often high dimensional, complex to parameterize,…
Big Data processing systems handle huge unstructured and structured data to store, process, and analyze through cluster analysis which helps in identifying unseen patterns to find the relationships between them. Clustering analysis over the…
The meaning of null in relational databases is a major source of confusion not only among database users but also among database textbook writers. The purpose of this article is to examine what database nulls could mean and to make some…
Increasingly more data is becoming available on the Web, estimates speaking of 1 billion documents in 2002. Most of the documents are Web pages whose data is considered to be in XML format, expecting it to eventually replace HTML. A common…
The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems…
From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath theorem from Database Dependency theory. Next, we leverage…
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…
A data store allows application processes to put and get data from a shared memory. In general, a data store cannot be modelled as a strictly sequential process. Applications observe non-sequential behaviours, called anomalies. The set of…
Graphs have become the best way we know of representing knowledge. The computing community has investigated and developed the support for managing graphs by means of digital technology. Graph databases and knowledge graphs surface as the…
A database is under construction to provide a complete collection of published basic properties of hypernuclei such as {\Lambda} binding energies, lifetimes, or excitation energies. From these values, averages with related errors are…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
We compute the number of points over finite fields of some algebraic varieties related to cluster algebras of finite type. More precisely, these varieties are the fibers of the projection map from the cluster variety to the affine space of…