Related papers: Sums and averages

Creating linguistic annotations requires more than just a reliable annotation scheme. Annotation can be a complex endeavour potentially involving many people, stages, and tools. This chapter outlines the process of creating end-to-end…

Interim analyses for group-sequential decision making are prevalent in clinical trials. Methodology is well established and has been routinely implemented over the last decades. Still, confusions and uncertainties on aspects of how to…

This note is a survey of $J$-spaces.

This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental…

We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.

Summarization systems are ultimately evaluated by human annotators and raters. Usually, annotators and raters do not reflect the demographics of end users, but are recruited through student populations or crowdsourcing platforms with skewed…

These are notes from a basic course in Several Complex Variables

Informal mathematical text underpins real-world quantitative reasoning and communication. Developing sophisticated methods of retrieval and abstraction from this dual modality is crucial in the pursuit of the vision of automating discovery…

In this paper, we provide formulas for partial sums of weighted averages over regular integers modulo $n$ of the $\gcd$-sum function with any arithmetic function. Many interesting applications of the results are also given.

Formal concepts and closed itemsets proved to be of big importance for knowledge discovery, both as a tool for concise representation of association rules and a tool for clustering and constructing domain taxonomies and ontologies.…

These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical…

In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.

These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.

Well-defined formal definitions for sentiment and opinion are extended to incorporate the necessary elements to provide a formal quantitative definition of reputation. This definition takes the form of a time-based index, in which each…

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…

These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

Equivalencies of many basic elementary inequalities are given

We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…