相关论文: Potpourri, 8

The goal of these talks was to explain how cohomology and other tools of algebraic topology are seen through the lens of n-category theory. Special topics include nonabelian cohomology, Postnikov towers, the theory of "n-stuff", and…

Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…

In this short note, we aim to discuss some summations due to Ramanujan, their generalizations and some allied series

Many things in mathematics seem lamost unreasonably nice. This includes objects, counterexamples, proofs. In this preprint I discuss many examples of this phenomenon with emphasis on the ring of polynomials in a countably infinite number of…

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…

There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to…

We prove an NP upper bound on a theory of integer-indexed integer-valued arrays that extends combinatory array logic with an ordering relation on the index set and the ability to express sums of elements. We compare our fragment with seven…

First we give a complex ball uniformization of the moduli space of 8 ordered points on the projective line by using the theory of periods of K3 surfaces. Next we give a projective model of this moduli space by using automorphic forms on a…

We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent…

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…

This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…

Recently, research efforts have gained pace to cater to varied user preferences while generating text summaries. While there have been attempts to incorporate a few handpicked characteristics such as length or entities, a holistic view…

This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…

A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.

This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…

Classroom discussions in English Language Arts have a positive effect on students' reading, writing and reasoning skills. Although prior work has largely focused on teacher talk and student-teacher interactions, we focus on three…

The annotation of textual information is a fundamental activity in Linguistics and Computational Linguistics. This article presents various observations on annotations. It approaches the topic from several angles including Hypertext,…

In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…