DG algebras with exterior homology

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is the integers, or the prime field of characteristic p>0, and n is greater than or equal to -1. The examples are unexpectedly interesting.Comment: 15 page

Homology of perfect complexes

It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective dimension, obstructions to realizing R as a closed fiber of some flat local homomorphism. Other applications include, as special cases, uniform proofs of known results on free actions of elementary abelian groups and of tori on finite CW complexes. The arguments use numerical invariants of objects in general triangulated categories, introduced here and called levels. They allow one to track, through changes of triangulated categories, homological invariants like projective dimension, as well as structural invariants like Loewy length. An intermediate result sharpens, with a new proof, the New Intersection Theorem for commutative algebras over fields. Under additional hypotheses on the ring $R$ stronger estimates are proved for Loewy lengths of modules of finite projective dimension.Comment: This version corrects an error in the statement (and proof) of Theorem 7.4 in the published version of the paper [Adv. Math. 223 (2010) 1731--1781]. These changes do not affect any other results or proofs in the paper. A corrigendum has been submitted

Two-Hop Routing with Traffic-Differentiation for QoS Guarantee in Wireless Sensor Networks

This paper proposes a Traffic-Differentiated Two-Hop Routing protocol for Quality of Service (QoS) in Wireless Sensor Networks (WSNs). It targets WSN applications having different types of data traffic with several priorities. The protocol achieves to increase Packet Reception Ratio (PRR) and reduce end-to-end delay while considering multi-queue priority policy, two-hop neighborhood information, link reliability and power efficiency. The protocol is modular and utilizes effective methods for estimating the link metrics. Numerical results show that the proposed protocol is a feasible solution to addresses QoS service differenti- ation for traffic with different priorities.Comment: 13 page

Predicting the Brand Popularity from the Brand Metadata

Social networks have become one of the primary sources of big data, where a variety of posts related to brands are liked, shared, and commented, which are collectively called as brand metadata. Due to the increased boom in E/M-commerce, buyers often refer the brand metadata as a valuable source of information to make their purchasing decision. From the literature study, we found that there are not many works on predicting the popularity of the brand based on the combination of brand metadata and comment’s thoughtfulness analysis. This paper proposes a novel framework to classify the comment’s as thoughtful favored or disfavored comment’s, and later combines them with the brand metadata to forecast the popularity of the brand in near future. The performance of the proposed framework is compared with some of the recent works w.r.t. thoughtful comment’s identification accuracy, execution time, prediction accuracy and prediction time, the results obtained are found to be very encouraging