In a previous article (cf. [DM]), the modularity of a large class of rigid Calabi-Yau threefolds was established. To make that result more explicit, we recall (and re-prove) a result of Serre giving a bound for the conductor of “integral” 2-dimensional compatible families of Galois representations and apply this result to give an algorithm that determines the level of a modular rigid Calabi-Yau...

Collaborative filtering (CF)-based recommender systems represent a promising solution for the rapidly growing mobile music market. However, in the mobile Web environment, a traditional CF system that uses explicit ratings to collect user preferences has a limitation: mobile customers find it difficult to rate their tastes directly because of poor interfaces and high telecommunication costs. Imp...

Collaborative filtering(CF) for the personalized recommendation is a successful and popular method in recommender systems. But the mainly researched and implemented cases focus on dealing with independent items with explicit feedback by users. For the domain of TV program recommendation in VOD service platform, we need to consider the unique characteristic and constraints of the domain. In this...

This paper explores the problem of user recommendations in group settings. Research in networked social behavior has found evidence that individuals tend to form connections to those having similar interests to their own. Known as homophily, this tendency has been shown to significantly inform the structure of social networks. Collaborative filtering (CF) techniques, however, typically do not t...

Understanding the microbial flora of the cystic fibrosis (CF) respiratory tract is of considerable importance, as patient morbidity and death are primarily caused by chronic respiratory infections. However, chronically colonized CF airways represent a surprisingly complex and diverse ecosystem. The precise contributions of different microbes to patient morbidity, and in particular the importanc...

As usual, Z,Q,C denote the ring of integers, the field of rational numbers and the field of complex numbers respectively. Let us fix a primitive cube root of unity ζ3 = −1+ √ −3 2 ∈ C. Let Q(ζ3) = Q( √ −3) be the third cyclotomic field and Z[ζ3] = Z +Z · ζ3 its ring of integers. We write λ for the (principal) maximal ideal (1− ζ3) · Z[ζ3] of Z[ζ3]. It is known [11, Th. 5 on p. 176] (see also [5...

since the emergence of the process-oriented approach to second language writing instruction two main questions have been what and how error feedback should be given to the students. the question of whether teachers should provide feedback on grammar in the writing assignments of english as a foreign language students, and if so how, has been a matter of considerable debate in the field of secon...

In this paper we continue to extend our previous investigation of continued fraction (CF) solutions for the stationary probability of discrete one-variable master equations which generally do not satisfy detailed balance. We derive explicit expressions, directly in terms of the elementary transition rates, for the continued fraction recursion coefficients. Further, we derive several approximate...

1 Alonzo Church, Ann. Math., 2nd ser., 33, 346-366 (1932), and 34, 839-864 (1933). S. C. Kleene, Ann. Math., 2nd ser., 35, 529-544 (1934). We shall refer to the latter paper as Kleene 1934. 2 Alonzo Church and J. B. Rosser, "Some Properties of Conversion." 3 Explicit formal definitions are given by S. C. Kleene, Amer. Jour. Math., 57, 153173 (1935). This paper, and a second part of it, forthcom...