The regularity of points in multi-projective spaces

Let I = p_1^{m_1} \cap ... \cap p_s^{m_s} be the defining ideal of a scheme of fat points in P^{n_1} x ... x P^{n_k} with support in generic position. When all the m_i's are 1, we explicitly calculate the Castelnuovo-Mumford regularity of I. In general, if at least one m_i >= 2, we give an upper bound for the regularity of I, which extends the result of Catalisano, Trung and Valla to the multi-projective case.Comment: 12 pages with minor revisions. To appear in JPA

Splittings of monomial ideals

We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bipartite graphs. Finally, we consider the frequency with which one can find particular splittings of monomial ideals and raise questions about ideals whose resolutions are characteristic-dependent.Comment: minor changes: added Cor. 3.10 and some references. To appear in Proc. Amer. Math. So

A conjecture on critical graphs and connections to the persistence of associated primes

We introduce a conjecture about constructing critically (s+1)-chromatic graphs from critically s-chromatic graphs. We then show how this conjecture implies that any unmixed height two square-free monomial ideal I, i.e., the cover ideal of a finite simple graph, has the persistence property, that is, Ass(R/I^s) \subseteq Ass(R/I^{s+1}) for all s >= 1. To support our conjecture, we prove that the statement is true if we also assume that \chi_f(G), the fractional chromatic number of the graph G, satisfies \chi(G) -1 < \chi_f(G) <= \chi(G). We give an algebraic proof of this result.Comment: 11 pages; Minor changes throughout the paper; to appear in Discrete Math

Motivational profiles of learning multiple foreign languages

Second language motivation has been well-researched in SLA and has a consistent positive correlation with learning achievement, which is empirically supported by many studies in different contexts with different second languages (Masgoret & Gardner, 2003). However, except for a few recent studies (Dörnyei & Chan, 2013; Henry & Cliffordson, 2013), little is known about how motivation differs when learners attempt to study more than one foreign language simultaneously. This paper reports on how university students in Vietnam are motivated to learn both English and Mandarin. Conceptualizing motivation via the L2 Motivational Self System, proposed and validated by Dörnyei and other scholars, 154 Vietnamese university students were given a motivation questionnaire. Using both quantitative and qualitative profile analyses, the results generally indicated that students have different motivations for learning English and Mandarin

Random walks on mutual microRNA-target gene interaction network improve the prediction of disease-associated microRNAs

Background: MicroRNAs (miRNAs) have been shown to play an important role in pathological initiation, progression and maintenance. Because identification in the laboratory of disease-related miRNAs is not straightforward, numerous network-based methods have been developed to predict novel miRNAs in silico. Homogeneous networks (in which every node is a miRNA) based on the targets shared between miRNAs have been widely used to predict their role in disease phenotypes. Although such homogeneous networks can predict potential disease-associated miRNAs, they do not consider the roles of the target genes of the miRNAs. Here, we introduce a novel method based on a heterogeneous network that not only considers miRNAs but also the corresponding target genes in the network model. Results: Instead of constructing homogeneous miRNA networks, we built heterogeneous miRNA networks consisting of both miRNAs and their target genes, using databases of known miRNA-target gene interactions. In addition, as recent studies demonstrated reciprocal regulatory relations between miRNAs and their target genes, we considered these heterogeneous miRNA networks to be undirected, assuming mutual miRNA-target interactions. Next, we introduced a novel method (RWRMTN) operating on these mutual heterogeneous miRNA networks to rank candidate disease-related miRNAs using a random walk with restart (RWR) based algorithm. Using both known disease-associated miRNAs and their target genes as seed nodes, the method can identify additional miRNAs involved in the disease phenotype. Experiments indicated that RWRMTN outperformed two existing state-of-the-art methods: RWRMDA, a network-based method that also uses a RWR on homogeneous (rather than heterogeneous) miRNA networks, and RLSMDA, a machine learning-based method. Interestingly, we could relate this performance gain to the emergence of "disease modules" in the heterogeneous miRNA networks used as input for the algorithm. Moreover, we could demonstrate that RWRMTN is stable, performing well when using both experimentally validated and predicted miRNA-target gene interaction data for network construction. Finally, using RWRMTN, we identified 76 novel miRNAs associated with 23 disease phenotypes which were present in a recent database of known disease-miRNA associations. Conclusions: Summarizing, using random walks on mutual miRNA-target networks improves the prediction of novel disease-associated miRNAs because of the existence of "disease modules" in these networks