Bilinear Forms on Finite Abelian Groups and Group-Invariant Butson Hadamard Matrices

Let $K$ be a finite abelian group and let $\exp(K)$ denote the least common multiple of the orders of the elements of $K$. A $BH(K,h)$ matrix is a $K$-invariant $|K|\times |K|$ matrix $H$ whose entries are complex $h$th roots of unity such that $HH^*=|K|I$, where $H^*$ denotes the complex conjugate transpose of $H$, and $I$ is the identity matrix of order $|K|$. Let $\nu_p(x)$ denote the $p$-adic valuation of the integer $x$. Using bilinear forms on $K$, we show that a $BH(K,h)$ exists whenever (i) $\nu_p(h) \geq \lceil \nu_p(\exp(K))/2 \rceil$ for every prime divisor $p$ of $|K|$ and (ii) $\nu_2(h) \ge 2$ if $\nu_2(|K|)$ is odd and $K$ has a direct factor $\mathbb{Z}_2$. Employing the field descent method, we prove that these conditions are necessary for the existence of a $BH(K,h)$ matrix in the case where $K$ is cyclic of prime power order

The DKAP Project The Country Report of Vietnam

Viet Nam is at the beginning of the Fourth Industrial Revolution. In order to grasp the opportunities that the revolution has brought about, and to successfully build the society of digital citizens, there must be the demand of enhancing the capacity and capability for students to meet international standards in terms of Information and Communications Technology (ICT) skills. Viet Nam was selected as one of the four countries (Viet Nam, Bangladesh, Fiji, and the Republic of Korea) to join UNESCO Bangkok’s “Digital Kids Asia Pacific (DKAP)” project, a comparative cross-national study with the aim to seek the understanding and address children’s ICT practices, attitudes, behaviors, and competency levels within an educational context. Thanks to the project, the Vietnamese research team completely conducted the survey in twenty (20) schools from five (5) provinces in Viet Nam. With the data on the digital citizenship competency levels of 1,061 10th grade students, the research team discovered the valuable findings to draw an initial big picture for Vietnamese policy makers, educators, and teachers about digital citizenship competencies of 15-year-old Vietnamese students

Economic Reform in Tanzania and Vietnam: A Comparative Commentary

The economic reforms in Tanzania and Vietnam represent the two typical cases of transition economies in Asia and Africa, particularrly the transformation of the two developing economies from the planned to the market mechanism. In this paper, the two authors, Brian - a British economist and Dinh - a Vietnamese economist, have, basing on a comparative approach, enquired into various economic and social aspects of the economic reforms in the two countries, including the demographic transition, the change in population growth, the investment in human capital, the growth of GDP, the structural sransformation, the linkage between gricultural growth, rural development, food production and poverty alleviation, the reform in the industrial sector and the state enterprises, the change of ownership , the role of the State, the capital formation, the role of the domestic savings, foreign aid, investment and trade, the gains and losses from globalisation, with an aim to find the answer to the question why in the two cases, Tanzania seemed to follow the donors’ guidance better than Vietnam, but achieved smaller successes?http://deepblue.lib.umich.edu/bitstream/2027.42/40092/3/wp706.pd

Inference and Analysis of Multilayered Mirna-Mediated Networks in Cancer

MicroRNAs (miRNAs) are small noncoding transcripts that can regulate gene expression, thereby controlling diverse biological processes. Aberrant disruptions of miRNA expression and their interactions with other biological agents (e.g., coding and noncoding transcripts) have been associated with several types of cancer. The goal of this dissertation is to use multidimensional genomic data to model two different gene regulation mechanisms by miRNAs in cancer. This dissertation results from two research projects. The first project investigates a miRNA-mediated gene regulation mechanism called competing endogenous RNA (ceRNA) interactions, which suggests that some transcripts can indirectly regulate one another\u27s activity through their interactions with a common set of miRNAs. Identification of context-specific ceRNA interactions is a challenging task. To address that, we proposed a computational method called Cancerin to identify genome-wide cancer-associated ceRNA interactions. Cancerin incorporates DNA methylation (DM), copy number alteration (CNA), and gene and miRNA expression datasets to construct cancer-specific ceRNA networks. Cancerin was applied to three cancer datasets from the Cancer Genome Atlas (TCGA) project. We found that the RNAs involved in ceRNA interactions were enriched with cancer-related genes and have high prognostic power. Moreover, the ceRNA modules in the inferred ceRNA networks were involved in cancer-associated biological processes. The second project investigates what biological functions are regulated by both miRNAs and transcription factors (TFs). While it has been known that miRNAs and TFs can coregulate common target genes having similar biological functions, it is challenging to associate specific biological functions to specific miRNAs and TFs. In this project, we proposed a computational method called CanMod to identify gene regulatory modules. Each module consists of miRNAs, TFs and their coregulated target genes. CanMod was applied on the breast cancer dataset from TCGA. Many hub regulators (i.e., miRNAs and TFs) found in the inferred modules were known cancer genes, and CanMod was able to find experimentally validated regulator-target interactions. In addition, the modules were associated with distinguishable and cancer-related biological processes. Given the biological findings obtained from Cancerin and CanMod, we believe that the two computational methods are valuable tools to explore novel miRNA involvement in cancer