Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

"Where is the value in education for me?": experiences and perspectives of Ontario secondary students at risk of non-completion of their Ontario Secondary School Diploma /

This study examined students considered at risk of non-completion of their Ontario Secondary School Diploma and aimed to offer insight into the questions, "What factors currently lead to school disconnect" and "How can these factors be addressed?" Eight students currently enrolled in an alternative learning environment participated in the study. Each was asked to take part in two, digitally recorded interviews that were subsequently transcribed by the researcher. The data were then coded and analysed according to specific themes: obstacles, empowerment, goals, views about success, opinions of school, and power of the teacher. From these themes, three broad focus areas emerged that were used to keep the data analysis focused: worldview, school effects, and self-image. Variances between the data collected and ideas presented in the current literature were highlighted as a reminder that when dealing with a human population, we cannot rely on textbook definitions and theory alone.

An exploratory study for the discovery of non-invasive hepatocellular carcinoma biomarkers among high-risk hepatitis C virus infected patients

Hepatocellular Carcinoma (HCC) is a major healthcare problem, representing the third most common cause of cancer-related mortality worldwide. Chronic infections with Hepatitis B virus (HBV) and/or Hepatitis C virus (HCV) are the major risk factors for the development of HCC. The incidence of HBV -associated HCC is in decline as a result of an effective HBV vaccine; however, since an equally effective HCV vaccine has not yet been developed, there are 130 million HCV infected patients worldwide who are at a high-risk for developing HCC. Because reliable parameters and/or tools for the early detection of HCC among high-risk individuals are severely lacking, HCC patients are always diagnosed at a late stage where surgical solutions or effective treatment are not possible. Using urine as a non-invasive sample source, two different approaches (proteomic-based and genomic-based approaches) were pursued with the common goal of discovering potential biomarker candidates for the early detection of HCC among high-risk chronic HCV infected patients. Urine was collected from 106 HCV infected Egyptian patients, 32 of whom had already developed HCC and 74 patients who were diagnosed as HCC-free at the time of initial sample collection. In addition to these patients, urine samples were also collected from 12 healthy control individuals. Total urinary proteins, Trans-renal nucleic acid (Tr-NA) and microRNA (miRNA) were isolated from urine using novel methodologies and silicon carbide-loaded spin columns. In the first, "proteomic-based", approach, liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) was used to identify potential candidates from pooled urine samples. This was followed by validating relative expression levels of proteins present in urine among all the patients using quantitative real time-PCR (qRT-PCR). This approach revealed that significant over-expression of three proteins: DJ-1, Chromatin Assembly Factor-1 (CAF-1) and 11 Moemen Abdalla HCC Biomarkers Heat Shock Protein 60 (HSP60), were characteristic events among HCC-post HCV infected patients. As a single-based HCC biomarker, CAF-1 over-expression identified HCC among HCV infected patients with a specificity of 90%, sensitivity of 66% and with an overall diagnostic accuracy of 78%. Moreover, the CAF-lIHSP60 tandem identified HCC among HCV infected patients with a specificity of 92%, sensitivity of 61 % and with an overall diagnostic accuracy of 77%. In the second genomic-based approach, two different approaches were processed. The first approach was the miRNA-based approach. The expression levels of miRNAs isolated from urine were studied using the Illumina MicroRNA Expression Profiling Assay. This was followed by qRT-PCR-based validation of deregulated expression of identified miRNA candidates among all the patients. This approach shed the light on the deregulated expression of a number of miRNAs, which may have a role in either the development of HCC among HCV infected patients (i.e. miR-640, miR-765, miR-200a, miR-521 and miR-520) or may allow for a better understanding of the viral-host interaction (miR-152, miR-486, miR-219, miR452, miR-425, miR-154 and miR-31). Moreover, the deregulated expression of both miR-618 and miR-650 appeared to be a common event among HCC-post HCV infected patients. The results of the search for putative targets of these two miRNA suggested that miR-618 may be a potent oncogene, as it targets the tumor-suppressor gene Low density lipoprotein-related protein 12 (LPR12), while miR-650 may be a potent tumor-suppressor gene, as it is supposed to downregulate the TNF receptor-associated factor-4 (TRAF4) oncogene. The specificity of miR-618 and miR-650 deregulated expression patterns for the early detection of HCC among HCV infected patients was 68% and 58%, respectively, whereas the sensitivity was 64% and 72%, respectively. When the deregulated expression of both miRNAs was combined as a tandem biomarker, the specificity and the sensitivity were 75% and 58% respectively. 111 Moemen Abdalla HCC Biomarkers In the second, "Trans-renal nucleic acid-based", approach, the urinary apoptotic nucleic acid (uaNA) levels of 70ng/mL or more were found to be a good predictor of HCC among chronic HCV infected patients. The specificity and the sensitivity of this diagnostic approach were 76% and 86%, respectively, with an overall diagnostic value of 81 %. The uaNA levels positively correlated to HCC disease progression as monitored by epigenetic changes of a panel of eight tumor-suppressor genes (TSGs) using methylation-sensitive PCR. Moreover, the pairing of high uaNA levels (:::: 70 ng/mL) and CAF-1 over-expreSSIOn produced a highly specific (l 00%) multiple-based HCC biomarker with an acceptable sensitivity of 64%, and with a diagnostic accuracy of 82%. In comparison to the previous pairing, the uaNA levels (:::: 70 ng/mL) in tandem with HSP60 over-expression was less specific (89%) but highly sensitive (72%), resulting in a diagnostic accuracy of 64%. The specificities of miR-650 deregulated expression in combination with either high uaNA content or HSP 60 over-expression were 82% and 79%, respectively, whereas, the sensitivities of these combinations were 64% and 58%, respectively. The potential biomarkers identified in this study compare favorably with the diagnostic accuracy of the a-fetoprotein levels test, which has a specificity of 75%, sensitivity of 68% and an overall diagnostic accuracy of 70%. Here we present an intriguing study which shows the significance of using urine as a noninvasive sample source for the identification of promising HCC biomarkers. We have also introduced new techniques for the isolation of different urinary macromolecules, especially miRNA, from urine. Furthermore, we strongly recommend the potential biomarkers indentified in this study as focal points of any future research on HCC diagnosis. A larger testing pool will determine if their use is practical for mass population screening. This explorative study identified potential targets that merit further investigation for the development of diagnostically accurate biomarkers isolated from 1-2 mL urine samples that were acquired in a non-invasive manner.