On the extremal number of edges in hamiltonian connected graphs

AbstractAssume that n and δ are positive integers with 3≤δ<n. Let hc(n,δ) be the minimum number of edges required to guarantee an n-vertex graph G with minimum degree δ(G)≥δ to be hamiltonian connected. Any n-vertex graph G with δ(G)≥δ is hamiltonian connected if |E(G)|≥hc(n,δ). We prove that hc(n,δ)=C(n−δ+1,2)+δ2−δ+1 if δ≤⌊n+3×(nmod2)6⌋+1, hc(n,δ)=C(n−⌊n2⌋+1,2)+⌊n2⌋2−⌊n2⌋+1 if ⌊n+3×(nmod2)6⌋+1<δ≤⌊n2⌋, and hc(n,δ)=⌈nδ2⌉ if δ>⌊n2⌋

Identification of microbial DNA in human cancer

<p>Abstract</p> <p>Background</p> <p>Microorganisms have been associated with many types of human diseases; however, a significant number of clinically important microbial pathogens remain to be discovered.</p> <p>Methods</p> <p>We have developed a genome-wide approach, called Digital Karyotyping Microbe Identification (DK-MICROBE), to identify genomic DNA of bacteria and viruses in human disease tissues. This method involves the generation of an experimental DNA tag library through Digital Karyotyping (DK) followed by analysis of the tag sequences for the presence of microbial DNA content using a compiled microbial DNA virtual tag library.</p> <p>Results</p> <p>To validate this technology and to identify pathogens that may be associated with human cancer pathogenesis, we used DK-MICROBE to determine the presence of microbial DNA in 58 human tumor samples, including brain, ovarian, and colorectal cancers. We detected DNA from Human herpesvirus 6 (HHV-6) in a DK library of a colorectal cancer liver metastasis and in normal tissue from the same patient.</p> <p>Conclusion</p> <p>DK-MICROBE can identify previously unknown infectious agents in human tumors, and is now available for further applications for the identification of pathogen DNA in human cancer and other diseases.</p

Carrier Screening for Spinal Muscular Atrophy (SMA) in 107,611 Pregnant Women during the Period 2005–2009: A Prospective Population-Based Cohort Study

BACKGROUND: Spinal muscular atrophy (SMA) is the most common neuromuscular autosomal recessive disorder. The American College of Medical Genetics has recently recommended routine carrier screening for SMA because of the high carrier frequency (1 in 25-50) as well as the severity of that genetic disease. Large studies are needed to determine the feasibility, benefits, and costs of such a program. METHODS AND FINDINGS: This is a prospective population-based cohort study of 107,611 pregnant women from 25 counties in Taiwan conducted during the period January 2005 to June 2009. A three-stage screening program was used: (1) pregnant women were tested for SMA heterozygosity; (2) if the mother was determined to be heterozygous for SMA (carrier status), the paternal partner was then tested; (3) if both partners were SMA carriers, prenatal diagnostic testing was performed. During the study period, a total of 2,262 SMA carriers with one copy of the SMN1 gene were identified among the 107,611 pregnant women that were screened. The carrier rate was approximately 1 in 48 (2.10%). The negative predictive value of DHPLC coupled with MLPA was 99.87%. The combined method could detect approximately 94% of carriers because most of the cases resulted from a common single deletion event. In addition, 2,038 spouses were determined to be SMA carriers. Among those individuals, 47 couples were determined to be at high risk for having offspring with SMA. Prenatal diagnostic testing was performed in 43 pregnant women (91.49%) and SMA was diagnosed in 12 (27.91%) fetuses. The prevalence of SMA in our population was 1 in 8,968. CONCLUSION: The main benefit of SMA carrier screening is to reduce the burden associated with giving birth to an affected child. In this study, we determined the carrier frequency and genetic risk and provided carrier couples with genetic services, knowledge, and genetic counseling

Outcome of Population-based Spinal Muscular Atrophy (SMA) Screening in Taiwan.

<p>*Data available from the Bureau of Health Promotion, Department of Health, Taiwan (<a href="http://www.bhp.doh.gov.tw/BHPnet/Portal/" target="_blank">http://www.bhp.doh.gov.tw/BHPnet/Portal/</a>).</p