Covering Points by Disjoint Boxes with Outliers

For a set of n points in the plane, we consider the axis--aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain n-k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+k log k) time for p=1, and O(n log n+k^p log^p k time for p = 2,3. For rectangles we get O(n + k^3) for p = 1 and O(n log n+k^{2+p} log^{p-1} k) time for p = 2,3. In all cases, our algorithms use O(n) space.Comment: updated version: - changed problem from 'cover exactly n-k points' to 'cover at least n-k points' to avoid having non-feasible solutions. Results are unchanged. - added Proof to Lemma 11, clarified some sections - corrected typos and small errors - updated affiliations of two author

Inscribing or Circumscribing a Histogon to a Convex Polygon

We consider two optimization problems of approximating a convex polygon, one by a largest inscribed histogon and the other by a smallest circumscribed histogon. An axis-aligned histogon is an axis-aligned rectilinear polygon such that every horizontal edge has an integer length. A histogon of orientation ? is a copy of an axis-aligned histogon rotated by ? in counterclockwise direction. The goal is to find a largest inscribed histogon and a smallest circumscribed histogon over all orientations in [0,?). Depending on whether the horizontal width of a histogon is predetermined or not, we consider several different versions of the problem and present exact algorithms. These optimization problems belong to shape analysis, classification, and simplification, and they have applications in various cost-optimization problems

PwRn1, a novel Ty3/gypsy-like retrotransposon of Paragonimus westermani: molecular characters and its differentially preserved mobile potential according to host chromosomal polyploidy

<p>Abstract</p> <p>Background</p> <p>Retrotransposons have been known to involve in the remodeling and evolution of host genome. These reverse transcribing elements, which show a complex evolutionary pathway with diverse intermediate forms, have been comprehensively analyzed from a wide range of host genomes, while the information remains limited to only a few species in the phylum Platyhelminthes.</p> <p>Results</p> <p>A LTR retrotransposon and its homologs with a strong phylogenetic affinity toward <it>CsRn1 </it>of <it>Clonorchis sinensis </it>were isolated from a trematode parasite <it>Paragonimus westermani </it>via a degenerate PCR method and from an insect species <it>Anopheles gambiae </it>by <it>in silico </it>analysis of the whole mosquito genome, respectively. These elements, designated <it>PwRn1 </it>and <it>AgCR-1 </it>– <it>AgCR-14 </it>conserved unique features including a t-RNA^Trpprimer binding site and the unusual CHCC signature of Gag proteins. Their flanking LTRs displayed >97% nucleotide identities and thus, these elements were likely to have expanded recently in the trematode and insect genomes. They evolved heterogeneous expression strategies: a single fused ORF, two separate ORFs with an identical reading frame and two ORFs overlapped by -1 frameshifting. Phylogenetic analyses suggested that the elements with the separate ORFs had evolved from an ancestral form(s) with the overlapped ORFs. The mobile potential of <it>PwRn1 </it>was likely to be maintained differentially in association with the karyotype of host genomes, as was examined by the presence/absence of intergenomic polymorphism and mRNA transcripts.</p> <p>Conclusion</p> <p>Our results on the structural diversity of <it>CsRn1</it>-like elements can provide a molecular tool to dissect a more detailed evolutionary episode of LTR retrotransposons. The <it>PwRn1</it>-associated genomic polymorphism, which is substantial in diploids, will also be informative in addressing genomic diversification following inter-/intra-specific hybridization in <it>P. westermani </it>populations.</p

Graphene for Controlled and Accelerated Osteogenic Differentiation of Human Mesenchymal Stem Cells

Modern tissue engineering strategies combine living cells and scaffold materials to develop biological substitutes that can restore tissue functions. Both natural and synthetic materials have been fabricated for transplantation of stem cells and their specific differentiation into muscles, bones and cartilages. One of the key objectives for bone regeneration therapy to be successful is to direct stem cells' proliferation and to accelerate their differentiation in a controlled manner through the use of growth factors and osteogenic inducers. Here we show that graphene provides a promising biocompatible scaffold that does not hamper the proliferation of human mesenchymal stem cells (hMSCs) and accelerates their specific differentiation into bone cells. The differentiation rate is comparable to the one achieved with common growth factors, demonstrating graphene's potential for stem cell research.Comment: 34 pages, 11 figures, 1 table, submitte

Cigarette Smoking and Risk of Lung Cancer in Korean Men: The Seoul Male Cancer Cohort Study

Lung cancer is the leading cause of cancer deaths in Korea. The aim of this study was to estimate lung cancer risk of cigarette smoking in Korean men by a 10-yr follow-up prospective cohort study using the primary databases. The number of subjects was 14,272 men, who had full information of smoking habits among participants in the Seoul Male Cancer Cohort Study (SMCC). Total 125,053 person-years were calculated by determining the number of days from the start of follow-up, January 1, 1993, until the date of lung cancer diagnosis, death from another cause, or the end of follow-up, December 31, 2002, followed by converting the number of days to years. The information of outcome was obtained by the database of Korea Central Cancer Registry, Seoul Regional Cancer Registry, and Korea Statistical Office. The relative risk (RR) and its 95% confidence interval (CI) values of smoking were calculated using Cox proportional hazards regression stratified on potential confounders. During the follow-up periods, 78 cases of lung cancer occurred. The cigarette smoking is the major risk factor and increases the 4.18-fold risk of lung cancer in Korean men. In order to control lung cancer, intervention of quitting smoking is needed

Preoperative serum HER2 extracellular domain levels in primary invasive breast cancer

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.Abstract Background Despite the preclinical outcomes and biologic significance of the presence of the human epidermal growth factor receptor-2 (HER2) extracellular domain (ECD), there is little evidence supporting the measurement of ECD levels in any clinical setting. The aim of this study was to determine the prevalence of elevated serum HER2 ECD levels, the association between these levels and tissue HER2 overexpression, and the potential clinical prognostic value of HER2 ECD in primary invasive breast cancer. Methods Serum HER2 ECD levels were examined preoperatively in 2,862 consecutive stage I–III primary breast cancer patients between 2007 and 2009. Serum HER2 ECD levels were measured by chemiluminescence immunoassay (ADVIA Centaur), and the tissue HER2 status was assessed by immunohistochemistry and fluorescence in situ hybridization. The cutoff value for the serum level of HER2 ECD was set at 15.2 ng/ml. Results Among the 2,862 patients, 126 (4.4%) had elevated serum HER2 ECD levels, and HER2 was overexpressed in the tumor tissue of 692 patients (24.2%), with a concordance of 78.7%. Multivariate analysis revealed that elevated serum HER2 ECD was a significant independent prognostic factor for worse distant-metastasis-free survival [DMFS; hazard ratio (HR) = 2.50, 95% confidence interval (CI) = 1.5–4.3, P = 0.001] and breast-cancer-specific survival (BCSS; HR = 2.0, 95% CI = 1.1–3.8, P = 0.036), which were much stronger in patients with tissue HER2-positive tumors (DMFS: HR = 3.8, 95% CI = 2.0–7.0, P < 0.001; BCSS: HR = 2.6, 95% CI = 1.2-5.3, P = 0.012). Conclusions Given the prevalence of HER2 expression, its measurement as an independent prognostic factor can be clinically useful, particularly in patients with tissue HER2-positive tumors