Cubic Augmentation of Planar Graphs

In this paper we study the problem of augmenting a planar graph such that it becomes 3-regular and remains planar. We show that it is NP-hard to decide whether such an augmentation exists. On the other hand, we give an efficient algorithm for the variant of the problem where the input graph has a fixed planar (topological) embedding that has to be preserved by the augmentation. We further generalize this algorithm to test efficiently whether a 3-regular planar augmentation exists that additionally makes the input graph connected or biconnected. If the input graph should become even triconnected, we show that the existence of a 3-regular planar augmentation is again NP-hard to decide.Comment: accepted at ISAAC 201

Planar subgraphs without low-degree nodes

We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k. If G is a unit disk graph, the problem is trivial to solve for k = 1. We show that even the slightest deviation from the trivial case (e.g., quasi unit disk graphs or k = 1) leads to NP-hard problems.Peer reviewe

Approximating the edge length of 2-edge connected planar geometric graphs on a set of points

Given a set P of n points in the plane, we solve the problems of constructing a geometric planar graph spanning P 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set P, respectively. First, we construct in O(nlogn) time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in O(nlogn) time a 2-edge connected geometric planar graph spanning P with max edge length bounded by √5 times the optimal, assuming that the set P forms a connected Unit Disk Graph. Second, we prove that 2 times the optimal is always sufficient if the set of points forms a 2 edge connected Unit Disk Graph and give an algorithm that runs in O(n 2) time. We also show that for κ ∈ O(√n), there exists a set P of n points in the plane such that even though the Unit Disk Graph spanning P is κ-vertex connected, there is no 2-edge connected geometric planar graph spanning P even if the length of its edges is allowed to be up to 17/16

Novel PTH gene mutations causing isolated hypoparathyroidism

Context: PTH gene mutations represent a rare cause of familial isolated hypoparathyroidism (FIH). These defects can cause hypoparathyroidism with increased or decreased serum levels of PTH through 1) impaired PTH synthesis; 2) induction of parathyroid cell apoptosis; or 3) secretion of bioinactive PTH molecules. Eight pathogenic mutations of this gene have been described previously. Objective: Through describing two novel mutations of the PTH gene, we aim to extend the molecular basis for FIH and further refine the proposed mechanisms by which PTH mutations cause hypoparathyroidism. Design: Proband case reports with extended family analysis. Patients and Other Participants: The probands in both kindreds presented before 10-days-of-age with hypocalcemia and elevated phosphate levels. Proband A had low PTH levels, while these levels were elevated in Proband B. Proband B was initially diagnosed with pseudohypoparathyroidism. Interventions: Methylation analysis of CpG dinucleotides within three GNAS differentially methylated regions; Whole genome sequencing; and PTH infusion with analysis of nephrogenous cyclic AMP. Results: Proband A had a novel heterozygous sequence change in exon 2 of the PTH gene, c.46_47delinsAA (p.Ala16Lys) and Proband B had a novel homozygous nucleotide transition in PTH exon 3 (c.128G>A; p.G43E) that led to replacement of glycine by glutamic acid at position 12 of PTH 1-84. PTH 1-34 infusion demonstrated that renal responsiveness to PTH was intact and not antagonized by circulating bioinactive PTH. Conclusions: PTH gene mutations are uncommon causes of hypoparathyroidism, but can be misdiagnosed as disorders of gland development or receptor function if PTH levels are decreased or elevated, respectively. Genetic testing should be considered early in the diagnostic approach to these presentations

ASSESSMENT OF THE CONSTRUCTION INDUSTRY PRACTICE IN PALESTINE BASED ON THE DESIGN FOR CONSTRUCTION SAFETY (DFCS) CONCEPT

Construction industry is characterized by poor safety performance subjecting workers at sites to great risks. Safety risks can be minimized, not only by improving safety measures at site but also by considering safety issues throughout the project lifecycle; from the schematic design up to the operation and maintenance phases. Design for Construction Safety (DfCS) should be considered a main criterion in the design of engineering projects. In the DfCS most hazards would be designed out or minimized before reaching the construction phase. In Palestine, the construction industry has many safety accidents and risks caused by inadequate considerations to safety requirements in the early stages of the project lifecycle. The main aim of the undertaken research is to enhance the safety performance of the construction industry in Palestine. The characteristics of the construction industry in Palestine were assessed based on the DfCS concept. The positive characteristics are to be strengthened while the negative ones should be avoided, or at least proactive measures should be taken to minimize their effects. The DfCS concept was applied to five case study buildings already constructed in Gaza Strip, Palestine. The results from the case studies determined the safety risks in need for improvements; the main of which included:(1) Designing the exterior and interior building edges in such a way to ensure worker protection during the construction and maintenance phases,(2) Designing the formworks required for architecture, civil, mechanical and electrical works and (3) Selection of noncombustible durable building materials which can be also handled

Synthesis and Evaluation of Novel DNA Minor Groove Binders as Antiamoebic Agents

The free-living amoeba Acanthamoeba castellanii is responsible for the central nervous infection granulomatous amoebic encephalitis and sight-threatening infection Acanthamoeba keratitis. Moreover, no effective treatment is currently present, and a combination drug therapy is used. In this study, twelve DNA minor groove binders (MGBs) were synthesized and tested for their antiamoebic activity via amoebicidal, encystation, excystation, and cytopathogenicity assays. It was found that the compounds MGB3, MGB6, MGB22, MGB24, and MGB16 significantly reduce amoeba viability to 76.20%, 59.45%, 66.5%, 39.32%, and 43.21%, respectively, in amoebicidal assays. Moreover, the compounds MGB6, MGB20, MGB22, MGB28, MGB30, MGB32, and MGB16 significantly inhibit Acanthamoeba cysts, leading to the development of only 46.3%, 39%, 30.3%, 29.6%, 27.8%, 41.5%, and 45.6% cysts. Additionally, the compounds MGB3, MGB4, MGB6, MGB22, MGB24, MGB28, MGB32, and MGB16 significantly reduce the re-emergence of cysts to trophozoites, with viable trophozoites being only 64.3%, 47.3%, 41.4%, 52.9%, 55.4%, 40.6%, 62.1%, and 51.7%. Moreover, the compounds MGB3, MGB4, and MGB6 exhibited the greatest reduction in amoeba-mediated host-cell death, with cell death reduced to 41.5%, 49.4%, and 49.5%. With the following determined, future in vivo studies can be carried out to understand the effect of the compounds on animal models such as mice