On existentially complete triangle-free graphs

For a positive integer k, we say that a graph is k-existentially complete if for every 0 ⩽ a ⩽ k, and every tuple of distinct vertices x1, …, xa, y1, …, yk−a, there exists a vertex z that is joined to all of the vertices x1, …, xa and to none of the vertices y1, …, yk−a. While it is easy to show that the binomial random graph Gn,1/2 satisfies this property (with high probability) for k = (1 − o(1)) log2n, little is known about the “triangle-free” version of this problem: does there exist a finite triangle-free graph G with a similar “extension property”? This question was first raised by Cherlin in 1993 and remains open even in the case k = 4. We show that there are no k-existentially complete triangle-free graphs on n vertices with k>8lognloglogn, for n sufficiently large

Partitioning a graph into monochromatic connected subgraphs

We show that every 2-edge‐colored graph on vertices with minimum degree at least\frac{2n - 5}{3} can be partitioned into two monochromatic connected subgraphs, provided

Simplified Production of Large Prototypes using Visible Slicing

Rapid Prototyping (RP) is a totally automatic generative manufacturing technique based on a “divide-and-conquer” strategy called ‘slicing’. Simple slicing used on 2.5-axis kinematics of the existing RP machines is responsible for the staircase error. Although thinner slices will have less error, the slice thickness has practical limits. Visible Slicing overcomes these limitations. A few visible slices exactly represent the object. Each visible slice can be realized using a 3- axis kinematics machine from two opposite directions. Visible slicing is implemented on Segmented Object Manufacturing (SOM) machine under development. SOM can produce soft large prototypes faster and cheaper with accuracy comparable to that of CNC machining.Mechanical Engineerin

BRAF and TERT mutations in papillary thyroid cancer patients of Latino ancestry.

Papillary thyroid cancer (PTC) is the second most commonly diagnosed malignancy in U.S. Latinas and in Colombian women. Studies in non-Latinos indicate that BRAF and TERT mutations are PTC prognostic markers. This study aimed to determine the prevalence and clinical associations of BRAF and TERT mutations in PTC Latino patients from Colombia. We analyzed mutations of BRAF (V600E) and TERT promoter (C228T, C250T) in tumor DNA from 141 patients (75 with classical variant PTC, CVPTC; 66 with follicular variant PTC, FVPTC) recruited through a multi-center study. Associations between mutations and clinical variables were evaluated with Fisher exact tests. Survival was evaluated with Kaplan-Meier plots. Double-mutant tumors (BRAF+/TERT+, n = 14 patients) were more common in CVPTC (P = 0.02). Relative to patients without mutations (n = 48), double mutations were more common in patients with large tumors (P = 0.03), lymph node metastasis (P = 0.01), extra-thyroid extension (P = 0.03), and advanced stage (P = 6.0 × 10-5). In older patients, TERT mutations were more frequent (mean age 51 years vs 45 years for wild type TERT, P = 0.04) and survival was lower (HR = 1.20; P = 0.017); however, given the small sample size, the decrease in survival was not statically significant between genotypes. Comparisons with published data in US whites revealed that Colombian patients had a higher prevalence of severe pathological features and of double-mutant tumors (10 vs 6%, P = 0.001). Mutations in both oncogenes show prognostic associations in Latinos from Colombia. Our study is important to advance Latino PTC precision medicine and replicates previous prognostic associations between BRAF and TERT in this population

The HABP2 G534E polymorphism does not increase nonmedullary thyroid cancer risk in Hispanics.

Familial nonmedullary thyroid cancer (NMTC) has not been clearly linked to causal germline variants, despite the large role that genetic factors play in risk. Recently, HABP2 G534E (rs7080536A) has been implicated as a causal variant in NMTC. We have previously shown that the HABP2 G534E variant is not associated with TC risk in patients from the British Isles. Hispanics are the largest and the youngest minority in the United States and NMTC is now the second most common malignancy in women from this population. In order to determine if the HABP2 G534E variant played a role in NMTC risk among Hispanic populations, we analyzed 281 cases and 1105 population-matched controls from a multicenter study in Colombia, evaluating the association through logistic regression. We found that the HABP2 G534E variant was not significantly associated with NMTC risk (P=0.843) in this Hispanic group. We also stratified available clinical data by multiple available clinicopathological variables and further analyzed the effect of HABP2 on NMTC presentation. However, we failed to detect associations between HABP2 G534E and NMTC risk, regardless of disease presentation (P≥0.273 for all cases). Therefore, without any significant associations between the HABP2 G534E variant and NMTC risk, we conclude that the variant is not causal of NMTC in this Hispanic population