A Space-Filling, Nonregular Tetrahedron

This activity is an investigation of a special nonregular tetrahedron that can be arranged to fill space without leaving any internal gaps in the same way that certain planar figures tessellate the plane. These tetrahedra can be connected together with hinges to make fun and interesting puzzles. More background information can be found in the paper An Amazing, Space-Filling, Non-Regular Tetrahedron by Joyce Frost and Peg Cagle, published by the IAS/Park City Mathematics Institute (available at mathforum.org/pcmi/hstp/resources/dodeca/)

Temporal and spatial sulfate variability in groundwater at a lignite mine, northeast Texas

Sulfate (SO₄ ²⁻) concentrations in the groundwater at the Luminant Monticello lignite mine, northeast Texas, vary with both time and space. SO₄ ²⁻ is monitored closely because it is a product of chemical reactions that can lead to acid mine drainage. Although acid mine drainage is not a problem at Monticello, SO₄ ²⁻ concentrations in some areas are high and correspond to high total dissolved solids (TDS), low pH groundwater. At Monticello, chloride, total dissolved iron, and total dissolved manganese concentrations also are variable. To examine this variability, 46 monitoring wells are divided into those: 1) screened in rock underneath the lignite seam (underburden); 2) screened in the rock over the lignite seam (overburden); and 3) screened in the reclaimed spoil. There is a wide range of SO₄ ²⁻ concentration across the mine with statistically significant differences between the SO₄ ²⁻ distributions for each well category. Three hypotheses may explain the spatial SO₄ ²⁻ variability: (1) The heterogeneity of the mined material (2) Flushing of SO₄ ²⁻ from the reclaimed section into the overburden (3) Exposing iron sulfides to oxidizing conditions when the water table is dropped by mine dewatering operations. Possible sources of SO₄ ²⁻ include the oxidation of pyrite and/or the dissolution of gypsum. Temporal SO₄ ²⁻ variability is evident in the SO₄ ²⁻ time series for each well. In the underburden, SO₄ ²⁻ seems to be approaching a steady state; however, some wells in the unmined overburden and reclaimed area have SO₄ ²⁻ trends that are increasing or are highly variable with time. Water table fluctuations or flushing caused by seasonal meteorological changes may control these trends. Correlation analyses show that for most underburden, overburden, and reclaim wells, SO₄ ²⁻ does not correlate with pH, indicating that acidity does not accompany the incorporation of SO₄ ²⁻ and that SO₄ ²⁻ may be advected from another part of the mine. Analysis of water level and SO₄ ²⁻ time series, as well as Cl⁻ and SO₄ ²⁻ time series, show that advection from reclaimed areas cannot account for every high SO₄ ²⁻ value or increasing SO₄ ²⁻ concentration in the overburden and reclaim. Groundwater in most overburden and reclaimed areas are at equilibrium with gypsum, indicating gypsum precipitation if SO₄ ²⁻ is flushed into the area and gypsum dissolution if SO₄ ²⁻ is flushed out. Time series analyses shows some of the wells with increasing SO₄ ²⁻ concentration to be approaching equilibrium. Also, most SO₄ ²⁻ time series have a seasonal component. Flushing from the reclaimed areas is considered to be the dominant process controlling SO₄ ²⁻ variability in the overburden. A combination of flushing and aqueous geochemical processes related to heterogeneity controls the SO₄ ²⁻ concentration in the reclaimed land.Geological Science

Overexpression of Glut1 and Glut3 in stage I nonsmall cell lung carcinoma is associated with poor survival

BACKGROUND. Increased expression of Glut1 and Glut2, has been reported in many human cancers, including nonsmall cell lung carcinoma (NSCLC). The aim of this study was to determine the biologic significance of Glut1 and Glut3 overexpression in Stage I NSCLC. METHODS. Using immunohistochemistry and polyclonal anti-Glut1 and anti-Glut3 antibodies, the authors immunostained sections of formalin fixed, paraffin embedded tissues from 289 Stage I NSCLCs. The Kaplan-Meier survival method, the log rank test, and Fisher\u27s exact test were used for statistical analysis. RESULTS. Of the 289 cases, 49 (17%) were negative for both Glut1 and Glut3, 239 (83%) were Glut1 positive, 61 (21%) were Glut3 positive, 179 (62%) were positive for Glut1 but negative for Glut3, 1 (0.3%) was positive for Glut3 but negative for Glut1, and 60 (21%) were positive for both Glut1 and Glut3. Only 1 of 50 Glut1 negative tumors (2%) was positive for Glut3, whereas 60 of 239 Glut1 positive tumors (25%) were positive for Glut3 (P \u3c 0.0001). Glut1 or Gluts were detected more often in poorly differentiated and undifferentiated tumors (P \u3c0.0001 and P = 0.0008, respectively). Overexpression of Glut1 and/or Glut3 was associated with poorer survival (P = 0.0133), especially in patients with well-differentiated and moderately differentiated tumors (P = 0.0017). CONCLUSIONS. In Stage I NSCLC, Glut3 overexpression likely occurs after Glut1 overexpression. The appearance of Glut1 positive clones is associated with aggressive biologic behavior, which is worsened by the emergence of Glut3 positive clones. Glut1 and Glut3 are significant of poor prognosis indicators in cases of NSCLC

Absence of prognostic significance of bcl-2 immunopositivity in non- small cell lung cancer: Analysis of 427 cases

The bcl-2 gene product inhibits apoptosis and is thought to participate in oncogenesis. Association of bcl-2 immunopositivity with improved prognosis of non-small cell lung cancers (NSCLG) is controversial. Although two studies have reported better survival in bcl-2immunopositive NSCLCs, a third series has contradicted this finding. The authors studied a relatively larger case series involving 427 patients for whom detailed information on long-term follow-up was available to determine the prognostic significance of bcl-2 expression. The study included 252 adenocarcinomas (AC), 111 squamous cell carcinomas (SCG), and 64 large cell carcinomas (LC). After antigen retrieval, sections were immunostained using a monoclonal anti-bcl2 antibody (1:60, Clone 124, Dako) and the avidin-bintin complex technique. Staining was scored as positive or negative mad also on a semiquantitative scale as 0, low (\u3c10%), moderate (10% to 75%), or extensive (\u3e75%). Bcl-2 immunoreactivity was correlated with survival using the actuarial survival method, Kaplan- Meier method, and log-rank test and was not associated with statistically significant differences in survival for NSCLCs (P = .5537). Differences in survival remained insignificant even after NSCLCs were stratified for cell type, stage, or grade, singly or in combination. Therefore, using this method, bcl-2 immunopositivity does not appear to act as an independent prognostic indicator in NSCLCs

High c-erbB-3 protein expression is associated with shorter survival in advanced non-small cell lung carcinomas

c-erbB-3 is a new member of the Type I growth factor receptor family that includes epidermal growth-factor receptor (also called c-erbB-1) and HER-2/neu (also called c-erbB-2). Frequency and significance of c-erbB-3 over expression in lung cancers have not been reported previously. A series of 549 cases of primary lung carcinomas were immunostained with a monoclonal anti-human c-erbB-3 antibody (Clone RTJ.1) using formalin-fixed, paraffin-embedded archival tissue. Sharp membranous staining or punctate cytoplasmic staining was interpreted as positive and scored 0 (\u3c 5% of tumor cells), 1 (5-9%), 2 (10-49%), or 3 (≤ 50%). Medical records were reviewed for clinical data, including stage and survival. Actuarial cumulative survival analysis with the Mantel-Cox test was performed on 443 cases that had a single primary site in the lung of pure non-small cell carcinoma (adenocarcinoma, squamous cell carcinoma, large cell carcinoma) and that also had follow-up data for more than 3 months. In all stages, squamous cell carcinoma showed the greatest rate of high c-erbB-3 positivity (score, 3) (34/119; 28.6%), followed by adenocarcinoma (41/256; 15.9%) and large cell carcinoma (7/66; 10.6%). Patients with high c-erbB-3 expression (score, 3) survived for significantly shorter times than did patients with low c-erbB-3-expression (score, 0-2) in Stages III and IV (P = 0.002), but not in Stage I or II non-small cell lung carcinomas. In conclusion, high c-erbB-3 expression in advanced non-small cell lung carcinomas might be an adverse prognostic factor. This finding suggests that c-erbB-3 might be a potential target for molecular therapy in advanced non-small cell lung carcinomas