Pascal\u27s Triangle, Pascal\u27s Pyramid, and the Trinomial Triangle

Many properties have been found hidden in Pascal\u27s triangle. In this paper, we will present several known properties in Pascal\u27s triangle as well as the properties that lift to different extensions of the triangle, namely Pascal\u27s pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle

Effects of Visual Deprivation on Dynamic Stability of Young and Older Adults during Treadmill Walking

Vision plays an essential role in human locomotion by providing information about the environment in which we navigate. Research has focused primarily on the effects of visual deprivation on human gait during overground walking; however, overground walking introduces several limitations such as fewer steps to analyze and uncontrolled gait speed between trials. The purpose of this study was to examine the effect of visual deprivation on dynamic stability during treadmill walking. Fifteen participants (six older adults 69.33 ± 4.88 yrs. and nine young adults 22.67 ± 1.87 yrs.) performed two 90-sec trials at their preferred walking speed on a treadmill: first with eyes open (EO) and then with eyes closed (EC). Prior to performing these two trials, participants walked on the treadmill approximately ten times with each lasting 12 sec to become acclimated to the treadmill. While wearing a safety harness, full-body kinematics were recorded during the two primary trials from 26 reflective markers using an 8-camera motion capture system. Spatial gait parameters including step length, step width, and foot landing angle were computed for both walking conditions. Measurements of dynamic stability were calculated as the variability (i.e., the standard deviation) of all gait parameters. Analyses of variance with repeated measures were used to analyze the gait parameters and stability measurements. The between-subject factor was the age (young vs. older) and the within-subject factor was the condition (EO vs. EC). Our results revealed no significant age by condition effect for all measurements of interest. However, a significant main effect of condition was detected for step length (p \u3c 0.001), foot angle (p \u3c 0.001), step length variability (p = 0.003), foot angle variability (p \u3c 0.001), and step width variability (p \u3c 0.001). Specifically, both age groups took a shorter step with reduced foot landing angle during EC walking in comparison with EO walking. Similarly, both age groups demonstrated reduced stability as indicated by the elevated variability of the step length, step width, and foot landing angle during EC gait than during EO gait. Our findings showed that both young and older adults adopted a “cautious gait” when walking without visual input. Furthermore, the dynamic stability was deteriorated while walking with visual information removed. Visual deprivation seems to affect both age groups equally. Although the finding from this project could provide guidance for designing fall prevention interventions targeting individuals with visual impairments, more studies based on large sample sizes are needed to examine comprehensively the impact of visual deprivation on dynamic stability and the risk of falls among humans

Platinum-Bismuth Bimetallic Catalysts: Synthesis, Characterization and Applications

Bimetallic catalysts have been explored and shown to exhibit unique characteristics which are not present in monometallic catalysts. Platinum is well known as an effective catalyst for oxidation and reduction reactions, and it can be made more effective when bismuth is introduced as a promotor. Thus, the effectiveness of the Pt-Bi catalyst was demonstrated in prior work. What is not clear, however, is the mechanism behind the catalyst function; why addition of bismuth to platinum decreases deactivation and increases selectivity, and how effective would the Pt-Bi catalyst be in deoxygenation reactions? In this work, the effectiveness of different variations of the Pt-Bi catalyst was explored for the deoxygenation of guaiacol. Methane was selected as the model reductant. Two Pt-Bi catalysts with different metal ratios were prepared, tested and characterized to reveal the catalyst’s structure. Methods used in characterization included SEM, TEM and BET measurements. Representative catalysts were then tested in a fixed-bed reactor for performance

Immigration in the 21st Century: Perspectives on Law and Policy

The program consisted of a keynote presentation by Linda Chavez, Chairman of the Center for Equal Opportunity, followed by a panel featuring Leticia Saucedo, Associate Professor of Law at the William S. Boyd School of Law, University of Nevada, Law Vegas; Andrea Rahal, Associate at McCandlish Holton, PC in Richmond; Robert Redmond, Jr., Partner at Williams Mullen in Richmond; Michael Hethmon, General Counsel for the Immigration Reform Law Institute; and Tim Freilich, Legal Director of the Legal Aid Justice Center\u27s Immigration Advocacy Program. Christopher Nugent, Senior Counsel at Holland & Knight, D.C. Office, served as moderator

SPFC: a tool to improve water management and hay production in the Crau region

Correspondance: [email protected] ; UMR SYSTEM équipe CONSYSTThis article deals with the development and application of SPFC, a model used to improve water and grassland production (HC) in this region of France. This model is composed of two sub-models: an irrigation model and a crop model. As the fields are border irrigated, these two sub-models are coupled. The crop model simulates dry matter, Leaf Area Index (LAI) and soil water reserve (SWR) variations. LAI and SWR are both used for border model updating: SWR for the deficit of saturation required by the infiltration equation and LAI for the roughness coefficient n. After calibration and validation, SPFC is then used to identify realistic management strategies for the irrigation and production system at the plot level. By scheduling irrigation when SWR is 50% depleted, would result in a low Dry Matter DM production loss (around 10%), reduced labour (8 irrigation events instead of 11) and in significant water saving compared with farmers' practices, on the basis of an average climatic scenario. Furthermore, this improvement of irrigation efficiency is not incompatible with groundwater recharge used for the potable water supply of the region

YAP1 Recruits c-Abl to Protect Angiomotin-Like 1 from Nedd4-Mediated Degradation

Tissue development and organ growth require constant remodeling of cell-cell contacts formed between epithelial cells. The Hippo signaling cascade curtails organ growth by excluding the transcriptional co-activator Yes Associated Protein 1 (YAP1) from the nucleus. Angiomotin family members recruit YAP1 to tight junctions [1], but whether YAP1 plays a specific role outside of the nucleus is currently unknown.The present study demonstrates that the E3 ubiquitin ligase Nedd4.2 targets Angiomotin-like 1 (AMOTL1), a family member that promotes the formation of epithelial tight junctions, for ubiquitin-dependent degradation. Unexpectedly, YAP1 antagonizes the function of Nedd4.2, and protects AMOTL1 against Nedd4.2-mediated degradation. YAP1 recruits c-Abl, a tyrosine kinase that binds and phosphorylates Nedd4.2 on tyrosine residues, thereby modifying its ubiquitin-ligase activity.Our results uncover a novel function for cytoplasmic YAP1. YAP1 recruits c-Abl to protect AMOTL1 against Nedd4.2-mediated degradation. Thus, YAP1, excluded from the nucleus, contributes to the maintenance of tight junctions

Patterns of nucleotide diversity at the regions encompassing the Drosophila insulin-like peptide (dilp) genes: demography vs positive selection in Drosophila melanogaster.

In Drosophila, the insulin-signaling pathway controls some life history traits, such as fertility and lifespan, and it is considered to be the main metabolic pathway involved in establishing adult body size. Several observations concerning variation in body size in the Drosophila genus are suggestive of its adaptive character. Genes encoding proteins in this pathway are, therefore, good candidates to have experienced adaptive changes and to reveal the footprint of positive selection. The Drosophila insulin-like peptides (DILPs) are the ligands that trigger the insulin-signaling cascade. In Drosophila melanogaster, there are several peptides that are structurally similar to the single mammalian insulin peptide. The footprint of recent adaptive changes on nucleotide variation can be unveiled through the analysis of polymorphism and divergence. With this aim, we have surveyed nucleotide sequence variation at the dilp1-7 genes in a natural population of D. melanogaster. The comparison of polymorphism in D. melanogaster and divergence from D. simulans at different functional classes of the dilp genes provided no evidence of adaptive protein evolution after the split of the D. melanogaster and D. simulans lineages. However, our survey of polymorphism at the dilp gene regions of D. melanogaster has provided some evidence for the action of positive selection at or near these genes. The regions encompassing the dilp1-4 genes and the dilp6 gene stand out as likely affected by recent adaptive events

The Drosophila FoxA Ortholog Fork Head Regulates Growth and Gene Expression Downstream of Target of Rapamycin

Forkhead transcription factors of the FoxO subfamily regulate gene expression programs downstream of the insulin signaling network. It is less clear which proteins mediate transcriptional control exerted by Target of rapamycin (TOR) signaling, but recent studies in nematodes suggest a role for FoxA transcription factors downstream of TOR. In this study we present evidence that outlines a similar connection in Drosophila, in which the FoxA protein Fork head (FKH) regulates cellular and organismal size downstream of TOR. We find that ectopic expression and targeted knockdown of FKH in larval tissues elicits different size phenotypes depending on nutrient state and TOR signaling levels. FKH overexpression has a negative effect on growth under fed conditions, and this phenotype is not further exacerbated by inhibition of TOR via rapamycin feeding. Under conditions of starvation or low TOR signaling levels, knockdown of FKH attenuates the size reduction associated with these conditions. Subcellular localization of endogenous FKH protein is shifted from predominantly cytoplasmic on a high-protein diet to a pronounced nuclear accumulation in animals with reduced levels of TOR or fed with rapamycin. Two putative FKH target genes, CG6770 and cabut, are transcriptionally induced by rapamycin or FKH expression, and silenced by FKH knockdown. Induction of both target genes in heterozygous TOR mutant animals is suppressed by mutations in fkh. Furthermore, TOR signaling levels and FKH impact on transcription of the dFOXO target gene d4E-BP, implying a point of crosstalk with the insulin pathway. In summary, our observations show that an alteration of FKH levels has an effect on cellular and organismal size, and that FKH function is required for the growth inhibition and target gene induction caused by low TOR signaling levels

WW domain-mediated interaction with Wbp2 is important for the oncogenic property of TAZ

The transcriptional co-activators YAP and TAZ are downstream targets inhibited by the Hippo tumor suppressor pathway. YAP and TAZ both possess WW domains, which are important protein–protein interaction modules that mediate interaction with proline-rich motifs, most commonly PPXY. The WW domains of YAP have complex regulatory roles as exemplified by recent reports showing that they can positively or negatively influence YAP activity in a cell and context-specific manner. In this study, we show that the WW domain of TAZ is important for it to transform both MCF10A and NIH3T3 cells and to activate transcription of ITGB2 but not CTGF, as introducing point mutations into the WW domain of TAZ (WWm) abolished its transforming and transcription-promoting ability. Using a proteomic approach, we discovered potential regulatory proteins that interact with TAZ WW domain and identified Wbp2. The interaction of Wbp2 with TAZ is dependent on the WW domain of TAZ and the PPXY-containing C-terminal region of Wbp2. Knockdown of endogenous Wbp2 suppresses, whereas overexpression of Wbp2 enhances, TAZ-driven transformation. Forced interaction of WWm with Wbp2 by direct C-terminal fusion of full-length Wbp2 or its TAZ-interacting C-terminal domain restored the transforming and transcription-promoting ability of TAZ. These results suggest that the WW domain-mediated interaction with Wbp2 promotes the transforming ability of TAZ

Relationship of metabolic syndrome and its components with -844 G/A and HindIII C/G PAI-1 gene polymorphisms in Mexican children

<p>Abstract</p> <p>Background</p> <p>Several association studies have shown that -844 G/A and <it>HindIII </it>C/G <it>PAI-1 </it>polymorphisms are related with increase of PAI-1 levels, obesity, insulin resistance, glucose intolerance, hypertension and dyslipidemia, which are components of metabolic syndrome. The aim of this study was to analyze the allele and genotype frequencies of these polymorphisms in <it>PAI-1 </it>gene and its association with metabolic syndrome and its components in a sample of Mexican mestizo children.</p> <p>Methods</p> <p>This study included 100 children with an age range between 6-11 years divided in two groups: a) 48 children diagnosed with metabolic syndrome and b) 52 children metabolically healthy without any clinical and biochemical alteration. Metabolic syndrome was defined as the presence of three or more of the following criteria: fasting glucose levels ≥ 100 mg/dL, triglycerides ≥ 150 mg/dL, HDL-cholesterol < 40 mg/dL, obesity BMI ≥ 95^thpercentile, systolic blood pressure (SBP) and diastolic blood pressure (DBP) ≥ 95^thpercentile and insulin resistance HOMA-IR ≥ 2.4. The -844 G/A and <it>HindIII </it>C/G <it>PAI-1 </it>polymorphisms were analyzed by PCR-RFLP.</p> <p>Results</p> <p>For the -844 G/A polymorphism, the G/A genotype (OR = 2.79; 95% CI, 1.11-7.08; <it>p </it>= 0.015) and the A allele (OR = 2.2; 95% CI, 1.10-4.43; <it>p </it>= 0.015) were associated with metabolic syndrome. The -844 G/A and A/A genotypes were associated with increase in plasma triglycerides levels (OR = 2.6; 95% CI, 1.16 to 6.04; <it>p </it>= 0.02), decrease in plasma HDL-cholesterol levels (OR = 2.4; 95% CI, 1.06 to 5.42; <it>p </it>= 0.03) and obesity (OR = 2.6; 95% CI, 1.17-5.92; <it>p </it>= 0.01). The C/G and G/G genotypes of the <it>HindIII </it>C/G polymorphism contributed to a significant increase in plasma total cholesterol levels (179 vs. 165 mg/dL; <it>p </it>= 0.02) in comparison with C/C genotype.</p> <p>Conclusions</p> <p>The -844 G/A <it>PAI-1 </it>polymorphism is related with the risk of developing metabolic syndrome, obesity and atherogenic dyslipidemia, and the <it>HindIII </it>C/G <it>PAI-1 </it>polymorphism was associated with the increase of total cholesterol levels in Mexican children.</p