Graph Saturation in Multipartite Graphs

Let $G$ be a fixed graph and let ${\mathcal F}$ be a family of graphs. A subgraph $J$ of $G$ is ${\mathcal F}$-saturated if no member of ${\mathcal F}$ is a subgraph of $J$, but for any edge $e$ in $E(G)-E(J)$, some element of ${\mathcal F}$ is a subgraph of $J+e$. We let $\text{ex}({\mathcal F},G)$ and $\text{sat}({\mathcal F},G)$ denote the maximum and minimum size of an ${\mathcal F}$-saturated subgraph of $G$, respectively. If no element of ${\mathcal F}$ is a subgraph of $G$, then $\text{sat}({\mathcal F},G) = \text{ex}({\mathcal F}, G) = |E(G)|$. In this paper, for $k\ge 3$ and $n\ge 100$ we determine $\text{sat}(K_3,K_k^n)$, where $K_k^n$ is the complete balanced $k$-partite graph with partite sets of size $n$. We also give several families of constructions of $K_t$-saturated subgraphs of $K_k^n$ for $t\ge 4$. Our results and constructions provide an informative contrast to recent results on the edge-density version of $\text{ex}(K_t,K_k^n)$ from [A. Bondy, J. Shen, S. Thomass\'e, and C. Thomassen, Density conditions for triangles in multipartite graphs, Combinatorica 26 (2006), 121--131] and [F. Pfender, Complete subgraphs in multipartite graphs, Combinatorica 32 (2012), no. 4, 483--495].Comment: 16 pages, 4 figure

The Effects of a Sleep Extension on Reactive Strength and Decision Making in Agility Tasks

This study examined the effect of extended sleep on reactive strength index (RSI) performance and decision-making skills of agility tasks. Participants (N = 15) volunteered for the study providing informed consent and were varsity student-athletes at Ithaca College. Participants attended five lab sessions over a six-week period with testing occurring at four of the lab sessions. Performance was measured by trials of the reactive strength index-drop jump test (RSI-DJ), a pre-planned change of direction (COD) test, and a reactive agility test (RAT). Participants were familiarized with testing protocols that were followed by a baseline period where habitual sleep patterns were recorded. After the two-week baseline period, participants were randomly assigned to either a sleep or control group. During the intervention period, the sleep group was required to extend their sleep by one-hour and the control group continued there habitual sleep patterns. The intervention period was two-weeks in duration. Each participant recorded sleep duration and quality throughout the duration of the study. Data were analyzed using a mixed design measures ANOVA. A pairwise comparison if the ANOVA yielded significant effects. The results showed participants from the sleep group increased their sleep duration by 11% and RSI by 5%. The reactive agility tests showed no significant changes; however, the sleep and control groups had faster decision making times upon posttest (5%). Practical application of this study is that extended sleep shows potential positive effects on reactive strength

List Distinguishing Parameters of Trees

A coloring of the vertices of a graph G is said to be distinguishing} provided no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, D(G), is the minimum number of colors in a distinguishing coloring of G. The distinguishing chromatic number of G, chi_D(G), is the minimum number of colors in a distinguishing coloring of G that is also a proper coloring. Recently the notion of a distinguishing coloring was extended to that of a list distinguishing coloring. Given an assignment L= {L(v) : v in V(G)} of lists of available colors to the vertices of G, we say that G is (properly) L-distinguishable if there is a (proper) distinguishing coloring f of G such that f(v) is in L(v) for all v. The list distinguishing number of G, D_l(G), is the minimum integer k such that G is L-distinguishable for any list assignment L with |L(v)| = k for all v. Similarly, the list distinguishing chromatic number of G, denoted chi_{D_l}(G) is the minimum integer k such that G is properly L-distinguishable for any list assignment L with |L(v)| = k for all v. In this paper, we study these distinguishing parameters for trees, and in particular extend an enumerative technique of Cheng to show that for any tree T, D_l(T) = D(T), chi_D(T)=chi_{D_l}(T), and chi_D(T) <= D(T) + 1.Comment: 10 page

Electron Accumulation on Naphthalene Diimide Photosensitized by [Ru(2,2′-Bipyridine)3]2+

In a molecular triad comprised of a central naphthalene diimide (NDI) unit flanked by two [Ru(bpy)3]2+ (bpy = 2,2′-bipyridine) sensitizers, NDI2– is formed after irradiation with visible light in deaerated CH3CN in the presence of excess triethylamine. The mechanism for this electron accumulation involves a combination of photoinduced and thermal elementary steps. In a structurally related molecular pentad with two peripheral triarylamine (TAA) electron donors attached covalently to a central [Ru(bpy)3]2+-NDI-[Ru(bpy)3]2+ core but no sacrificial reagents present, photoexcitation only leads to NDI– (and TAA+), whereas NDI2– is unattainable due to rapid electron transfer events counteracting charge accumulation. For solar energy conversion, this finding means that fully integrated systems with covalently linked photosensitizers and catalysts are not necessarily superior to multicomponent systems, because the fully integrated systems can suffer from rapid undesired electron transfer events that impede multielectron reactions on the catalyst

Porous silica spheres as indoor air pollutant scavengers

Porous silica spheres were investigated for their effectiveness in removing typical indoor air pollutants, such as aromatic and carbonyl-containing volatile organic compounds (VOCs), and compared to the commercially available polymer styrene-divinylbenzene (XAD-4). The silica spheres and the XAD-4 resin were coated on denuder sampling devices and their adsorption efficiencies for volatile organic compounds evaluated using an indoor air simulation chamber. Real indoor sampling was also undertaken to evaluate the affinity of the silica adsorbents for a variety of indoor VOCs. The silica sphere adsorbents were found to have a high affinity for polar carbonyls and found to be more efficient than the XAD-4 resin at adsorbing carbonyls in an indoor environment

PITX1, a specificity determinant in the HIF-1α-mediated transcriptional response to hypoxia

Hypoxia is an important developmental cue for multicellular organisms but it is also a contributing factor for several human pathologies, such as stroke, cardiovascular diseases and cancer. In cells, hypoxia activates a major transcriptional program coordinated by the Hypoxia Inducible Factor (HIF) family. HIF can activate more than one hundred targets but not all of them are activated at the same time, and there is considerable cell type variability. In this report we identified the paired-like homeodomain pituitary transcription factor (PITX1), as a transcription factor that helps promote specificity in HIF-1α dependent target gene activation. Mechanistically, PITX1 associates with HIF-1β and it is important for the induction of certain HIF-1 dependent genes but not all. In particular, PITX1 controls the HIF-1α-dependent expression of the histone demethylases; JMJD2B, JMJD2A, JMJD2C and JMJD1B. Functionally, PITX1 is required for the survival and proliferation responses in hypoxia, as PITX1 depleted cells have higher levels of apoptotic markers and reduced proliferation. Overall, our study identified PITX1 as a key specificity factor in HIF-1α dependent responses, suggesting PITX1 as a protein to target in hypoxic cancers

Mechanical Properties of Collagen Fibrils

AbstractThe formation of collagen fibers from staggered subfibrils still lacks a universally accepted model. Determining the mechanical properties of single collagen fibrils (diameter 50–200nm) provides new insights into collagen structure. In this work, the reduced modulus of collagen was measured by nanoindentation using atomic force microscopy. For individual type 1 collagen fibrils from rat tail, the modulus was found to be in the range from 5 GPa to 11.5GPa (in air and at room temperature). The hypothesis that collagen anisotropy is due to the subfibrils being aligned along the fibril axis is supported by nonuniform surface imprints performed by high load nanoindentation