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

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

Scalar Absorption and the Breaking of the World Volume Conformal Invariance

We investigate a version of fixed scalars for non-dilatonic branes which correspond to dilatations of the brane world-volume. We obtain a cross-section whose world-volume interpretation falls out naturally from an investigation of the breaking of conformal invariance by the irrelevant Born-Infeld corrections to Yang-Mills theory. From the same irrelevant world-volume operator we obtain the leading correction to the cross-sections of minimal scalars. This correction can be obtained in supergravity via an improved matching of inner and outer solutions to the minimal wave equation.Comment: 20 pages, 2 figures. Minor change

An Exploratory Study of Suboxone (Buprenorphine/ Naloxone) Film Splitting: Cutting Methods, Content Uniformity, and Stability

Suboxone films are U.S. Food and Drug Administration approved to treat opioid dependence. While the package insert states that films should not be cut, physicians often prescribe film fractions for treatment and tapering. There is no data to support this practice, and this study was initiated to evaluate cutting methods, content uniformity, and stability of split films. Suboxone 8-mg buprenorphine/2-mg naloxone films were split using four methods: 1) ruler/razor cut, 2) scissor cut, 3) fold/rip, and 4) fold/scissor cut. United States Pharmacopeia Chapter \u3c905\u3e was used to evaluate the weight variation and content uniformity of split films. The stability of split films stored in polybags was evaluated over 7 days. A stability-indicating high-performance liquid chromatography method was used for content uniformity and stability evaluation. The weight variation results were acceptable for the half films from all four cutting methods, but this was not true for the quarter films. The method of ruler/razor cut was determined most favorable and used for the content uniformity test. Based on the high-performance liquid chromatography results, the half films from the ruler/razor cut method met the passing criteria of United States Pharmacopeia Chapter \u3c905\u3e with acceptance values of 9.8 to 10.4 for buprenorphine and 8.4 to 11.5 for naloxone (≤15 is considered passing). The stability results indicated that both actives retained \u3e97.7% of initial strength. Four cutting methods were found to be acceptable for splitting Suboxone films into half but not quarter fractions. The half films from the ruler/razor cut method also passed United States Pharmacopeia Chapter \u3c905\u3e content uniformity test. Both actives remained stable for 7 days when the half films were stored in polybags at room temperature

Nernst branes in gauged supergravity

We study static black brane solutions in the context of N = 2 U(1) gauged supergravity in four dimensions. Using the formalism of first-order flow equations, we construct novel extremal black brane solutions including examples of Nernst branes, i.e. extremal black brane solutions with vanishing entropy density. We also discuss a class of non-extremal generalizations which is captured by the first-order formalism.Comment: 44 pages, 3 figures, v2: added appendix B and references, minor typographic changes, v3: added some clarifying remarks, version published in JHE

Best supportive care for idiopathic pulmonary fibrosis: Current gaps and future directions

Best supportive care (BSC) is generally defined as all the interventions and the multiprofessional approach aimed to improve and optimise quality of life (QoL) in patients affected by progressive diseases. In this sense, it excludes and might be complementary to other interventions directly targeting the disease. BSC improves survival in patients with different types of cancer. Patients with idiopathic pulmonary fibrosis (IPF) experience a vast range of symptoms during the natural history of the disease and might have a beneficial effect of BSC interventions. This review highlights the current evidence on interventions targeting QoL and gaps for the clinical assessment of BSC in the treatment of IPF patients. Very few interventions to improve QoL or improve symptom control are currently supported by well-designed studies. Sound methodology is paramount in evaluating BSC in IPF, as well as the use of validated tools to measure QoL and symptom control in this specific group of patients

Quantum Moduli Spaces of N=1N=1 String Theories

Generically, string models with $N=1$ supersymmetry are not expected to have moduli beyond perturbation theory; stringy non-perturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat directions. In this note, we describe models where some subspace of the moduli space survives non-perturbatively. Discrete $R$ symmetries forbid any inherently stringy effects, and dynamical considerations control the field-theoretic effects. The surviving subspace is a space of high symmetry; the system is attracted to this subspace by a potential which we compute. Models of this type may be useful for considerations of duality and raise troubling cosmological questions about string theory. Our considerations also suggest a mechanism for fixing the expectation value of the dilaton.Comment: 26 pages; uses harvmac. Footnote re fixing dilaton adde