Let α(G) and β(G), denote the size of a largest independent set and the clique cover number of an undirected graph G. Let H be an interval graph with V (G) = V (H) and E(G) ⊆ E(H), and let φ(G,H) denote the maximum of β(G[W ]) α(G[W ]) overall induced subgraphs G[W ] of G that are cliques in H . The main result of this paper is to prove that for any graph G β(G) ≤ 2α(H)φ(G,H)(logα(H) + 1), wher...

We consider a piecewise analytic expanding map f : [0, 1] → [0, 1] of degree d which preserves orientation, and an analytic positive potential g : [0, 1] → R. We address the analysis of the following problem: for a given analytic potential β log g, where β is a real constant, it is well known that there exists a real analytic (with a complex analytic extension to a small complex neighborhood of...

Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |G which induces a bi-invariant metric dG(x, y) = |Ad(yx−1)|G on G. We prove the existence of a constant β ≈ .23 (independent of G) such that for any closed subgroup H ( G, the diameter of the quotient G/H (in the induced metric) is ≥ β.

Classically, G protein-coupled receptor (GPCR) stimulation promotes G protein signaling at the plasma membrane, followed by rapid β-arrestin-mediated desensitization and receptor internalization into endosomes. However, it has been demonstrated that some GPCRs activate G proteins from within internalized cellular compartments, resulting in sustained signaling. We have used a variety of biochemi...

Let G be a well covered graph, that is, all maximal independent sets of G have the same cardinality, and let ik denote the number of independent sets of cardinality k in G. We investigate the roots of the independence polynomial i(G, x)= ∑ ik xk . In particular, we show that if G is a well covered graph with independence number β, then all the roots of i(G, x) lie in in the disk |z| ≤β (this is...

Synthesis of poly(vinyl chloride-g-β-butyrolactone) [poly(VC-g-BL)] graft copolymer was carried out by means “click” chemistry terminally propargyl polyβ-butyrolactone ester (PBL-propargyl) and polyvinyl chloride with pendant azido group (PVC-N3). PVC-N3 synthesized reaction purified PVC sodium azide. PBL-propargyl obtained the β-butyrolactone alcohol ring-opening polymerization. By using PBL-p...

We consider the algorithmic problem of community detection in networks. Given an undirected friendship graph G = (V, E), a subset S ⊆ V is an (α, β)-community if: • Every member of the community is friends with an α-fraction of the community; • Every non-member is friends with at most a β-fraction of the community. Arora et al [AGSS12] gave a quasi-polynomial time algorithm for enumerating all ...

Type 2 diabetes (T2D) has emerged as a major threat to human health in most parts of the world. Therapeutic strategies aimed at improving pancreatic β cell function are predicted to prove beneficial for the treatment of T2D. In the present study, we demonstrate that drug-mediated, chronic, and selective activation of β cell G(q) signaling greatly improve β cell function and glucose homeostasis ...

Deregulation of the Wnt/β-catenin signaling pathway is a hallmark of colon cancer. Mutations in the adenomatous polyposis coli (APC) gene occur in the vast majority of colorectal cancers and are an initiating event in cellular transformation. Cells harboring mutant APC contain elevated levels of the β-catenin transcription coactivator in the nucleus which leads to abnormal expression of genes c...

Genetic factors influencing Hb F content in adult red blood cells include β-thalassemia genotypes, co-inheritance of α-thalassemia traits and single nucleotide polymorphisms (SNPs). Genotyping of α- and β-thalassemia and five SNPs in β-globin gene cluster previously identified in genome-wide association studies as being markers of elevated Hb F in β-thalassemia were performed in 81 subjects dia...