On (t,r) Broadcast Domination Numbers of Grids

The domination number of a graph $G = (V,E)$ is the minimum cardinality of any subset $S \subset V$ such that every vertex in $V$ is in $S$ or adjacent to an element of $S$. Finding the domination numbers of $m$ by $n$ grids was an open problem for nearly 30 years and was finally solved in 2011 by Goncalves, Pinlou, Rao, and Thomass\'e. Many variants of domination number on graphs have been defined and studied, but exact values have not yet been obtained for grids. We will define a family of domination theories parameterized by pairs of positive integers $(t,r)$ where $1 \leq r \leq t$ which generalize domination and distance domination theories for graphs. We call these domination numbers the $(t,r)$ broadcast domination numbers. We give the exact values of $(t,r)$ broadcast domination numbers for small grids, and we identify upper bounds for the $(t,r)$ broadcast domination numbers for large grids and conjecture that these bounds are tight for sufficiently large grids.Comment: 28 pages, 43 figure

Implications of the Ticket to Work and Self-Sufficiency Program for Young Adults

On December 17, 1999, President Clinton signed the Ticket to Work and Work Incentives Improvement Act (P.L. 106-170) into law establishing in section 101(a) the Ticket to Work and Self-Sufficiency Program (Ticket to Work Program) as well as several other provisions to support the movement of beneficiaries with disabilities who receive Supplemental Security Income (SSI) and Social Security Disability Insurance (SSDI) into employment. The Ticket to Work Program was established to expand the universe of providers available to beneficiaries with disabilities as they are afforded the opportunity to choose from whom they access their needed employment services and supports. The Ticket to Work Program also increased provider incentives to serve these individuals. The Social Security Administration (SSA) administers this new program with the support of Maximus, Inc, the entity contracted with by the SSA to serve as the program manager. The SSA is currently contracting with agencies to serve as Employment Networks (EN). These ENs perform an array of duties under the law, including providing employment services, vocational rehabilitation (VR) services, and other support services to assist individuals with disabilities to obtain and maintain employment. Under this program, the SSA is directed to provide to beneficiaries with disabilities who meet certain eligibility criteria a Ticket they may use to obtain employment services, VR services and/or other support services from an EN of their choice. “A Ticket under the Ticket to Work and Self-Sufficiency Program is a document that provides evidence of SSA’s agreement to pay an EN or a State VR agency for providing employment services, VR services and/or other support services to a Ticket recipient who requests such services.” (SSA 2001, p. 12) The Ticket to Work Program will be phased in nationally over a three-year period beginning in January, 2002, with beneficiaries in 13 states: Arizona, Colorado, Delaware, Florida, Illinois, Iowa, Massachusetts, New York, Oklahoma, Oregon, South Carolina, Vermont and Wisconsin. The remaining states will be included by January, 2004

Learning from Other Communities

This paper reflects a synopsis of the work in person/family-centered planning representative of its implementation across a variety of disability service systems, including prisons, schools, community-based service agencies and institutional settings. The authors who have contributed to this paper have direct experience in the field working with individuals who have disability labels of severe and persistent mental illness, mental retardation and developmental disabilities, and learning disabilities. It is their hope that this paper will serve to guide the emerging best practice in the design and delivery of person-centered service delivery systems

Evolving injury profiles amid advancing sport: Musculoskeletal injuries in ringball players

Background: Ringball, a sport historically derived from conventional basketball and netball, demonstrates the evolution of traditional sport. The variations between these sports may predispose players to different risk factors and consequent injuries and their impact, yet they are usually considered comparably. Objective: To determine the prevalence of musculoskeletal injuries and to profile injuries based on location, severity, and mechanisms of occurrence. A further objective was to compare the injuries sustained in ringball with that of basketball and netball. Methods: A questionnaire-based study, administered to 110 ringball players in KwaZulu-Natal, South Africa, was applied. Data were described and compared using frequencies/ percentages for categorical variables. Results: Seventy-six ringball players completed the questionnaire (69% response rate). The prevalence of at least one injury during/after the last or current season was 80% (n=61). The most commonly reported injury was to the foot/ankle (36%; n=33) followed by the knee (29%; n=27) and wrist (9%; n=8). The most common mechanisms of injury reported were landing (15%; n=9), jumping (9%; n=5), goal shooting (7%; n=4), defending (7%; n=4) and collision (7%; n=4). Discussion: Ringball shares similar injuries to that of basketball/netball, with foot/ankle injuries being the most prevalent. The prevalence of other injuries in ringball differed from basketball/netball, suggesting variations between these sports as a contributor to the injuries described. Conclusion: The evolution of sport and the modifications in rules/techniques may create a nuanced injury profile to those commonly identified. The combination of a sport’s uniqueness/modification and its similarities to other sports warrants the need for more tailored approaches to injury prevention and a platform for future research

Weighted Birkhoff Averages and the Parameterization Method

This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles in area preserving maps. The recipe requires only a finite data set sampled from the quasiperiodic circle. Our approach, being based on the parameterization method, uses a Newton scheme to iteratively solve a conjugacy equation describing the invariant circle. A critical step in properly formulating the conjugacy equation is to determine the rotation number of the quasiperiodic subsystem. For this we exploit a the weighted Birkhoff averaging method. This approach facilities accurate computation of the rotation number given nothing but the already mentioned orbit data. The weighted Birkhoff averages also facilitate the computation of other integral observables like Fourier coefficients of the parameterization of the invariant circle. Since the parameterization method is based on a Newton scheme, we only need to approximate a small number of Fourier coefficients with low accuracy to find a good enough initial approximation so that Newton converges. Moreover, the Fourier coefficients may be computed independently, so we can sample the higher modes to guess the decay rate of the Fourier coefficients. This allows us to choose, a-priori, an appropriate number of modes in the truncation. We illustrate the utility of the approach for explicit example systems including the area preserving Henon map and the standard map. We present example computations for invariant circles with period as low as 1 and up to more than 100. We also employ a numerical continuation scheme to compute large numbers of quasiperiodic circles in these systems. During the continuation we monitor the Sobolev norm of the Parameterization to automatically detect the breakdown of the family.Comment: 38 pages, 15 figure

The β-blocker Nebivolol Is a GRK/β-arrestin Biased Agonist

Nebivolol, a third generation β-adrenoceptor (β-AR) antagonist (β-blocker), causes vasodilation by inducing nitric oxide (NO) production. The mechanism via which nebivolol induces NO production remains unknown, resulting in the genesis of much of the controversy regarding the pharmacological action of nebivolol. Carvedilol is another β-blocker that induces NO production. A prominent pharmacological mechanism of carvedilol is biased agonism that is independent of Gαs and involves G protein-coupled receptor kinase (GRK)/β-arrestin signaling with downstream activation of the epidermal growth factor receptor (EGFR) and extracellular signal-regulated kinase (ERK). Due to the pharmacological similarities between nebivolol and carvedilol, we hypothesized that nebivolol is also a GRK/β-arrestin biased agonist. We tested this hypothesis utilizing mouse embryonic fibroblasts (MEFs) that solely express β2-ARs, and HL-1 cardiac myocytes that express β1- and β2-ARs and no detectable β3-ARs. We confirmed previous reports that nebivolol does not significantly alter cAMP levels and thus is not a classical agonist. Moreover, in both cell types, nebivolol induced rapid internalization of β-ARs indicating that nebivolol is also not a classical β-blocker. Furthermore, nebivolol treatment resulted in a time-dependent phosphorylation of ERK that was indistinguishable from carvedilol and similar in duration, but not amplitude, to isoproterenol. Nebivolol-mediated phosphorylation of ERK was sensitive to propranolol (non-selective β-AR-blocker), AG1478 (EGFR inhibitor), indicating that the signaling emanates from β-ARs and involves the EGFR. Furthermore, in MEFs, nebivolol-mediated phosphorylation of ERK was sensitive to pharmacological inhibition of GRK2 as well as siRNA knockdown of β-arrestin 1/2. Additionally, nebivolol induced redistribution of β-arrestin 2 from a diffuse staining pattern into more intense punctate spots. We conclude that nebivolol is a β2-AR, and likely β1-AR, GRK/β-arrestin biased agonist, which suggests that some of the unique clinically beneficial effects of nebivolol may be due to biased agonism at β1- and/or β2-ARs. © 2013 Erickson et al

Effects of pH, Dosage, Temperature and Mixing Speed on The Efficiency of Water Melon Seed in Removing the Turbidity and Colour of Atabong River, Awka-Ibom State, Nigeria

Studies were carried out to determine the effects of operating parameters such as temperature, pH, dosage and mixing speed on the efficiency of watermelon seed in removing the turbidity and colour of Atabong River, which serves the people of Eket and their environs in Akwa-Ibom State. Results obtained showed that at an ideal pH of 7.5, temperature of 25oC, dosage of 0.6g/l and mixing speed of 120rpm the water melon coagulum removed turbidity and colour of the raw river water by 87.9% and 84.3% respectively. At this optimum conditions, water melon coagulum decreased the raw water turbidity from 67.7 to 8.18 NTU and colour, 318 to 50 TCU. The findings have demonstrated the effectiveness of water melon seeds as a possible replacement for chemicals like alum and ferric salts normally used in coagulation-flocculation water treatment

(2S,4'R,5'R)-(E)-tert-Butyl 2-acetyl-2-(2-oxo-5-phenyl-1,3- dioxolan-4-ylmethyl)-5-phenylpent-4-enoate

The title compound, C₂₇H₃₀O₆, was prepared by monodihydroxylation of the bis-olefin (E,E)-tert-butyl 2-acetyl-2-cinnamyl-5-phenylpent-4-enoate using standard Sharpless asymmetric dihydroxylation conditions, followed by treatment with 1,1'-carbonyl diimidazole. In the crystal structure, the phenyl rings form an intramolecular edge-to-face C-H… π contact with an interplanar angle of 56.4° and a H…centroid distance of 3.03 Å.David J. Fox ; Daniel Sejer Pedersen and Stuart Warre

Use of intensity quotients and differences in absolute structure refinement

Several methods for absolute structure refinement were tested using single-crystal X-ray diffraction data collected using Cu Kα radiation for 23 crystals with no element heavier than oxygen: conventional refinement using an inversion twin model, estimation using intensity quotients in SHELXL2012, estimation using Bayesian methods in PLATON, estimation using restraints consisting of numerical intensity differences in CRYSTALS and estimation using differences and quotients in TOPAS-Academic where both quantities were coded in terms of other structural parameters and implemented as restraints. The conventional refinement approach yielded accurate values of the Flack parameter, but with standard uncertainties ranging from 0.15 to 0.77. The other methods also yielded accurate values of the Flack parameter, but with much higher precision. Absolute structure was established in all cases, even for a hydrocarbon. The procedures in which restraints are coded explicitly in terms of other structural parameters enable the Flack parameter to correlate with these other parameters, so that it is determined along with those parameters during refinement