The sum number of the cocktail party graph

A graph G is called a sum graph if there exists a labelling of the vertices of G by distinct positive integers such that the vertices labelled u and v are adjacent if and only if there exists a vertex labelled u + v. If G is not a sum graph, adding a finite number of isolated vertices to it will always yield a sum graph, and the sum number oe(G) of G is the smallest number of isolated vertices that will achieve this result. A labelling that realizes G + K oe(G) as a sum graph is said to be optimal. In this paper we consider G = H m;n , the complete n-partite graph on n 2 sets of m 2 nonadjacent vertices. We give an optimal labelling to show that oe(H 2;n ) = 4n \Gamma 5, and in the general case we give constructive proofs that oe(H m;n ) 2 \Omega\Gamma mn) and oe(H m;n ) 2 O(mn 2 ). We conjecture that oe(H m;n ) is asymptotically greater than mn, the cardinality of the vertex set; if so, then H m;n is the first known graph with this property. We also provide for the first time an optimal labelling of the complete bipatite graph Kmn whose smallest label is 1

Providing the Context for Intentional Learning

This article is written in response to Sharon Derry's article “Remediating Academic Difficulties Through Strategy Training: The Acquisition of Useful Knowledge.” The features of effective strategy instruction, to which Derry refers, are illustrated by examining the nature of the decisions the teacher confronts; specifically, determining the purposes of instruction, the context in which instruction occurs, and the roles of the teacher and students in instruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69150/2/10.1177_074193259001100608.pd

The effect of growth rate on reproductive outcomes in replacement dairy heifers in seasonally calving, pasture-based systems

peer-reviewedThe effect of average daily gain (ADG) on reproductive outcomes in replacement dairy heifers was investigated. All heifers were managed in the typical Irish spring calving, pasture-based system, where the herd calves in 1 block between January and April and the majority of the diet comprises grazed grass. Heifer calves (n = 399) from 7 herds were weighed at birth and at the beginning of the breeding season, and ADG was calculated. Service dates and pregnancy diagnosis results were recorded, and conception dates were calculated. Days open (DO) was defined as the number of days between the beginning of the breeding season and conception. Genetic data were retrieved from the Irish Cattle Breeding Federation database. A Cox proportional hazard model was constructed to identify variables with a significant effect on DO. An accelerated failure time model was used to predict survival curves and median survival times for different combinations of the significant variables. The ADG ranged from 0.41 to 0.91 kg/d, with a median of 0.70 kg/d. Frailty effect of farm within year, maintenance subindex of the economic breeding index, and ADG had a significant effect on DO. Derived from the final accelerated failure time model, the predicted median DO for a heifer with an ADG of 0.40, 0.70, or 0.90 kg/d aged 443 d at the beginning of the breeding season and with a maintenance subindex in the second tercile were 27, 16, and 11 d, respectively

The effect of dairy heifer pre-breeding growth rate on first lactation milk yield in spring-calving, pasture-based herds

peer-reviewedOptimising heifer growth rate may offer an opportunity to improve lifetime milk yield per cow, enhancing the environmental and economic efficiency of dairy farming operations. The effect of dairy heifer pre-breeding average daily weight gain (ADGPB) on first lactation milk yield was investigated. This observational study employed a data set comprising 265 Holstein-Friesian, or Holstein-Friesian-cross-Jersey heifers from seven commercial, spring-calving, pasture-based dairy herds, where the major component of the diet was grazed grass. These were weighed at birth and prior to breeding and ADGPB was calculated. Milk recordings were performed throughout the heifers' first lactation and 305-day yield figures calculated from these records. Yields were corrected to 4% fat and 3.1% protein to create standardised 305-day milk yield (SMY), which was the outcome of interest. Median ADGPB was 0.72 kg/day. Median 305-day yield was 5 967 kg. Linear regression was used to investigate the effect of weight and genetic, age and first calving factors on SMY. Pre-breeding average daily weight gain, age at first calving and predicted transmitting abilities for milk protein production and calving interval were all significant in the final model, which also included the random effects of farm and month of calving within year. ADGPB was quadratically related to first lactation SMY, with an ADGPB of 0.82 kg/day corresponding to the maximum predicted SMY. The model predicted that a heifer growing at 0.82 kg/day would produce 1 120 kg more SMY than a heifer growing at 0.55 kg/day, 218 kg more than a heifer growing at 0.7 kg/day and 103 kg more than a heifer growing at 0.90 kg/day. Manipulation of heifer growth rate may offer a viable method of increasing first lactation milk yield

Balloon Measurements of Cosmic Ray Muon Spectra in the Atmosphere along with those of Primary Protons and Helium Nuclei over Mid-Latitude

We report here the measurements of the energy spectra of atmospheric muons and of the cosmic ray primary proton and helium nuclei in a single experiment. These were carried out using the MASS superconducting spectrometer in a balloon flight experiment in 1991. The relevance of these results to the atmospheric neutrino anomaly is emphasized. In particular, this approach allows uncertainties caused by the level of solar modulation, the geomagnetic cut-off of the primaries and possible experimental systematics to be decoupled in the comparison of calculated fluxes of muons to measured muon fluxes. The muon observations cover the momentum and depth ranges of 0.3-40 GeV/c and 5-886 g/cmsquared, respectively. The proton and helium primary measurements cover the rigidity range from 3 to 100 GV, in which both the solar modulation and the geomagnetic cut-off affect the energy spectra at low energies.Comment: 31 pages, including 17 figures, simplified apparatus figure, to appear in Phys. Rev.

Arc-continent collision: The making of an orogen

Peer Reviewe

Low-viscosity route to high-molecular-weight water-soluble polymers: exploiting the salt sensitivity of poly(N-acryloylmorpholine)

We report a new one-pot low-viscosity synthetic route to high molecular weight non-ionic water-soluble polymers based on polymerization-induced self-assembly (PISA). The RAFT aqueous dispersion polymerization of N-acryloylmorpholine (NAM) is conducted at 30 °C using a suitable redox initiator and a poly(2-hydroxyethyl acrylamide) (PHEAC) precursor in the presence of 0.60 M ammonium sulfate. This relatively low level of added electrolyte is sufficient to salt out the PNAM block, while steric stabilization is conferred by the relatively short salt-tolerant PHEAC block. A mean degree of polymerization (DP) of up to 6000 was targeted for the PNAM block, and high NAM conversions (>96%) were obtained in all cases. On dilution with deionized water, the as-synthesized sterically stabilized particles undergo dissociation to afford molecularly dissolved chains, as judged by dynamic light scattering and 1H NMR spectroscopy studies. DMF GPC analysis confirmed a high chain extension efficiency for the PHEAC precursor, but relatively broad molecular weight distributions were observed for the PHEAC-PNAM diblock copolymer chains (Mw/Mn > 1.9). This has been observed for many other PISA formulations when targeting high core-forming block DPs and is tentatively attributed to chain transfer to polymer, which is well known for polyacrylamide-based polymers. In fact, relatively high dispersities are actually desirable if such copolymers are to be used as viscosity modifiers because solution viscosity correlates closely with Mw. Static light scattering studies were also conducted, with a Zimm plot indicating an absolute Mw of approximately 2.5 × 106 g mol-1 when targeting a PNAM DP of 6000. Finally, it is emphasized that targeting such high DPs leads to a sulfur content for this latter formulation of just 23 ppm, which minimizes the cost, color, and malodor associated with the organosulfur RAFT agent

Milagrito: a TeV air-shower array

Milagrito, a large, covered water-Cherenkov detector, was the world's first air-shower-particle detector sensitive to cosmic gamma rays below 1 TeV. It served as a prototype for the Milagro detector and operated from February 1997 to May 1998. This paper gives a description of Milagrito, a summary of the operating experience, and early results that demonstrate the capabilities of this technique.Comment: 38 pages including 24 figure

Music intervention to relieve anxiety and pain in adults undergoing cardiac surgery: A systematic review and meta-Analysis

Objectives Previous studies have reported beneficial effects of perioperative music on patients' anxiety and pain. We performed a systematic review and meta-Analysis of randomised controlled trials investigating music interventions in cardiac surgery. Methods Five electronic databases were systematically searched. Primary outcomes were patients' postoperative anxiety and pain. Secondary outcomes were hospital length of stay, opioid use, vital parameters and time on mechanical ventilation. PRISMA guidelines were followed and PROSPERO database registration was completed (CRD42020149733). A meta-Analysis was performed using random effects models and pooled standardised mean differences (SMD) with 95% confidence intervals were calculated. Results Twenty studies were included for qualitative analysis (1169 patients) and 16 (987 patients) for meta-Analysis. The first postoperative mu