The group theoretic Rubik\u27s Cube

Cyclic fads often boomerang our childhood toys, sending them back to us with renewed popularity during our adulthood. Recently, Rubik\u27s Cube has made a startling comeback and is once again a staple in most toy stores. Invented by Erno Rubik in his hometown of Budapest, Hungary, the original \Magic Cube was released in 1974. Upon its world debut in 1980, the toy named after this Hungarian architect became an instant classic. Over 350 billion Rubik\u27s Cubes have been sold worlwide [sic] over the past 30 years, making it easily the top-selling puzzle toy in documented history. This seemingly innocuous puzzle has frazzled countless children, and perhaps even more adults. The mathematical complexity of the Cube attracted group theorists and other mathematicians upon its release over three decades ago, and the many layers of its structure continue to intrigue the mathematics community. Most of us place emphasis on unscralmbing [sic] the Cube, solving the puzzle. Rather than focusing on the construction of algorithms or solutions to the Cube, we chose to take a group theoretic approach to analyzing this infamous toy. Here, treating Rubik\u27s Cube as a group, we will examine subgroups of the Cube, particularly those constructed via semidirect products. These constructions aid us in describing the possible color arrangements of the Cube

Disrupted Maturation of the Microbiota and Metabolome among Extremely Preterm Infants with Postnatal Growth Failure

Growth failure during infancy is a major global problem that has adverse effects on long-term health and neurodevelopment. Preterm infants are disproportionately affected by growth failure and its effects. Herein we found that extremely preterm infants with postnatal growth failure have disrupted maturation of the intestinal microbiota, characterized by persistently low diversity, dominance of pathogenic bacteria within the Enterobacteriaceae family, and a paucity of strictly anaerobic taxa including Veillonella relative to infants with appropriate postnatal growth. Metabolomic profiling of infants with growth failure demonstrated elevated serum acylcarnitines, fatty acids, and other byproducts of lipolysis and fatty acid oxidation. Machine learning algorithms for normal maturation of the microbiota and metabolome among infants with appropriate growth revealed a pattern of delayed maturation of the microbiota and metabolome among infants with growth failure. Collectively, we identified novel microbial and metabolic features of growth failure in preterm infants and potentially modifiable targets for intervention

Milrinone in congenital diaphragmatic hernia - a randomized pilot trial: study protocol, review of literature and survey of current practices.

Background:Congenital diaphragmatic hernia (CDH) is commonly associated with pulmonary hypoplasia and pulmonary hypertension (PH). PH associated with CDH (CDH-PH) is frequently resistant to conventional pulmonary vasodilator therapy including inhaled nitric oxide (iNO) possibly due to right and left ventricular dysfunction. Milrinone is an intravenous inotrope and lusitrope with pulmonary vasodilator properties and has been shown anecdotally to improve oxygenation in PH. We developed this pilot study to determine if milrinone infusion would improve oxygenation in neonates ≥36 weeks postmenstrual age (PMA) with CDH. Methods/design:Data on pulmonary vasodilator management and outcome of CDH patients was collected from 18 university NICUs affiliated with the Neonatal Research Network (NRN) from 2011 to 2012. The proposed pilot will be a masked, placebo-controlled, multicenter, randomized trial of 66 infants with CDH with an oxygenation index (OI) ≥10 or oxygen saturation index (OSI) ≥5. The primary outcome is the oxygenation response, as determined by change in OI at 24 h after initiation of study drug. As secondary outcomes, we will determine oxygenation at 48 h and 72 h post-infusion, right ventricular pressures on echocardiogram and the incidence of systemic hypotension, arrhythmias, intracranial hemorrhage, survival without extracorporeal membrane oxygenation, and chronic lung disease (oxygen need at 28 days postnatal age). Finally, we will evaluate the pulmonary and nutritional status at 4, 8 and 12 months of age using a phone questionnaire. Results:Three hundred thirty-seven infants with CDH were admitted to NRN NICUs in 2011 and 2012 of which 275 were ≥36 weeks PMA and were exposed to the following pulmonary vasodilators: iNO (39%), sildenafil (17%), milrinone (17%), inhaled epoprostenol (6%), intravenous epoprostenol (3%), and intravenous PGE1 (1%). ECMO was required in 36% of patients. Survival to discharge was 71%. Discussion:CDH is an orphan disease with high mortality with few randomized trials evaluating postnatal management. Intravenous milrinone is a commonly used medication in neonatal/pediatric intensive care units and is currently used in 17% of patients with CDH within the NRN. This pilot study will provide data and enable further studies evaluating pulmonary vasodilator therapy in CDH. Trial registration:ClinicalTrials.gov; NCT02951130; registered 14 October 2016

Astrometric Confirmation and Preliminary Orbital Parameters of the Young Exoplanet 51 Eridani b with the Gemini Planet Imager

We present new Gemini Planet Imager observations of the young exoplanet 51 Eridani b that provide further evidence that the companion is physically associated with 51 Eridani. Combining this new astrometric measurement with those reported in the literature, we significantly reduce the posterior probability that 51 Eridani b is an unbound foreground or background T-dwarf in a chance alignment with 51 Eridani to 2 7 10-7, an order of magnitude lower than previously reported. If 51 Eridani b is indeed a bound object, then we have detected orbital motion of the planet between the discovery epoch and the latest epoch. By implementing a computationally efficient Monte Carlo technique, preliminary constraints are placed on the orbital parameters of the system. The current set of astrometric measurements suggest an orbital semimajor axis of AU, corresponding to a period of years (assuming a mass of 1.75 Mo for the central star), and an inclination of deg. The remaining orbital elements are only marginally constrained by the current measurements. These preliminary values suggest an orbit that does not share the same inclination as the orbit of the distant M-dwarf binary, GJ 3305, which is a wide physically bound companion to 51 Eridani.Peer reviewed: YesNRC publication: Ye