Dilations of partial representations of Hopf algebras

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory.Comment: 25 pages. Corrected several typos, final version to appear in Journal of the London Mathematical Societ

The State of External Law\u27s Effect on the Arbitration Process. III. A Commentary on the External Law Papers and IV. Panel Discussion

Marilyn Teitelbaum: I think I have the best of all worlds because I can read these great papers, without having to prepare one of my own, and like all lawyers I like to talk. So, I can share my views, that sometimes diverge from both of the views just presented, particularly the view from the management perspective. In one part of Ted St. Antoine’s paper that was not discussed with you today, he says that the external law question may be a “tempest in a tea pot.” My words would be similar—“much ado about nothing.” I think there is a fairly easy way to deal with the problem. I, as representative of “the union,” used to be the one that was always trying to bring in external law. I still do that, but now I do it in a different way. I agree that the arbitrator’s authority comes from the contract and I try to make things easier for the arbitrators by not asking them to decide external law as such. But, if I want the law to be considered, I word the issue in a way that I can argue external law under the contract. For example, if it’s an NLRA violation, I may define the issue as, “Did the employer violate the collective bargaining agreement by unilaterally changing the terms and conditions of employment?” Or if it’s a discharge case involving sex or race discrimination, “Did the employer violate the just cause clause of the contract by discharging the grievant because of her sex.

Inverse-designed diamond photonics

Diamond hosts optically active color centers with great promise in quantum computation, networking, and sensing. Realization of such applications is contingent upon the integration of color centers into photonic circuits. However, current diamond quantum optics experiments are restricted to single devices and few quantum emitters because fabrication constraints limit device functionalities, thus precluding color center integrated photonic circuits. In this work, we utilize inverse design methods to overcome constraints of cutting-edge diamond nanofabrication methods and fabricate compact and robust diamond devices with unique specifications. Our design method leverages advanced optimization techniques to search the full parameter space for fabricable device designs. We experimentally demonstrate inverse-designed photonic free-space interfaces as well as their scalable integration with two vastly different devices: classical photonic crystal cavities and inverse-designed waveguide-splitters. The multi-device integration capability and performance of our inverse-designed diamond platform represents a critical advancement toward integrated diamond quantum optical circuits

A double-blind randomized controlled trial of maternal postpartum deworming to improve infant weight gain in the Peruvian Amazon

Background : Nutritional interventions targeting the critical growth and development period before two years of age can have the greatest impact on health trajectories over the life course. Compelling evidence has demonstrated that interventions investing in maternal health in the first 1000 days of life are beneficial for both mothers and their children. One such potential intervention is deworming integrated into maternal postpartum care in areas where soil-transmitted helminth (STH) infections are endemic. Methodology/Principal Findings : From February to August 2014, 1010 mother-infant pairs were recruited into a trial aimed at assessing the effectiveness of maternal postpartum deworming on infant and maternal health outcomes. Following delivery, mothers were randomly assigned to receive either single-dose 400 mg albendazole or placebo. Participants were followed-up at 1 and 6 months postpartum. There was no statistically significant difference in mean weight gain between infants in the experimental and control groups (mean difference: -0.02; 95% CI: -0.1, 0.08) at 6 months of age. Further, deworming had no effect on measured infant morbidity indicators. However, ad hoc analyses restricted to mothers who tested positive for STHs at baseline suggest that infants of mothers in the experimental group had greater mean length gain in cm (mean difference: 0.8; 95% CI: 0.1, 1.4) and length-for-age z-score (mean difference: 0.5; 95% CI: 0.2, 0.8) at 6 months of age. Conclusions/Significance : In a study population composed of both STH-infected and uninfected mothers, maternal postpartum deworming was insufficient to impact infant growth and morbidity indicators up to 6 months postpartum. Among STH-infected mothers, however, important improvements in infant length gain and length-for-age were observed. The benefits of maternal postpartum deworming should be further investigated in study populations having higher overall prevalences and intensities of STH infections and, in particular, where whipworm and hookworm infections are of public health concern