An Obstruction to Quantization of the Sphere

In the standard example of strict deformation quantization of the symplectic sphere $S^2$, the set of allowed values of the quantization parameter $\hbar$ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including $S^2$) in which $\hbar$ can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing $S^2$ is never connected.Comment: 23 page. v2: changed sign conventio

Unique Molecular Features in High-Risk Histology Endometrial Cancers

Endometrial cancer is the most common gynecologic malignancy in the United States and the sixth most common cancer in women worldwide. Fortunately, most women who develop endometrial cancer have low-grade early-stage endometrioid carcinomas, and simple hysterectomy is curative. Unfortunately, 15% of women with endometrial cancer will develop high-risk histologic tumors including uterine carcinosarcoma or high-grade endometrioid, clear cell, or serous carcinomas. These high-risk histologic tumors account for more than 50% of deaths from this disease. In this review, we will highlight the biologic differences between low- and high-risk carcinomas with a focus on the cell of origin, early precursor lesions including atrophic and proliferative endometrium, and the potential role of stem cells. We will discuss treatment, including standard of care therapy, hormonal therapy, and precision medicine-based or targeted molecular therapies. We will also discuss the impact and need for model systems. The molecular underpinnings behind this high death to incidence ratio are important to understand and improve outcomes

Preliminary Canopy Removal Experiments in Algal Dominated Communities Low on the Shore and in the Shallow Subtidal on the Isle of Man

The algal dominated communities immediately above and below the low-water spring level on a moderately exposed Manx shore were investigated by canopy removal experiments. Fucus serratus, Laminaria digitata and L. hyperborea were removed. Competition was shown to be important in determining the zonation of L. digitata and the distribution along the wave exposure gradient of other species such as Alaria esculenta, Desmarestia aculeata and D. viridis, and L. saccharina. Many species of algal epiphytes were early colonizers of canopy removal areas suggesting that competition from canopy algae usually restricts them to an epiphytic habit. The results indicate that interactions between macrophytes are much more important than grazing in structuring these communities

Time, institutional support and quality of decision making in child protection:A cross-country analysis

This paper examines perceptions of time and institutional support for decision making and staff confidence in child welfare staffs ultimate decisions – examining differences and similarities between and within the service-oriented Nordic countries (Norway and Finland) and the risk-oriented Anglo-American countries (England and California). The study identifies a high degree of work pressure across all the countries, lines of predominantly vertical institutional support and relatively high confidence in decisions. Finland stands out with higher perceived work pressure and with a horizontal support line, whereas England stands out with workers having a lower degree of confidence in their own and others’ decisions

A model for the orientational ordering of the plant microtubule cortical array

The plant microtubule cortical array is a striking feature of all growing plant cells. It consists of a more or less homogeneously distributed array of highly aligned microtubules connected to the inner side of the plasma membrane and oriented transversely to the cell growth axis. Here we formulate a continuum model to describe the origin of orientational order in such confined arrays of dynamical microtubules. The model is based on recent experimental observations that show that a growing cortical microtubule can interact through angle dependent collisions with pre-existing microtubules that can lead either to co-alignment of the growth, retraction through catastrophe induction or crossing over the encountered microtubule. We identify a single control parameter, which is fully determined by the nucleation rate and intrinsic dynamics of individual microtubules. We solve the model analytically in the stationary isotropic phase, discuss the limits of stability of this isotropic phase, and explicitly solve for the ordered stationary states in a simplified version of the model.Comment: 15 pages, 5 figure