Entanglement entropy on a fuzzy sphere with a UV cutoff

We introduce a UV cutoff into free scalar field theory on the noncommutative (fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows us to control the effective nonlocality scale of the theory. In the resulting fuzzy geometry, we establish which degrees of freedom lie within a specific geometric subregion and compute the associated vacuum entanglement entropy. Entanglement entropy for regions smaller than the effective nonlocality scale is extensive, while entanglement entropy for regions larger than the effective nonlocality scale follows the area law. This reproduces features previously obtained in the strong coupling regime through holography. We also show that mutual information is unaffected by the UV cutoff.Comment: Significantly revised with improved methodology, 16 pages, 8 figure

PRDM14 is expressed in germ cell tumors with constitutive overexpression altering human germline differentiation and proliferation.

Germ cell tumors (GCTs) are a heterogeneous group of tumors occurring in gonadal and extragonadal locations. GCTs are hypothesized to arise from primordial germ cells (PGCs), which fail to differentiate. One recently identified susceptibility loci for human GCT is PR (PRDI-BF1 and RIZ) domain proteins 14 (PRDM14). PRDM14 is expressed in early primate PGCs and is repressed as PGCs differentiate. To examine PRDM14 in human GCTs we profiled human GCT cell lines and patient samples and discovered that PRDM14 is expressed in embryonal carcinoma cell lines, embryonal carcinomas, seminomas, intracranial germinomas and yolk sac tumors, but is not expressed in teratomas. To model constitutive overexpression in human PGCs, we generated PGC-like cells (PGCLCs) from human pluripotent stem cells (PSCs) and discovered that elevated expression of PRDM14 does not block early PGC formation. Instead, we show that elevated PRDM14 in PGCLCs causes proliferation and differentiation defects in the germline

The importance of Implementing Literacy Strategies in a Mathematics Classroom

The purpose of this ACTION research study is to explore the influence of literacy on mathematical proficiency levels. The correlation will use the data to formulate some strategies for the classroom in order to increase confidence in both subject areas