Here dw denotes the Lebesgue measure on the unit sphere, normalized to make ∫ S2 dw = 1. The famous Moser-Trudinger inequality says that J1 is bounded below by a non-positive constant C1. Later Onofri [6] showed that C1 can be taken to be 0. (Another proof was also given by OsgoodPhillips-Sarnack [7].) On the other hand, if we restrict Jα to the class of G of functions g for which e2g has centr...

Amacrine cells in the mammalian retina are famously diverse in shape and function. Here, we show that two wide-field GABA amacrine cells, S1 and S2, have stereotyped synaptic contacts with the appropriate morphology and distribution to perform specific functions. S1 and S2 both supply negative feedback to rod bipolar terminals and thus provide a substrate for lateral inhibition in the rod pathw...

We consider closed topological 4-manifolds M $M$ with universal cover S 2 × ${S^2\times {S^2}}$ and Euler characteristic χ ( ) = 1 $\chi (M) 1$ . All such manifolds π ≅ Z / 4 $\pi =\pi _1(M)\cong {\mathbb {Z}/{4}}$ are homotopy equivalent. In this case, we show that there four homeomorphism types, propose a candidate for smooth example is not homeomorphic to the geometric quotient. If \cong \ma...

Organic fertilizer applications and subsurface drainage are two important measures for improving coastal saline soil; however, nitrous oxide (N2O) emissions from soil under a combination of these seldom evaluated. In this study, cultivated with sunflowers (Helianthus annuus L.) was employed as an experimental system. Prior to the experiment, soils were buried three different spacings (10 m (S1)...

Primary cultures of granule cells (GC) from rat cerebellar cortex were used to determine whether bioelectric activity, via a Ca(2+)/calmodulin-dependent kinase (CaMK) signaling cascade, modulates expression and exon selection in the inositol trisphosphate receptor type 1 (IP(3)R1). IP(3)R1 contains or lacks three exons (S1, S2, and S3) that are regulated in a regionally and temporally specific ...

Empirical density plots (Fig A to J) suggest that π̂IBD for pairs of parasite samples within and across clinics loosely follow a mixture distribution over three classes: 1) near zero π̂IBD shown in green; 2) low to intermediate π̂IBD shown in shades of blue; and 3) high π̂IBD, which notably rarefies with distance, and is colored red if sufficiently dense to be visible, and otherwise outlined in bla...

All tools used in the online tutorial (www.rnaseq.wiki) are referenced below (in bold) along with alternative tools in each category. Where possible a citation is provided. Links are also provided to help the user evaluate the code and the level of maintenance. Where possible the link goes directly to a source controlled repository such as a git repo. Additional lists of tools can be found here...

The nomenclature used here (see also Fig. S1) was built on classical dental serial homologies. The work of Hershkovitz [2] was a major source for defining homologous structures and naming them, but other sources were also considered [3-7]. These works emphasized dental structures that are expressed as relief on tooth crowns. Structures expressed as depressions, in particular groove systems, wer...