Minimal surfaces and eigenvalue problems

We show that metrics that maximize the k-th Steklov eigenvalue on surfaces with boundary arise from free boundary minimal surfaces in the unit ball. We prove several properties of the volumes of these minimal submanifolds. For free boundary minimal submanifolds in the ball we show that the boundary volume is reduced up to second order under conformal transformations of the ball. For two-dimensional stationary integer multiplicity rectifiable varifolds that are stationary for deformations that preserve the ball, we prove that the boundary length is reduced under conformal transformations. We also give an overview of some of the known results on extremal metrics of the Laplacian on closed surfaces, and give a survey of our recent results from [FS2] on extremal metrics for Steklov eigenvalues on compact surfaces with boundary.Comment: 17 pages. To appear in Contemporary Mathematic

Slow intermixing of cells during Xenopus embryogenesis contributes to the consistency of the blastomere fate map

The relatively consistent fates of the blastomeres of the frog embryo could result from (i) predetermination of the blastomeres or (ii) reproducible morphogenetic cell movements. In some species, the mixing of the cells during development provides a test between these alternative hypotheses. If blastomeres are predetermined, then random intermixing of the descendants with neighboring cells could not alter their fate. To follow cell mixing during Xenopus development, fluorescent dextran lineage tracers were microinjected into identified blastomeres at the 16-cell stage. The labelled descendants of the injected blastomeres were followed over several stages of embryogenesis. After gastrulation, the labelled descendants formed relatively coherent groups in characteristic regions of the embryo. By larval stages, most of the labelled descendants were still located in characteristic regions. However, coherence was less pronounced and individual descendants were located in many regions of the embryo. Hence, cell mixing is a slow, but progressive, process throughout Xenopus development. This is in sharp contrast to the extensive mixing that occurs during the early development of other vertebrates, such as zebrafish and mice. The slow cell mixing in Xenopus development suggests a simple mechanism for the consistent fates of cleavage-stage blastomeres. The stereotyped cell movements of embryogenesis redistribute the largely coherent descendants to characteristic locations in the embryo. The small amount of mixing that does occur would result in variable locations of a small proportion of the descendants; this could contribute to the observed variability of the blastomere fate map. Because cell mixing during Xenopus development is insufficient to challenge possible lineage restrictions, additional experiments must be performed to establish when and if lineage restrictions occur

Observations on the action of digitalis in man

In recent years evidence has been produced that makes clearer certain points that have been observed by clinicians during the administration of digitalis for therapeutic purposes, that helps to indicate with more certainty the effect that can be expected in a particular case, and that enables the drug to be administered with greater efficiency.The author of this thesis has worked in collaboration with others in producing some of this evidence, and some of the results have already been published as follows:-1. Certain Effects of Digitalis on the Heart. Cohn and Fraser. International Congress of Medicine. London,1913.2. The Influence of Digitalis on the T wave of the Human Electrocardiogram. Cohn, Fraser and Jamieson. Journal of Experimental Medicine. Vol.XXI,June,1915.The Author of this thesis had clinical charge of the cases employed in the investigations. The electrocardiographic records were made and analysed by him under the direction of Dr.A.E.Cohn,but for the analysis and discussion here presented the author is entirely responsible. The preparation of this thesis was commenced in 1914 but was interrupted by the war.In a field of this nature, where so many observers have been engaged, it is necessary to indicate the work of others, whether previous or contemporary, to such an extent that the sequence 1. of thought may he maintained, hut it is impossible to refer to much work of importance that has helped to build up the present knowledge of the actions of the digitalis bodies.The observations will be recorded in so far as they apply to our knowledge of the action of digitalis in human beings on :-(I) the normal pace-maker of the heart; (II) the auriculo-ventricular conducting mechanism; (III) the ventricular muscle

Supporting siblings of children with a special educational need or disability : an evaluation of Sibs Talk, a one‐to‐one intervention delivered by staff in mainstream schools

A group often overlooked for specific supports in schools are siblings of children with a disability, special educational needs or a serious long‐term condition (SEND). In this article we review the current sibling research and identify a lack of literature on interventions, particularly within a school context. We then present a description of Sibs Talk, an example of a new school‐based intervention to support siblings. Sibs Talk is a ten‐session, one‐to‐one intervention approach for schools to complete with Key Stage 2 children who have a brother or sister with SEND. Finally, we present an initial evaluation of the effectiveness of Sibs Talk, using a pre and post evaluation format with a sample of 55 children from 11 schools. The data presented in this evaluation indicate that Sibs Talk may have contributed to positive outcomes for participating children

Regulation of cAMP responses by the G12/13 pathway converges on adenylyl cyclase VII

Regulation of intracellular cyclic adenosine 3’, 5’-monophosphate (cAMP) by multiple pathways enables differential function of this ubiquitous second messenger in a context dependent manner. Modulation of Gs-stimulated intracellular cAMP has long been known to be modulated by the Gi and Gq/Ca2+ pathways. Recently, the G13 pathway was also shown to facilitate cAMP responses in murine macrophage cells. We report here that this synergistic regulation of cAMP synthesis by the Gs and G13 pathways is mediated by a specific isoform of adenylyl cyclase, AC7. Furthermore, this signaling paradigm exists in several hematopoietic lineages and can be recapitulated by exogenous expression of AC7 in HEK 293 cells. Mechanistic characterization of this synergistic interaction indicates that it occurs downstream of receptor activation and it can be mediated by the alpha subunit of either G12 or G13. Our results demonstrate that AC7 is a specific downstream effector of the G12/13 pathway