Nonlinear bound states on weakly homogeneous spaces

We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schr\"odinger equations. We examine two constrained minimization problems, which give rise to such solutions. One yields what we call $F_\lambda$-minimizers, the other energy minimizers. We produce such ground state solutions on a class of Riemannian manifolds called weakly homogeneous spaces, and establish smoothness, positivity, and decay properties. We also identify classes of Riemannian manifolds with no such minimizers, and classes for which essential uniqueness of positive solutions to the associated elliptic PDE fails.Comment: 49 page

Title VII\u27s Anti-Retaliation Provision Prohibits Any Employer Conduct That Might Dissuade a Reasonable Worker from Making or Supporting a Charge of Discrimination: \u3cem\u3eBurlington Northern & Santa Fe Railway Co. v. White\u3c/em\u3e

The United States Supreme Court held that Title VII\u27s anti-retaliation provision is not limited to workplace-related conduct that affects the terms and conditions of employment, but rather prohibits any employer conduct constituting a materially adverse action - i.e., one that well might dissuade a reasonable worker from making or supporting a charge of discrimination. Burlington N. & Santa Fe Ry. Co. v. White, 126 S. Ct. 2405 (2006)

Mechanically Compliant Grating Reflectors for Optomechanics

We demonstrate micromechanical reflectors with a reflectivity as large as 99.4% and a mechanical quality factor Q as large as 7.8*10^5 for optomechanical applications. The reflectors are silicon nitride membranes patterned with sub-wavelength grating structures, obviating the need for the many dielectric layers used in conventional mirrors. We have employed the reflectors in the construction of a Fabry-Perot cavity with a finesse as high as F=1200, and used the optical response to probe the mechanical properties of the membrane. By driving the cavity with light detuned to the high-frequency side of a cavity resonance, we create an optical antidamping force that causes the reflector to self-oscillate at 211 kHz

A Human Perspective of Contractor Prequalification

The contractor prequalification topic has had much written on it over the last two decades. In the past it has been primarily viewed in terms of the appropriate selection of contractors for construction projects. There has been extensive research interest into the functional and process driven aspects of contractor prequalification. However, there has been little research taking a more holistic view of contractor prequalification in terms of the human aspects that surround it. Hence, gaining a wider appreciation on how prequalification systems affect the major stakeholders seems warranted. The use of soft systems thinking allowed for an in-depth and contextual analysis of prequalification issues. This necessitated unstructured in-depth interviews to be carried out with senior industry practitioners. Sifting through their respective experiences allowed for an alternative view of contractor prequalification systems. It allowed a very human perspective of prequalification to emerge. The research suggests that viewing prequalification systems from a human perspective provides a fuller picture of their true benefits and limitations

Linking vegetation change, carbon sequestration and biodiversity

1. Despite recent interest in linkages between above- and belowground communities and their consequences for ecosystem processes, much remains unknown about their responses to long-term ecosystem change. We synthesize multiple lines of evidence from a long-term ‘natural experiment’ to illustrate how ecosystem retrogression (the decline in ecosystem processes due to long-term absence of major disturbance) drives vegetation change, and thus aboveground and belowground carbon (C) sequestration, and communities of consumer biota. 2. Our study system involves 30 islands in Swedish boreal forest that form a 5000 year fire-driven retrogressive chronosequence. Here, retrogression leads to lower plant productivity and slower decomposition, and a community shift from plants with traits associated with resource acquisition to those linked with resource conservation. 3. We present consistent evidence that aboveground ecosystem C sequestration declines, while belowground and total C storage increases linearly for at least 5000 years following fire absence. This increase is driven primarily by changes in vegetation characteristics, impairment of decomposer organisms and absence of humus combustion. 4. Data from contrasting trophic groups show that during retrogression, biomass or abundance of plants and decomposer biota decreases, while that of aboveground invertebrates and birds increases, due to different organisms accessing resources via distinct energy channels. Meanwhile, diversity measures of vascular plants and aboveground (but not belowground) consumers respond positively to retrogression. 5. We show that taxonomic richness of plants and aboveground consumers are positively correlated with total ecosystem C storage, suggesting that conserving old growth forests simultaneously maximizes biodiversity and C sequestration. However, we find little observational or experimental evidence that plant diversity is a major driver of ecosystem C storage on the islands relative to other biotic and abiotic factors. 6. Synthesis. Our study reveals that across contrasting islands differing in exposure to a key extrinsic driver (historical disturbance regime and resulting retrogression), there are coordinated responses of soil fertility, vegetation, consumer communities, and ecosystem C sequestration, which all feed back to one another. It also highlights the value of well replicated natural experiments for tackling questions about aboveground-belowground linkages over temporal and spatial scales that are otherwise unachievable

Impulse oscillometry identifies peripheral airway dysfunction in children with adenosine deaminase deficiency.

Adenosine deaminase-deficient severe combined immunodeficiency (ADA-SCID) is characterized by impaired T-, B- and NK-cell function. Affected children, in addition to early onset of infections, manifest non-immunologic symptoms including pulmonary dysfunction likely attributable to elevated systemic adenosine levels. Lung disease assessment has primarily employed repetitive radiography and effort-dependent functional studies. Through impulse oscillometry (IOS), which is effort-independent, we prospectively obtained objective measures of lung dysfunction in 10 children with ADA-SCID. These results support the use of IOS in the identification and monitoring of lung function abnormalities in children with primary immunodeficiencies

Primary neurons that express the L2/HNK-1 carbohydrate during early development in the zebrafish

In zebrafish, many nerve pathways in both the CNS and periphery are pioneered by a small and relatively simple set of ‘primary’ neurons that arise in the early embryo. We now have used monoclonal antibodies to show that, as they develop, primary neurons of several functional classes express on their surfaces the L2/HNK-1 tetrasaccharide that is associated with a variety of cell surface adhesion molecules. We have studied the early labeling patterns of these neurons, as well as some non-neural cells, and found that the time of onset and intensity of immunolabeling vary specifically according to cell type. The first neuronal expression is by Rohon-Beard and trigeminal ganglion neurons, both of which are primary sensory neurons that mediate touch sensitivity. These cells express the epitope very strongly on their growth cones and axons, permitting study of their development unobscured by labeling in other cells. Both types initiate axogenesis at the same early time, and appear to be the first neurons in the embryo to do so. Their peripheral neurites display similar branching patterns and have similar distinctive growth cone morphologies. Their central axons grow at the same rate along the same longitudinal fiber pathway, but in opposite directions, and where they meet they appear to fasciculate with one another. The similarities suggest that Rohon-Beard and trigeminal ganglion neurons, despite their different positions, share a common program of early development. Immunolabeling is also specifically present on a region of the brain surface where the newly arriving trigeminal sensory axons will enter the brain. Further, the trigeminal expression of the antigen persists in growth cones during the time that they contact an individually identified central target neuron, the Mauthner cell, which also expresses the epitope. These findings provide descriptive evidence for possible roles of L2/HNK-1 immunoreactive molecules in axonal growth and synaptogenesis