Negative type and bi-lipschitz embeddings into Hilbert space

The usual theory of negative type (and $p$-negative type) is heavily dependent on an embedding result of Schoenberg, which states that a metric space isometrically embeds in some Hilbert space if and only if it has 2-negative type. A generalisation of this embedding result to the setting of bi-lipschitz embeddings was given by Linial, London and Rabinovich. In this article we use this newer embedding result to define the concept of distorted p-negative type and extend much of the known theory of p-negative type to the setting of bi-lipschitz embeddings. In particular we show that a metric space $(X; d_X)$ has $p$-negative type with distortion $C$ $(0 \le p < \infty$, $1 \le C < 1$) if and only if $(X; d^{p/2}_X$) admits a bi-lipschitz embedding into some Hilbert space with distortion at most $C$. Analogues of strict $p$-negative type and polygonal equalities in this new setting are given and systematically studied. Finally, we provide explicit examples of these concepts in the bi-lipschitz setting for the bipartite graphs $K_{m,n}$ and the Hamming cube $H_n$

Therapeutic Implications of Targeting AKT Signaling in Melanoma

Identification of key enzymes regulating melanoma progression and drug resistance has the potential to lead to the development of novel, more effective targeted agents for inhibiting this deadly form of skin cancer. The Akt3, also known as protein kinase B gamma, pathway enzymes regulate diverse cellular processes including proliferation, survival, and invasion thereby promoting the development of melanoma. Accumulating preclinical evidence demonstrates that therapeutic agents targeting these kinases alone or in combination with other pathway members could be effective for the long-term treatment of advanced-stage disease. However, currently, no selective and effective therapeutic agent targeting these kinases has been identified for clinical use. This paper provides an overview of the key enzymes of the PI3K pathway with emphasis placed on Akt3 and the negative regulator of this kinase called PTEN (phosphatase and tensin homolog deleted on chromosome 10). Mechanisms regulating these enzymes, their substrates and therapeutic implications of targeting these proteins to treat melanoma are also discussed. Finally, key issues that remain to be answered and future directions for interested researchers pertaining to this signaling cascade are highlighted

Factors associated with not testing for HIV and consistent condom use among men in Soweto, South Africa.

BackgroundBesides access to medical male circumcision, HIV testing, access to condoms and consistent condom use are additional strategies men can use to prevent HIV acquisition. We examine male behavior toward testing and condom use.ObjectiveTo determine factors associated with never testing for HIV and consistent condom use among men who never test in Soweto.MethodsA cross-sectional survey in Soweto was conducted in 1539 men aged 18-32 years in 2007. Data were collected on socio-demographic and behavioral characteristics to determine factors associated with not testing and consistent condom use.ResultsOver two thirds (71%) of men had not had an HIV test and the majority (55%, n = 602) were young (18-23). Of those not testing, condom use was poor (44%, n = 304). Men who were 18-23 years (aOR: 2.261, CI: 1.534-3.331), with primary (aOR: 2.096, CI: 1.058-4.153) or high school (aOR: 1.622, CI: 1.078-2.439) education, had sex in the last 6 months (aOR: 1.703, CI: 1.055-2.751), and had ≥1 sexual partner (aOR: 1.749, CI: 1.196-2.557) were more likely not to test. Of those reporting condom use (n = 1036, 67%), consistent condom use was 43% (n = 451). HIV testing did not correlate with condom use.ConclusionLow rates of both condom use and HIV testing among men in a high HIV prevalence setting are worrisome and indicate an urgent need to develop innovative behavioral strategies to address this shortfall. Condom use is poor in this population whether tested or not tested for HIV, indicating no association between condom use and HIV testing

Effects of wild and farm-grown macroalgae on the growth of juvenile South African abalone Haliotis midae Linnaeus

The effect of various macroalgal diets on the growth of grow-out (> 20 mm shell length) South African abalone Haliotis midae was investigated on a commercial abalone farm. The experiment consisted of four treatments: fresh kelp blades (Ecklonia maxima [Osbeck] Papenfuss) (~ 10 % protein); farmed, protein-enriched Ulva lactuca Linnaeus (~26 % protein) grown in aquaculture effluent; wild U. lactuca (~ 20 % protein); and a combination (mixed) diet of kelp blades + farmed U. lactuca. Abalone grew best on the combination diet (0.423 ± 0.02% weight dayˉ¹ SGR [specific growth rate]; 59.593 ± 0.02 µm dayˉ¹ DISL [daily increment in shell length]; 1.093 final CF [condition factor]) followed by the kelp only diet (0.367 ± 0.02 % weight dayˉ¹ SGR; 53.148 ± 0.02 µm dayˉ¹ DISL; 1.047 final CF), then the farmed, protein-enriched U. lactuca only diet (0.290 ± 0.02% weight dayˉ¹ SGR; 42.988 ± 0.03 µm dayˉ¹ DISL; 1.013 final CF) that in turn outperformed the wild U. lactuca only diet (-0.079 ± 0.01 % weight dayˉ¹ SGR; 3.745 ± 0.02 µm dayˉ¹ DISL; 0.812 final CF). The results suggest that protein alone could not have accounted for the differences produced by the varieties of U. lactuca and that the gross energy content is probably important.Web of Scienc

Roundness, Negative Type and Bi-lipschitz Embeddings Into Hilbert Space

In this thesis we study certain roundness inequalities in metric spaces. The properties roundness and generalised roundness of metric spaces were originally introduced by Enflo where they were used to act as obstructions to uniform embeddings. Since then the relation of these properties to other embeddings such as isometric embeddings and coarse embeddings of metric spaces has been the subject of much study. A major result in this area is that generalised roundness, and the equivalent property of $p$-negative type, can act as a sufficient condition for certain isometric embeddings into Euclidean space. In particular a finite metric space $(X,d_{X})$ embeds isometrically into some Euclidean space if and only if it has $2$-negative type. We start by studying roundness in the setting of Banach spaces. Here we are able to unify and expand upon results of Enflo that aid in the calculation of the maximal roundness of many classical Banach spaces. We then consider the problem of computing the maximal roundness of more general Banach spaces whose unit spheres are easy to visualise but whose norm is more complicated to write down. In doing so we are led naturally to a slightly broader class of inequalities than that of the usual roundness. This new class of inequalities is then shown to have a close connection to the geometric concepts of smoothness and convexity. In the next section of this thesis we investigate the possibility of an analogous class of inequalities in the setting of generalised roundness, or equivalently $p$-negative type. Our starting point is a theorem of Linial, London and Rabinovich which characterises those finite metric spaces that admit a bi-lipschitz embedding into some Euclidean space with a given amount of distortion. Using this we are able to define the new concept of distorted $p$-negative type which we then show is a generalisation of the usual $p$-negative type. Due to the theorem of Linial, London and Rabinovich the concept of distorted $p$-negative type acts a sufficient condition for certain bi-lipschitz embeddings into Euclidean space. In particular we show that a finite metric space $(X,d_{X})$ admits a bi-lipschitz embedding into some Euclidean space with distortion at most $C$ if and only if it has $2$-negative type with distortion $C$. We are also able to prove an analogous result for infinite metric spaces. We then proceed to generalise the properties of the usual $p$-negative type such as strictness and polygonal equalities to this distorted setting. Explicit examples of finite metric spaces with distorted $p$-negative type and examples of their distorted polygonal equalities are then given. Finally, we prove a certain linearisation of the theorem of Linial, London and Rabinovich which provides a complete characterisation of those Banach spaces that are linearly isomorphic to a Hilbert space with a given level of distortion

The roles of anti-GM1 complex antibodies in autoimmune neuropathies

Anti-ganglioside antibodies have been implicated in autoimmune neuropathies for several decades. They are thought to elicit injury through binding to sites in the peripheral nervous system, where they activate the complement pathway to induce cell death. Patient serum is therefore regularly screened for these antibodies to aid in the diagnosis of various conditions. Recent work has found that complexes composed of gangliosides and other glycolipids can improve the detection of these antibodies beyond the signals detected to the single ganglioside species. In MMN research, complexes comprised of GM1 and GalC have been found to significantly enhance antibody detection in patient sera. In certain patients, however, antibody binding was only detected against these complexes and not the single antigens. This led some researchers to hypothesise that an unidentified class of antibody may have arisen that binds specifically to a neoepitope formed by the combination of the two glycolipids. It has also been hypothesised that that this complex may be the true target of immune mediated attack in MMN. This thesis sought to address this hypothesis by either cloning these antibodies directly from patient serum or through active immunisations with mice. Analysis of previously generated human monoclonal antibodies indicated that their behaviours were modified by complexes containing particular gangliosides or glycolipids. Furthermore, the antibodies behaviours were found to diverge, when they were screened against complexes comprised of gangliosides and different concentrations of accessory lipids. These findings suggested that the accessory lipids were interacting with the ganglioside headgroups to modify the presentation of different binding epitopes. This indicated that conformational modulation, rather than neo-epitope formation, may be responsible for complex enhancement Cloning antibodies from patient sera was unsuccessful but examination of the screening techniques suggested that the appearance of complex-dependent antibodies may have been an artefact. Attempts to induce complex-specific responses in mice were similarly unsuccessful but several anti-ganglioside and anti-sulfatide antibodies were created. The subsequent chapters focused on the characterisation of these antibodies and indicated that most of them bound well to solid-phase assays, cells and tissue and may therefore be of use in future studies. Taken together, the data from this thesis suggests that complex-dependent antibodies may not exist but are merely low concentrations of anti-ganglioside antibodies that are cis-enhanced by particular lipids. Future work should therefore focus on assessing how the ganglioside microenvironment modifies epitope presentation and how this affects the binding capabilities of antiganglioside antibodies

Accounting for Accountability: A Discourse Analysis of Psychiatric Nurses’ Experience of a Patient Suicide

Whilst the experience of a patient suicide is likely to have a significant impact upon the nurses who had been providing care, little work has actually explored this experience in any depth. In this article we explore how two psychiatric nurses construct and orient to accountability when talking of their experiences of a patient suicide. Discourse analysis was used to explore particular phases that the nurses oriented to in their accounts: scene setting; risk assessment; attributing for the suicide. Findings highlight the different, sometimes contradictory, ways the nurses attended to interactional concerns relating to implicit accountability and potential inferences of blame. Analysis of the nurses’ talk can make a valuable contribution to understanding the nature and the impact of ‘accountability’ in a mental health setting and so help nurses and other professionals gain an insight into their practice. The results from this study suggest that as a consequence of internalising fundamentally unrealisable expectations regarding suicide prevention, nurses can hold themselves to blame raising significant concerns around their needs in terms of support, which may not be recognised. This paper also makes a valuable contribution to our methodological understanding and the value of using discourse analysis in this setting