Equivalence after extension for compact operators on Banach spaces

In recent years the coincidence of the operator relations equivalence after extension and Schur coupling was settled for the Hilbert space case, by showing that equivalence after extension implies equivalence after one-sided extension. In this paper we investigate consequences of equivalence after extension for compact Banach space operators. We show that generating the same operator ideal is necessary but not sufficient for two compact operators to be equivalent after extension. In analogy with the necessary and sufficient conditions on the singular values for compact Hilbert space operators that are equivalent after extension, we prove the necessity of similar relationships between the $s$-numbers of two compact Banach space operators that are equivalent after extension, for arbitrary $s$-functions. We investigate equivalence after extension for operators on $\ell^{p}$-spaces. We show that two operators that act on different $\ell^{p}$-spaces cannot be equivalent after one-sided extension. Such operators can still be equivalent after extension, for instance all invertible operators are equivalent after extension, however, if one of the two operators is compact, then they cannot be equivalent after extension. This contrasts the Hilbert space case where equivalence after one-sided extension and equivalence after extension are, in fact, identical relations. Finally, for general Banach spaces $X$ and $Y$, we investigate consequences of an operator on $X$ being equivalent after extension to a compact operator on $Y$. We show that, in this case, a closed finite codimensional subspace of $Y$ must embed into $X$, and that certain general Banach space properties must transfer from $X$ to $Y$. We also show that no operator on $X$ can be equivalent after extension to an operator on $Y$, if $X$ and $Y$ are essentially incomparable Banach spaces

Estimated use of abacavir among adults and children enrolled in public sector antiretroviral therapy programmes in Gauteng Province, South Africa

In South Africa, abacavir (ABC) is currently recommended as part of first- and second-line antiretroviral therapy (ART) for HIV-positive paediatric patients. Concerns about overprescribing of the drug, particularly to adults, led to an analysis of ABC use in public sector ART programmes. We investigated current prescription of the drug to adults and children accessing ART in 4 public sector programmes across Gauteng Province, South Africa. ABC was almostexclusively prescribed to children initiating ART and adults requiring regimen changes due to drug toxicities. Patterns of ABC use among HIV-positive paediatric patients followed national ART treatment guidelines on the application of the drug. Although ABC is commonly used in the private sectorfor adults, the current national ART treatment guidelines for adults and adolescents should include ABC as an alternative to standard first- or second-line ART

Estimated use of abacavir among adults and children enrolled in public sector antiretroviral therapy programmes in Gauteng, South Africa

In South Africa, abacavir (ABC) is currently recommended as part of first- and second-line antiretroviral therapy (ART) for HIV-positive paediatric patients. Concerns about overprescribing of the drug, particularly to adults, led to an analysis of ABC use in public sector ART programmes. We investigated current prescription of the drug to adults and children accessing ART in 4 public sector programmes across Gauteng Province, South Africa. ABC was almost exclusively prescribed to children initiating ART and adults requiring regimen changes due to drug toxicities. Patterns of ABC use among HIV-positive paediatric patients followed national ART treatment guidelines on the application of the drug. Although ABC is commonly used in the private sector for adults, the current national ART treatment guidelines for adults and adolescents should include ABC as an alternative to standard first- or second-line ART

HIV care intervention - limited resources, limitless opportunities

This case is intended to inspire HIV caregivers and patients that, even in the most trying circumstances of limited resources, AIDS can be managed effectively with highly active antiretroviral therapy (HAART) and perseverance. Southern African Journal of HIV Medicine Vol. 7 (1) 2006: pp. 44-4

Abnormal synaptic pruning during adolescence underlying the development of psychotic disorders

PURPOSE OF REVIEW: Excessive synaptic pruning has first been suggested by Irwin Feinberg (1982) as an important pillar in the pathophysiology in schizophrenia (SCZ). This article reviews recent developments highlighting factors implicated in aberrant synaptic pruning and its contribution to disease onset and emergence of cognitive symptoms in SCZ. Unraveling these factors provides new insights for potential prevention and treatment strategies for psychotic disorders. RECENT FINDINGS: Increased pruning in SCZ was recently confirmed by a positron emission tomography-study employing the novel tracer [11C]UCB-J, demonstrating the consequential loss of synaptic density. Recent evidence supports the contributing role of astrocytes and increased complement-mediated microglial pruning in disease onset and cognitive symptoms in SCZ. Increased microglial pruning is mediated specifically by C4. Furthermore, environmental factors (e.g., infections and stress) can lead to dysbiosis which was recently linked to microglial activation and pruning in SCZ. SUMMARY: Recent findings render the pruning machinery a potential target for early treatment and prevention in individuals at high risk for SCZ. Minocycline can improve cognition in SCZ, probably by reducing excessive pruning. Probiotics might also have beneficial effects on cognition, although recent findings are not encouraging. N-acetyl-cysteine recovers functional connectivity in SCZ both in vitro and in vivo, making it an interesting candidate

Evidence for a kilometre-scale seismically slow layer atop the core-mantle boundary from normal modes

Geodynamic modelling and seismic studies have highlighted the possibility that a thin layer of low seismic velocities, potentially molten, may sit atop the core-mantle boundary but has thus far eluded detection. In this study we employ normal modes, an independent data type to body waves, to assess the visibility of a seismically slow layer atop the core-mantle boundary to normal mode centre frequencies. Using forward modelling and a dataset of 353 normal mode observations we find that some centre frequencies are sensitive to one-dimensional kilometre-scale structure at the core-mantle boundary. Furthermore, a global slow and dense layer 1 - 3 km thick is better-fitting than no layer. The well-fitting parameter space is broad with a wide range of possible seismic parameters, which precludes inferring a possible composition or phase. Our methodology cannot uniquely detect a layer in the Earth but one should be considered possible and accounted for in future studies