The Liouville Theorem for a Quasi-Linear Elliptic Partial Differential Equation

The classical Liouville Theorem of analytic function theory can be stated in either of two equivalent forms: The Liouville Theorem states: If f(w) is analytic and bounded throughout the finite w-plane, then f(w) is constant. If z(x, y) is a real valued function of the real variables x and y which is a solution of zxx + zyy = 0 and is bounded either above or below throughout the finite plane, then z(x, y) is a constant. Here we are concerned with the question of whether or not the second formulation of the above theorem is valid for solutions of more general elliptic partial differential equations

The Liouville Theorem for a Quasi-Linear Elliptic Partial Differential Equation

The classical Liouville Theorem of analytic function theory can be stated in either of two equivalent forms: The Liouville Theorem states: If f(w) is analytic and bounded throughout the finite w-plane, then f(w) is constant. If z(x, y) is a real valued function of the real variables x and y which is a solution of zxx + zyy = 0 and is bounded either above or below throughout the finite plane, then z(x, y) is a constant. Here we are concerned with the question of whether or not the second formulation of the above theorem is valid for solutions of more general elliptic partial differential equations

Health Disparities in Boys and Men of Color

http://dx.doi.org/10.2105/ajph.2011.30064

Evaluation of a library of FDA-approved drugs for their ability to potentiate antibiotics against multidrug resistant Gram-negative pathogens

The Prestwick library was screened for antibacterial activity or 'antibiotic-resistance breaking' (ARB) potential against four species of Gram-negative pathogens. Discounting known antibacterials, the screen identified very few ARB hits, which were strain/drug specific. These ARB hits included antimetabolites (zidovudine, floxuridine, didanosine, gemcitabine), anthracyclines (daunorubicin, mitoxantrone, epirubicin) and psychoactive drugs (gabapentin, fluspirilene, oxethazaine). This suggests that there are few approved drugs which could be directly repositioned as adjunct-antibacterials and these will need robust testing to validate efficacy. [Abstract copyright: © Crown copyright 2019.

The carbon balance of South America: A review of the status, decadal trends and main determinants

Copyright © 2012 European Geosciences Union. This is the published version available at http://www.biogeosciences-discuss.net/9/627/2012/bgd-9-627-2012.htmlWe attempt to summarize the carbon budget of South America and relate it to its dominant controls: population and economic growth, changes in land use practices and a changing atmospheric environment and climate. Flux estimation methods which we consider sufficiently reliable are fossil fuel emission inventories, biometric analysis of old-growth rainforests, estimation of carbon release associated with deforestation based on remote sensing and inventories, and finally inventories of agricultural exports. Other routes to estimating land-atmosphere CO2 fluxes include atmospheric transport inverse modelling and vegetation model predictions but are hampered by the data paucity and the need for improved parameterisation. The available data we analyze suggest that South America was a net source to the atmosphere during the 1980s (∼0.3–0.4 Pg C yr−1) and close to neutral (∼0.1 Pg C yr−1) in the 1990s with carbon uptake in old-growth forests nearly compensating carbon losses due to fossil fuel burning and deforestation. Annual mean precipitation over tropical South America measured by Amazon River discharge has a long-term upward trend, although over the last decade, dry seasons have tended to be drier and longer (and thus wet seasons wetter), with the years 2005 and 2010 experiencing strong droughts. It is currently unclear what the effect of these climate changes on the old-growth forest carbon sink will be but first measurements suggest it may be weakened. Based on scaling of forest census data the net carbon balance of South America seems to have been an increased source roughly over the 2005–2010 period (a total of ∼1 Pg C of dead tree biomass released over several years) due to forest drought response. Finally, economic development of the tropical forest regions of the continent is advancing steadily with exports of agricultural products being an important driver and witnessing a strong upturn over the last decade

Detection of early changes in the post-radiosurgery vestibular schwannoma microenvironment using multinuclear MRI

From Springer Nature via Jisc Publications RouterHistory: received 2021-03-01, accepted 2021-07-05, registration 2021-07-21, pub-electronic 2021-08-03, online 2021-08-03, collection 2021-12Publication status: PublishedFunder: CRUK and EPSRC Cancer Imaging Centre in Cambridge and Manchester; doi: http://dx.doi.org/10.13039/501100014679; Grant(s): C8742/A18097, C8742/A18097, C8742/A18097, C8742/A18097, C8742/A18097Funder: Manchester Academic Health Sciences centre (MAHSC)Abstract: Stereotactic radiosurgery (SRS) is an established, effective therapy against vestibular schwannoma (VS). The mechanisms of tumour response are, however, unknown and in this study we sought to evaluate changes in the irradiated VS tumour microenvironment through a multinuclear MRI approach. Five patients with growing sporadic VS underwent a multi-timepoint comprehensive MRI protocol, which included diffusion tensor imaging (DTI), dynamic contrast-enhanced (DCE) MRI and a spiral 23Na-MRI acquisition for total sodium concentration (TSC) quantification. Post-treatment voxelwise changes in TSC, DTI metrics and DCE-MRI derived microvascular biomarkers (Ktrans, ve and vp) were evaluated and compared against pre-treatment values. Changes in tumour TSC and microvascular parameters were observable as early as 2 weeks post-treatment, preceding changes in structural imaging. At 6 months post-treatment there were significant voxelwise increases in tumour TSC (p < 0.001) and mean diffusivity (p < 0.001, repeated-measures ANOVA) with marked decreases in tumour microvascular parameters (p < 0.001, repeated-measures ANOVA). This study presents the first in vivo evaluation of alterations in the VS tumour microenvironment following SRS, demonstrating that changes in tumour sodium homeostasis and microvascular parameters can be imaged as early as 2 weeks following treatment. Future studies should seek to investigate these clinically relevant MRI metrics as early biomarkers of SRS response

The influence of the accessory genome on bacterial pathogen evolution

Bacterial pathogens exhibit significant variation in their genomic content of virulence factors. This reflects the abundance of strategies pathogens evolved to infect host organisms by suppressing host immunity. Molecular arms-races have been a strong driving force for the evolution of pathogenicity, with pathogens often encoding overlapping or redundant functions, such as type III protein secretion effectors and hosts encoding ever more sophisticated immune systems. The pathogens’ frequent exposure to other microbes, either in their host or in the environment, provides opportunities for the acquisition or interchange of mobile genetic elements. These DNA elements accessorise the core genome and can play major roles in shaping genome structure and altering the complement of virulence factors. Here, we review the different mobile genetic elements focusing on the more recent discoveries and highlighting their role in shaping bacterial pathogen evolution