Acceleration of generalized hypergeometric functions through precise remainder asymptotics

We express the asymptotics of the remainders of the partial sums {s_n} of the generalized hypergeometric function q+1_F_q through an inverse power series z^n n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k} may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z=1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added several references, added comparison to other methods, and added discussion of recursion stabilit

Two-loop HTL Thermodynamics with Quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.Comment: 33 pages, 6 figure

Mesodermal Progenitor Cells (MPCs) Differentiate into Mesenchymal Stromal Cells (MSCs) by Activation of Wnt5/Calmodulin Signalling Pathway

Mesenchymal Stromal Cells (MSCs) remain poorly characterized because of the absence of manifest physical, phenotypic, and functional properties in cultured cell populations. Despite considerable research on MSCs and their clinical application, the biology of these cells is not fully clarified and data on signalling activation during mesenchymal differentiation and proliferation are controversial. The role of Wnt pathways is still debated, partly due to culture heterogeneity and methodological inconsistencies. Recently, we described a new bone marrow cell population isolated from MSC cultures that we named Mesodermal Progenitor Cells (MPCs) for their mesenchymal and endothelial differentiation potential. An optimized culture method allowed the isolation from human adult bone marrow of a highly pure population of MPCs (more than 97%), that showed the distinctive SSEA-4+CD105+CD90(neg) phenotype and not expressing MSCA-1 antigen. Under these selective culture conditions the percentage of MSCs (SSEA-4(neg)CD105+CD90(bright) and MSCA-1+), in the primary cultures, resulted lower than 2%.We demonstrate that MPCs differentiate to MSCs through an SSEA-4+CD105+CD90(bright) early intermediate precursor. Differentiation paralleled the activation of Wnt5/Calmodulin signalling by autocrine/paracrine intense secretion of Wnt5a and Wnt5b (p<0.05 vs uncondictioned media), which was later silenced in late MSCs (SSEA-4(neg)). We found the inhibition of this pathway by calmidazolium chloride specifically blocked mesenchymal induction (ID₅₀ =  0.5 µM, p<0.01), while endothelial differentiation was unaffected.The present study describes two different putative progenitors (early and late MSCs) that, together with already described MPCs, could be co-isolated and expanded in different percentages depending on the culture conditions. These results suggest that some modifications to the widely accepted MSC nomenclature are required

Benthic pH gradients across a range of shelf sea sediment types linked to sediment characteristics and seasonal variability

This study used microelectrodes to record pH profiles in fresh shelf sea sediment cores collected across a range of different sediment types within the Celtic Sea. Spatial and temporal variability was captured during repeated measurements in 2014 and 2015. Concurrently recorded oxygen microelectrode profiles and other sedimentary parameters provide a detailed context for interpretation of the pH data. Clear differences in profiles were observed between sediment type, location and season. Notably, very steep pH gradients exist within the surface sediments (10–20 mm), where decreases greater than 0.5 pH units were observed. Steep gradients were particularly apparent in fine cohesive sediments, less so in permeable sandier matrices. We hypothesise that the gradients are likely caused by aerobic organic matter respiration close to the sediment–water interface or oxidation of reduced species at the base of the oxic zone (NH4+, Mn2+, Fe2+, S−). Statistical analysis suggests the variability in the depth of the pH minima is controlled spatially by the oxygen penetration depth, and seasonally by the input and remineralisation of deposited organic phytodetritus. Below the pH minima the observed pH remained consistently low to maximum electrode penetration (ca. 60 mm), indicating an absence of sub-oxic processes generating H+ or balanced removal processes within this layer. Thus, a climatology of sediment surface porewater pH is provided against which to examine biogeochemical processes. This enhances our understanding of benthic pH processes, particularly in the context of human impacts, seabed integrity, and future climate changes, providing vital information for modelling benthic response under future climate scenarios