"Magic" numbers in Smale's 7th problem

Smale's 7-th problem concerns N-point configurations on the 2-dim sphere which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the pairs in a configuration; here, r is the chordal distance between the points forming a pair. More generally, V_0(r) may be replaced by the standardized Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to 0, and the sphere may be replaced by other compact manifolds. This paper inquires into the concavity of the map from the integers N>1 into the minimal average standardized Riesz pair-energies v_s(N) of the N-point configurations on the 2-sphere for various real s. It is known that v_s(N) is strictly increasing for each real s, and for s<2 also bounded above, hence "overall concave." It is (easily) proved that v_{-2}(N) is even locally strictly concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental data of putatively minimal average Riesz pair-energies v_s^x(N) for s in {-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally strictly concave, while v_s^x(N) is not always locally strictly concave for s in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific empirical set of integers). It is found that the empirical map C^{x}_+(s), with s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The integers in C^{x}_+(0) are few and far between, forming a curious sequence of numbers, reminiscent of the "magic numbers" in nuclear physics. It is conjectured that the "magic numbers" in Smale's 7-th problem are associated with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised version, to appear in J. Stat. Phys. under the different title: `Optimal N point configurations on the sphere: "Magic" numbers and Smale's 7th problem

CD4 and CD8 counts of Bacillus Calmette Guerin (BCG) vaccinated neonates in parts of Edo and Delta States, Nigeria

This study examines the cellular immune factors responsible for combating infections by assessing CD4 and CD8 counts of neonates (pre and post BCG vaccination). A total of 373 blood samples were collected from neonates that visited the immunization clinics at Irrua Specialist Teaching Hospital (ISTH), Irrua and Federal Medical Centre (FMC), Asaba, Nigeria. CD4 and CD8 easy count kit (Partec, Germany) was used for the determination of CD4 and CD8  count respectively, while the samples were analysed using SL-blue Cyflow. At ISTH Irrua, 191 samples were analyzed (130:60; pre and post vaccination), while at Asaba, 182 samples were analysed (120:62; pre and post vaccination). The results showed that CD4 count was significantly higher for Pre vaccination than Post vaccination at both locations. At FMC Asaba, the CD4 count for females was significantly higher than in males (pre-BCG vaccination), while CD4 count was not significantly affected by gender at Irrua, ISTH. CD8 increases in both locations but was not significantly affected by gender. The findings of this study therefore suggests that there is a cell mediated immune response to BCG vaccine by both the male and female neonates and this is associated with a decrease in CD4 count (post vaccination).Keywords: Edo, Delta, Male, Female, Neonates, BCG, CD4, CD

Understanding the power of the prime minister : structure and agency in models of prime ministerial power

Understanding the power of the prime minister is important because of the centrality of the prime minister within the core executive of British government, but existing models of prime ministerial power are unsatisfactory for various reasons. This article makes an original contribution by providing an overview and critique of the dominant models of prime ministerial power, highlighting their largely positivist bent and the related problem of the prevalence of overly parsimonious conceptions of the structural contexts prime ministers face. The central argument the paper makes is that much of the existing literature on prime ministerial power is premised on flawed understandings of the relationship between structure and agency, that this leads to misunderstandings of the real scope of prime ministerial agency, as well as its determinants, and that this can be rectified by adopting a strategic-relational view of structure and agency

Nucleosomes in serum of patients with early cerebral stroke

Background: Nucleosomes are cell death products that are elevated in serum of patients with diseases that are associated with massive cell destruction. We investigated the kinetics of circulating nucleosomes after cerebral stroke and their correlation with the clinical status. Methods: In total, we analyzed nucleosomes by ELISA in sera of 63 patients with early stroke daily during the first week after onset. For correlation with the clinical pathology, patients were grouped into those with medium to slight functional impairment (Barthel Index BI >= 50) and those with severe functional impairment (BI = 50 showed a continuous increase in nucleosomes until day 5 (median: 523 arbitrary units, AU) followed by a slow decline. In contrast, patients with BI = 50 (497 AU; p = 0.031). Concerning the infarction volume, nucleosomes showed significant correlations for the concentrations on day 3 (r = 0.43; p = 0.001) and for the area under the curve (r = 0.34; p = 0.016). Conclusion: Even if nucleosomes are nonspecific cell death markers, their release into serum after cerebral stroke correlates with the gross functional status as well as with the infarction volume and can be considered as biochemical correlative to the severity of stroke. Copyright (c) 2006 S. Karger AG, Basel

Direct Formation of Supermassive Black Holes via Multi-Scale Gas Inflows in Galaxy Mergers

Observations of distant bright quasars suggest that billion solar mass supermassive black holes (SMBHs) were already in place less than a billion years after the Big Bang. Models in which light black hole seeds form by the collapse of primordial metal-free stars cannot explain their rapid appearance due to inefficient gas accretion. Alternatively, these black holes may form by direct collapse of gas at the center of protogalaxies. However, this requires metal-free gas that does not cool efficiently and thus is not turned into stars, in contrast with the rapid metal enrichment of protogalaxies. Here we use a numerical simulation to show that mergers between massive protogalaxies naturally produce the required central gas accumulation with no need to suppress star formation. Merger-driven gas inflows produce an unstable, massive nuclear gas disk. Within the disk a second gas inflow accumulates more than 100 million solar masses of gas in a sub-parsec scale cloud in one hundred thousand years. The cloud undergoes gravitational collapse, which eventually leads to the formation of a massive black hole. The black hole can grow to a billion solar masses in less than a billion years by accreting gas from the surrounding disk.Comment: 26 pages, 4 Figures, submitted to Nature (includes Supplementary Information

Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit

We will investigate the influence of the inhomogeneity of the universe, especially that of the Lema{\^i}tre-Tolman-Bondi (LTB) model, on a gravitationally bound local system such as the solar system. We concentrate on the dynamical perturbation to the planetary motion and derive the leading order effect generated from the LTB model. It will be shown that there appear not only a well-known cosmological effect arisen from the homogeneous and isotropic model, such as the Robertson-Walker (RW) model, but also the additional terms due to the radial inhomogeneity of the LTB model. We will also apply the obtained results to the problem of secular increase in the astronomical unit, reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of the universe cannot have a significant effect for explaining the observed $d{\rm AU}/dt = 15 \pm 4 ~{\rm [m/century]}$.Comment: 12 pages, no figure, accepted for publication in Journal of Astrophysics and Astronom

b-Initiated processes at the LHC: a reappraisal

Several key processes at the LHC in the standard model and beyond that involve $b$ quarks, such as single-top, Higgs, and weak vector boson associated production, can be described in QCD either in a 4-flavor or 5-flavor scheme. In the former, $b$ quarks appear only in the final state and are typically considered massive. In 5-flavor schemes, calculations include $b$ quarks in the initial state, are simpler and allow the resummation of possibly large initial state logarithms of the type $\log \frac{{\cal Q}^2}{m_b^2}$ into the $b$ parton distribution function (PDF), ${\cal Q}$ being the typical scale of the hard process. In this work we critically reconsider the rationale for using 5-flavor improved schemes at the LHC. Our motivation stems from the observation that the effects of initial state logs are rarely very large in hadron collisions: 4-flavor computations are pertubatively well behaved and a substantial agreement between predictions in the two schemes is found. We identify two distinct reasons that explain this behaviour, i.e., the resummation of the initial state logarithms into the $b$-PDF is relevant only at large Bjorken $x$ and the possibly large ratios ${\cal Q}^2/m_b^2$'s are always accompanied by universal phase space suppression factors. Our study paves the way to using both schemes for the same process so to exploit their complementary advantages for different observables, such as employing a 5-flavor scheme to accurately predict the total cross section at NNLO and the corresponding 4-flavor computation at NLO for fully exclusive studies.Comment: Fixed typo in Eq. (A.10) and few typos in Eq. (C.2) and (C.3

High Proliferation Rate and a Compromised Spindle Assembly Checkpoint Confers Sensitivity to the MPS1 Inhibitor BOS172722 in Triple-Negative Breast Cancers

BOS172722 (CCT289346) is a highly potent, selective, and orally bioavailable inhibitor of spindle assembly checkpoint kinase MPS1. BOS172722 treatment alone induces significant sensitization to death, particularly in highly proliferative triple-negative breast cancer (TNBC) cell lines with compromised spindle assembly checkpoint activity. BOS172722 synergizes with paclitaxel to induce gross chromosomal segregation defects caused by MPS1 inhibitor-mediated abrogation of the mitotic delay induced by paclitaxel treatment. In in vivo pharmacodynamic experiments, BOS172722 potently inhibits the spindle assembly checkpoint induced by paclitaxel in human tumor xenograft models of TNBC, as measured by inhibition of the phosphorylation of histone H3 and the phosphorylation of the MPS1 substrate, KNL1. This mechanistic synergy results in significant in vivo efficacy, with robust tumor regressions observed for the combination of BOS172722 and paclitaxel versus either agent alone in long-term efficacy studies in multiple human tumor xenograft TNBC models, including a patient-derived xenograft and a systemic metastasis model. The current target indication for BOS172722 is TNBC, based on their high sensitivity to MPS1 inhibition, the well-defined clinical patient population with high unmet need, and the synergy observed with paclitaxel

Meropenem vs standard of care for treatment of neonatal late onset sepsis (NeoMero1): A randomised controlled trial.

BACKGROUND: The early use of broad-spectrum antibiotics remains the cornerstone for the treatment of neonatal late onset sepsis (LOS). However, which antibiotics should be used is still debatable, as relevant studies were conducted more than 20 years ago, recruited in single centres or countries, evaluated antibiotics not in clinical use anymore and had variable inclusion/exclusion criteria and outcome measures. Moreover, antibiotic-resistant bacteria have become a major problem in many countries worldwide. We hypothesized that efficacy of meropenem as a broad-spectrum antibiotic is superior to standard of care regimens (SOC) in empiric treatment of LOS and aimed to compare meropenem to SOC in infants aged 44 weeks meeting the Goldstein criteria of sepsis, were randomized in a 1:1 ratio to receive meropenem or one of the two SOC regimens (ampicillin+gentamicin or cefotaxime+gentamicin) chosen by each site prior to the start of the study for 8-14 days. The primary outcome was treatment success (survival, no modification of allocated therapy, resolution/improvement of clinical and laboratory markers, no need of additional antibiotics and presumed/confirmed eradication of pathogens) at test-of-cure visit (TOC) in full analysis set. Stool samples were tested at baseline and Day 28 for meropenem-resistant Gram-negative organisms (CRGNO). The primary analysis was performed in all randomised patients and in patients with culture confirmed LOS. Proportions of participants with successful outcome were compared by using a logistic regression model adjusted for the stratification factors. From September 3, 2012 to November 30th 2014, total of 136 patients (instead of planned 275) in each arm were randomized; 140 (52%) were culture positive. Successful outcome at TOC was achieved in 44/136 (32%) in the meropenem arm vs. 31/135 (23%) in the SOC arm (p = 0.087). The respective numbers in patients with positive cultures were 17/63 (27%) vs. 10/77 (13%) (p = 0.022). The main reason of failure was modification of allocated therapy. Treatment emergent adverse events occurred in 72% and serious adverse events in 17% of patients, the Day 28 mortality was 6%. Cumulative acquisition of CRGNO by Day 28 occurred in 4% of patients in the meropenem and 12% in the SOC arm (p = 0.052). CONCLUSIONS: Within this study population, we found no evidence that meropenem was superior to SOC in terms of success at TOC, short term hearing disturbances, safety or mortality were similar in both treatment arms but the study was underpowered to detect the planned effect. Meropenem treatment did not select for colonization with CRGNOs. We suggest that meropenem as broad-spectrum antibiotic should be reserved for neonates who are more likely to have Gram-negative LOS, especially in NICUs where microorganisms producing extended spectrum- and AmpC type beta-lactamases are circulating

Synthetic Lethality of Chk1 Inhibition Combined with p53 and/or p21 Loss During a DNA Damage Response in Normal and Tumor Cells

Cell cycle checkpoints ensure genome integrity and are frequently compromised in human cancers. A therapeutic strategy being explored takes advantage of checkpoint defects in p53-deficient tumors in order to sensitize them to DNA-damaging agents by eliminating Chk1-mediated checkpoint responses. Using mouse models, we demonstrated that p21 is a key determinant of how cells respond to the combination of DNA damage and Chk1 inhibition (combination therapy) in normal cells as well as in tumors. Loss of p21 sensitized normal cells to the combination therapy much more than did p53 loss and the enhanced lethality was partially blocked by CDK inhibition. In addition, basal pools of p21 (p53 independent) provided p53 null cells with protection from the combination therapy. Our results uncover a novel p53-independent function for p21 in protecting cells from the lethal effects of DNA damage followed by Chk1 inhibition. As p21 levels are low in a significant fraction of colorectal tumors, they are predicted to be particularly sensitive to the combination therapy. Results reported in this study support this prediction