"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

Transmission dynamics of malaria in Nigeria.

Background: Two of the problems of malaria parasite vector control in Nigeria are the diversity of Anopheline vectors and large size of the country. Anopheline distribution and transmission dynamics of malaria were therefore compared between four ecotypes in Nigeria during the rainy season. Methods: Polymerase chain reaction (PCR) was used in molecular identification after morphological identification microscopically. Enzyme linked immunorsorbent assay (ELISA) was used for the blood meal analysis and sporozoite detection. Results: Five species were identified out of 16,410 anophelines collected. An. gambiae s.s made up approximately 29.2%-36.6% of the population in each zone. All five species acted as vectors for P. falciparum. An. gambiae s.s had the highest sporozoite rate. The most infected mosquitoes were found in the rain forest. More blood meals were taken from bovids, except the savannah forest, where 73.3%were on humans and Human Blood index (HBI) was 57.3%. The Entomological inoculation rate (EIR) was a mean of 13.6 ib/p but was highest in the rainforest zone. Conclusions and limitations: This study demonstrates the complex distribution of anophelines and theconsiderable variations in the intensity of malaria transmission in Nigeria. We highlight the need to consider diverse epidemiological situations when planning countrywide control programmes

Antibacterial effects of cyanogenic glucoside isolated from the stem bark of Bauhinia rufescens Lam

The chemical contents and in vitro antibacterial effects of the n-butanol column fractions, stem bark methanol extracts of Bauhinia rufescens Lam. were evaluated in Gram-positive and Gram-negative bacteria using disc diffusion technique. The n-butanol soluble portion from the stem bark methanol extract was successively eluted to afford 10 pooled fractions by comparison of TLC chromatograms. The bioactive fraction (fraction D) was further chromatographed using the bioassay guided protocol to afford 4 sub-fractions from which a pure compound was isolated and characterized using spectral studies as: (4S, 6R)-(Z)-6-(â-Dglucopyranosyloxy)-4-hydroxy-2-cyclohexenyl-Ä1,á-acetonitrile–a cyclohexenyl cyano methylene known commonly as menisdaurin. Test bacteria were Bacillus subtilis, Corynaebacterium spp., Escherichia coli and Shigella dysenteriae. The diameters of inhibition zone on the Gram-positive bacteria was found in the range from11.83±0.17 (n-butanol Fraction D) to 17.33±0.67 (Fraction D2-8); while on Gram-negative organism the values ranged from  11.50±0.29 (n-butanol Fraction D) to 19.67±0.33 (Fraction D2-8). The activity index (AI) showed that Fraction D2-8 (51.18%) and Compound I [menisdaurin] (127.36%) was highly sensitive to Corynaebacterium spp. and E. coli when computed with Erythromycin and Gentamicin respectively. Highest AI was exhibited by Fraction D2-8 (93.89%) against S. dysenteriae when computed with ciprofloxacin. In continuation of our chemical studies and search for bioactive compounds from medicinal plants; this work, therefore, was aimed at characterizing and testing the antibacterial efficacy of the isolated compound in order to further confirm our earlier reports on use of this part of B. rufescens in some parts of Northern Nigeria as atreatment against diarrhoea and dysentery. This is the first report of the isolation and antibacterial activity of menisdaurin from B. rufescens.© 2013 International Formulae Group. All rights reserved.Keywords: Antibacterial, Bauhinia rufescens, cyanogenic glucoside, isolation, menisdaurin

Targeted Molecular Imaging in Adrenal Disease—An Emerging Role for Metomidate PET-CT

Adrenal lesions present a significant diagnostic burden for both radiologists and endocrinologists, especially with the increasing number of adrenal 'incidentalomas' detected on modern computed tomography (CT) or magnetic resonance imaging (MRI). A key objective is the reliable distinction of benign disease from either primary adrenal malignancy (e.g., adrenocortical carcinoma or malignant forms of pheochromocytoma/paraganglioma (PPGL)) or metastases (e.g., bronchial, renal). Benign lesions may still be associated with adverse sequelae through autonomous hormone hypersecretion (e.g., primary aldosteronism, Cushing's syndrome, phaeochromocytoma). Here, identifying a causative lesion, or lateralising the disease to a single adrenal gland, is key to effective management, as unilateral adrenalectomy may offer the potential for curing conditions that are typically associated with significant excess morbidity and mortality. This review considers the evolving role of positron emission tomography (PET) imaging in addressing the limitations of traditional cross-sectional imaging and adjunctive techniques, such as venous sampling, in the management of adrenal disorders. We review the development of targeted molecular imaging to the adrenocortical enzymes CYP11B1 and CYP11B2 with different radiolabeled metomidate compounds. Particular consideration is given to iodo-metomidate PET tracers for the diagnosis and management of adrenocortical carcinoma, and the increasingly recognized utility of $^{11}$C-metomidate PET-CT in primary aldosteronism.NIHR Cambridge Biomedical Research Centr

Effects on the maternofetal unit of the rabbit model after substitution of the amniotic fluid with perfluorocarbons

Objectives: Exchanging amniotic fluid (AF) with perfluorocarbon (PFC) may serve as a medium for fetoscopic surgery. This study evaluates the distribution and physiologic effects of intraamniotic PFC as a medium for fetoscopy. Methods: Fetuses of 17 pregnant rabbits underwent either exchange of the AF with PFC, electrolyte solution (ES), or control. The quality of vision during fetoscopy was assessed in AF and PFC. After 6 h, we determined the distribution of PFC in the maternofetal unit. Results: Quality of vision during fetoscopy was better in PFC than with AF. There was no difference in fetal survival between the study groups. PFC was demonstrated on X-ray in the pharynx of 4 fetuses, and the esophagus in 1. Conclusions: PFC provided an ideal medium for fetoscopy without fetal compromise. Copyright (c) 2005 S. Karger AG, Basel

Barriers and facilitators to human immunodeficiency virus sero-status disclosure in a tertiary health facility in Kano, Nigeria

Disclosure of Human Immunodeficiency Virus (HIV) sero-status to sexual partners, family and friends is essential in preventing HIV transmission. An array of benefits has been associated with disclosure; such as early referral to care and treatment, reduced stigma and increased social support. Objectives: We determined the prevalence, barriers and facilitators to HIV sero-status disclosure among clients attending the Antiretroviral (ARV) clinic in AminuKano-Teaching Hospital, Kano. Method: A descriptive cross-sectional study was conducted among 231 HIV positive patients attending ARV clinic at AKTH using a systematic sampling technique. Interviewer-administered semi-structured questionnaire was used to obtain respondent's socio-demographic characteristics, disclosure status, barriers and facilitators of HIV sero-status disclosure. We conducted univariate, bivariate and multivariate analysis using SPSS version 22, and a p- value ≤0.05 was considered as the level of significance. Results: The mean age of the respondents was 35 ± 8.64 years with a male to female sex distribution of 53% to 47 % respectively. Majority were not married (74.0%) and two thirds (67%) were Muslims. This study found that 60% of the respondents had disclosed their HIV sero-status and 97% of them had done so voluntarily. The fear of divorce/neglect (p&lt;0.01, aOR=0.017, 95% CI=0.02-0.15) and fear of stigma (p&lt;0.01, aOR=0.03, 95% CI= 0.00-0.03) were found as barriers to HIV sero-status disclosure. Financial difficulties (p&lt;0.01, aOR=3.03, 95% CI=1.16-5.61) and the need for improved access to necessary medical care (p=0.04, aOR=6.52, 95% CI=1.85-23.15) were found to facilitate HIV sero status disclosure. Conclusion: The study found a low HIV sero-status disclosure in Kano. Disclosure being major recommendation by World Health Organisation and the Centres for Disease Control and Prevention requires strengthening during patients counselling and education sessions

Antiplasmodial and larvicidal flavonoids from Derris trifoliata

From the dichloromethane-methanol (1:1) extract of the seed pods of Derris trifoliata, a new flavanone derivative (S)-lupinifolin 4´-methyl ether was isolated. In addition, the known flavonoids lupinifolin and rotenone were identified. The structures were determined on the basis of spectroscopic evidence. Lupinfolin showed moderate in vitro antiplasmodial activity against the D6 (chloroquine-sensitive) and W2 (chloroquineresistant)strains of Plasmodium falciparum. The different parts of this plant showed larvicidal activities against Aedes aegypti and rotenoids were identified as the active principles

Hannah Arendt

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