Super-resolution in confocal scanning microscopy: generalized inversion formulae

It was shown in previous papers that the resolution of a confocal scanning microscope can be significantly improved by measuring, for each scanning position, the full diffraction image and by inverting these data to recover the value of the object at the confocal point. In the present work, the authors generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use of the data samples recorded at other scanning positions. This leads them to a family of generalized inversion formulae, either exact or approximate. Some previously known formulae are re-derived here as special cases in a particularly simple way.

1.° Codicis Theodosiani, sive potius breviarii Aniani interpretationum fragmenta. — 2.° Theodosii Junioris et Valentiniani III. novellae constitutiones. — 3.° Gaii Institutionum fragmenta. — 4.° Julii Pauli sententiarum fragmenta. — 5.° Gregoriani, Hermogeniani et Papianei codicum fragmenta. — 6.° Formulae veteres : finis desideratur

Colbertinus

1.° M. Pauli Veneti libri tres de conditionibus et consuetudinibus orientalium regionum : interprete Francisco Pipino, Bononiensi, ordinis Fratrum Praedicatorum. — 2.° Epistola Presbyteri Joannis, quam misit Imperatori Frederico Barba-rubea. — 3.° Vita Machometi ; qualiter seduxit Terram sanctam, sive, Ecclesiam Orientalem. — 4.° Gesta Romanorum, sive potiùs, fabulae aniles et insulsae sub nominibus Romanorum Imperatorum. — 5.° Formulae variarum orationum, tam Presbyteri, quàm cujuscumque fidelis. — 6.° Confessio multùm spiritualis, composita per Cardinalem sancti Sixti. — 7.° Decretum Concilii Florentini super unione Graecorum, anno 1439. — 8.° Eugenii, Papae IV. bulla de unione Graecorum ; data eodem anno. — 9.° Ejusdem bulla super reductione Armenorum.

Ludovici de Targny

Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

Effects of bovine alpha-lactalbumin and casein glycomacropeptide-enriched infant formulae on faecal microbiota in healthy term infants

Objective: Certain milk factors may promote the growth of a host-friendly gastrointestinal microbiota, for example, one that is predominated by bifidobacteria, a perceived healthpromoting genus. This may explain why breast-fed infants experience fewer intestinal infections than their formula-fed counterparts who are believed to have a more diverse microbiota, which is similar to that of adults. The effects of formulas supplemented with 2 such ingredients from bovine milk, a-lactalbumin (alpha-lac) and casein glycomacropeptide (GMP), on gut flora were investigated in this study. Patients and Methods: Six-week-old (4-8 wk), healthy term infants were randomised to a standard infant formula or 1 of 2 test formulae enriched in alpha-Jac with higher or lower GMP until 6 months. Faecal bacteriology was determined by the culture-independent procedure fluorescence in situ hybridisation. Results: There was a large fluctuation of bacterial counts within groups with no statistically significant differences between groups. Although all groups showed a. predominance of bifidobacteria, breast-fed infants had a small temporary increase in counts. Other bacterial levels varied in formula-fed groups, which overall showed an adult-like faecal microflora. Conclusions: It can be speculated that a prebiotic effect for alpha-lac and GMP is achieved only with low starting populations of beneficial microbiota (eg, infants not initially breast-fed.

Physiological and bifidogenic effects of prebiotic supplements in infant formulae

This randomized controlled trial involving 110 healthy neonates studied physiological and bifidogenic effects of galactooligosaccharides (GOS), oligofructose and long-chain inulin (FOS) in formula. Subjects were randomized to Orafti Synergy1 (50 oligofructose: 50 FOS) 0.4g/dl or 0.8g/dl, GOS:FOS (90:10) 0.8g/dl or a standard formula according to Good Clinical Practise (GCP) guidelines. A breast-fed group was included for comparison. Outcome parameters were weight, length, intake, stool characteristics, crying, regurgitation, vomiting, adverse events and fecal bacterial population counts. Statistical analyses used non-parametric tests. During the first month of life weight, length, intake and crying increased significantly in all groups. Regurgitation and vomiting scores were low and similar. Stool frequency decreased significantly and similarly in all formula groups but was lower than in the breast-fed. All prebiotic groups maintained soft stools, only slightly harder than those of breast-fed infants. The standard group had significantly harder stools at wks 2 and 4 compared to 1 (P<0.001 & P=0.0279). The total number of fecal bacteria increased in all prebiotic groups (9.82, 9.73 and 9.91 to 10.34, 10.38 and 10.37, respectively, log10 cells/g feces, P=0.2298) and resembled more the breast-fed pattern. Numbers of lactic acid bacteria, bacteroides and clostridia were comparable. In the SYN1 0.8 g/dl and GOS:FOS groups Bifidobacterium counts were significantly higher at D14 & 28 compared to D3 and comparable to the breast-fed group. Tolerance and growth were normal. In conclusion, stool consistency and bacterial composition of infants taking SYN1 0.8 g/dl or GOS:FOS supplemented formula was closer to the breast-fed pattern. There was no risk for dehydration.