Sample size determination in combinatorial chemistry.

Combinatorial chemistry is gaining wide appeal as a technique for generating molecular diversity. Among the many combinatorial protocols, the split/recombine method is quite popular and particularly efficient at generating large libraries of compounds. In this process, polymer beads are equally divided into a series of pools and each pool is treated with a unique fragment; then the beads are recombined, mixed to uniformity, and redivided equally into a new series of pools for the subsequent couplings. The deviation from the ideal equimolar distribution of the final products is assessed by a special overall relative error, which is shown to be related to the Pearson statistic. Although the split/recombine sampling scheme is quite different from those used in analysis of categorical data, the Pearson statistic is shown to still follow a chi2 distribution. This result allows us to derive the required number of beads such that, with 99% confidence, the overall relative error is controlled to be less than a pregiven tolerable limit L1. In this paper, we also discuss another criterion, which determines the required number of beads so that, with 99% confidence, all individual relative errors are controlled to be less than a pregiven tolerable limit L2 (0 < L2 < 1).

Bioenergetic scaling: metabolic design and body-size constraints in mammals.

The cytosolic phosphorylation ratio ([ATP]/[ADP][P(i)]) in the mammalian heart was found to be inversely related to body mass with an exponent of -0.30 (r = 0.999). This exponent is similar to -0.25 calculated for the mass-specific O2 consumption. The inverse of cytosolic free [ADP], the Gibbs energy of ATP hydrolysis (delta G'ATP), and the efficiency of ATP production (energy captured in forming 3 mol of ATP per cycle along the mitochondrial respiratory chain from NADH to 1/2 O2) were all found to scale with body mass with a negative exponent. On the basis of scaling of the phosphorylation ratio and free cytosolic [ADP], we propose that the myocardium and other tissues of small mammals represent a metabolic system with a higher driving potential (a higher delta G'ATP from the higher [ATP]/[ADP][P(i)]) and a higher kinetic gain [(delta V/Vmax)/delta [ADP]] where small changes in free [ADP] produce large changes in steady-state rates of O2 consumption. From the inverse relationship between mitochondrial efficiency and body size we calculate that tissues of small mammals are more efficient than those of large mammals in converting energy from the oxidation of foodstuffs to the bond energy of ATP. A higher efficiency also indicates that mitochondrial electron transport is not the major site for higher heat production in small mammals. We further propose that the lower limit of about 2 g for adult endotherm body size (bumblebee-bat, Estrucan shrew, and hummingbird) may be set by the thermodynamics of the electron transport chain. The upper limit for body size (100,000-kg adult blue whale) may relate to a minimum delta G'ATP of approximately 55 kJ/mol for a cytoplasmic phosphorylation ratio of 12,000 M-1.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

Disk halo size measured in individuals with monofocal versus diffractive multifocal intraocular lenses

PURPOSE: To compare disk halo size in response to a glare source in eyes with an aspheric apodized diffractive multifocal intraocular lens (IOL) or aspheric monofocal IOL. SETTING: Rementeria Ophthalmological Clinic, Madrid, Spain. DESIGN: Prospective randomized masked study. METHOD: Halo radius was measured using a vision monitor (MonCv3) with low-luminance optotypes in eyes that had cataract surgery and bilateral implantion of an Acrysof Restor SN6AD1 multifocal IOL or Acrysof IQ monofocal IOL 6 to 9 months previously. The visual angle subtended by the disk halo radius was calculated in minutes of arc (arcmin). Patient complaints of halo disturbances were recorded. Monocular uncorrected distance visual acutity (UDVA) and corrected distance visual acuity (CDVA) were measured using high-contrast (96%) and low-contrast (10%) logMAR letter charts. RESULTS: The study comprised 39 eyes of 39 subjects (aged 70 to 80 years); 21 eyes had a multifocal IOL and 18 eyes a monofocal IOL. The mean halo radius was 35 arcmin larger in the multifocal IOL group than the monofocal group (P<.05). Greater halo effects were reported in the multifocal IOL group (P<.05). The mean monocular high-contrast UDVA and low-contrast UDVA did not vary significantly between groups, whereas the mean monocular high-contrast CDVA and low-contrast CDVA were significantly worse at 0.12 logMAR and 0.13 logMAR in the multifocal than in the monofocal IOL group, respectively (P <.01). A significant positive correlation was detected by multiple linear regression between the halo radius and low-contrast UDVA in the multifocal IOL group (r = 0.72, P<.001). CONCLUSIONS: The diffractive multifocal IOL gave rise to a larger disk halo size, which was correlated with a worse low-contrast UDVA.

Finite size effects in the specific heat of glass-formers

We report clear finite size effects in the specific heat and in the relaxation times of a model glass former at temperatures considerably smaller than the Mode Coupling transition. A crucial ingredient to reach this result is a new Monte Carlo algorithm which allows us to reduce the relaxation time by two order of magnitudes. These effects signal the existence of a large correlation length in static quantities.