Shannon Entropy Loss in Mixed-Radix Conversions

This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size 2J to a set of arbitrary size n. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed n value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, n, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size J of the source domain 2J. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino.     

ESCA studies of metal-oxygen surfaces using argon and oxygen ion-bombardment

ESCA has been used to monitor alterations of catalytically and electrochemically important metal-oxygen surfaces following exposure to Ar⁺ and O₂⁺ ion bombardment. This treatment resulted not only in sputtering, but also, in many cases, in reduction to the corresponding metal or lower oxide. A model based on bulk thermodynamic free energy considerations Is proposed to explain this phenomenon. We have also exploited this approach to obtain an in-depth concentration profile of various oxidation states of an element, to selectively prepare desired surface oxide compositio and to aid in interpreting complex O ls spectra. Results obtained from metal-oxygen surfaces for Ni, Ru and Mo are presented. Ni₂O₃ and RuO₃, which are gross defect structures of the bulk species, are present on NiO and RuO₂ respectively, with the former being confined to the surface layers. The MoO₂, on the other hand, is covered with a surface layer of MoO₃ present as a regular crystal structure.     

An experimental study of a turbulent shear layer at a clean and contaminated free-surface

An experimental study was performed to measure the flow properties of a vertically-orientated shear layer in the vicinity of a free-surface. The effect of surface contamination on the near surface flow field was also determined. Digital Particle Image Velocimetry was used to measure instantaneous and averaged velocity, vorticity, and Reynolds stresses. Results show that the presence of surfactants can cause directional shifts of the shear layer, as well as an overall damping of the turbulence in the vicinity of the free-surface, except in the vicinity of a Reynolds ridge where an increase in Reynolds stress was observed.     

Dynamic combinatorial libraries of metalloporphyrins: templated amplification of disulfide-linked oligomers

Disulfide-linked cyclic porphyrin oligomers from dimer to tetramer can be selected and amplified virtually quantitatively from a dynamic combinatorial library using bis-thiol substituted zinc(II) porphyrin units with appropriate amine donor templates.     

Variable coordination geometries at the diiron(II) active site of ribonucleotide reductase R2

The R2 subunit of Escherichia coli ribonucleotide reductase contains a dinuclear iron center that generates a catalytically essential stable tyrosyl radical by one electron oxidation of a nearby tyrosine residue. After acquisition of Fe(II) ions by the apo protein, the resulting diiron(II) center reacts with O(2) to initiate formation of the radical. Knowledge of the structure of the reactant diiron(II) form of R2 is a prerequisite for a detailed understanding of the O(2) activation mechanism. Whereas kinetic and spectroscopic studies of the reaction have generally been conducted at pH 7.6 with reactant produced by the addition of Fe(II) ions to the apo protein, the available crystal structures of diferrous R2 have been obtained by chemical or photoreduction of the oxidized diiron(III) protein at pH 5-6. To address this discrepancy, we have generated the diiron(II) states of wildtype R2 (R2-wt), R2-D84E, and R2-D84E/W48F by infusion of Fe(II) ions into crystals of the apo proteins at neutral pH. The structures of diferrous R2-wt and R2-D48E determined from these crystals reveal diiron(II) centers with active site geometries that differ significantly from those observed in either chemically or photoreduced crystals. Structures of R2-wt and R2-D48E/W48F determined at both neutral and low pH are very similar, suggesting that the differences are not due solely to pH effects. The structures of these "ferrous soaked" forms are more consistent with circular dichroism (CD) and magnetic circular dichroism (MCD) spectroscopic data and provide alternate starting points for consideration of possible O(2) activation mechanisms.     

Solid-phase approach towards the synthesis of functionalized imidazo[1,2-b]pyrazol-2-ones

The solid-phase synthesis of a series of imidazo[1,2-b]pyrazol-2-ones, an interesting 5,5-fused ring system, based on diverse set of hydrazine acids and malanonitriles is described. The method involves formation of 5-aminopyrazoles on solid support and subsequent cyclizative cleavage off the resin. Compounds were obtained in acceptable to excellent yields and are suitable for biological evaluation without further purification.