Tiny families of functions with random properties: A quality-size trade-off for hashing

We present three explicit constructions of hash functions, which exhibit a trade-off between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudorandom property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing property—mapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction property—mapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle, respectively, the extreme situations when the range is very large or very small. We provide lower bounds showing that our constructions are nearly optimal, and mention some applications of the new constructions. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 315–343 (1997)     

Signatures of a Concentration‐Dependent Flory χ Parameter: Swelling and Collapse of Coils and Brushes

The quality of solvents of polymers is often described in terms of the Flory χ parameter typically assumed to depend only on the temperature, T. In certain polymer‐solvent systems fitting the experimental data enforces the replacement of (χT) by a concentration‐dependent χ_eff. In turn, this modifies the swelling and collapse behavior. These effects are studied, in the framework of a mean‐field theory, for isolated coils and for planar brushes. The ϕ dependence of χ_eff gives rise to three main consequences: (i) shift in the cross‐over between Gaussian and self‐avoidance regimes; (ii) a possibility of first‐order collapse transition for isolated flexible coils; (iii) the possibility of a first‐order phase transition leading to a vertical phase separation within the brush. The discussion relates these effects directly to thermodynamic measurements and does not involve a specific microscopic model. The implementation for the case of poly(N‐isopropylamide) (PNIPAM) brushes is discussed.

ϕ vs. z plots, for brushes with N = 300, σ/a² = 18 (σ/R = 0.019) characterized by different χ_eff.     

Techniques for bounding the convergence rate of genetic algorithms

The main purpose of the present paper is the study of computational aspects, and primarily the convergence rate, of genetic algorithms (GAs). Despite the fact that such algorithms are widely used in practice, little is known so far about their theoretical properties, and in particular about their long‐term behavior. This situation is perhaps not too surprising, given the inherent hardness of analyzing nonlinear dynamical systems, and the complexity of the problems to which GAs are usually applied. In the present paper we concentrate on a number of very simple and natural systems of this sort, and show that at least for these systems the analysis can be properly carried out. Various properties and tight quantitative bounds on the long‐term behavior of such systems are established. It is our hope that the techniques developed for analyzing these simple systems prove to be applicable to a wider range of genetic algorithms, and contribute to the development of the mathematical foundations of this promising optimization method. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 111–138, 1999     

A Hybrid DNA Aptamer–Dendrimer Nanomaterial for Targeted Cell Labeling

Antibodies are natural nanomaterials and have been widely used for targeted cell labeling. However, the applications of antibodies are often limited by their large size and instability. The purpose of this study is to develop a new type of multifunctional nanomaterial that is comprised of a nucleic acid aptamer and a dendrimer, both of which are stable. This nanomaterial is ≈8 nm in size. Moreover, it could not only carry multiple signal molecules, but also bind to target cancer cells with high affinity and specificity. This sub‐10 nm multifunctional nanomaterial is expected to be useful in basic biomedical research and clinical medicine.

     

The effect of annealing ambient on carrier recombination in boron implanted silicon

The selection of either an oxidising or inert ambient during high temperature annealing is shown to affect dopant activation and electron–hole recombination in boron implanted silicon samples. Samples implanted with B at fluence between 3 × 10¹⁴ cm^–2 to 3 × 10¹⁵ cm^–2 are shown to have lower dopant activation after oxidation at 1000 °C compared to an equivalent anneal in an inert ambient. In addition, emitter recombination is shown to be up to 15 times higher after oxidation compared with an inert anneal for samples with equivalent passivation from deposited Al₂O₃ films. The observed increase in recombination for oxidised samples is attributed to the enhanced formation of boron‐interstitial defect clusters and dislocation loops under oxidising conditions. It is also shown that an inert anneal for 10 minutes at 1000 °C prior to oxidation has no significant impact on sheet resistance or recombination compared with a standard oxidation process.

     

Accelerating CFD–DEM simulation of processes with wide particle size distributions

Size-reduction systems have been extensively used in industry for many years. Nevertheless, reliable engineering tools to be used to predict the comminution of particles are scarce. Computational fluid dynamics(CFD)–discrete element model(DEM) numerical simulation may be used to predict such a complex phenomenon and therefore establish a proper design and optimization model for comminution systems.They may also be used to predict attrition in systems where particle attrition is significant. Therefore,empirical comminution functions(which are applicable for any attrition/comminution process), such as:strength distribution, selection, equivalence, breakage, and fatigue, have been integrated into the threedimensional CFD–DEM simulation tool. The main drawback of such a design tool is the long computational time required owing to the large number of particles and the minute time-step required to maintain a steady solution while simulating the flow of particulate materials with very fine particles.The present study developed several methods to accelerate CFD–DEM simulations: reducing the number of operations carried out at the single-particle level, constructing a DEM grid detached from the CFD grid enabling a no binary search, generating a sub-grid within the DEM grid to enable a no binary search for fine particles, and increasing the computational time-step and eliminating the finest particles in the simulation while still tracking their contribution to the process.The total speedup of the simulation process without the elimination of the finest particles was a factor of about 17. The elimination of the finest particles gave additional speedup of a factor of at least 18.Therefore, the simulation of a grinding process can run at least 300 times faster than the conventional method in which a standard no binary search is employed and the smallest particles are tracked.     

RNA encapsidation by SV40-derived nanoparticles follows a rapid two-state mechanism

Remarkably, uniform virus-like particles self-assemble in a process that appears to follow a rapid kinetic mechanism. The mechanisms by which spherical viruses assemble from hundreds of capsid proteins around nucleic acid, however, are yet unresolved. Using time-resolved small-angle X-ray scattering (TR-SAXS), we have been able to directly visualize SV40 VP1 pentamers encapsidating short RNA molecules (500mers). This assembly process yields T = 1 icosahedral particles comprised of 12 pentamers and one RNA molecule. The reaction is nearly one-third complete within 35 ms, following a two-state kinetic process with no detectable intermediates. Theoretical analysis of kinetics, using a master equation, shows that the assembly process nucleates at the RNA and continues by a cascade of elongation reactions in which one VP1 pentamer is added at a time, with a rate of approximately 10(9) M(-1) s(-1). The reaction is highly robust and faster than the predicted diffusion limit. The emerging molecular mechanism, which appears to be general to viruses that assemble around nucleic acids, implicates long-ranged electrostatic interactions. The model proposes that the growing nucleo-protein complex acts as an electrostatic antenna that attracts other capsid subunits for the encapsidation process.     

The neutrino as a tachyon

We investigate the hypothesis that at least one of the known neutrinos travels faster than light. The current experimental situation is examined within this purview.     

Hydroxynitrile lyase catalysed synthesis of heterocyclic (R)- and (S)-cyanohydrins

Heterocyclic saturated five- and six-membered ring ketones sometimes bearing a methyl substituent were reacted with HCN under enzyme catalysis using recombinant hydroxynitrile lyase from Hevea brasiliensis, as a rule (S)-selective, and Prunus amygdalus, (R)-selective. The resulting cyanohydrins were stereochemically characterised. The steric outcome of these transformations was interpreted by molecular modelling.