Structural characterization of crystalline ternary inclusion compounds at the air-water interface

Crystalline ternary inclusion monolayers consisting of a two-dimensional hydrogen-bonded host network of guanidinium (G) ions and organosulfonate (S) amphiphiles, and biphenylalkane guests, can be generated at the air-water interface through synergistic structural enforcement by hydrogen bonding and host-guest packing. Surface pressure-area isotherms of the 4'-hexadecylbiphenyl-4-sulfonate (C16BPS) amphiphile in the presence of G, with or without guest, are characterized by lift-off molecular areas expected for the GS sheet based on single-crystal X-ray structures of homologous bulk crystals. Intercalation of biphenylalkane guests (4-C(n)()H(2)(n)()(+1)-C(6)H(4)-C(6)H(5), n = 1, 4, 6, 10, 16; denoted CnBP) between organosulfonate hydrophobes, which define pocketlike cavities in the GS monolayer host, afford ternary inclusion monolayers with a 1:1 host-guest stoichiometry. These inclusion monolayers are less compressible than the guest-free host, consistent with dense packing of the biphenylalkane moieties of the host and the biphenylalkane guests. The inclusion monolayers are distinguished from the amorphous guest-free host and from selected guanidinium-free mixed monolayers by structural characterization with grazing-angle incidence X-ray diffraction (GIXD). The GIXD data for the ternary (G)C16BPS:C16BP and (G)C16BPS:C6BP inclusion monolayers obtained upon compression are consistent with a rectangular unit cell. The dimensions of these unit cells and refinement of the GIXD data suggest a "rotated shifted ribbon" GS hydrogen-bonding motif similar to that observed in some bulk GS crystals, including (G)(ethylbiphenylsulfonate). GIXD reveals that (G)C16BPS:C16BP and (G)C16BPS:C6BP are more crystalline than the corresponding guanidinium-free mixed monolayers. The (G)C16BPS:C6BP inclusion monolayer is stable upon compression, even though the alkyl-alkyl host-guest interactions are reduced due to the shorter hexyl substituents of the guest, demonstrating an important reinforcing role for the hydrogen-bonded GS sheet. The structure of a C16BPS:tetracosane (C24) mixed monolayer is independent of G; the unit cell symmetry and dimensions suggest a structure governed by alkyl-alkane interactions that prohibit formation of a GS network. These results illustrate that the existence of ternary inclusion monolayers with an intact GS network requires guest molecules that are structurally homologous with the hydrophobes of the host, in this case biphenylalkanes. The observation of these inclusion compounds suggests an approach for introducing functional nonamphiphilic molecules to an air-water interface through inclusion in a well-defined host.     

Heterogeneous Electrofreezing of Super-Cooled Water on Surfaces of Pyroelectric Crystals is Triggered by Trigonal Planar Ions

Electrofreezing experiments of super-cooled water (SCW) with different ions, performed directly on the charged hemihedral faces of pyroelectric LiTaO₃ and AgI crystals, in the presence and in the absence of pyroelectric charge are reported. It is demonstrated that bicarbonate (HCO₃⁻) ions elevate the icing temperature near the positively charged faces. In contrast, the hydronium (H₃O⁺) slightly reduces the icing temperature. Molecular dynamics simulations suggest that the hydrated trigonal planar HCO₃⁻ ions self-assemble with water molecules near the surface of the AgI crystal as clusters of slightly different configuration from those of the ice-like hexagons. These clusters, however, have a tendency to serve as embryonic nuclei for ice crystallization. Consequently, we predicted and experimentally confirmed that the trigonal planar ions of NO₃⁻ and guanidinium (Gdm⁺), at appropriate concentrations, elevate the icing temperature near the positive and negative charged surfaces, respectively. On the other hand, the Cl⁻ and SO₄²⁻ ions of different configurations reduce the icing temperature.     

Data compression and prediction in neural networks

We study the relationship between data compression and prediction in single-layer neural networks of limited complexity. Quantifying the intuitive notion of Occam's razor using Rissanen's minimum complexity framework, we investigate the model-selection criterion advocated by this principle. While we find that the criterion works well for large sample sizes (as it must for consistency), the behavior for finite sample sizes is rather complex, depending intricately on the relationship between the complexity of the hypothesis space and the target space. We also show that the limited networks studied perform efficient data compression, even in the error full regime.     

On random mapping patterns

Random mapping patterns may be represented by unlabelled directed graphs in which each point has out-degree one. We determine the asymptotic behaviour of various parameters associated with such graphs, such as the expected number of points belonging to cycles and the expected number of components. Dedicated to Paul Erdős on his seventieth birthday     

Electronic structure for sliding charge density waves

We present a model for the electron system in NbSe₃ based on its quasi one-dimensional metallic properties. In a one-dimensional metal phonon drag of 2K_F-phonons takes place at temperatures higher than θ_D, since the phonon-electron scattering rate τ^?1_ph?el is greater than the phonon-phonon rate τ^?1_ph?ph. this situation is in contrast to the situation in three dimensional metals, where phonon drag takes place only at very low temperatures. Our model explains the transport properties of the material including the electrical conductivity anistropy, the conductivity in a strong electric field, and the Hall effect data.     

The Avidin-Biotin complex in solid phase radioimmunoassays

A solid-phase radioimmunoassay is described in which biotin conjugated antibodies are used to replace¹²⁵I labeled antibodies to individual antigens. The amount of antigen present is subsequently determined by the binding of¹²⁵I-labeled avidin. This method is appealing for a variety of reasons. (a) Only one¹²⁵I-labeled protein (avidin) need be prepared and characterized for all affinity systems, (b) There is no need to purify individual antibodies. (c) Biotin can be attached to antibodies under mild conditions. (d) The size, physical characteristics, and biological activity of the biotin-derived antibody are only nominally affected. (e) The biotin-avidin complex is of exceptionally high affinity and stability, (f) Introduction of biotin groups into the antibodies leads to amplified radioactive tracer binding, (g) Avidin and biotin are commercially available.     

On the log-product of the subtree-sizes of random trees

We determine the asymptotic behavior of the expected value and the variance of the log-product of the subtree-sizes of trees T_n belonging to simply generated families of rooted trees. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 197–212, 1998