Dynamics of learning for the binary perceptron problem

A polynomial learning algorithm for a perceptron with binary bonds and random patterns is investigated within dynamic mean field theory. A discontinuous freezing transition is found at a temperature where the entropy is still positive. Critical slowing down is observed approaching this temperature from above. The fraction of errors resulting from this learning procedure is finite in the thermodynamic limit for all temperatures and all finite values of the number of patterns per bond. Monte-Carlo simulations on larger samples (N127) are in quantitative agreement. Simulations on smaller samples indicate a finite bound for the existence of perfect solutions in agreement with the replica theory and the zero entropy criterion. This suggests that perfect solutions exist also in larger samples but cannot be found with a polynomial procedure as expected for a combinatorial hard problem.     

Mineral?le

Ohne Zusammenfassung     

Influence of madelung (interatomic Coulomb) energy on Wolfsberg–Helmholz calculations

A model is presented for the estimation of ionicities in molecules and complex ions. The model uses the minimization of total energy by the method of differential ionization energies. The effect of Madelung corrections to the energies is considered, and the model is refined by evaluating the covalent-bond energies. Wolfsberg–Helmholz calculations have been applied to the same type of model, also incorporating Madelung corrections. The Madelung corrections make the metal ionization energy curves less steep, and the ligand ionization energies are nearly invariant with charge. This creates a situation which has previously been artificially imposed by selecting the ligand ionization energies to give desirable terms in the Wolfsberg–Helmholz secular determinant. The effect of Madelung energy is shown to be the primary influence in describing the ionicity and total energy of a chromophore; covalent bonding effects are shown to be secondary when the ligands and the central atom have fairly different electronegativities.     

Elastic interaction and the phase transition in coherent metal-hydrogen systems

We study the statistical mechanics of hydrogen dissolved in metals. The underlying model is based on the assumption that the dominant attractive interaction between the protons in the metal is of an elastic nature.

In the first part of the paper we review some general properties of the elastic interaction. We then discuss the importance of boundary conditions for the form of the elastic interaction, which turns out to be of the Curie-Weiss type with macroscopic range.

In the second part we investigate the a-a' (‘gas-liquid’) phase transition in the hydrogen lattice fluid. The long-range part of the elastic interaction is treated in mean field approximation. In the canonical ensemble as opposed to the grand canonical ensemble one finds no co-existing phases near the critical point. Instead there is a continuous transition which changes into a first-order transition at tricritical points. In the temperature-density region which normally corresponds to the two-phase co-existence region the hydrogen density is inhomogeneous and varies on a macroscopic scale.

The peculiar nature of the a-a' phase transition is due to the long-range character of the elastic interaction, which ultimately results from the requirement of coherency of the host crystal. We argue that coherent metal-hydrogen systems offer examples of real systems where the classical theory of phase transitions applies.     

PHOSPHORORGANISCHE VERBINDUNGEN 88.1 OPTISCH AKTIVE PHOSPHINIGSÄUREAMIDE DARSTELLUNG,EIGENSCHAFTEN UND ABSOLUTE KONFIGURATION

Abstract

Optisch aktive Amidophosphoniumsalze, z.B. (7a) und (7b), werden elektroreduktiv unter Retention in die bisher unbekannten Phosphinigsäureamide (4a) und (4b) überführt. Die absolute Konfiguration von (4a) und (4b) wird durch chemische Korrelation mit Verbindungen bekannter absoluter Konfiguration ermittelt. Durch Umsetzung von optisch aktivem (4b) mit Trifluoressigsäure-p-kresylester erhält man unter Retention Ethyl-phenyl-phosphinigsäure p-kresylester (13).

Optically active amidophosphonium salts (e.g. 7a, 7b) may be electrochemically reduced with retention of configuration at phosphorus to the corresponding phosphinous acid amides (4a, 4b), previously unreported compounds. The absolute configuration were deduced through further chemical reaction under known stereochemical control to products of defined absolute configuration. Reaction of optically active (4b) with para-cresyl trifluoroacetate gives the ethyl–phenyl phosphinous acid para-cresyl ester (13) under retention of configuration.     

Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile

In the present paper, an efficient method of damping structural vibrations using the acoustic black hole effect is further investigated experimentally. This method is based on some specific properties of flexural wave propagation in tapered plates (wedges) of power-law profile that have to be partially covered by narrow thin strips of absorbing layers. Ideally, if the power-law exponent of the profile is equal or larger than two, the flexural wave never reaches the sharp edge and therefore never reflects back, which constitutes the acoustic black hole effect. It has been previously established theoretically and confirmed experimentally that this method of damping structural vibrations is very efficient even in the presence of edge truncations. The present work describes the results of the experimental studies of the effects of manufacturing intolerances on damping flexural vibrations in wedge-like structures of power-law profile. In particular, the effect of mechanical damage resulting from the use of cutting tools to wedge tips is investigated, including tip curling and early truncation, as well as the placement of absorbing layers on different wedge surfaces. Also, the effects of welded and glued bonding of wedge attachments to basic rectangular plates (strips) are investigated. The results show that, although the above-mentioned geometrical and material imperfections reduce the damping efficiency by varying degrees, the method of damping structural vibrations using the acoustic black hole effect is robust enough and can be used widely without the need of high precision manufacturing.