Gibbs states of the Hopfield model with extensively many patterns

We consider the Hopfield model withM(N)=N patterns, whereN is the number of neurons. We show that if is sufficiently small and the temperature sufficiently low, then there exist disjoint Gibbs states for each of the stored patterns, almost surely with respect to the distribution of the random patterns. This solves a provlem left open in previous work. The key new ingredient is a self-averaging result on the free energy functional. This result has considerable additional interest and some consequences are discussed. A similar result for the free energy of the Sherrington-Kirkpatrick model is also given.     

Recent results from the TCV tokamak

During the first two years of operation, the TCV tokamak has produced a large variety of plasma shapes and magnetic configurations, with 1.0B _tor1.46T,I _p800kA,k2.05, –0.71. A new shape control algorithm, based on a finite element reconstruction of the plasma current in real time, has been implemented. Vertical growth rates up to 1000s^–1 have been stabilized using the external coil system. Ohmic H-modes with Troyon factors ( _tor aB/I _p) up to two and densities up to 2.25×10²⁰m^–3, corresponding to the Greenwald limit, have been obtained in diverted discharges. Limiter H-modes with line averaged electron densities up to 1.7×10²⁰m^–3 have been obtained in elongated D-shaped plasmas with 360 kAI _P600 kA.Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.This work was partly supported by the Fonds National Suisse de la Recherche Scientifique.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Internal dynamics of flexible molecules: Cyclohexane

Summary The international motions of a single cyclohexane molecule are studied by molecular dynamics calculations. Classical trajectories are calculated by integrating Newton's equation of motion. The potential functions used are essentially the same as in Allinger's MM2 program which is widely applied for calculations on conformational energies of organic molecules.Geometries and relative energies are reported for all stable low energy conformers and some transition states of cyclohexane. Vibrational frequencies of classical oscillations of individual bonds — computed for ethane as reference system — are close to the experimental values.Two trajectories of the molecular dynamics of cyclohexane were simulated. In the first we were able to follow the process of ring inversion: chair twisted forms inverted chair. The reaction path is analysed in detail and compared with static approaches. The second trajectory shows the correlated reorientation of the possible twisted forms alone. This process is known as pseudorotation.Dedicated to Prof. Dr. Karl Schlögl     

Synthesis and absolute configuration of clemastine and its isomers (author's transl)]

Synthesis and Absolute Configuration of Clemastine and its Isomers. Condensation of 4-chloro-α-methylbenzhydrylalkohol ( 1 ) with 2-(2-chloroethyl)-1-methylpyrrolidine ( 2 ) gave an isomeric mixture of 2-[2-(p-chloro-α-methyl-=-phenylbenzyloxy)ethyl]-1-methylpyrrolidine ( 3 ) and 4-(p-chloro-=-phenylbenzyloxy)-1-methyl-hexahydroazepin ( 4 ). The separation of the four possible optically active isomers of 3 is described and their absolute configuration established by degradation to (R)- and (S)-1-methyl-2-pyrrolidineethanol ( 6 ), respectively, and by an X-ray cristallographic analysis of the quarternary methiodide of the isomer 3-A . Clemastine (3-A) is (+)-(2R)-2-[2-((αR)-(p-chloro-α-methyl-α-phenylbenzyloxy)ethyl)]-1-methylpyrrolidine.     

Enantioselective Alternating Terpolymerization of Styrene and Ethene with Carbon Monoxide. Preliminary communication

In spite of the higher reactivity of styrene with respect to ethene for the alternating copolymerization with carbon monoxide, catalyzed by chiral (dihydrooxazole)(phosphino)palladium complexes, ethene is preferentially (and randomly) enchained in terpolymerization experiments; enantioface selection for styrene is comparably high in both copolymerization and terpolymerization processes.     

Structural, textural, and electronic properties of a nanosized mesoporous ZnxTi1-xO2-) solid solution prepared by a supercritical drying route

Mesoporous nanosized TiO2 and Zn(x)Ti(1-x)O(2-x) solid solution having a Zn content below 10 mol % with a particles size between 13 and 17 nm are prepared by a template-free sol-gel method followed by high-temperature supercritical drying in 2-propanol. The structural, textural, and electronic properties of the obtained nanomaterials are methodically investigated by using XRD, SEM, TEM, ED, HREM, EDX, ICP-OES, N(2) adsorption-desorption, Raman spectroscopy, and diffuse reflectance UV-vis spectroscopy. It is shown that the proposed synthesis technique leads to the formation of a Zn(x)Ti(1-x)O(2-x) solid solution based on the anatase crystal structure rather than a two-phase sample. High-resolution electron microscopy and electron diffraction indicate that the distribution of zinc atoms over the anatase structure does not lead to a considerable deformation of the crystal structure.     

Sparsely substituted chlorins as core constructs in chlorophyll analogue chemistry. I. Synthesis

Five routes to stable chlorins bearing 0 or 1 meso substituents have been investigated, among which reaction of a 9-bromo-1-formyldipyrromethane and 2,3,4,5-tetrahydro-1,3,3-trimethyldipyrrin proved most effective. Application of this route afforded metallochlorins [Cu(II), Zn(II), and Pd(II)] including the chlorin lacking any β-pyrrole and meso substituents.     

Evaluation of cellulase preparations for hydrolysis of hardwood substrates

Seven cellulase preparations from Penicillium and Trichoderma spp. were evaluated for their ability to hydrolyze the cellulose fraction of hardwoods (yellow poplar and red maple) pretreated by organosolv extraction, as well as model cellulosic substrates such as filter paper. There was no significant correlation among hydrolytic performance on pretreated hardwood, based on glucose release, and filter paper activity. However, performance on pretreated hardwood showed significant correlations to the levels of endogenous β-glucosidase and xylanase activities in the cellulase preparation. Accordingly, differences in performance were reduced or eliminated following supplementation with a crude β-glucosidase preparation containing both activities. These results complement a previous investigation using softwoods pretreated by either organosolv extraction or steam explosion. Cellulase preparations that performed best on hardwood also showed superior performance on the softwood substrates.     

Micropatterning chemical oscillations: waves, autofocusing, and symmetry breaking

Arrays of chemical oscillators are micropatterned by Wet Stamping. The technique is used to demonstrate that chemical waves can be initiated and controlled in oscillatory systems and that such waves can give rise to phenomena not observed in excitable media. Interoscillator coupling and synchronization, kinetic autofocusing, and twist-symmetry breaking are a consequence of the dependence of the oscillation phase on the local concentrations of reagents and on systems' geometry. Conditions under which a generic oscillatory system would exhibit such behaviors are determined.