Reconstruction on Trees and Spin Glass Transition

Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol from the information received at the leaves. In the large system limit, reconstruction is possible when the channel noise is smaller than a threshold.We show that this threshold coincides with the dynamical (replica symmetry breaking) glass transition for an associated statistical physics problem. Motivated by this correspondence, we derive a variational principle which implies new rigorous bounds on the reconstruction threshold. Finally, we apply a standard numerical procedure used in statistical physics, to predict the reconstruction thresholds in various channels. In particular, we prove a bound on the reconstruction problem for the antiferromagnetic “Potts” channels, which implies, in the noiseless limit, new results on random proper colorings of infinite regular trees.This relation to the reconstruction problem also offers interesting perspective for putting on a clean mathematical basis the theory of glasses on random graphs. PACS: 02.50.−r (Probability theory, stochastic processes, and statistics), 64.70.Pf (Glass transitions), 89.75.Hc (Networks and genealogical trees)     

On the Dynamics of the Glass Transition on Bethe Lattices

The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transition upon decreasing the temperature or increasing the degree of constrainedness. Our analysis is based upon a detailed study of large scale rearrangements which control the slow dynamics of the system close to the dynamical transition. Particular attention is devoted to the neighborhood of a zero temperature tricritical point. Both the approach and several key results are conjectured to be valid in a considerably more general context. PACS Numbers:75.50.Lk (Spin glasses), 64.70.Pf (Glass transitions), 89.20.Ff (Computer science     

Photoluminescence emissions of ceramics: a marker of production technology

Photoluminescence (PL) measurements have been performed on different sets of ceramic shards; the results obtained from the ceramic bodies of lustred majolicas produced in Iraq, Italy and Spain are reported. Non-lustred samples are analysed for comparison. The spectra obtained from all the lustred samples show PL emission bands that are attributed to the presence of α-quartz and diopside. The photoluminescence of the lustre-decorated ceramics is possibly a fingerprint of the particular production technology of lustre. PACS 81.05.Mh; 78.55.Hx     

Propositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics (PNL), we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.     

Turbo codes: the phase transition

Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In reference [1] they are mapped onto a class of disordered spin models. The analytical calculations concerning these models are reported here. We prove the existence of a no-error phase and compute its local stability threshold. As a byproduct, we gain some insight into the dynamics of the decoding algorithm. Received 14 March 2000     

Probing the order-to-chaos region in superdeformed 151Tb and 196Pb nuclei with continuum gamma transitions

The gamma decay associated with the warm rotation of the superdeformed nuclei 151Tb and 196Pb has been measured with the EUROBALL IV array. Several independent quantities provide a stringent test of the population and decay dynamics in the superdeformed well. A Monte Carlo simulation of the gamma decay based on microscopic calculations gives remarkable agreement with the data only assuming a large enhancement of the B(E1) strength for 1-2 MeV gamma rays, which may be related to the evidence for octupole vibrations in both mass regions.     

Studies for a Diastereoselective Synthesis of the Tetracyclic Diterpenic Diol Stemarin: A Model Study for a New Preparation of the Key Intermediate and the Synthesis of (+)-18-Deoxystemarin

Methods for a stereoselective preparation of compounds of type 2b , a key intermediate of a previous synthesis of the tetracyclic diterpene stemarin ( la ), have been tested on model compounds 5a, 5c , and 8a . Thus, (±)-(1RS,6SR,8SR,11SR)-hydroxytricyclo[6.2.2.0^l,6]dodecan-9-one ( 5a ) was transformed by the Mitsunobu reaction into (±)-(1RS,6SR,8SR,11RS)-11-(benzoyloxy)tricyclot[6.2.2.0^1,6]dodecan-9-one ( 6b ; Scheme 2). The latter was also obtained from (±)-(1RS,6SR,8SR,11RS)-11-[(4)-toluenesulfonyloxy]tricyclo[6.2.2.0^1,6]dodecan-9-one ( 5c ) by the action of Et₄N (PhCOO) in acetone. Compound 6b was then converted into (±)-(1RS,6RS,8RS,9RS)-tricyclo[6.2.2.0^1,6]dodecan-9-ol ( 8b ), a model for 2b . Compound 8b was also prepared from its epimer 8a by the Mitsunobu reaction via ester 7b . The inversion of configuration of bicyclo[2.2.2]octan-2-ols or derivates was not previously described. The model studies paved the way to the diastereoselective synthesis of (+)-18-deoxystemarin ( 1b ) via 12β-hydroxy-13-methyl-9β,13β-ethano-9β-podocarpan-15-one ( 10a ) and 13-methyl-9β,13β-ethano-9β-podpcarpan-12α-ol ( 11b ).     

“Gold corrosion”: red stains on a gold Austrian Ducat

Femtosecond laser induced adsorption site changes of CO at nanoparticulate palladium aggregates have been investigated using laser light at =400 nm and pulse lengths of 70 fs. The average sizes of the aggregates grown by evaporating palladium atoms onto an epitaxial Al₂O₃ film on NiAl(110) were varied between 100 and 6000 atoms per island. Amorphous aggregates grown at 120 K and crystalline aggregates grown at 300 K have been investigated. Beyond laser-induced migration of CO already reported for nanosecond experiments, adsorbate-induced surface roughening is apparent from Fourier-transform infrared reflection absorption spectroscopy. The laser-induced processes are correlated to the presence of higher local adsorbate densities and a substantial population of edge sites. A model is suggested attributing surface roughening to the formation of local hot spots after coherent electronic excitation via heating through highly vibrationally excited adsorbate states and energetic channelling along chains of elevated local adsorbate densities. The processes are most efficient for intermediate aggregate sizes. In contrast to nanosecond experiments, a few percent of CO molecules are desorbed during the femtosecond experiments from smaller aggregates. PACS 82.53.St