Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Typical behavior of relays in communication channels

The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and- forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units. © 2007 The American Physical Society.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

Intercultural transfer and artistic innovation:German musicians in Victorian Britain

Throughout the nineteenth century, German classical music production was an aesthetic point of reference for British concert audiences. As a consequence, a sizeable number of German musicians were to be found in Britain as performers, conductors, teachers, musicologists and managers. They acted as agents of intercultural transfer, disseminating performance and organisational practices which had a transformative effect on British musical life. This article moves away from a focus on high-profile visiting artists such as Mendelssohn Bartholdy or Wagner and argues that the extent to which transfer took place can be better assessed by concentrating on the cohort of those artists who remained permanently. Some of these are all but forgotten today, but were household names in Victorian Britain. The case studies have been selected for the range of genres they represent and include Joseph Mainzer (choral singing), Carl Rosa (opera), August Manns, Carl Hallé and Julius Seligmann (orchestral music), and Friedrich Niecks (musicology). On a theoretical level, the concept of ‘intercultural transfer’ is applied in order to determine aspects such as diffusion, adaptation or sustainability of artistic elements within the new cultural context. The approach confirms that ‘national’ cultures do not develop indigenously but always through cross-national interaction. Während des neunzehnten Jahrhunderts war die klassische Musikszene Deutschlands ästhetischer Bezugpunkt für das britische Konzertpublikum. Dies hatte zur Folge, dass vermehrt Deutsche als Musiker, Dirigenten, Lehrer, Musikwissenschaftler und Manager in Großbritannien tätig wurden. Sie fungierten als Vermittler interkulturellen Transfers, indem sie aufführungs- und organisationstechnische Praktiken verbreiteten und damit zu einer Transformation des britischen Musiklebens beitrugen. Vorliegender Artikel konzentriert sich weniger auf bekannte Künstler mit kurzfristigen Engagements (z. B. Mendelssohn Bartholdy, Wagner), und argumentiert vielmehr, dass sich das Ausmaß des Transfers besser über solche Musiker feststellen lässt, die sich längerfristig ansiedelten. Einige davon waren allgemein bekannte Persönlichkeiten im Königreich, sind heute aber vergessen. Die Auswahl der Fallstudien gibt einen Überblick über verschiedene Gattungen und beinhaltet Joseph Mainzer (Chorgesang), Carl Rosa (Oper), August Manns, Carl Hallé und Julius Seligmann (Orchestermusik), sowie Friedrich Niecks (Musikwissenschaft). Auf der Theorieebene wird das Konzept des ‘interkulturellen Transfers’ herangezogen, um Aspekte wie Diffusion, Anpassung oder Nachhaltigkeit künstlerischer Elemente im neuen kulturellen Kontext zu beleuchten. Der Ansatz bestätigt, dass sich ‘nationale’ Kulturen nicht indigen entwickeln sondern immer im Austausch mit anderen Kulturen