Critical behavior in a cross-situational lexicon learning scenario

The associationist account for early word-learning is based on the co-occurrence between objects and words. Here we examine the performance of a simple associative learning algorithm for acquiring the referents of words in a cross-situational scenario affected by noise produced by out-of-context words. We find a critical value of the noise parameter $\gamma_c$ above which learning is impossible. We use finite-size scaling to show that the sharpness of the transition persists across a region of order $\tau^{-1/2}$ about $\gamma_c$, where $\tau$ is the number of learning trials, as well as to obtain the learning error (scaling function) in the critical region. In addition, we show that the distribution of durations of periods when the learning error is zero is a power law with exponent -3/2 at the critical point

Temperature dependence of single-particle properties in nuclear matter

The single-nucleon potential in hot nuclear matter is investigated in the framework of the Brueckner theory by adopting the realistic Argonne V18 or Nijmegen 93 two-body nucleon-nucleon interaction supplemented by a microscopic three-body force. The rearrangement contribution to the single-particle potential induced by the ground state correlations is calculated in terms of the hole-line expansion of the mass operator and provides a significant repulsive contribution in the low-momentum region around and below the Fermi surface. Increasing temperature leads to a reduction of the effect, while increasing density makes it become stronger. The three-body force suppresses somewhat the ground state correlations due to its strong short-range repulsion, increasing with density. Inclusion of the three-body force contribution results in a quite different temperature dependence of the single-particle potential at high enough densities as compared to that adopting the pure two-body force. The effects of three-body force and ground state correlations on the nucleon effective mass are also discussed.Comment: 14 pages, 5 figure