The threshold behavior of the K-satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to the abrupt appearance of logical contradictions in all solutions and not to the progressive decreasing of the number of these solutions down to zero. A physical interpretation is given for the different cases $K=1\mathrm{}$, $K=2\mathrm{}$, and $K\ge 3$.

A Comment on the Letter by Taejin Lee, Phys. Rev. Lett. 74, 4967 (1995).

A Comment on the Letter by Arlen Anderson, Phys. Rev. Lett. 74, 621 (1995). The authors of the Letter offer a Reply.

A Comment on the Letter by Arlen Anderson, Phys. Rev. Lett. 74, 621 (1995). The authors of the Letter offer a Reply.

A Comment on the Letter by Arlen Anderson, Phys. Rev. Lett. 74, 621 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by (Ltr. I) K. R. W. Jones, (Ltr. II) Lajos Diósi, and (Ltr. III) I. R. Senitzky.

A Comment on the Letter by Chin-Kun Hu, Chai-Yu Lin, and Jau-Ann Chen, Phys. Rev. Lett. 75, 193 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by J-P. Hovi and Amnon Aharony.

We develop here a dynamic linear response theory of many-body nonextensive systems based on the maximization of the Tsallis entropy associated with the density matrix and the concomitant suitably defined mean total energy, number, etc., where the averaging is over the qth power of the density matrix, q being a parameter characterizing the nonextensivity. This formulation is shown to preserve causality (Kramers-Kronig), time reversal, and Onsager reciprocity, while a different form of fluctuation-dissipation theorem is obtained. The traditional theory for extensive systems is obtained in the special case where $q=1\mathrm{}$.

A Comment on the Letter by Nathan Poliatzky, Phys. Rev. Lett. 70, 2507 (1993). The authors of the Letter offer a Reply.

A Reply to the Comment by Zhong-Qi Ma.

We show a direct connection between a cellular automaton and integrable nonlinear wave equations. We also present the $N$-soliton formula for the cellular automaton. Finally, we propose a general method for constructing such integrable cellular automata and their $N$-soliton solutions.

We present a new approach for clustering, based on the physical properties of an inhomogeneous ferromagnetic model. We do not assume any structure of the underlying distribution of the data. A Potts spin is assigned to each data point and short range interactions between neighboring points are introduced. Spin-spin correlations, measured (by Monte Carlo procedure) in a superparamagnetic regime in which aligned domains appear, serve to partition the data points into clusters. Our method outperforms other algorithms for toy problems as well as for real data.

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Dynamical current redistribution (DCR) in noisy resistors is discussed. Contrary to a common assumption in many theories and in the interpretation of many experiments, DCR can cause large-amplitude non-Gaussian (NG) noise for statistically independent fluctuators. NG effects are predicted to be large near the percolation threshold and near the metal-insulator transition. We report the first observations of NG noise in semiconductor superlattices and attribute this to DCR. We also show that DCR is the most likely explanation of NG noise in several other systems.

A Comment on the Letter by A. Muriel, Phys. Rev. Lett. 75, 2255 (1995).

A Comment on the Letter by A. Muriel, Phys. Rev. Lett. 75, 2255 (1995).

The general impossibility of determining the state of a single quantum system is proved for arbitrary measuring schemes, including a succession of measurements. Some recently proposed methods are critically examined. A scheme for tomographic measurements on a single copy of a radiation field is devised, showing that the system state is perturbed however weak the system-apparatus interaction is, due to the need of preparing the apparatus in a highly “squeezed” state.

It is argued that ultraviolet absorption by a DNA molecule (which gets biochemically attached to nearby photolyase enzyme so that the effect of uv absorption becomes macroscopically discernible) constitutes an intriguing example of quantum measurement. We point out that this does not merely illustrate the quantum measurement paradox in the hitherto unexplored arena of biological macromolecules, but is also instructive in highlighting specific difficulties inherent in various approaches to the measurement problem.

We investigated the spectrum of the ${}^{16}{\mathrm{O}}_2$ molecule by high-sensitivity laser spectroscopy and searched for transitions involving states which are antisymmetric under the exchange of the nuclei. These states are forbidden by the symmetrization postulate of quantum mechanics. This is the first reported experiment to test the symmetrization postulate for integer-spin particles to high precision. Our data set an upper limit of $5\times {10}^{-7\mathrm{}}$ to a possible violation of this postulate.