The time-dependent evolution equation for the connection strength of a three-layer feed-forward neural network derived from optimizing the information rate is solved accurately at the long-time limit. It is shown that (1) the receptive field is given by the eigenvector of the maximum eigenvalue of the evolution equation, (2) the morphology of the receptive field is divided by a parameter $k_2$ into distinct regions, (3) the receptive field obeys parity invariance for high values of $k_2$ but breaks the parity invariance for values of $k_2$ less than -0.891$C_Q$, and (4) the analytic expressions for the receptive fields are derived. Differences of our results from the theory of Marr and Hildreth [Proc. R. Soc. London Ser. B 207, 187 (1980)] of edge-detection based on the center-surround ${\nabla }^2$G filters are presented.

We study a simple nonlinear model that mimics many features of the DNA molecule, where the source of the nonlinearity is the hydrogen bonds between nucleotides. We find an asymptotic solution of the equations of motion in the limit of small amplitudes. For an arbitrary initial condition, however, the equations of motion have to be integrated numerically. In this case we find essentially two different regimes, one in which an initial pulselike disturbance is pinned, and another one in which it propagates along the chain. In this latter case, propagation is a linear effect, in which the nonlinearity plays little role.

We have analyzed a self-organization occurring in an open ferromagnetic Ising system on a square lattice in contact with a heat bath and subject to an external source of energy. The system follows a stochastic dynamics composed of two processes: one of the Glauber type, which simulates the contact of the system with the heat bath, and the other of the Kawasaki type, which simulates the continuous flux of energy into the system. When the flux is small, the stationary state is paramagnetic at high temperatures and ferromagnetic at low temperatures. By increasing the flux, the ferromagnetic state is destroyed and the system reaches a new stationary state of high energy identified with the antiferromagnetic ordered state.

The thermodynamic formalism for dynamical systems is applied to a class of mappings of ‘‘laminar-turbulent’’ temporal intermittency. The corresponding statistical system is shown to be a lattice gas with many-body interactions of clustering type. This one-dimensional system bears a close analogy with the Fisher-Felderhof droplet model of condensation. The abnormal dynamic fluctuations give rise to a phase transition. The critical behaviors, which depend solely on the characteristic exponent z of the original map, are studied analytically, and a number of unexpected results are obtained. In the pressure-temperature plane, the intermittant state is located on a critical line that separates the chaotic (‘‘turbulent’’) state from the periodic (‘‘laminar’’) state. The transition from one phase to the other may be of first order if z<2. On the other hand, for 2≤z, the ‘‘sporadic state’’ introduced by Gaspard and Wang [Proc. Natl. Acad. Sci. U.S.A. 85, 4591 (1988)] is existent and corresponds to a codimension-two point on the critical curve.

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

The effects of a forced flow on dendritic growth rate are studied theoretically. By using a solvability condition, one determines the eigenvalue C=${\rho }^2$V/${\mathrm{Dd}}_0$ as a function of the velocity of the forced flow in the two-dimensional model. Even in the presence of crystalline anisotropy, no solutions for eigenvalues can be found when the flow velocity is larger than a critical velocity. The results are compared critically with recent experiments.

It is shown that for a given angular orbital configuration, the expression for multicenter molecular integrals of higher principal quantum number Slater orbitals can be generalized in a systematic approach.

The negative ions of the rare gases (He, Ne, Ar, Kr, Xe, and Rn) and some actinides (Pu, Am, Bk, Cf, and Es) have been calculated self-consistently by the generalized exchange local-spin-density-functional theory with self-interaction correction and correlation. The electron affinities were obtained as the differences between the statistical total energies of the negative ions and neutral atoms; the electron affinities were positive around several millirydbergs. Consequently, the negative ions are predicted stable for the rare gases and actinides.

We examine semiclassically the reduction in bond length of the deuterium molecule when it forms astride a localized electronic charge concentration. For the types of charge concentration generally expected in the valence shells of high-Z atoms, bond-length reductions of several times over the vacuum length are suggested. Implications for cold nuclear fusion are discussed.

The divergence of a semiclassical series of wave functions due to the presence of one or two turning points is investigated. The asymptotic expansion of higher semiclassical corrections ${\phi }_n$ with respect to the inverse power of the order number n is obtained. Amazingly, the expansion terms are subject to the same recurrence relations as the terms of the initial expansion with respect to Planck’s constant ħ. Quantitative criteria for obtaining maximally accurate semiclassical wave functions are derived.

Collective rotational motion of strongly correlated atomic electrons is investigated by using the self-consistent cranking model. The intrinsic wave function and the moment of inertia are analyzed as a function of angular velocity of rotation. Origin of the ‘‘rotational contraction’’ is ascribed to the effect of quantum-mechanical shell structure.

The dielectronic recombination cross sections associated with the 2s→2p transition in Li-like carbon and oxygen ions in the presence of small electric fields have been calculated in the distorted-wave approximation. By convoluting the product of the electron velocity and the theoretical cross section with the experimental velocity distribution, we compare our calculations with recent measurements of high-resolution recombination rates 〈vσ(v)〉 by Andersen et al. With the exception of the magnitude of the low-energy peak due to the 2p4l resonances, the agreement between experiment and theory is excellent in ${\mathrm{C}}^{3+}$ for a field in the interaction region of just over 3 V/cm. In the case of ${\mathrm{O}}^{5+}$, however, there is good agreement between experiment and theory for the low-Rydberg states, but there appear to be discrepancies between the measured rates and the theoretical rates for the high-Rydberg states, where the effects of fields are important.

The ‘‘label-free’’ operator has recently been used to calculate individual properties of each atom in a pair. Large values of individual induced-dipole moments have thus been obtained. We explain the origin of such artificial values. We also show why this approach is not consistent with quantum-mechanical principles and leads to logical inconsistencies. Such a formalism cannot be used to calculate individual properties of an atom in a pair. However, we specify the conditions for which this formalism could be extended to be useful in calculating global exchange properties of the total pair.

A specific experiment demonstrates unambiguously that the ${\mathrm{He}}^{+}$ ion signal coming from single collisions between a ${\mathrm{He}}^{\mathrm{*}}$(2 ${}_{}{}^1{}_{}{}^{}$,3S) beam on a He${(1\mathrm{}}^1$S) target in the presence of a laser field cannot be produced by the two-step process involving 2 ${}_{}{}^1{}_{}{}^{}2$ ${}_{}{}^1{}_{}{}^{}P$ collisional excitation followed by $2^1$P photoionization. This evidence gives support to the conclusion that the laser-assisted collision is the ionizing mechanism.

The resonant electron-capture process is studied for the lightly charged ions of the K isoelectronic sequence with 19 electrons, where the inversion of the ground-state configuration takes place due to strong electron-electron correlation. An anomaly in the capture cross section is found around ${\mathrm{Sc}}^{2+}$. The usual separation of the dielectronic recombination process into the intra- and intershell excitation transitions is no longer meaningful for these ions.

We analyze the autoionization widths of doubly excited states of two-electron atoms using the (K,T${)}^A$ classification scheme introduced previously. It is shown that the widths of all the states along each truncated rotor series are comparable except for the last two states. This novel systematics is interpreted qualitatively in terms of the molecular or the correlated motion of the two electrons, except for the last two states which are explained in terms of the independent-electron model.

High-resolution spectra (0.07 and 0.14 Å, full width at half-maximum) are presented for the region between 860 and 918 Å of the photoionization spectrum of atomic chlorine. Comparison is made with several many-body theories. Significant disagreement with theory is found, particularly with the widths and profiles of the sharp autoionizing resonances.

It is shown that a dynamical phase transition is typically present in chaotic Hamiltonian systems due to the intermittent motion near regular islands. The transition shows up in the spectrum of the Rényi entropies $K_q$ as a jump from a finite $K_1$ to zero at q=1+0. Numerical measurements have been carried out for the correlation entropy $K_2$.

Recent results for heat transport between parallel plates are compared. Theoretical predictions are obtained from an exact solution to the nonlinear Bhatnagar, Gross, and Krook [Phys. Rev. 94, 511 (1954)] kinetic model for the Boltzmann equation. The temperature profiles are compared with corresponding results from a molecular-dynamics simulation using stochastic boundary conditions. Good agreement is obtained for the wide range of Knudsen numbers and temperature gradients considered, including states far from equilibrium.

Most of the results of the recent paper by A. Redondo [Phys. Rev. A 39, 4366 (1989)] are both well-known and well documented in literature. Parts of the first-order density matrix history are briefly reviewed.