Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

Coherent molecular solitons in Bose-Einstein condensates

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEG, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output. [S0031-9007(98)07283-4].

Thermal diffusion in molecular dynamics simulations of thin film diamond deposition

Molecular dynamics simulations of carbon atom depositions are used to investigate energy diffusion from the impact zone. A modified Stillinger-Weber potential models the carbon interactions for both sp2 and sp3 bonding. Simulations were performed on 50 eV carbon atom depositions onto the (111) surface of a 3.8 x 3.4 x 1.0 nm diamond slab containing 2816 atoms in 11 layers of 256 atoms each. The bottom layer was thermostated to 300 K. At every 100th simulation time step (27 fs), the average local kinetic energy, and hence local temperature, is calculated. To do this the substrate is divided into a set of 15 concentric hemispherical zones, each of thickness one atomic diameter (0.14 nm) and centered on the impact point. A 50-eV incident atom heats the local impact zone above 10 000 K. After the initial large transient (200 fs) the impact zone has cooled below 3000 K, then near 1000 K by 1 ps. Thereafter the temperature profile decays approximately as described by diffusion theory, perturbed by atomic scale fluctuations. A continuum model of classical energy transfer is provided by the traditional thermal diffusion equation. The results show that continuum diffusion theory describes well energy diffusion in low energy atomic deposition processes, at distance and time scales larger than 1.5 nm and 1-2 ps, beyond which the energy decays essentially exponentially. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Unsupervised cell nucleus segmentation with active contours

The task of segmenting cell nuclei from cytoplasm in conventional Papanicolaou (Pap) stained cervical cell images is a classical image analysis problem which may prove to be crucial to the development of successful systems which automate the analysis of Pap smears for detection of cancer of the cervix. Although simple thresholding techniques will extract the nucleus in some cases, accurate unsupervised segmentation of very large image databases is elusive. Conventional active contour models as introduced by Kass, Witkin and Terzopoulos (1988) offer a number of advantages in this application, but suffer from the well-known drawbacks of initialisation and minimisation. Here we show that a Viterbi search-based dual active contour algorithm is able to overcome many of these problems and achieve over 99% accurate segmentation on a database of 20 130 Pap stained cell images. (C) 1998 Elsevier Science B.V. All rights reserved.

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

Integrability of a t - J model with impurities

A t - J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1).

Atoms in squeezed light fields

Squeezed light is of interest as an example of a non-classical state of the electromagnetic field and because of its applications both in technology and in fundamental quantum physics. This review concentrates on one aspect of squeezed light, namely its application in atomic spectroscopy. The general properties, detection and application of squeezed light are first reviewed. The basic features of the main theoretical methods (master equations, quantum Langevin equations, coupled systems) used to treat squeezed light spectroscopy are then outlined. The physics of squeezed light interactions with atomic systems is dealt with first for the simpler case of two-level atoms and then for the more complex situation of multi-level atoms and multi-atom systems. Finally the specific applications of squeezed light spectroscopy are reviewed.

Chaotic dynamics of cold atoms in far-off-resonant donut beams

We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the (x,y) plant for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos. [S1063-651X(99)03903-3].

Autoinhibition by an internal nuclear localization signal revealed by the crystal structure of mammalian importin alpha

Importin alpha is the nuclear import receptor that recognizes classical monopartite and bipartite nuclear localization signals (NLSs). The structure of mouse importin alpha has been determined at 2.5 Angstrom resolution. The structure shows a large C-terminal domain containing armadillo repeats, and a less structured N-terminal importin beta-binding domain containing an internal NLS bound to the NLS-binding site. The structure explains the regulatory switch between the cytoplasmic, high-affinity form, and the nuclear, low-affinity form for NLS binding of the nuclear import receptor predicted by the current models of nuclear import. Importin beta conceivably converts the low- to high-affinity form by binding to a site overlapping the autoinhibitory sequence. The structure also has implications for understanding NLS recognition, and the structures of armadillo and HEAT repeats.

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

Novel solitons in parametric amplifiers and atom lasers

We review recent developments in quantum and classical soliton theory, leading to the possibility of observing both classical and quantum parametric solitons in higher-dimensional environments. In particular, we consider the theory of three bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium this corresponds to the process of sum frequency generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. Potential applications include an ultrafast photonic AND-gate. The simplest quantum solitons or energy eigenstates (bound-state solutions) of the interacting field Hamiltonian are obtained exactly in three space dimensions. They have a point-like structure-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with the imposition of a momentum cut-off on the nonlinear couplings. The case of three-dimensional matter-wave solitons in coupled atomic/molecular Bose-Einstein condensates is discussed.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.