Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Body girth as an alternative to body mass for establishing condition indexes in field studies: a validation in the king penguin.

Body mass and body condition are often tightly linked to animal health and fitness in the wild and thus are key measures for ecophysiologists and behavioral ecologists. In some animals, such as large seabird species, obtaining indexes of structural size is relatively easy, whereas measuring body mass under specific field circumstances may be more of a challenge. Here, we suggest an alternative, easily measurable, and reliable surrogate of body mass in field studies, that is, body girth. Using 234 free-living king penguins (Aptenodytes patagonicus) at various stages of molt and breeding, we measured body girth under the flippers, body mass, and bill and flipper length. We found that body girth was strongly and positively related to body mass in both molting (R(2) = 0.91) and breeding (R(2) = 0.73) birds, with the mean error around our predictions being 6.4%. Body girth appeared to be a reliable proxy measure of body mass because the relationship did not vary according to year and experimenter, bird sex, or stage within breeding groups. Body girth was, however, a weak proxy of body mass in birds at the end of molt, probably because most of those birds had reached a critical depletion of energy stores. Body condition indexes established from ordinary least squares regressions of either body girth or body mass on structural size were highly correlated (r(s) = 0.91), suggesting that body girth was as good as body mass in establishing body condition indexes in king penguins. Body girth may prove a useful proxy to body mass for estimating body condition in field investigations and could likely provide similar information in other penguins and large animals that may be complicated to weigh in the wild.

Several neuronal and axonal types form long intrinsic connections in the cat primary auditory cortical field (AI).

Intrinsic connections in the cat primary auditory field (AI) as revealed by injections of Phaseolus vulgaris leucoagglutinin (PHA-L) or biocytin, had an anisotropic and patchy distribution. Neurons, labelled retrogradely with PHA-L were concentrated along a dorsoventral stripe through the injection site and rostral to it; the spread of rostrally located neurons was greater after injections into regions of low rather than high characteristic frequencies. The intensity of retrograde labelling varied from weak and granular to very strong and Golgi-like. Out of 313 Golgi like retrogradely labelled neurons 79.6% were pyramidal, 17.2% multipolar, 2.6% bipolar, and 0.6% bitufted; 13.4% were putatively inhibitory, i.e. aspiny or sparsely spiny multipolar, or bitufted. Individual anterogradely labelled intrinsic axons were reconstructed for distances of 2 to 7 mm. Five main types were distinguished on the basis of the branching pattern and the location of synaptic specialisations. Type 1 axons travelled horizontally within layers II to VI and sent collaterals at regular intervals; boutons were only present in the terminal arborizations of these collaterals. Type 2 axons also travelled horizontally within layers II to VI and had rather short and thin collateral branches; boutons or spine-like protrusions occurred in most parts of the axon. Type 3 axons travelled obliquely through the cortex and formed a single terminal arborization, the only site where boutons were found. Type 4 axons travelled for some distance in layer I; they formed a heterogeneous group as to their collaterals and synaptic specializations. Type 5 axons travelled at the interface between layer VI and the white matter; boutons en passant, spine-like protrusions, and thin short branches with boutons en passant were frequent all along their trajectory. Thus, only some axonal types sustain the patchy pattern of intrinsic connectivity, whereas others are involved in a more diffuse connectivity.

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Weak approximations. A Malliavin calculus approach

We introduce a variation of the proof for weak approximations that issuitable for studying the densities of stochastic processes which areevaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations fordensities and distributions can also be achieved. We apply theseideas to the case of stochastic differential equations with boundaryconditions and the composition of two diffusions.

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.

Vertically coupled double quantum rings at zero magnetic field

Within local-spin-density functional theory, we have investigated the ¿dissociation¿ of few-electron circular vertical semiconductor double quantum ring artificial molecules at zero magnetic field as a function of interring distance. In a first step, the molecules are constituted by two identical quantum rings. When the rings are quantum mechanically strongly coupled, the electronic states are substantially delocalized, and the addition energy spectra of the artificial molecule resemble those of a single quantum ring in the few-electron limit. When the rings are quantum mechanically weakly coupled, the electronic states in the molecule are substantially localized in one ring or the other, although the rings can be electrostatically coupled. The effect of a slight mismatch introduced in the molecules from nominally identical quantum wells, or from changes in the inner radius of the constituent rings, induces localization by offsetting the energy levels in the quantum rings. This plays a crucial role in the appearance of the addition spectra as a function of coupling strength particularly in the weak coupling limit.

Exchange-correlation effects on quantum wires with spin-orbit interactions under the influence of in-plane magnetic fields.

Within the noncollinear local spin-density approximation, we have studied the ground state structure of a parabolically confined quantum wire submitted to an in-plane magnetic field, including both Rashba and Dresselhaus spin-orbit interactions. We have explored a wide range of linear electronic densities in the weak (strong) coupling regimes that appear when the ratio of spin-orbit to confining energy is small (large). These results are used to obtain the conductance of the wire. In the strong coupling limit, the interplay between the applied magnetic field¿irrespective of the in-plane direction, the exchange-correlation energy, and the spin-orbit energy-produces anomalous plateaus in the conductance vs linear density plots that are otherwise absent, or washes out plateaus that appear when the exchange-correlation energy is not taken into account.

Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

Double folding with a density-dependent effective interaction and it s analytical approximation

The real part of the optical potential for heavy ion elastic scattering is obtained by double folding of the nuclear densities with a density-dependent nucleon-nucleon effective interaction which was successful in describing the binding, size, and nucleon separation energies in spherical nuclei. A simple analytical form is found to differ from the resulting potential considerably less than 1% all through the important region. This analytical potential is used so that only few points of the folding need to be computed. With an imaginary part of the Woods-Saxon type, this potential predicts the elastic scattering angular distribution in very good agreement with experimental data, and little renormalization (unity in most cases) is needed.

Particle in an electromagnetic field: The Lorentz-Dirac equation

A new method to solve the Lorentz-Dirac equation in the presence of an external electromagnetic field is presented. The validity of the approximation is discussed, and the method is applied to a particle in the presence of a constant magnetic field.

Classical solutions of the leading-logarithm approximation with non-trivial topology

Exact solutions of the classical equations corresponding to the leading-logarithm approximation are obtained. They are classified by an (integer) topological number.