Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

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.

Integrable Kondo impurities in the one-dimensional supersymmetric extended Hubbard model

An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local moments of the impurities are presented as a non-trivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

Using Lindenmayer systems to model morphogenesis in a tropical pasture legume Stylosanthes scabra

This paper summarizes the processes involved in designing a mathematical model of a growing pasture plant, Stylosanthes scabra Vog. cv. Fitzroy. The model is based on the mathematical formalism of Lindenmayer systems and yields realistic computer-generated images of progressive plant geometry through time. The processes involved in attaining growth data, retrieving useful growth rules, and constructing a virtual plant model are outlined. Progressive output morphological data proved useful for predicting total leaf area and allowed for easier quantification of plant canopy size in terms of biomass and total leaf area.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

New integrable model of correlated electrons with off-diagonal long-range order from so(5) symmetry

We present a new integrable model for correlated electrons which is based on so(5) symmetry. By using an eta-pairing realization we construct eigenstates of the Hamiltonian with off-diagonal long-range order. It is also shown that these states lie in the ground state sector. We exactly solve the model on a one-dimensional lattice by the Bethe ansatz.

Ameloblast apoptosis and IGF-1 receptor expression in the continuously erupting rat incisor model

Enamel-producing cells (ameloblasts) pass through several phenotypic and functional stages during enamel formation. In the transition between secretory and maturation stages, about one quarter of the ameloblasts suddenly undergo apoptosis. We have studied this phenomenon using the continuously erupting rat incisor model. A special feature of this model is that all stages of ameloblast differentiation are presented within a single longitudinal section of the developing tooth. This permits investigation of the temporal sequence of gene and growth factor receptor expression during ameloblast differentiation and apoptosis. We describe the light and electron microscopic morphology of ameloblast apoptosis and the pattern of insulin-like growth factor-1 receptor expression by ameloblasts in the continuously erupting rat incisor model. In the developing rat incisor, ameloblast apoptosis is associated with downregulated expression of the insulin-like growth factor-1 receptor. These data are consistent with the hypothesis that ameloblasts are hard wired for apoptosis and that insulin-like growth factor-1 receptor expression is required to block the default apoptotic pathway. Possible mechanisms of insulin-like growth factor-1 inhibition of ameloblast apoptosis are presented. The rat incisor model may be useful in studies of physiological apoptosis as it presents apoptosis in a predictable pattern in adult tissues.

RWMODEL II: Computer simulation of the Rescorla-Wagner model of Pavlovian conditioning

RWMODEL II simulates the Rescorla-Wagner model of Pavlovian conditioning. It is written in Delphi and runs under Windows 3.1 and Windows 95. The program was designed for novice and expert users and can be employed in teaching, as well as in research. It is user friendly and requires a minimal level of computer literacy but is sufficiently flexible to permit a wide range of simulations. It allows the display of empirical data, against which predictions from the model can be validated.

Estimation of contribution of changes in classic risk factors to trends in coronary-event rates across the WHO MONICA Project populations

Background From the mid-1980s to mid-1990s, the WHO MONICA Project monitored coronary events and classic risk factors for coronary heart disease (CHD) in 38 populations from 21 countries. We assessed the extent to which changes in these risk factors explain the variation in the trends in coronary-event rates across the populations. Methods In men and women aged 35-64 years, non-fatal myocardial infarction and coronary deaths were registered continuously to assess trends in rates of coronary events. We carried out population surveys to estimate trends in risk factors. Trends in event rates were regressed on trends in risk score and in individual risk factors. Findings Smoking rates decreased in most male populations but trends were mixed in women; mean blood pressures and cholesterol concentrations decreased, body-mass index increased, and overall risk scores and coronary-event rates decreased. The model of trends in 10-year coronary-event rates against risk scores and single risk factors showed a poor fit, but this was improved with a 4-year time lag for coronary events. The explanatory power of the analyses was limited by imprecision of the estimates and homogeneity of trends in the study populations. Interpretation Changes in the classic risk factors seem to partly explain the variation in population trends in CHD. Residual variance is attributable to difficulties in measurement and analysis, including time lag, and to factors that were not included, such as medical interventions. The results support prevention policies based on the classic risk factors but suggest potential for prevention beyond these.

A model for assembly and activation of the GM-CSF, IL-3 and IL-5 receptors: Insights from activated mutants of the common beta subunit

Granulocyte-macrophage colony stimulating factor (GM-CSF), Interleukin-3 (IL-3) and Interleukin-5 (IL-5) have overlapping, pleiotropic effects on hematopoietic cells, including neutrophils, eosinophils, monocytes and early progenitor cells. The high-affinity receptors for human GM-CSF, IL-3, and IL-5 share a common beta-subunit (h beta(c)), which is essential for signalling and plays a major role in recruiting intracellular signalling molecules. While activation of the cytoplasmic tyrosine kinase JAK2 appears to be the initiating event for signalling, the immediate events that trigger this are still unclear. We have isolated a number of activated mutants of h beta(c), which can be grouped into classes defined by their state of receptor phosphorylation, their requirement for alpha subunit as a cofactor, and their activities in primary cells and cell lines. We discuss these findings with regard to the stoichiometry, activation, and signalling of the normal GM-CSF/IL-3/IL-5 receptor complexes. Specifically, this work has implications for the role of the ligand-specific alpha-subunits in initiating the signalling through the beta-subunit, the role of beta subunit dimerization as a receptor trigger, and the function of receptor tyrosine phosphorylation in generating growth and survival signals. Based on the properties of the activated mutants and the recent structures of erythropoietin receptor (Epo-R) complexes, we propose a model in which (1) activation of h beta(c) can occur via alternative states that differ with respect to stoichiometry and subunit assembly, but which all mediate proliferative responses, and (2) each of the different classes of activated mutants mimics one of these alternative states. (C) 2000 International Society for Experimental Hematology. Published by Elsevier Science Inc.

Grazers and diggers: Exploitation competition and coexistence among foragers with different feeding strategies on a single resource

A mathematical model is presented that describes a system where two consumer species compete exploitatively for a single renewable resource. The resource is distributed in a patchy but homogeneous environment; that is, all patches are intrinsically identical. The two consumer species are referred to as diggers and grazers, where diggers deplete the resource within a patch to lower densities than grazers. We show that the two distinct feeding strategies can produce a heterogeneous resource distribution that enables their coexistence. Coexistence requires that grazers must either move faster than diggers between patches or convert the resources to population growth much more efficiently than diggers. The model shows that the functional form of resource renewal within a patch is also important for coexistence. These results contrast with theory that considers exploitation competition for a single resource when the resource is assumed to be well mixed throughout the system.

Optimal release strategies for biological control agents: an application of stochastic dynamic programming to population management

1. Establishing biological control agents in the field is a major step in any classical biocontrol programme, yet there are few general guidelines to help the practitioner decide what factors might enhance the establishment of such agents. 2. A stochastic dynamic programming (SDP) approach, linked to a metapopulation model, was used to find optimal release strategies (number and size of releases), given constraints on time and the number of biocontrol agents available. By modelling within a decision-making framework we derived rules of thumb that will enable biocontrol workers to choose between management options, depending on the current state of the system. 3. When there are few well-established sites, making a few large releases is the optimal strategy. For other states of the system, the optimal strategy ranges from a few large releases, through a mixed strategy (a variety of release sizes), to many small releases, as the probability of establishment of smaller inocula increases. 4. Given that the probability of establishment is rarely a known entity, we also strongly recommend a mixed strategy in the early stages of a release programme, to accelerate learning and improve the chances of finding the optimal approach.