Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

The protease inhibitor cystatin C is differentially expressed among dendritic cell populations, but does not control antigen presentation

Dendritic cells (DC) undergo complex developmental changes during maturation. The MHC class H (MHC H) molecules of immature DC accumulate in intracellular compartments, but are expressed at high levels on the plasma membrane upon DC maturation. It has been proposed that the cysteine protease inhibitor cystatin C (CyC) plays a pivotal role in the control of this process by regulating the activity of cathepsin S, a protease involved in removal of the MHC H chaperone E, and hence in the formation of MHC H-peptide complexes. We show that CyC is differentially expressed by mouse DC populations. CD8(+) DC, but not CD4(+) or CD4(-)CD8(-) DC, synthesize CyC, which accumulates in MHC II(+)Lamp(+) compartments. However, II processing and MHC H peptide loading proceeded similarly in all three DC populations. We then analyzed MHC H localization and Ag presentation in CD8(+) DC, bone marrow-derived DC, and spleen-derived DC lines, from CyC-deficient mice. The absence of CyC did not affect the expression, the subcellular distribution, or the formation of peptide-loaded MHC II complexes in any of these DC types, nor the efficiency of presentation of exogenous Ags. Therefore, CyC is neither necessary nor sufficient to control MHC II expression and Ag presentation in DC. Our results also show that CyC expression can differ markedly between closely related cell types, suggesting the existence of hitherto unrecognized mechanisms of control of CyC expression.

Image calibration to like-values in mapping shallow water quality from multitemporal data

The applicability of image calibration to like-values in mapping water quality parameters from multitemporal images is explored, Six sets of water samples were collected at satellite overpasses over Moreton Bay, Brisbane, Australia. Analysis of these samples reveals that waters in this shallow bay are mostly TSS-dominated, even though they are occasionally dominated by chlorophyll as well. Three of the images were calibrated to a reference image based on invariant targets. Predictive models constructed from the reference image were applied to estimating total suspended sediment (TSS) and Secchi depth from another image at a discrepancy of around 35 percent. Application of the predictive model for TSS concentration to another image acquired at a time of different water types resulted in a discrepancy of 152 percent. Therefore, image calibration to like-values could be used to reliably map certain water quality parameters from multitemporal TM images so long as the water type under study remains unchanged. This method is limited in that the mapped results could be rather inaccurate if the water type under study has changed considerably. Thus, the approach needs to be refined in shallow water from multitemporal satellite imagery.

Drinfield twists and alegebraic Bethe ansatz of the supersymmetric t-J model

We construct the Drinfeld twists (factorizing F-matrices) for the supersymmetric t-J model. Working in the basis provided by the F-matrix (i.e. the so-called F-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2\1) invariant t-J model.

Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

How configurations of binocular disparity determine whether stereoscopic slant or stereoscopic occlusion is seen

A partially occluded contour and a slanted contour may generate identical binocular horizontal disparities. We investigated conditions promoting an occlusion resolution indicated by an illusory contour in depth along the aligned ends of horizontally disparate line sets. For a set of identical oblique lines with a constant width added to one eye's view, strength, depth, and stability of the illusory contour were poor, whereas for oblique lines of alternating orientations the illusory contours were strong, indicating a reliance on vertical size disparities rather than vertical positional disparities in generating perceived occlusion. For horizontal lines, occlusion was seen when the lines were of different lengths and absolute width disparity was invariant across the set. In all line configurations, when the additional length was on the wrong eye to be attributed to differential occlusion, lines appeared slanted consistent with their individual horizontal disparities. This rules out monocular illusory contours as the determining factor.

Limiting conditional distributions for birth-death processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on whether or not the process is evanescent. In the former case we shall relax the condition that absorption is certain. Furthermore, we shall allow for the possibility that the minimal process might be explosive, so that the transition rates alone will not necessarily determine the birth-death process uniquely. Although we shall be concerned mainly with the minimal process, our most general results hold for any birth-death process whose transition probabilities satisfy both the backward and the forward Kolmogorov differential equations.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Embryonic development of the nervous system of the temnocephalid flatworm Craspedella pedum

The nervous system of temnocephalid flatworms consists of the brain and three pairs of longitudinal connectives extending into the trunk and tail. The connectives are crosslinked by an invariant number of regularly spaced commissures. Branches of the connectives innervate the tentacles of the head and the sucker organ in the tail. A set of nerve rings encircling the pharynx and connected to the brain and connectives constitute the pharyngeal nervous system. The nervous system is formed during early embryogenesis when the embryo represents a multilayered mesenchymal mass of cells. Gastrulation and the formation of separate epithelial germ layers that characterize most other animal groups are absent. The brain arises as a bilaterally symmetric condensation of postmitotic cells in the deep layers of the anterior region of the embryonic mesenchyme. The pattern of axon outgrowth, visualized by labeling with anti-acetylated tubulin (acTub) antibody, shows marked differences from the pattern observed in other flatworm taxa. in regard to the number of neurons that express the acTub epitope. Acetylated tubulin is only expressed in neurons that form long axon tracts. In other flatworm species, such as the typhloplanoid Mesostoma and the polyclad Imogine, which were investigated by us with the acTub antibody (Hartenstein and Ehlers [2000] Dev. Genes Evol. 210:399-415; Younossi-Hartenstein and Hartenstein [2000] Dev. Genes Evol. 210:383-398), only a small number of pioneer neurons become acTub positive during the embryonic period. By contrast, in temnocephalids, most, if not all, neurons express acTub and form long, large-diameter axons. Initially, the brain commissure, pharyngeal nerve ring, and the connectives are laid down. Commissural tracts and tentacle nerves branching off the connectives appear later. We speculate that the precocious differentiation of the nervous system may be related to the fact that temnocephalids move by muscle action, and possess a massive and complex muscular system when they hatch. In addition, they have muscular specializations such as the anterior tentacles and the posterior sucker that are used as soon as they hatch. By contrast, juveniles of Mesostoma and larvae of polyclads move predominantly by ciliary action that may not require a complex neural circuitry for coordination. (C) 2001 Wiley-Liss, Inc.

Colourful objects through animal eyes

To understand how bees, birds, and fish may use colour vision for food selection and mate choice, we reconstructed views of biologically important objects taking into account the receptor spectral sensitivities. Reflectance spectra a of flowers, bird plumage, and fish skin were used to calculate receptor quantum catches. The quantum catches were then coded by red, green, and blue of a computer monitor; and powers, birds, and fish were visualized in animal colours. Calculations were performed for different illumination conditions. To simulate colour constancy, we used a von Kries algorithm, i.e., the receptor quantum catches were scaled so that the colour of illumination remained invariant. We show that on land this algorithm compensates reasonably well for changes of object appearance caused by natural changes of illumination, while in water failures of von Kries colour constancy are prominent. (C) 2000 John Wiley & Sons, Inc.

On the relation between the conditional moment closure and unsteady flamelets

We consider the relation between the conditional moment closure (CMC) and the unsteady flamelet model (FM). The CMC equations were originally constructed as global equations, while FM was derived asymptotically for a thin reaction zone. The recent tendency is to use FM-type equations as global equations. We investigate the possible consequences and suggest a new version of FM: coordinate-invariant FM (CIFM). Unlike FM, CIFM complies with conditional properties of the exact transport equations which are used effectively in CMC. We analyse the assumptions needed to obtain another global version of FM: representative interactive flamelets (RIF), from original FM and demonstrate that, in homogeneous turbulence, one of these assumptions is equivalent to the main CMC hypothesis.