Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Determinant representations of correlation functions for the supersymmetric t-J model

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

Valuing ecological functions of biodiversity in changbaishan mountain biosphere reserve in northeast china

Conservation of biodiversity can generate considerable indirect economic value and this is being increasingly recognized in China. For a forest ecosystem type of a nature reserve, the most important of its values are its ecological functions which provide human beings and other living things with beneficial environmental services. These services include water conservancy, soil protection, CO2 fixation and O-2 release, nutrient cycling, pollutant decomposition, and disease and pest control. Based on a case study in Changbaishan Mountain Biosphere Reserve in Northeast China, this paper provides a monetary valuation of these services by using opportunity cost and alternative cost methods. Using such an approach, this reserve is valued at 510.11 million yuan (USD 61.68 mill.) per year, 10 times higher than the opportunity cost (51.78 mill. yuan/ha.a) for regular timber production. While China has heeded United Nations Environmental Program (UNEP)'s call for economic evaluation of ecological functions, the assessment techniques used need to be improved in China and in the West for reasons mentioned.

Mapping the royal road and other hierarchical functions

In this paper we present a technique for visualising hierarchical and symmetric, multimodal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over {0, 1}(n), for n less than or equal to 16). The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.

The functions of societies and the evolution of group living: Spider societies as a test case

Many models have been advanced to suggest how different expressions of sociality have evolved and are maintained. However these models ignore the function of groups for the particular species in question. Here we present a new perspective on sociality where the function of the group takes a central role. We argue that sociality may have primarily a reproductive, protective, or foraging function, depending on whether it enhances the reproductive, protective or foraging aspect of the animal's life (sociality may serve a mixture of these functions). Different functions can potentially cause the development of the same social behaviour. By identifying which function influences a particular social behaviour we can determine how that social behaviour will change with changing conditions, and which models are most pertinent. To test our approach we examined spider sociality, which has often been seen as the poor cousin to insect sociality. By using our approach we found that the group characteristics of eusocial insects is largely governed by the reproductive function of their groups, while the group characteristics of social spiders is largely governed by the foraging function of the group. This means that models relevant to insects may not be relevant to spiders. It also explains why eusocial insects have developed a strict caste system while spider societies are more egalitarian. We also used our approach to explain the differences between different types of spider groups. For example, differences in the characteristics of colonial and kleptoparasitic groups can be explained by differences in foraging methods, while differences between colonial and cooperative spiders can be explained by the role of the reproductive function in the formation of cooperative spider groups. Although the interactions within cooperative spider colonies are largely those of a foraging society, demographic traits and colony dynamics are strongly influenced by the reproductive function. We argue that functional explanations help to understand the social structure of spider groups and therefore the evolutionary potential for speciation in social spiders.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Growth factors and cytokines modulate gene expression of cell-surface proteoglycans in human periodontal ligament cells

Cell-surface proteoglycans have been known to be involved in many functions including interactions with components of the extracellular microenvironment, and act as co-receptors which bind and modify the action of various growth factors and cytokines. The purpose of this study was to determine the regulation by growth factors and cytokines on cell-surface proteoglycan gene expression in cultured human periodontal ligament (PDL) cells. Subconfluent, quiescent PDL cells were treated with various concentrations of serum, bFGF, PDGF-BB, TGF-beta1, IL-1 beta, and IFN-gamma. RT-PCR technique was used, complemented with Northern blot for syndecan-1, to examine the effects of these agents on the mRNA expression of five cell-surface proteoglycans (syndecan-1, syndecan-2, syndecan-4, glypican and betaglycan). Syndecan-1 mRNA levels increased in response to serum, bFGF and PDGF-BB, but decreased in response to TGF-beta1, IL-1 beta and IFN-gamma. In contrast, syndecan-2 mRNA levels were upregulated by TCF-beta1 and IL-1 beta stimulation, but remained unchanged with the other agents. Betaglycan gene expression decreased in response to serum, but was upregulated by TCF-beta1 and unchanged by the other stimulants. Additionally, syndecan-4 and glypican were not significantly altered in response to the regulator molecules studied, with the exception that glypican is decreased in response to IFN-gamma. These data demonstrate that the gene expression of the five cell-surface proteoglycans studied is differentially regulated in PDL cells lending support to the nation of distinct functions for these cell-surface proteoglycans. (C) 2001 Wiley-Liss, inc.

Suppression of keratinocyte growth and differentiation by transforming growth factor beta 1 involves multiple signaling pathways

Transforming growth factor beta1 treatment of keratinocytes results in a suppression of differentiation, an induction of extracellular matrix production, and a suppression of growth. In this study we utilized markers specific for each of these functions to explore the signaling pathways involved in mediating these transforming-growth-factor-beta1-induced activities. In the first instance, we found that the induction of extracellular matrix production (characterized by 3TP-Lux reporter activity) was induced in both keratinocytes and a keratinocyte-derived carcinoma cell line, SCC25, in a dose-dependent manner. Furthermore, transforming growth factor beta1 also suppressed the differentiation-specific marker gene, transglutaminase type 1, in both keratinocytes and SCC25 cells. In contrast, transforming growth factor beta1 inhibited proliferation of keratinocytes but did not cause growth inhibition in the SCC25 cells. Transforming-growth-factor-beta1-induced growth inhibition of keratinocytes was characterized by decreases in DNA synthesis, accumulation of hypophosphorylated Rb, and the inhibition of the E2F:Rb-responsive promoter, cdc2, and an induction of the p21 promoter. When the negative regulator of transforming growth factor beta1 signaling, SMAD7, was overexpressed in keratinocytes it could prevent transforming-growth-factor-beta1-induced activation of the 3TP-Lux and the p21 promoter. SMAD7 could also prevent the suppression of the transglutaminase type 1 by transforming growth factor beta1 but it could not inhibit the repression of the cdc2 promoter. These data indicate that the induction of 3TP-Lux and p21 and the suppression of transglutaminase type 1 are mediated by a different proximate signaling pathway to that regulating the suppression of the cdc2 gene. Combined, these data indicate that the regulation of transforming growth factor beta1 actions are complex and involve multiple signaling pathways.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

The Three-dimensional Solution Structure of NaD1, a New Floral Defensin from Nicotiana alata and its Application to a Homology Model of the Crop Defense Protein alfAFP

NMR spectroscopy and simulated annealing calculations have been used to determine the three-dimensional structure of NaD1, a novel antifungal and insecticidal protein isolated from the flowers of Nicotiana alata. NaD1 is a basic, cysteine-rich protein of 47 residues and is the first example of a plant defensin from flowers to be characterized structurally. Its three-dimensional structure consists of an a-helix and a triple-stranded anti-parallel beta-sheet that are stabilized by four intramolecular disulfide bonds. NaD1 features all the characteristics of the cysteine-stabilized up motif that has been described for a variety of proteins of differing functions ranging from antibacterial insect defensins and ion channel-perturbing scorpion toxins to an elicitor of the sweet taste response. The protein is biologically active against insect pests, which makes it a potential candidate for use in crop protection. NaD1 shares 31% sequence identity with alfAFP, an antifungal protein from alfalfa that confers resistance to a fungal pathogen in transgenic potatoes. The structure of NaD1 was used to obtain a homology model of alfAFP, since NaD1 has the highest level of sequence identity with alfAFP of any structurally characterized antifungal defensin. The structures of NaD1 and alfAFP were used in conjunction with structure - activity data for the radish defensin Rs-AFP2 to provide an insight into structure-function relationships. In particular, a putative effector site was identified in the structure of NaD1 and in the corresponding homology model of alfAFP. (C) 2002 Elsevier Science Ltd. All rights reserved.