Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

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.

Measurement Function Design for Visual Tracking Applications

Extracting human postural information from video sequences has proved a difficult research question. The most successful approaches to date have been based on particle filtering, whereby the underlying probability distribution is approximated by a set of particles. The shape of the underlying observational probability distribution plays a significant role in determining the success, both accuracy and efficiency, of any visual tracker. In this paper we compare approaches used by other authors and present a cost path approach which is commonly used in image segmentation problems, however is currently not widely used in tracking applications.

Common multiples of complete graphs

A graph H is said to divide a graph G if there exists a set S of subgraphs of G, all isomorphic to H, such that the edge set of G is partitioned by the edge sets of the subgraphs in S. Thus, a graph G is a common multiple of two graphs if each of the two graphs divides G.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Using FCD Mapper Software and Landsat Images to Assess Forest Canopy Density in Landscapes in Australia and the Philippines

Using Landsat imagery, forest canopy density (FCD) estimated with the FCD Mapper®, was correlated with predominant height (PDH, measured as the average height of the tallest 50 trees per hectare) for 20 field plots measured in native forest at Noosa Heads, south-east Queensland, Australia. A corresponding image was used to calculate FCD in Leyte Island, the Philippines and was validated on the ground for accuracy. The FCD Mapper was produced for the International Tropical Timber Organisation and estimates FCD as an index of canopy density using reflectance characteristics of Landsat Enhanced Thematic (ETM) Mapper images. The FCD Mapper is a ‘semi-expert’ computer program which uses interactive screens to allow the operator to make decisions concerning the classification of land into bare soil, grass and forest. At Noosa, a positive strong nonlinear relationship (r2 = 0.86) was found between FCD and PDH for 15 field plots with variable PDH but complete canopy closure. An additional five field plots were measured in forest with a broken canopy and the software assessed these plots as having a much lower FCD than forest with canopy closure. FCD estimates for forest and agricultural land in the island of Leyte and subsequent field validation showed that at appropriate settings, the FCD Mapper differentiated between tropical rainforest and banana or coconut plantation. These findings suggest that in forests with a closed canopy this remote sensing technique has promise for forest inventory and productivity assessment. The findings also suggest that the software has promise for discriminating between native forest with a complete canopy and forest which has a broken canopy, such as coconut or banana plantation.

Fast evolution strategies

Evolution strategies are a class of general optimisation algorithms which are applicable to functions that are multimodal, nondifferentiable, or even discontinuous. Although recombination operators have been introduced into evolution strategies, the primary search operator is still mutation. Classical evolution strategies rely on Gaussian mutations. A new mutation operator based on the Cauchy distribution is proposed in this paper. It is shown empirically that the new evolution strategy based on Cauchy mutation outperforms the classical evolution strategy on most of the 23 benchmark problems tested in this paper. The paper also shows empirically that changing the order of mutating the objective variables and mutating the strategy parameters does not alter the previous conclusion significantly, and that Cauchy mutations with different scaling parameters still outperform the Gaussian mutation with self-adaptation. However, the advantage of Cauchy mutations disappears when recombination is used in evolution strategies. It is argued that the search step size plays an important role in determining evolution strategies' performance. The large step size of recombination plays a similar role as Cauchy mutation.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Squeezing-induced complete transparency in two-level systems

The modification of the statistical properties of vacuum fluctuations, via quadrature squeezing, can dramatically reduce the absorptive and dispersive properties of two-level atoms. We show that for some range of parameter values the system exhibits zero absorption accompanied by zero dispersion of the probe field. This complete transparency is attributed to the coherent population oscillations induced by the squeezed vacuum.

Studies of evolutionary temperature adaptation: Muscle function and locomotor performance in Antarctic fish

1, Studies of evolutionary temperature adaptation of muscle and locomotor performance in fish are reviewed with a focus on the Antarctic fauna living at subzero temperatures. 2. Only limited data are available to compare the sustained and burst swimming kinematics and performance of Antarctic, temperate and tropical species. Available data indicate that low temperatures limit maximum swimming performance and this is especially evident in fish larvae. 3, In a recent study, muscle performance in the Antarctic rock cod Notothenia coriiceps at 0 degrees C was found to be sufficient to produce maximum velocities during burst swimming that were similar to those seen in the sculpin Myoxocephalus scorpius at 10 degrees C, indicating temperature compensation of muscle and locomotor performance in the Antarctic fish. However, at 15 degrees C, sculpin produce maximum swimming velocities greater than N, coriiceps at 0 degrees C, 4, It is recommended that strict hypothesis-driven investigations using ecologically relevant measures of performance are undertaken to study temperature adaptation in Antarctic fish, Recent detailed phylogenetic analyses of the Antarctic fish fauna and their temperate relatives will allow a stronger experimental approach by helping to separate what is due to adaptation to the cold and what is due to phylogeny alone.

Spectroscopic identification of a dinuclear metal centre in manganese(II)-activated aminopeptidase P from Escherichia coli: implications for human prolidase

Electron paramagnetic resonance (EPR) spectra and X-ray absorption (EXAFS and XANES) data have been recorded for the manganese enzyme aminopeptidase P (AMPP, PepP protein) from Escherichia coli. The biological function of the protein, a tetramer of 50-kDa subunits, is the hydrolysis of N-terminal Xaa-Pro peptide bonds. Activity assays confirm that the enzyme is activated by treatment with Mn2+. The EPR spectrum of Mn2+-activated AMPP at liquid-He temperature is characteristic of an exchange-coupled dinuclear Mn(II) site, the Mn-Mn separation calculated from the zero-field splitting D of the quintet state being 3.5 (+/- 0.1) Angstrom. In the X-ray absorption spectrum of Mn2+-activated AMPP at the Mn K edge, the near-edge features are consistent with octahedrally coordinated Mn atoms in oxidation state +2. EXAFS data, limited to k less than or equal to 12 Angstrom(-1) by traces of Fe in the protein, are consistent with a single coordination shell occupied predominantly by O donor atoms at an average Mn-ligand distance of 2.15 Angstrom, but the possibility of a mixture of O and N donor atoms is not excluded. The Mn-Mn interaction at 3.5 Angstrom, is not detected in the EXAFS, probably due to destructive interference from light outer-shell atoms. The biological function, amino acid sequence and metal-ion dependence of E. coli AMPP are closely related to those of human prolidase, an enzyme that specifically cleaves Xaa-Pro dipeptides. Mutations that lead to human prolidase deficiency and clinical symptoms have been identified. Several known inhibitors of prolidase also inhibit AMPP. When these inhibitors are added to Mn2+-activated AMPP, the EPR spectrum and EXAFS remain unchanged. It can be inferred that the inhibitors either do not bind directly to the Mn centres, or substitute for existing Mn ligands without a significant change in donor atoms or coordination geometry. The conclusions from the spectroscopic measurements on AMPP have been verified by, and complement, a recent crystal structure analysis.

Key residues characteristic of GATA N-fingers are recognized by FOG

Protein-protein interactions play significant roles in the control of gene expression. These interactions often occur between small, discrete domains within different transcription factors. In particular, zinc fingers, usually regarded as DNA-binding domains, are now also known to be involved in mediating contacts between proteins. We have investigated the interaction between the erythroid transcription factor GATA-1 and its partner, the 9 zinc finger protein, FOG (Friend of GATA). We demonstrate that this interaction represents a genuine finger-finger contact, which is dependent on zinc coordinating residues within each protein. We map the contact domains to the core of the N-terminal zinc finger of GATA-1 and the 6th zinc finger of FOG. Using a scanning substitution strategy we identify key residues within the GATA-1 N-finger which are required for FOG binding. These residues are conserved in the N-fingers of all GATA proteins known to bind FOG, but are not found in the respective C-fingers, This observation may, therefore, account for the particular specificity of FOG for N-fingers, Interestingly, the key N-finger residues are seen to form a contiguous surface, when mapped onto the structure of the N-finger of GATA-1.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

Structure/function studies of S100A8/A9

The functional importance of members of the S100 Ca2+-binding protein family is recently emerging. A variety of activities, several of which are apparently opposing, are attributed to S100A8, a protein implicated in embryogenesis, growth, differentiation, and immune and inflammatory processes. Murine (m) S100A8 was initially described as a chemoattractant (CP-10) for myeloid cells. It is coordinately expressed with mS100A9 (MRP14) in neutrophils and the non-covalent heterodimer is presumed to be the functional intracellular species. The extracellular chemotactic activity of mS100A8, however, is not dependent on mS100A9 and occurs at concentrations (10(-13)-10(-11) M) at which the non-covalent heterodimer would probably dissociate. This review focuses on the structure and post-translational modifications of mS100A8/A9 and their effects on function, particularly chemotaxis.