Interference in hyperbolic space

The interference in a phase space algorithm of Schleich and Wheeler [Nature 326, 574 (1987)] is extended to the hyperbolic space underlying the group SU(1,1). The extension involves introducing the notion of weighted areas. Analytic expressions for the asymptotic forms for overlaps between the eigenstates of the generators of su(1,1) thus obtained are found to be in excellent agreement with the numerical results.[S1050-2947(98)08602-8].

Category-theoretic fibration as an abstraction mechanism in information systems

This paper examines the problem of establishing a formal relationship of abstraction and refinement between abstract enterprise models and the concrete information systems which implement them. It introduces and justifies a number of reasonableness requirements, which turn out to justify the use of category theoretic concepts, particularly fibrations, to precisely specify a semantics for enterprise models which enables them to be considered as abstractions of the conceptual models from which the implementing information systems are built. The category-theoretic concepts are developed towards the problem of testing whether a system satisfies the fibration axioms, and are applied to case studies to demonstrate their practicability.

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

R-estimator of location of the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

OntoRama: Browsing RDF ontologies using a hyperbolic-style browser

This paper presents a Java-based hyperbolic-style browser designed to render RDF files as structured ontological maps. The program was motivated by the need to browse the content of a web-accessible ontology server: WEB KB-2. The ontology server contains descriptions of over 74,500 object types derived from the WordNet 1.7 lexical database and can be accessed using RDF syntax. Such a structure creates complications for hyperbolic-style displays. In WEB KB-2 there are 140 stable ontology link types and a hyperbolic display needs to filter and iconify the view so different link relations can be distinguished in multi-link views. Our browsing tool, OntoRama, is therefore motivated by two possibly interfering aims: the first to display up to 10 times the number of nodes in a hyperbolic-style view than using a conventional graphics display; secondly, to render the ontology with multiple links comprehensible in that view.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

The critical power function is dependent on the duration of the predictive exercise tests chosen

The linear relationship between work accomplished (W-lim) and time to exhaustion (t(lim)) can be described by the equation: W-lim = a + CP.t(lim). Critical power (CP) is the slope of this line and is thought to represent a maximum rate of ATP synthesis without exhaustion, presumably an inherent characteristic of the aerobic energy system. The present investigation determined whether the choice of predictive tests would elicit significant differences in the estimated CP. Ten female physical education students completed, in random order and on consecutive days, five art-out predictive tests at preselected constant-power outputs. Predictive tests were performed on an electrically-braked cycle ergometer and power loadings were individually chosen so as to induce fatigue within approximately 1-10 mins. CP was derived by fitting the linear W-lim-t(lim) regression and calculated three ways: 1) using the first, third and fifth W-lim-t(lim) coordinates (I-135), 2) using coordinates from the three highest power outputs (I-123; mean t(lim) = 68-193 s) and 3) using coordinates from the lowest power outputs (I-345; mean t(lim) = 193-485 s). Repeated measures ANOVA revealed that CPI123 (201.0 +/- 37.9W) > CPI135 (176.1 +/- 27.6W) > CPI345 (164.0 +/- 22.8W) (P < 0.05). When the three sets of data were used to fit the hyperbolic Power-t(lim) regression, statistically significant differences between each CP were also found (P < 0.05). The shorter the predictive trials, the greater the slope of the W-lim-t(lim) regression; possibly because of the greater influence of 'aerobic inertia' on these trials. This may explain why CP has failed to represent a maximal, sustainable work rate. The present findings suggest that if CP is to represent the highest power output that an individual can maintain for a very long time without fatigue then CP should be calculated over a range of predictive tests in which the influence of aerobic inertia is minimised.

Bishadowing and hyperbolicity

Shadowing of a dynamical system is often used to justify the validity of computer simulations of the system, and in numerical calculations an inverse form of the shadowing concept is also of some interest. In this paper we characterize the notion of shadowing in terms of stability, and express the notion of hyperbolicity using the concept of inverse shadowing.

Calorimetric demonstration of the potential of molecular crowding to emulate the effect of an allosteric activator on pyruvate kinase kinetics

A method based on isothermal calorimetry is described for the direct kinetic assay of pyruvate kinase. In agreement with earlier findings based on the standard coupled assay system for this enzyme in the presence of a fixed ADP concentration, the essentially rectangular hyperbolic dependence of initial velocity upon phosphoenolpyruvate concentration is rendered sigmoidal by the allosteric inhibitor phenylalanine. This effect of phenylalanine can be countered by including a high concentration of a space- filling osmolyte such as proline in the reaction mixtures. This investigation thus affords a dramatic example that illustrates the need to consider potential consequences of thermodynamic nonideality on the kinetics of enzyme reactions in crowded molecular environments such as the cell cytoplasm.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Quantitative description of the interaction between folate and the folate-binding protein from cow's milk

A detailed study has been carried out on the dependence of folate binding on the concentration of FBP (folate-binding protein) at pH 5.0, conditions selected to prevent complications arising from the pre-existing self-association of the acceptor. In contrast with the mandatory requirement that reversible interaction of ligand with a single acceptor site should exhibit a unique, rectangular hyperbolic binding curve, results obtained by ultrafiltration for the FBP-folate system required description in terms of (i) a sigmoidal relationship between concentrations of bound and free folate and (ii) an inverse dependence of affinity on FBP concentration. These findings have been attributed to the difficulties in determining the free ligand concentration in the FBP-folate mixtures for which reaction is essentially stoichiometric. This explanation also accounts for the similar published behaviour of the FBP-folate system at neutral pH, which had been attributed erroneously to acceptor self-association, a phenomenon incompatible with the experimental findings because of its prediction of a greater affinity for folate with increasing FBP concentration.

Effect of nitrogen supply on leaf appearance, leaf growth, leaf nitrogen economy and photosynthetic capacity in maize (Zea mays L.)

Leaf area growth and nitrogen concentration per unit leaf area, N-a (g m(-2) N) are two options plants can use to adapt to nitrogen limitation. Previous work indicated that potato (Solanum tuberosum L.) adapts the size of leaves to maintain Na and photosynthetic capacity per unit leaf area. This paper reports on the effect of N limitation on leaf area production and photosynthetic capacity in maize, a C4 cereal. Maize was grown in two experiments in pots in glasshouses with three (0.84-6.0 g N pot(-1)) and five rates (0.5-6.0 g pot(-1)) of N. Leaf tip and ligule appearance were monitored and final individual leaf area was determined. Changes with leaf age in leaf area, leaf N content and light-saturated photosynthetic capacity, P a,, were measured on two leaves per plant in each experiment. The final area of the largest leaf and total plant leaf area differed by 16 and 29% from the lowest to highest N supply, but leaf appearance rate and the duration of leaf expansion were unaffected. The N concentration of expanding leaves (N-a or %N in dry matter) differed by at least a factor 2 from the lowest to highest N supply. A hyperbolic function described the relation between P-max and N-a. The results confirm the 'maize strategy': leaf N content, photosynthetic capacity, and ultimately radiation use efficiency is more sensitive to nitrogen limitation than are leaf area expansion and light interception. The generality of the findings is discussed and it is suggested that at canopy level species showing the 'potato strategy' can be recognized from little effect of nitrogen supply on radiation use efficiency, while the reverse is true for species showing the 'maize strategy' for adaptation to N limitation. (c) 2004 Elsevier B.V. All rights reserved.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.