Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

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 power system control scheme based on security visualisation in parameter space

Power system real time security assessment is one of the fundamental modules of the electricity markets. Typically, when a contingency occurs, it is required that security assessment and enhancement module shall be ready for action within about 20 minutes’ time to meet the real time requirement. The recent California black out again highlighted the importance of system security. This paper proposed an approach for power system security assessment and enhancement based on the information provided from the pre-defined system parameter space. The proposed scheme opens up an efficient way for real time security assessment and enhancement in a competitive electricity market for single contingency case

Modeling control objectives for business process compliance

Business process design is primarily driven by process improvement objectives. However, the role of control objectives stemming from regulations and standards is becoming increasingly important for businesses in light of recent events that led to some of the largest scandals in corporate history. As organizations strive to meet compliance agendas, there is an evident need to provide systematic approaches that assist in the understanding of the interplay between (often conflicting) business and control objectives during business process design. In this paper, our objective is twofold. We will firstly present a research agenda in the space of business process compliance, identifying major technical and organizational challenges. We then tackle a part of the overall problem space, which deals with the effective modeling of control objectives and subsequently their propagation onto business process models. Control objective modeling is proposed through a specialized modal logic based on normative systems theory, and the visualization of control objectives on business process models is achieved procedurally. The proposed approach is demonstrated in the context of a purchase-to-pay scenario.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].

Solute transport by surface runoff from low-angle slopes: theory and application

The removal of chemicals in solution by overland how from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface-mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff: to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright (C) 2000 John Wiley & Sons, Ltd.

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.

Mathematical constraints on a theory of human memory - Response

Colonius suggests that, in using standard set theory as the language in which to express our computational-level theory of human memory, we would need to violate the axiom of foundation in order to express meaningful memory bindings in which a context is identical to an item in the list. We circumvent Colonius's objection by allowing that a list item may serve as a label for a context without being identical to that context. This debate serves to highlight the value of specifying memory operations in set theoretic notation, as it would have been difficult if not impossible to formulate such an objection at the algorithmic level.

Children and economic development: Family size, gender preferences and human capital formation - theory and Indian cases

In the light of Gary Becker's economic theory of the family, considers how economic cost and benefit factors can influence the size of families that parents decide to have. Some support for the importance of such factors is found from results of structured interviews with wives in Kondh-dominated villages in western Orissa. These results are at variance with the hypothesis of Malthus about population growth. Factors that may alter the optimal family size as development proceeds are discussed. It is found in our sampling that, on the whole, there is a preference for daughters rather than sons although this is not as strong in the Kondh-dominated villages as in poor villages in the Santal tribal belt of West Bengal. While in the Kondh-dominated villages some discrimination in access to education in favour of boys compared to girls is present, little such or no such discrimination occurs in relation to access to food and medical attention. In the villages surveyed in the West Bengal Santal tribal belt, discrimination in favour of boys is more pronounced than in the Kondh-dominated area in Orissa. While economic considerations help to explain gender discrimination between boys and girls, we find that social and cultural factors also play a major role. Parents in a similar economic situation seem to display substantially different patterns of gender discrimination between children depending on their social and cultural content. It seems that the extent to which economic theories of the family explain family preferences and behaviour depend significantly on the social and cultural context in which they are to be applied.

Status, legitimacy and ingroup bias in the context of an organizational merger

Adopting an intergroup perspective, the research was designed to examine predictors of employee responses to an organizational merger. Data were collected from 120 employees of a newly merged scientific organization. As predicted from social identity theory, the most negative responses to the merger were apparent among the employees of the low status premerger organization. There was also evidence of ingroup bias among both groups of employees involved in the merger—as expected, the bias was most marked on the status-irrelevant dimensions for the employees of the lower status organization, but most marked on the status-relevant dimensions for the employees of the high status organization. Also, in support of social identity theory, the perceived legitimacy of the basis for the status differentiation between the groups was associated with more positive responses to the merger among employees of the low status premerger organization, but with poorer responses among employees of the high status premerger organization. There was consistent evidence that the status by legitimacy interaction was mediated through the extent to which employees of the newly merged organization perceived a common ingroup identity