Time complexity analysis of the stochastic diffusion search

The Stochastic Diffusion Search algorithm -an integral part of Stochastic Search Networks is investigated. Stochastic Diffusion Search is an alternative solution for invariant pattern recognition and focus of attention. It has been shown that the algorithm can be modelled as an ergodic, finite state Markov Chain under some non-restrictive assumptions. Sub-linear time complexity for some settings of parameters has been formulated and proved. Some properties of the algorithm are then characterised and numerical examples illustrating some features of the algorithm are presented.

Ideological dominance in recreation provision: towards a theory of Local Authority response to Compulsory Competitive Tendering in Britain

This paper considers how the delivery of public leisure services in Britain has been affected by the imposition of Compulsory Competitive Tendering (CCT) on the management of facilities. In particular, it focuses on the changing relationship between the central and local levels of government, theorising a tripartite local response to CCT, incorporating local statism, post-Fordist rejection of CCT and post- Fordist compliance with the aims of the central administration. The paper then discusses the actual implementation of CCT, relating the theorised responses to those witnessed in practice. This results in the delineation of a continuum of stances, ranging from pragmatic forms of local statism, such as the protection of the former direct labour force, to centrist attempts to combine the ethics of socialism with the mechanics of the market, to an outright rejection of state organisation and control. The paper concludes that although legitimate attempts have been made to protect local services, the outcome of the CCT process has undoubtedly been the regeneration of public leisure provision away from its service roots towards a market model of provision.

Public leisure provision under Compulsory Competitive Tendering: the maintenance of ideological dominance?

Although much has been written about the effect on services of public sector restructuring, little is yet available on public leisure provision. This omission is addressed by considering how the delivery of public leisure services in Britain has been affected by the imposition of Compulsory Competitive Tendering (CCT). In particular, it focuses on the changing relationship between the central and local levels of government recognising, on the part of local government, a continuum of structural responses to central initiatives which have, in some cases, conspired to reduce the impact of CCT on public leisure provision. The paper concludes that although attempts have been made to protect local services, the outcome of the CCT process has been the regeneration of public leisure provision away from its service roots, but within an enduring ideological paradigm of conservative professionalism.

Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

Equidistributing Meshes with Constraints

Adaptive methods which “equidistribute” a given positive weight function are now used fairly widely for selecting discrete meshes. The disadvantage of such schemes is that the resulting mesh may not be smoothly varying. In this paper a technique is developed for equidistributing a function subject to constraints on the ratios of adjacent steps in the mesh. Given a weight function $f \geqq 0$ on an interval $[a,b]$ and constants $c$ and $K$, the method produces a mesh with points $x_0 = a,x_{j + 1} = x_j + h_j ,j = 0,1, \cdots ,n - 1$ and $x_n = b$ such that\[ \int_{xj}^{x_{j + 1} } {f \leqq c\quad {\text{and}}\quad \frac{1} {K}} \leqq \frac{{h_{j + 1} }} {{h_j }} \leqq K\quad {\text{for}}\, j = 0,1, \cdots ,n - 1 . \] A theoretical analysis of the procedure is presented, and numerical algorithms for implementing the method are given. Examples show that the procedure is effective in practice. Other types of constraints on equidistributing meshes are also discussed. The principal application of the procedure is to the solution of boundary value problems, where the weight function is generally some error indicator, and accuracy and convergence properties may depend on the smoothness of the mesh. Other practical applications include the regrading of statistical data.

Temporal constraints on linear BRDF model parameters

Linear models of bidirectional reflectance distribution are useful tools for understanding the angular variability of surface reflectance as observed by medium-resolution sensors such as the Moderate Resolution Imaging Spectrometer. These models are operationally used to normalize data to common view and illumination geometries and to calculate integral quantities such as albedo. Currently, to compensate for noise in observed reflectance, these models are inverted against data collected during some temporal window for which the model parameters are assumed to be constant. Despite this, the retrieved parameters are often noisy for regions where sufficient observations are not available. This paper demonstrates the use of Lagrangian multipliers to allow arbitrarily large windows and, at the same time, produce individual parameter sets for each day even for regions where only sparse observations are available.

On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

On a stochastic Trotter formula with application to spontaneous localization models

We consider the relation between so called continuous localization models—i.e. non-linear stochastic Schrödinger evolutions—and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.

Structure, conduct and the stochastic volatility of food markets: theory and empirics

The relationship between price volatility and competition is examined. Atheoretic, vector auto regressions on farm prices of wheat and retail prices of derivatives (flour, bread, pasta, bulgur and cookies) are compared to results from a dynamic, simultaneous-equations model with theory-based farm-to-retail linkages. Analytical results yield insights about numbers of firms and their impacts on demand- and supply-side multipliers, but the applications to Turkish time series (1988:1-1996:12) yield mixed results.

A normative method to analyse workarounds in a healthcare environment: motivations, consequences, and constraints

Healthcare information systems have the potential to enhance productivity, lower costs, and reduce medication errors by automating business processes. However, various issues such as system complexity and system abilities in a relation to user requirements as well as rapid changes in business needs have an impact on the use of these systems. In many cases failure of a system to meet business process needs has pushed users to develop alternative work processes (workarounds) to fill this gap. Some research has been undertaken on why users are motivated to perform and create workarounds. However, very little research has assessed the consequences on patient safety. Moreover, the impact of performing these workarounds on the organisation and how to quantify risks and benefits is not well analysed. Generally, there is a lack of rigorous understanding and qualitative and quantitative studies on healthcare IS workarounds and their outcomes. This project applies A Normative Approach for Modelling Workarounds to develop A Model of Motivation, Constraints, and Consequences. It aims to understand the phenomenon in-depth and provide guidelines to organisations on how to deal with workarounds. Finally the method is demonstrated on a case study example and its relative merits discussed.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.