Computational Methods for Reconstruction and Analysis of Genome-Scale Metabolic Networks

Metabolism is the cellular subsystem responsible for generation of energy from nutrients and production of building blocks for larger macromolecules. Computational and statistical modeling of metabolism is vital to many disciplines including bioengineering, the study of diseases, drug target identification, and understanding the evolution of metabolism. In this thesis, we propose efficient computational methods for metabolic modeling. The techniques presented are targeted particularly at the analysis of large metabolic models encompassing the whole metabolism of one or several organisms. We concentrate on three major themes of metabolic modeling: metabolic pathway analysis, metabolic reconstruction and the study of evolution of metabolism. In the first part of this thesis, we study metabolic pathway analysis. We propose a novel modeling framework called gapless modeling to study biochemically viable metabolic networks and pathways. In addition, we investigate the utilization of atom-level information on metabolism to improve the quality of pathway analyses. We describe efficient algorithms for discovering both gapless and atom-level metabolic pathways, and conduct experiments with large-scale metabolic networks. The presented gapless approach offers a compromise in terms of complexity and feasibility between the previous graph-theoretic and stoichiometric approaches to metabolic modeling. Gapless pathway analysis shows that microbial metabolic networks are not as robust to random damage as suggested by previous studies. Furthermore the amino acid biosynthesis pathways of the fungal species Trichoderma reesei discovered from atom-level data are shown to closely correspond to those of Saccharomyces cerevisiae. In the second part, we propose computational methods for metabolic reconstruction in the gapless modeling framework. We study the task of reconstructing a metabolic network that does not suffer from connectivity problems. Such problems often limit the usability of reconstructed models, and typically require a significant amount of manual postprocessing. We formulate gapless metabolic reconstruction as an optimization problem and propose an efficient divide-and-conquer strategy to solve it with real-world instances. We also describe computational techniques for solving problems stemming from ambiguities in metabolite naming. These techniques have been implemented in a web-based sofware ReMatch intended for reconstruction of models for 13C metabolic flux analysis. In the third part, we extend our scope from single to multiple metabolic networks and propose an algorithm for inferring gapless metabolic networks of ancestral species from phylogenetic data. Experimenting with 16 fungal species, we show that the method is able to generate results that are easily interpretable and that provide hypotheses about the evolution of metabolism.

Statistical and Information-Theoretic Methods for Data-Analysis

In this Thesis, we develop theory and methods for computational data analysis. The problems in data analysis are approached from three perspectives: statistical learning theory, the Bayesian framework, and the information-theoretic minimum description length (MDL) principle. Contributions in statistical learning theory address the possibility of generalization to unseen cases, and regression analysis with partially observed data with an application to mobile device positioning. In the second part of the Thesis, we discuss so called Bayesian network classifiers, and show that they are closely related to logistic regression models. In the final part, we apply the MDL principle to tracing the history of old manuscripts, and to noise reduction in digital signals.

Automated Discovery of Structured Process Models: Discover Structured vs. Discover and Structure

This paper addresses the problem of discovering business process models from event logs. Existing approaches to this problem strike various tradeoffs between accuracy and understandability of the discovered models. With respect to the second criterion, empirical studies have shown that block-structured process models are generally more understandable and less error-prone than unstructured ones. Accordingly, several automated process discovery methods generate block-structured models by construction. These approaches however intertwine the concern of producing accurate models with that of ensuring their structuredness, sometimes sacrificing the former to ensure the latter. In this paper we propose an alternative approach that separates these two concerns. Instead of directly discovering a structured process model, we first apply a well-known heuristic technique that discovers more accurate but sometimes unstructured (and even unsound) process models, and then transform the resulting model into a structured one. An experimental evaluation shows that our “discover and structure” approach outperforms traditional “discover structured” approaches with respect to a range of accuracy and complexity measures.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

Comparative study of different formulations and solution methods for two phase flow in saturated porous media

Six models (Simulators) are formulated and developed with all possible combinations of pressure and saturation of the phases as primary variables. A comparative study between six simulators with two numerical methods, conventional simultaneous and modified sequential methods are carried out. The results of the numerical models are compared with the laboratory experimental results to study the accuracy of the model especially in heterogeneous porous media. From the study it is observed that the simulator using pressure and saturation of the wetting fluid (PW, SW formulation) is the best among the models tested. Many simulators with nonwetting phase as one of the primary variables did not converge when used along with simultaneous method. Based on simulator 1 (PW, SW formulation), a comparison of different solution methods such as simultaneous method, modified sequential and adaptive solution modified sequential method are carried out on 4 test problems including heterogeneous and randomly heterogeneous problems. It is found that the modified sequential and adaptive solution modified sequential methods could save the memory by half and as also the CPU time required by these methods is very less when compared with that using simultaneous method. It is also found that the simulator with PNW and PW as the primary variable which had problem of convergence using the simultaneous method, converged using both the modified sequential method and also using adaptive solution modified sequential method. The present study indicates that pressure and saturation formulation along with adaptive solution modified sequential method is the best among the different simulators and methods tested.

Geometric integration applied to moving mesh methods and degenerate Lagrangians

Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation, but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this thesis we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. The proposed methods are readily applicable to (weakly) non-degenerate field theories---numerical results for the Sine-Gordon equation are presented.

In an attempt to extend our approach to degenerate field theories, in the last part of this thesis we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for variational integration. Our main observation is that the evolution takes place on the primary constraint and the 'Hamiltonian' equations of motion can be formulated as an index 1 differential-algebraic system. We then proceed to construct variational Runge-Kutta methods and analyze their properties. The general properties of Runge-Kutta methods depend on the 'velocity' part of the Lagrangian. If the 'velocity' part is also linear in the position coordinate, then we show that non-partitioned variational Runge-Kutta methods are equivalent to integration of the corresponding first-order Euler-Lagrange equations, which have the form of a Poisson system with a constant structure matrix, and the classical properties of the Runge-Kutta method are retained. If the 'velocity' part is nonlinear in the position coordinate, we observe a reduction of the order of convergence, which is typical of numerical integration of DAEs. We also apply our methods to several models and present the results of our numerical experiments.

Efficient methods for empirical tests of behavioral economics theories in laboratory and field experiments

In the quest for a descriptive theory of decision-making, the rational actor model in economics imposes rather unrealistic expectations and abilities on human decision makers. The further we move from idealized scenarios, such as perfectly competitive markets, and ambitiously extend the reach of the theory to describe everyday decision making situations, the less sense these assumptions make. Behavioural economics has instead proposed models based on assumptions that are more psychologically realistic, with the aim of gaining more precision and descriptive power. Increased psychological realism, however, comes at the cost of a greater number of parameters and model complexity. Now there are a plethora of models, based on different assumptions, applicable in differing contextual settings, and selecting the right model to use tends to be an ad-hoc process. In this thesis, we develop optimal experimental design methods and evaluate different behavioral theories against evidence from lab and field experiments.

We look at evidence from controlled laboratory experiments. Subjects are presented with choices between monetary gambles or lotteries. Different decision-making theories evaluate the choices differently and would make distinct predictions about the subjects' choices. Theories whose predictions are inconsistent with the actual choices can be systematically eliminated. Behavioural theories can have multiple parameters requiring complex experimental designs with a very large number of possible choice tests. This imposes computational and economic constraints on using classical experimental design methods. We develop a methodology of adaptive tests: Bayesian Rapid Optimal Adaptive Designs (BROAD) that sequentially chooses the "most informative" test at each stage, and based on the response updates its posterior beliefs over the theories, which informs the next most informative test to run. BROAD utilizes the Equivalent Class Edge Cutting (EC²) criteria to select tests. We prove that the EC² criteria is adaptively submodular, which allows us to prove theoretical guarantees against the Bayes-optimal testing sequence even in the presence of noisy responses. In simulated ground-truth experiments, we find that the EC² criteria recovers the true hypotheses with significantly fewer tests than more widely used criteria such as Information Gain and Generalized Binary Search. We show, theoretically as well as experimentally, that surprisingly these popular criteria can perform poorly in the presence of noise, or subject errors. Furthermore, we use the adaptive submodular property of EC² to implement an accelerated greedy version of BROAD which leads to orders of magnitude speedup over other methods.

We use BROAD to perform two experiments. First, we compare the main classes of theories for decision-making under risk, namely: expected value, prospect theory, constant relative risk aversion (CRRA) and moments models. Subjects are given an initial endowment, and sequentially presented choices between two lotteries, with the possibility of losses. The lotteries are selected using BROAD, and 57 subjects from Caltech and UCLA are incentivized by randomly realizing one of the lotteries chosen. Aggregate posterior probabilities over the theories show limited evidence in favour of CRRA and moments' models. Classifying the subjects into types showed that most subjects are described by prospect theory, followed by expected value. Adaptive experimental design raises the possibility that subjects could engage in strategic manipulation, i.e. subjects could mask their true preferences and choose differently in order to obtain more favourable tests in later rounds thereby increasing their payoffs. We pay close attention to this problem; strategic manipulation is ruled out since it is infeasible in practice, and also since we do not find any signatures of it in our data.

In the second experiment, we compare the main theories of time preference: exponential discounting, hyperbolic discounting, "present bias" models: quasi-hyperbolic (α, β) discounting and fixed cost discounting, and generalized-hyperbolic discounting. 40 subjects from UCLA were given choices between 2 options: a smaller but more immediate payoff versus a larger but later payoff. We found very limited evidence for present bias models and hyperbolic discounting, and most subjects were classified as generalized hyperbolic discounting types, followed by exponential discounting.

In these models the passage of time is linear. We instead consider a psychological model where the perception of time is subjective. We prove that when the biological (subjective) time is positively dependent, it gives rise to hyperbolic discounting and temporal choice inconsistency.

We also test the predictions of behavioral theories in the "wild". We pay attention to prospect theory, which emerged as the dominant theory in our lab experiments of risky choice. Loss aversion and reference dependence predicts that consumers will behave in a uniquely distinct way than the standard rational model predicts. Specifically, loss aversion predicts that when an item is being offered at a discount, the demand for it will be greater than that explained by its price elasticity. Even more importantly, when the item is no longer discounted, demand for its close substitute would increase excessively. We tested this prediction using a discrete choice model with loss-averse utility function on data from a large eCommerce retailer. Not only did we identify loss aversion, but we also found that the effect decreased with consumers' experience. We outline the policy implications that consumer loss aversion entails, and strategies for competitive pricing.

In future work, BROAD can be widely applicable for testing different behavioural models, e.g. in social preference and game theory, and in different contextual settings. Additional measurements beyond choice data, including biological measurements such as skin conductance, can be used to more rapidly eliminate hypothesis and speed up model comparison. Discrete choice models also provide a framework for testing behavioural models with field data, and encourage combined lab-field experiments.

Estimates of growth and comparisons of growth rates determined from length- and age-based models for populations of purple wrasse (Notolabrus fucicola)

Growth of a temperate reefa-ssociated fish, the purple wrasse (Notolabrus fucicola), was examined from two sites on the east coast of Tasmania by using age- and length-based models. Models based on the von Bertalanffy growth function, in the standard and a reparameterized form, were constructed by using otolith-derived age estimates. Growth trajectories from tag-recaptures were used to construct length-based growth models derived from the GROTAG model, in turn a reparameterization of the Fabens model. Likelihood ratio tests (LRTs) determined the optimal parameterization of the GROTAG model, including estimators of individual growth variability, seasonal growth, measurement error, and outliers for each data set. Growth models and parameter estimates were compared by bootstrap confidence intervals, LRTs, and randomization tests and plots of bootstrap parameter estimates. The relative merit of these methods for comparing models and parameters was evaluated; LRTs combined with bootstrapping and randomization tests provided the most insight into the relationships between parameter estimates. Significant differences in growth of purple wrasse were found between sites in both length- and age-based models. A significant difference in the peak growth season was found between sites, and a large difference in growth rate between sexes was found at one site with the use of length-based models.

A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example

We present a method to integrate environmental time series into stock assessment models and to test the significance of correlations between population processes and the environmental time series. Parameters that relate the environmental time series to population processes are included in the stock assessment model, and likelihood ratio tests are used to determine if the parameters improve the fit to the data significantly. Two approaches are considered to integrate the environmental relationship. In the environmental model, the population dynamics process (e.g. recruitment) is proportional to the environmental variable, whereas in the environmental model with process error it is proportional to the environmental variable, but the model allows an additional temporal variation (process error) constrained by a log-normal distribution. The methods are tested by using simulation analysis and compared to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. In the traditional method, the estimates of recruitment were provided by a model that allowed the recruitment only to have a temporal variation constrained by a log-normal distribution. We illustrate the methods by applying them to test the statistical significance of the correlation between sea-surface temperature (SST) and recruitment to the snapper (Pagrus auratus) stock in the Hauraki Gulf–Bay of Plenty, New Zealand. Simulation analyses indicated that the integrated approach with additional process error is superior to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. The results suggest that, for the snapper stock, recruitment is positively correlated with SST at the time of spawning.

Construction of habitat suitability models (HSMs) for benthic macroinvertebrate and their applications to instream environmental flows: A case study in Xiangxi River of Three Gorges Reservior region, China

Based on a long-term ecological monitoring, the present study chose the most dominant benthic macroinvertebrate (Baetis spp.) as target organisms in Xiangxi River, built the habitat suitability models (HSMs) for water depth, current velocity and substrate, respectively, which is the first aquatic organisms model for habitat suitability in the Chinese Mainland with a long-term consecutive in situ measurement. In order to protect the biointegrity and function of the river ecosystem, the theory system of instream environmental flow should be categorized into three hierarchies, namely minimum required instream flow (hydrological level), minimum instream environmental flow (biospecies level), and optimum instream environmental flow (ecosystem level). These three hierarchies of instream environmental flow models were then constructed with the hydrological and weighted usable area (WUA) method. The results show that the minimum required instream flow of Xiangxi River calculated by the Tennant method (10% of the mean annual flow) was 0.615 m(3) s(-1); the minimum instream environmental flow accounted for 19.22% of the mean annual flow (namely 1.182 m(3) s(-1)), which was the damaged river channel. ow in the dry season; and 42.91% of the mean annual flow (namely 2.639 m(3) s(-1)) should be viewed as the optimum instream environmental flow in order to protect the health of the river ecosystem, maintain the instream biodiversity, and reduce the impact of small hydropower stations nearby the Xiangxi River. We recommend that the hydrological and biological methods can help establish better instream environmental. ow models and design best management practices for use in the small hydropower station project. (C) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Instrumental and interpretive methods in evaluating urban programmes

The turn within urban policy to address increasingly complex social, economic and environmental problems has exposed some of the fragility of traditional measurement models and their reliance on the rational paradigm. This article looks at the experiences of the European Union (EU) Programme for Peace and Reconciliation in Northern Ireland and its particular attempt to construct new District Partnerships to deliver area-based regeneration programmes. It highlights the need to combine instrumental and interpretative evaluation methods in an attempt to explain the wider contribution of governance to conflict resolution and participatory practice in local development. It concludes by highlighting the value of conceptual approaches that deal with the politics of evaluation and the distributional effects of policy interventions designed to create new relationships within and between multiple stakeholders.

Time Efficient Assessment and Feedback Methods for Large Computer-Aided-Design Cohorts

Timely and individualized feedback on coursework is desirable from a student perspective as it facilitates formative development and encourages reflective learning practice. Faculty however are faced with a significant and potentially time consuming challenge when teaching larger cohorts if they are to provide feedback which is timely, individualized and detailed. Additionally, for subjects which assess non-traditional submissions, such as Computer-Aided-Design (CAD), the methods for assessment and feedback tend not to be so well developed or optimized. Issues can also arise over the consistency of the feedback provided. Evaluations of Computer-Assisted feedback in other disciplines (Denton et al, 2008), (Croft et al, 2001) have shown students prefer this method of feedback to traditional “red pen” marking and also that such methods can be more time efficient for faculty.
Herein, approaches are described which make use of technology and additional software tools to speed up, simplify and automate assessment and the provision of feedback for large cohorts of first and second year engineering students studying modules where CAD files are submitted electronically. A range of automated methods are described and compared with more “manual” approaches. Specifically one method uses an application programming interface (API) to interrogate SolidWorks models and extract information into an Excel spreadsheet, which is then used to automatically send feedback emails. Another method describes the use of audio recordings made during model interrogation which reduces the amount of time while increasing the level of detail provided as feedback.
Limitations found with these methods and problems encountered are discussed along with a quantified assessment of time saving efficiencies made.

Optimal control and numerical optimization applied to epidemiological models

A relação entre a epidemiologia, a modelação matemática e as ferramentas computacionais permite construir e testar teorias sobre o desenvolvimento e combate de uma doença. Esta tese tem como motivação o estudo de modelos epidemiológicos aplicados a doenças infeciosas numa perspetiva de Controlo Ótimo, dando particular relevância ao Dengue. Sendo uma doença tropical e subtropical transmitida por mosquitos, afecta cerca de 100 milhões de pessoas por ano, e é considerada pela Organização Mundial de Saúde como uma grande preocupação para a saúde pública. Os modelos matemáticos desenvolvidos e testados neste trabalho, baseiam-se em equações diferenciais ordinárias que descrevem a dinâmica subjacente à doença nomeadamente a interação entre humanos e mosquitos. É feito um estudo analítico dos mesmos relativamente aos pontos de equilíbrio, sua estabilidade e número básico de reprodução. A propagação do Dengue pode ser atenuada através de medidas de controlo do vetor transmissor, tais como o uso de inseticidas específicos e campanhas educacionais. Como o desenvolvimento de uma potencial vacina tem sido uma aposta mundial recente, são propostos modelos baseados na simulação de um hipotético processo de vacinação numa população. Tendo por base a teoria de Controlo Ótimo, são analisadas as estratégias ótimas para o uso destes controlos e respetivas repercussões na redução/erradicação da doença aquando de um surto na população, considerando uma abordagem bioeconómica. Os problemas formulados são resolvidos numericamente usando métodos diretos e indiretos. Os primeiros discretizam o problema reformulando-o num problema de optimização não linear. Os métodos indiretos usam o Princípio do Máximo de Pontryagin como condição necessária para encontrar a curva ótima para o respetivo controlo. Nestas duas estratégias utilizam-se vários pacotes de software numérico. Ao longo deste trabalho, houve sempre um compromisso entre o realismo dos modelos epidemiológicos e a sua tratabilidade em termos matemáticos.

School funding and education policy-making models in Ontario /

The purpose of this thesis is to examine various policy implementation models, and to determine what use they are to a government. In order to insure that governmental proposals are created and exercised in an effective manner, there roust be some guidelines in place which will assist in resolving difficult situations. All governments face the challenge of responding to public demand, by delivering the type of policy responses that will attempt to answer those demands. The problem for those people in positions of policy-making responsibility is to balance the competitive forces that would influence policy. This thesis examines provincial government policy in two unique cases. The first is the revolutionary recommendations brought forth in the Hall -Dennis Report. The second is the question of extending full -funding to the end of high school in the separate school system. These two cases illustrate how divergent and problematic the policy-making duties of any government may be. In order to respond to these political challenges decision-makers must have a clear understanding of what they are attempting to do. They must also have an assortment of policy-making models that will insure a policy response effectively deals with the issue under examination. A government must make every effort to insure that all policymaking methods are considered, and that the data gathered is inserted into the most appropriate model. Currently, there is considerable debate over the benefits of the progressive individualistic education approach as proposed by the Hall -Dennis Committee. This debate is usually intensified during periods of economic uncertainty. Periodically, the province will also experience brief yet equally intense debate on the question of separate school funding. At one level, this debate centres around the efficiency of maintaining two parallel education systems, but the debate frequently has undertones of the religious animosity common in Ontario's history. As a result of the two policy cases under study we may ask ourselves these questions: a) did the policies in question improve the general quality of life in the province? and b) did the policies unite the province? In the cases of educational instruction and finance the debate is ongoing and unsettling. Currently, there is a widespread belief that provincial students at the elementary and secondary levels of education are not being educated adequately to meet the challenges of the twenty-first century. The perceived culprit is individual education which sees students progressing through the system at their own pace and not meeting adequate education standards. The question of the finance of Catholic education occasionally rears its head in a painful fashion within the province. Some public school supporters tend to take extension as a personal religious defeat, rather than an opportunity to demonstrate that educational diversity can be accommodated within Canada's most populated province. This thesis is an attempt to analyze how successful provincial policy-implementation models were in answering public demand. A majority of the public did not demand additional separate school funding, yet it was put into place. The same majority did insist on an examination of educational methods, and the government did put changes in place. It will also demonstrate how policy if wisely created may spread additional benefits to the public at large. Catholic students currently enjoy a much improved financial contribution from the province, yet these additional funds were taken from somewhere. The public system had it funds reduced with what would appear to be minimal impact. This impact indicates that government policy is still sensitive to the strongly held convictions of those people in opposition to a given policy.