While the bulk of topography on Earth is generated and maintained by variations in the thickness and density of crust and lithosphere, a significant time-variable contribution is expected as a result of convective flow in the underlying mantle. For over three decades, this dynamic topography has been calculated numerically from inferred density structure and radial viscosity profiles. Resulting models predict ±2 km of long wavelength (i.e., ~ 20,000 km) dynamic topography with minor contributions at wavelengths shorter than ~ 5,000 km. Recently, observational studies have revealed that, at the longest wavelengths, dynamic topography variation is ~ 30% that predicted, with ±1 km amplitudes recovered at shorter wavelengths. Here, the existing database of water-loaded basement depths is streamlined, revised and augmented. By fitting increasingly sophisticated thermal models to a combined database of these oceanic basement depths and corrected heat flow measurements, the average thermal structure of oceanic lithosphere is constrained. Significantly, optimal models are consistent with invariable geochemical and seismological constraints whilst yielding similar values of mantle potential temperature and plate thickness, irrespective of whether heat flow, subsidence or both are fit. After recalculating residual depth anomalies relative to optimal age-depth subsidence and combining them with continental constraints from gravity anomalies, a global spherical harmonic representation is generated. Although, long wavelength dynamic topography increases by ~ 40% in the revised observation-based model, spectral analysis confirms that a fundamental discrepancy between observations and predictions remains. Significantly, residual depth anomalies reveal a ~4,000 km-scale eastward tilt across the Indian Peninsula. This asymmetry extends onshore from the high-elevation Western Ghats in the west to the Krishna-Godavari floodplains in the east. Calibrated inverse modelling of drainage networks suggest that the tilt of the peninsula grew principally in Neogene times with vertical motions linked to asthenospheric temperature anomalies. Uplift rates of up to 0.1 mm a⁻¹ place important constraints on the spatio-temporal evolution of dynamic topography and suggest that rates of transient vertical motion exceed those predicted by many modelling studies. Most numerical models excise the upper ~ 300 km of Earth's mantle and are unable to reconstruct the wavelength and rate of uplift observed across Peninsular India. By contrast, through conversion of upper mantle shear wave velocities to density using a calibrated anelastic parameterisation, it is shown that shorter wavelength (i.e., ≤ 5,000 km) dynamic topography, can mostly be explained by ±150°C asthenospheric temperature anomalies. Inclusion of anelastically corrected density structure in whole-mantle instantaneous flow models also serves to reduce discrepancy between predictions and observations of dynamic topography at long wavelengths. Residual mismatch between observations and predictions is further improved if the basal 300-600 km of large low shear wave velocity regions in the deep mantle are geochemically distinct and negatively buoyant. Finally, inverse modelling of geoid, dynamic topography, gravity and core-mantle boundary topography observations using adapted density structure suggests that geodynamic constraints can be acceptably fit using plausible radial viscosity profiles, contradicting a long-standing assertion that modest long wavelength dynamic topography is incompatible with geoid observations.

<p>This thesis consists of three papers in dynamic political economy:</p><p>"Ideology and the Determination of Public Policy Over Time" investigates how public policy responds to persistent ideological shocks in dynamic politico-economic equilibrium. We develop a tractable model to analyse the dynamic interactions among ideology, public policy and individuals' intertemporal choice. Analytical solutions are obtained to characterize the Markov perfect equilibrium. Our main finding is that the relationship between ideology and the size of government turns out to be non-monotonic. In particular, a right-leaning ideological wave may lead to higher taxation, which makes the size of government much less distinctive under different political regimes. Incorporating ideological uncertainty per se has its theoretical relevance. Sufficient ideological uncertainty helps pin down a unique equilibrium. This is in contrast with recent works on dynamic political economy which feature multiple equilibria and have no sharp empirical predictions.</p><p>"Dynamic Inequality and Social Security" analyses the dynamic politico-economic equilibrium of a model where the repeated voting on social security and the evolution of household characteristics are mutually affected over time. Political decision-making is represented by probabilistic voting a la Lindbeck and Weibull (1987). We analytically characterize the unique Markov perfect equilibrium. The equilibrium social security tax rate are shown to be increasing in wealth inequality. The dynamic interaction between inequality and social security leads to growing social security programmes. The predictions of our model are broadly consistent with empirical evidence. We also perform some normative analysis, showing that the politico-economic mechanism tends to induce too large social security transfers in the long run.</p><p>"A Markovian Social Contract of Social Security" analyses the sustainability and evolution of the pay-as-you-go social security system in a majority voting framework with intra-cohort heterogeneity. We find that there exists a Markovian social contract through which the self-interested middle-aged median voter has incentives to support the system. This is in contrast with the approaches in the existing literature, which either resorts to the imperfect temporal separation of contributions and benefits, or builds the expectation of future social security benefits on variables that are payoff-irrelevant for future policymakers. Correspondingly, our model has a number of distinctive empirical implications. First, the social security tax rate converges along an increasing path to the steady state. Second, the growth of social security is negatively correlated with income inequality. Third, the impact of income inequality on the equilibrium social contract induces a non-monotonic relationship between income inequality and social security. These predictions are broadly consistent with the data from the OECD countries.</p>

To date, group scheduling research has primarily focused on examining the performance of different group heuristics under various experimental conditions. However, the dynamic selection of group heuristics has not received sufficient attention from researchers. The objective of this paper is to demonstrate a mechanism for the dynamic selection of group heuristics from several candidate alternatives by exploiting real time information from the Flexible Manufacturing System (FMS). In this regard, two tools, viz., Analytic Hierarchy Process (AHP) and Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER), are used to develop models for part type and family selection. The experimental results indicate that the performance of the proposed models are better than the common group scheduling heuristics under varied experimental conditions. / Singapore-MIT Alliance (SMA)

We provide two different neighborhood construction techniques for creating exponentially large neighborhoods that are searchable in polynomial time using dynamic programming. We illustrate both of these approaches on very large scale neighborhood search techniques for the traveling salesman problem. Our approaches are intended both to unify previously known results as well as to offer schemas for generating additional exponential neighborhoods that are searchable in polynomial time. The first approach is to define the neighborhood recursively. In this approach, the dynamic programming recursion is a natural consequence of the recursion that defines the neighborhood. In particular, we show how to create the pyramidal tour neighborhood, the twisted sequences neighborhood, and dynasearch neighborhoods using this approach. In the second approach, we consider the standard dynamic program to solve the TSP. We then obtain exponentially large neighborhoods by selecting a polynomially bounded number of states, and restricting the dynamic program to those states only. We show how the Balas and Simonetti neighborhood and the insertion dynasearch neighborhood can be viewed in this manner. We also show that one of the dynasearch neighborhoods can be derived directly from the 2-exchange neighborhood using this approach.

Thesis (Ph. D.)--Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1984. / Bibliography: p. 325-328.

This thesis consists of three papers in dynamic political economy: "Ideology and the Determination of Public Policy Over Time" investigates how public policy responds to persistent ideological shocks in dynamic politico-economic equilibrium. We develop a tractable model to analyse the dynamic interactions among ideology, public policy and individuals' intertemporal choice. Analytical solutions are obtained to characterize the Markov perfect equilibrium. Our main finding is that the relationship between ideology and the size of government turns out to be non-monotonic. In particular, a right-leaning ideological wave may lead to higher taxation, which makes the size of government much less distinctive under different political regimes. Incorporating ideological uncertainty per se has its theoretical relevance. Sufficient ideological uncertainty helps pin down a unique equilibrium. This is in contrast with recent works on dynamic political economy which feature multiple equilibria and have no sharp empirical predictions. "Dynamic Inequality and Social Security" analyses the dynamic politico-economic equilibrium of a model where the repeated voting on social security and the evolution of household characteristics are mutually affected over time. Political decision-making is represented by probabilistic voting a la Lindbeck and Weibull (1987). We analytically characterize the unique Markov perfect equilibrium. The equilibrium social security tax rate are shown to be increasing in wealth inequality. The dynamic interaction between inequality and social security leads to growing social security programmes. The predictions of our model are broadly consistent with empirical evidence. We also perform some normative analysis, showing that the politico-economic mechanism tends to induce too large social security transfers in the long run. "A Markovian Social Contract of Social Security" analyses the sustainability and evolution of the pay-as-you-go social security system in a majority voting framework with intra-cohort heterogeneity. We find that there exists a Markovian social contract through which the self-interested middle-aged median voter has incentives to support the system. This is in contrast with the approaches in the existing literature, which either resorts to the imperfect temporal separation of contributions and benefits, or builds the expectation of future social security benefits on variables that are payoff-irrelevant for future policymakers. Correspondingly, our model has a number of distinctive empirical implications. First, the social security tax rate converges along an increasing path to the steady state. Second, the growth of social security is negatively correlated with income inequality. Third, the impact of income inequality on the equilibrium social contract induces a non-monotonic relationship between income inequality and social security. These predictions are broadly consistent with the data from the OECD countries.

In this thesis we investigate important issues in the area of dynamic pricing for revenue management. Studying the effect of competition and strategic consumer behavior, we characterize the dynamic pricing policies for retailers who sell homogeneous goods in multi-period, discrete time, finite horizon settings. In the first essay an impatient consumer visits only one of two competing retailers in each period. If he does not purchase the good, he visits the competing retailer in the ensuing period. Compared to the corresponding single store monopoly, when the consumer’s valuation is uniformly distributed, prices decline exponentially rather than linearly, with a dramatically lower initial price, and a substantially lower system profit. The model is extended to accommodate many consumers, who may be either identical or similar, a more general valuation distribution, and situations wherein capacities are limited. The base case of a centralized two-store monopoly is also examined. In the second essay the consumer may return to the same retailer with some certain probability. This probability is either affected by market structure characteristics, or it may depend on the consumer’s experience at the last store visited. The robustness of the exponential decline of prices is reinforced. It occurs even when a strong retailer faces competition from a relatively much weaker retailer. We investigate the impact of the return probabilities on prices, profits, and consumer surplus. The model is extended to an oligopoly, and to situations with many similar consumers. The effect of strategic consumer behavior on prices and profits is revealed in the third essay. Characterizing the pricing policies arising in a two-period monopoly and duopoly settings, we find that strategic consumer behavior inflicts larger losses to a duopoly than to a monopoly. A lower strategic consumers’ discounting factor, which is beneficial to a monopoly, may be harmful to a duopoly. Ignoring strategic consumer behaviour is costly to a monopoly, but may, on the other hand, be beneficial to a duopoly. An extension to three periods is studied, and with longer horizons the model is analyzed for the case when all the consumers are strategic.

Measuring human behavioral patterns has broad application across different sciences. An individuals social, proximal and geographical contact patterns can have significant importance in Delay Tolerant Networking (DTN) and epidemiological modeling. Recent advances in computer science have not only provided the opportunity to record these behaviors with considerably higher temporal resolution and phenomenological accuracy, but also made it possible to record specific aspects of the behaviors which have been previously difficult to measure.<p> This thesis presents a data collection system using tiny sensors which is capable of recording humans proximal contacts and their visiting pattern to a set of geographical locations. The system also collects information on participants health status using weekly surveys. The system is tested on a population of 36 participants and 11 high-traffic public places. The resulting dataset offers rich information on human proximal and geographic contact patterns cross-linked with their health information.<p> In addition to the basic analysis of the dataset, the collected data is applied to two different applications. In DTNs the dataset is used to study the importance of public places as relay nodes, and described an algorithm that takes advantage of stationary nodes to improve routing performance and load balancing in the network. In epidemiological modeling, the collected dataset is combined with data on H1N1 infection spread over the same time period and designed a model on H1N1 pathogen transmission based on these data. Using the collected high-resolution contact data as the models contact patterns, this work represents the importance of contact density in addition to contact diversity in infection transmission rate. It also shows that the network measurements which are tied to contact duration are more representative of the relation between centrality of a person and their chance of contracting the infection.

<p>Neural networks are mathematical formulations that can be "trained" to perform certain functions. One particular application of these networks of interest in this thesis is to "model" a physical system using only input-output information. The physical system and the neural network are subjected to the same inputs. The neural network is then trained to produce an output which is the same as the physical system for any input. This neural network model so created is essentially a "blackbox" representation of the physical system. This approach has been used at the University of Saskatchewan to model a load sensing pump (a component which is used to create a constant flow rate independent of variations in pressure downstream of the pump). These studies have shown the versatility of neural networks for modeling dynamic and non-linear systems; however, these studies also indicated challenges associated with the morphology of neural networks and the algorithms to train them. These challenges were the motivation for this particular research.</p> <p>Within the Fluid Power Research group at the University of Saskatchewan, a "global" objective of research in the area of load sensing pumps has been to apply dynamic neural networks (DNN) in the modeling of loads sensing systems.. To fulfill the global objective, recurrent generalized neural network (RGNN) morphology along with a non-gradient based training approach called the complex algorithm (CA) were chosen to train a load sensing pump neural network model. However, preliminary studies indicated that the combination of recurrent generalized neural networks and complex training proved ineffective for even second order single-input single-output (SISO) systems when the initial synaptic weights of the neural network were chosen at random.</p> <p>Because of initial findings the focus of this research and its objectives shifted towards understanding the capabilities and limitations of recurrent generalized neural networks and non-gradient training (specifically the complex algorithm). To do so a second-order transfer function was considered from which an approximate recurrent generalized neural network representation was obtained. The network was tested under a variety of initial weight intervals and the number of weights being optimized. A definite trend was noted in that as the initial values of the synaptic weights were set closer to the "exact" values calculated for the system, the robustness of the network and the chance of finding an acceptable solution increased. Two types of training signals were used in the study; step response and frequency based training. It was found that when step response and frequency based training were compared, step response training was shown to produce a more generalized network.</p> <p>Another objective of this study was to compare the use of the CA to a proven non-gradient training method; the method chosen was genetic algorithm (GA) training. For the purposes of the studies conducted two modifications were done to the GA found in the literature. The most significant change was the assurance that the error would never increase during the training of RGNNs using the GA. This led to a collapse of the population around a specific point and limited its ability to obtain an accurate RGNN.</p> <p>The results of the research performed produced four conclusions. First, the robustness of training RGNNs using the CA is dependent upon the initial population of weights. Second, when using GAs a specific algorithm must be chosen which will allow the calculation of new population weights to move freely but at the same time ensure a stable output from the RGNN. Third, when the GA used was compared to the CA, the CA produced more generalized RGNNs. And the fourth is based upon the results of training RGNNs using the CA and GA when step response and frequency based training data sets were used, networks trained using step response are more generalized in the majority of cases.</p>

The bounded Fatou components for certain quadratic polynomials are attached to each other at the boundary and form chain-like structures called ``bubble rays". In the context of mating quadratic polynomials, these bubble rays can serve as a replacement for external rays. The main objective of this thesis is to apply this idea to the mating of starlike quadratics.