Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

A diagnostic framework for demand amplification problems in supply chains

This dissertation delivers a framework to diagnose the Bull-Whip Effect (BWE) in supply chains and then identify methods to minimize it. Such a framework is needed because in spite of the significant amount of literature discussing the bull-whip effect, many companies continue to experience the wide variations in demand that are indicative of the bull-whip effect. While the theory and knowledge of the bull-whip effect is well established, there still is the lack of an engineering framework and method to systematically identify the problem, diagnose its causes, and identify remedies. ^ The present work seeks to fill this gap by providing a holistic, systems perspective to bull-whip identification and diagnosis. The framework employs the SCOR reference model to examine the supply chain processes with a baseline measure of demand amplification. Then, research of the supply chain structural and behavioral features is conducted by means of the system dynamics modeling method. ^ The contribution of the diagnostic framework, is called Demand Amplification Protocol (DAMP), relies not only on the improvement of existent methods but also contributes with original developments introduced to accomplish successful diagnosis. DAMP contributes a comprehensive methodology that captures the dynamic complexities of supply chain processes. The method also contributes a BWE measurement method that is suitable for actual supply chains because of its low data requirements, and introduces a BWE scorecard for relating established causes to a central BWE metric. In addition, the dissertation makes a methodological contribution to the analysis of system dynamic models with a technique for statistical screening called SS-Opt, which determines the inputs with the greatest impact on the bull-whip effect by means of perturbation analysis and subsequent multivariate optimization. The dissertation describes the implementation of the DAMP framework in an actual case study that exposes the approach, analysis, results and conclusions. The case study suggests a balanced solution between costs and demand amplification can better serve both firms and supply chain interests. Insights pinpoint to supplier network redesign, postponement in manufacturing operations and collaborative forecasting agreements with main distributors.^

An integrated multi-agent framework for optimizing time, cost and environmental impact of construction processes

Environmentally conscious construction has received a significant amount of research attention during the last decades. Even though construction literature is rich in studies that emphasize the importance of environmental impact during the construction phase, most of the previous studies failed to combine environmental analysis with other project performance criteria in construction. This is mainly because most of the studies have overlooked the multi-objective nature of construction projects. In order to achieve environmentally conscious construction, multi-objectives and their relationships need to be successfully analyzed in the complex construction environment. The complex construction system is composed of changing project conditions that have an impact on the relationship between time, cost and environmental impact (TCEI) of construction operations. Yet, this impact is still unknown by construction professionals. Studying this impact is vital to fulfill multiple project objectives and achieve environmentally conscious construction. This research proposes an analytical framework to analyze the impact of changing project conditions on the relationship of TCEI. This study includes green house gas (GHG) emissions as an environmental impact category. The methodology utilizes multi-agent systems, multi-objective optimization, analytical network process, and system dynamics tools to study the relationships of TCEI and support decision-making under the influence of project conditions. Life cycle assessment (LCA) is applied to the evaluation of environmental impact in terms of GHG. The mixed method approach allowed for the collection and analysis of qualitative and quantitative data. Structured interviews of professionals in the highway construction field were conducted to gain their perspectives in decision-making under the influence of certain project conditions, while the quantitative data were collected from the Florida Department of Transportation (FDOT) for highway resurfacing projects. The data collected were used to test the framework. The framework yielded statistically significant results in simulating project conditions and optimizing TCEI. The results showed that the change in project conditions had a significant impact on the TCEI optimal solutions. The correlation between TCEI suggested that they affected each other positively, but in different strengths. The findings of the study will assist contractors to visualize the impact of their decision on the relationship of TCEI.

Essays on city size distribution and real estate bubbles

This is a dissertation about urban systems; within this broad subject I tackle three issues, one that focuses on an observed inter-city relationship and two that focus on an intra-city phenomenon. In Chapter II I adapt a model of random emergence of economic opportunities from the firm growth literature to the urban dynamics situation and present several predictions for urban system dynamics. One of these predictions is that the older the city the larger and more diversified it is going to be on average, which I proceed to verify empirically using two distinct datasets. In Chapter III I analyze the Residential Real Estate Bubble that took place in Miami-Dade County from 1999 to 2006. I adopt a Spatial-Economic model developed for the Paris Bubble episode of 1984–1993 and formulate an innovative test of the results in terms of speculative intensity on the basis of proxies of investor activity available in my dataset. My results support the idea that the best or more expensive areas are also where the greatest speculative activity takes place and where the rapid increase in prices begins. The most significant departure from previous studies that emerges in my results is the absence of a wider gap between high priced areas and low priced areas in the peak year. I develop a measure of dispersion in value among areas and contrast the Miami-Dade and Paris episodes. In Chapter IV I analyze the impact on tax equity of a Florida tax-limiting legislation known as Save Our Homes. I first compare homesteaded and non-homesteaded properties, and second, look within the subset of homesteaded properties. I find that non-homesteaded properties increase their share of taxes paid relative to homesteaded properties during an up market, but that this is reversed during a down market. For the subset of homesteaded properties I find that the impact on tax equity of SOH will depend on differential growth rates among higher and lower valued homes, but during times of rapid home price appreciation, in a scenario of no differential growth rates in property values, SOH increases progressivity relative to the prior system.

Frameworks for Systemic and Structural Analysis of Financial Innovations in Infrastructure

Financial innovations have emerged globally to close the gap between the rising global demand for infrastructures and the availability of financing sources offered by traditional financing mechanisms such as fuel taxation, tax-exempt bonds, and federal and state funds. The key to sustainable innovative financing mechanisms is effective policymaking. This paper discusses the theoretical framework of a research study whose objective is to structurally and systemically assess financial innovations in global infrastructures. The research aims to create analysis frameworks, taxonomies and constructs, and simulation models pertaining to the dynamics of the innovation process to be used in policy analysis. Structural assessment of innovative financing focuses on the typologies and loci of innovations and evaluates the performance of different types of innovative financing mechanisms. Systemic analysis of innovative financing explores the determinants of the innovation process using the System of Innovation approach. The final deliverables of the research include propositions pertaining to the constituents of System of Innovation for infrastructure finance which include the players, institutions, activities, and networks. These static constructs are used to develop a hybrid Agent-Based/System Dynamics simulation model to derive propositions regarding the emergent dynamics of the system. The initial outcomes of the research study are presented in this paper and include: (a) an archetype for mapping innovative financing mechanisms, (b) a System of Systems-based analysis framework to identify the dimensions of Systems of Innovation analyses, and (c) initial observations regarding the players, institutions, activities, and networks of the System of Innovation in the context of the U.S. transportation infrastructure financing.

Freshwater Resource Supply Modeling for Developed and Undeveloped Watersheds

Globally, the current state of freshwater resource management is insufficient and impeding the chance at a sustainable future. Human interference within the natural hydrologic cycle is becoming dangerously irreversible and the need to redefine resource managerial approaches is imminent. This research involves the development of a coupled natural-human freshwater resource supply model using a System Dynamics approach. The model was applied to two case studies, Somalia, Africa and the Phoenix Active Management Area in Arizona, USA. It is suggested that System Dynamic modeling would be an invaluable tool for achieving sustainable freshwater resource management in individual watersheds. Through a series of thought experiments, a thorough understanding of the systems’ dynamic behaviors is obtainable for freshwater resource managers and policy-makers to examine various courses of action for alleviating freshwater supply concerns. This thesis reviews the model, its development and an analysis of several thought experiments applied to the case studies.

Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Hydrological dynamics between a coastal aquifer and the adjacent estuarine system, Biscayne Bay, South Florida

Geochemical and geophysical approaches have been used to investigate the freshwater and saltwater dynamics in the coastal Biscayne Aquifer and Biscayne Bay. Stable isotopes of oxygen and hydrogen, and concentrations of Sr2+ and Ca2+ were combined in two geochemical mixing models to provide estimates of the various freshwater inputs (precipitation, canal water, and groundwater) to Biscayne Bay and the coastal canal system in South Florida. Shallow geophysical electromagnetic and direct current resistivity surveys were used to image the geometry and stratification of the saltwater mixing zone in the near coastal (less than 1km inland) Biscayne Aquifer. The combined stable isotope and trace metal models suggest a ratio of canal input-precipitation-groundwater of 38%–52%–10% in the wet season and 37%–58%–5% in the dry season with an error of 25%, where most (20%) of the error was attributed to the isotope regression model, while the remaining 5% error was attributed to the Sr2+/Ca2+ mixing model. These models suggest rainfall is the dominate source of freshwater to Biscayne Bay. For a bay-wide water budget that includes saltwater and freshwater mixing, fresh groundwater accounts for less than 2% of the total input. A similar Sr 2+/Ca2+ tracer model indicates precipitation is the dominate source in 9 out of 10 canals that discharge into Biscayne Bay. The two-component mixing model converged for 100% of the freshwater canal samples in this study with 63% of the water contributed to the canals coming from precipitation and 37% from groundwater inputs ±4%. There was a seasonal shift from 63% precipitation input in the dry season to 55% precipitation input in the wet season. The three end-member mixing model converged for only 60% of the saline canal samples possibly due to non-conservative behavior of Sr2+ and Ca2+ in saline groundwater discharging into the canal system. Electromagnetic and Direct Current resistivity surveys were successful at locating and estimating the geometry and depth of the freshwater/saltwater interface in the Biscayne Aquifer at two near coastal sites. A saltwater interface that deepened as the survey moved inland was detected with a maximum interpreted depth to the interface of 15 meters, approximately 0.33 km inland from the shoreline. ^

Diel Patterns of Patch Reef Community Dynamics in a Caribbean Back-Reef System

Back-reef seascapes represent critical habitat for juvenile and adult fishes. Patch reef, seagrass, and mangrove habitats form a heterogeneous mosaic, often linked by species that use reefs as structure during the day and make foraging migrations into soft-bottom habitat at night. Artificial reefs are used to model natural patch reefs, however may not function equivalently as fish habitat. To study the relative value of natural and artificial patch reefs as fish habitat, these communities in the Sea of Abaco, Bahamas were compared using roving diver surveys and time-lapse photography. Diel turnover in fish abundance, recorded with time-lapse photography and illuminated by infrared light, was quantified across midday, dusk, and night periods to explore possible effects of reef type (artificial vs. natural) on these patterns. Diurnal communities on natural reefs exhibited greater fish abundance, species richness, and functional diversity compared to artificial reefs. Furthermore, both types of reef communities exhibited a significant shift across the diel period, characterized by a decline in total fish density at night, especially for grunts (Haemulidae). Cross-habitat foraging migrations by diurnal or nocturnal species, such as haemulids, are likely central drivers of this twilight turnover and can represent important energy and nutrient subsidies. Time-lapse surveys provided more consistent measures of reef fish assemblages for the smaller artificial reef habitats, yet underestimated abundance of certain taxa and species richness on larger patch habitats when compared to the roving diver surveys. Time-lapse photography complemented with infrared light represent a valuable non-invasive approach to studying behavior of focal species and their fine-scale temporal dynamics in shallow-reef communities.