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. ^

The non-linear acousto-mechanical and thermodynamic response of spherical absorbers to laser pulses of various temporal profiles

This study is to theoretically investigate shockwave and microbubble formation due to laser absorption by microparticles and nanoparticles. The initial motivation for this research was to understand the underlying physical mechanisms responsible for laser damage to the retina, as well as the predict threshold levels for damage for laser pulses with of progressively shorter durations. The strongest absorbers in the retina are micron size melanosomes, and their absorption of laser light causes them to accrue very high energy density. I theoretically investigate how this absorbed energy is transferred to the surrounding medium. For a wide range of conditions I calculate shockwave generation and bubble growth as a function of the three parameters; fluence, pulse duration and pulse shape. In order to develop a rigorous physical treatment, the governing equations for the behavior of an absorber and for the surrounding medium are derived. Shockwave theory is investigated and the conclusion is that a shock pressure explanation is likely to be the underlying physical cause of retinal damage at threshold fluences for sub-nanosecond pulses. The same effects are also expected for non-biological micro and nano absorbers. ^

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

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. ^

Mitigating inconsistencies by coupling data cleaning, filtering, and contextual data validation in wireless sensor networks

With the advent of peer to peer networks, and more importantly sensor networks, the desire to extract useful information from continuous and unbounded streams of data has become more prominent. For example, in tele-health applications, sensor based data streaming systems are used to continuously and accurately monitor Alzheimer's patients and their surrounding environment. Typically, the requirements of such applications necessitate the cleaning and filtering of continuous, corrupted and incomplete data streams gathered wirelessly in dynamically varying conditions. Yet, existing data stream cleaning and filtering schemes are incapable of capturing the dynamics of the environment while simultaneously suppressing the losses and corruption introduced by uncertain environmental, hardware, and network conditions. Consequently, existing data cleaning and filtering paradigms are being challenged. This dissertation develops novel schemes for cleaning data streams received from a wireless sensor network operating under non-linear and dynamically varying conditions. The study establishes a paradigm for validating spatio-temporal associations among data sources to enhance data cleaning. To simplify the complexity of the validation process, the developed solution maps the requirements of the application on a geometrical space and identifies the potential sensor nodes of interest. Additionally, this dissertation models a wireless sensor network data reduction system by ascertaining that segregating data adaptation and prediction processes will augment the data reduction rates. The schemes presented in this study are evaluated using simulation and information theory concepts. The results demonstrate that dynamic conditions of the environment are better managed when validation is used for data cleaning. They also show that when a fast convergent adaptation process is deployed, data reduction rates are significantly improved. Targeted applications of the developed methodology include machine health monitoring, tele-health, environment and habitat monitoring, intermodal transportation and homeland security.

Disturbance regime and limits on benefits of refuge use for fishes in a fluctuating hydroscape

Refuge habitats increase survival rate and recovery time of populations experiencing environmental disturbance, but limits on the ability of refuges to buffer communities are poorly understood. We hypothesized that importance of refuges in preventing population declines and alteration in community structure has a non-linear relationship with severity of disturbance. In the Florida Everglades, alligator ponds are used as refuge habitat by fishes during seasonal drying of marsh habitats. Using an 11-year record of hydrological conditions and fish abundance in 10 marshes and 34 alligator ponds from two regions of the Everglades, we sought to characterize patterns of refuge use and temporal dynamics of fish abundance and community structure across changing intensity, duration, and frequency of drought disturbance. Abundance in alligator ponds was positively related to refuge size, distance from alternative refugia (e.g. canals), and abundance in surrounding marsh prior to hydrologic disturbance. Variables negatively related to abundance in alligator ponds included water level in surrounding marsh and abundance of disturbance-tolerant species. Refuge community structure did not differ between regions because the same subset of species in both regions used alligator ponds during droughts. When time between disturbances was short, fish abundance declined in marshes, and in the region with the most spatially extensive pattern of disturbance, community structure was altered in both marshes and alligator ponds because of an increased proportion of species more resistant to disturbance. These changes in community structure were associated with increases in both duration and frequency of hydrologic disturbance. Use of refuge habitat had a modal relationship with severity of disturbance regime. Spatial patterns of response suggest that decline in refuge use was because of decreased effectiveness of refuge habitat in reducing mortality and providing sufficient time for recovery for fish communities experiencing reduced time between disturbance events.

Mitigating Inconsistencies by Coupling Data Cleaning, Filtering, and Contextual Data Validation in Wireless Sensor Networks

With the advent of peer to peer networks, and more importantly sensor networks, the desire to extract useful information from continuous and unbounded streams of data has become more prominent. For example, in tele-health applications, sensor based data streaming systems are used to continuously and accurately monitor Alzheimer's patients and their surrounding environment. Typically, the requirements of such applications necessitate the cleaning and filtering of continuous, corrupted and incomplete data streams gathered wirelessly in dynamically varying conditions. Yet, existing data stream cleaning and filtering schemes are incapable of capturing the dynamics of the environment while simultaneously suppressing the losses and corruption introduced by uncertain environmental, hardware, and network conditions. Consequently, existing data cleaning and filtering paradigms are being challenged. This dissertation develops novel schemes for cleaning data streams received from a wireless sensor network operating under non-linear and dynamically varying conditions. The study establishes a paradigm for validating spatio-temporal associations among data sources to enhance data cleaning. To simplify the complexity of the validation process, the developed solution maps the requirements of the application on a geometrical space and identifies the potential sensor nodes of interest. Additionally, this dissertation models a wireless sensor network data reduction system by ascertaining that segregating data adaptation and prediction processes will augment the data reduction rates. The schemes presented in this study are evaluated using simulation and information theory concepts. The results demonstrate that dynamic conditions of the environment are better managed when validation is used for data cleaning. They also show that when a fast convergent adaptation process is deployed, data reduction rates are significantly improved. Targeted applications of the developed methodology include machine health monitoring, tele-health, environment and habitat monitoring, intermodal transportation and homeland security.