Projected sequential Gaussian processes: flexible interpolation for large data sets

Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential framework for inference in such projected processes is presented, where the observations are considered one at a time. We introduce a C++ library for carrying out such projected, sequential estimation which adds several novel features. In particular we have incorporated the ability to use a generic observation operator, or sensor model, to permit data fusion. We can also cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the variogram parameters is based on maximum likelihood estimation. We illustrate the projected sequential method in application to synthetic and real data sets. We discuss the software implementation and suggest possible future extensions.

Cathodic protection of reinforced concrete:anodic processes in cements and related electrolytes

The nature and kinetics of electrode reactions and processes occurring for four lightweight anode systems which have been utilised in reinforced concrete cathodic protection systems have been studied. The anodes investigated were flame sprayed zinc, conductive paint and two activated titanium meshes. The electrochemical properties of each material were investigated in rapidly stirred de-oxygenated electrolytes using anodic potentiodynamic polarisation. Conductive coating electrodes were formed on glass microscope slides, whilst mesh strands were immersed directly. Oxygen evolution occurred preferentially for both mesh anodes in saturated Ca (OH)2/CaC12 solutions but was severely inhibited in less alkaline solutions and significant current only passed in chloride solutions. The main reactions for conductive paint was based on oxygen evolution in all electrolytes, although chlorides increased the electrical activity. Self-corrosion of zinc was controlled by electrolyte composition and the experimental set-up, chlorides increasing the electrical activity. Impressed current cathodic protection was applied to 25 externally exposed concrete slabs over a period of 18 months to investigate anode degradation mechanisms at normal and high current densities. Specimen chloride content, curing and reinforcement depth were also variables. Several destructive and non-destructive methods for assessing the performance of anodes were evaluated including a site instrument for quantitative "instant-off- potential measurements. The impact of cathodic protection on the concrete substrate was determined for a number of specimens using appropriate methods. Anodic degradation rates were primarily influenced by current density, followed by cemendtious alkalinity, chloride levels and by current distribution. Degradation of cementitious overlays and conductive paint substrates proceeded by sequential neutralisation of cement phases, with some evidence of paint binder oxidation. Sprayed zinc progressively formed an insulating layer of hydroxide complexes, which underwent pitting_ attack in the presence of sufficient chlorides, whilst substrate degradation was minimal. Adhesion of all anode systems decreased with increasing current density. The influence of anode material on the ionic gradients which can develop during cathodic protection was investigated. A constant current was passed through saturated cement paste prisms containing calcium chloride to central cathodes via anodes applied or embedded at each end. Pore solution was obtained from successive cut paste slices for anion and cation analyses. Various experimental errors reduced the value of the results. Characteristic S-shaped profiles were not observed and chloride ion profiles were ambiguous. Mesh anode specimens were significantly more durable than the conductive coatings in the high humidity environment. Limited results suggested zinc ion migration to the cathode region. Electrical data from each investigation clearly indicated a decreasing order of anode efficiency by specific anode material.

Modeling high-speed network traffic with truncated α-stable processes

It has been reported that high-speed communication network traffic exhibits both long-range dependence (LRD) and burstiness, which posed new challenges in network engineering. While many models have been studied in capturing the traffic LRD, they are not capable of capturing efficiently the traffic impulsiveness. It is desirable to develop a model that can capture both LRD and burstiness. In this letter, we propose a truncated a-stable LRD process model for this purpose, which can characterize both LRD and burstiness accurately. A procedure is developed further to estimate the model parameters from real traffic. Simulations demonstrate that our proposed model has a higher accuracy compared to existing models and is flexible in capturing the characteristics of high-speed network traffic. © 2012 Springer-Verlag GmbH.

Wind power forecasts using Gaussian processes and numerical weather prediction

Since wind at the earth's surface has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safe and economic use of wind energy. In this paper, we investigated a combination of numeric and probabilistic models: a Gaussian process (GP) combined with a numerical weather prediction (NWP) model was applied to wind-power forecasting up to one day ahead. First, the wind-speed data from NWP was corrected by a GP, then, as there is always a defined limit on power generated in a wind turbine due to the turbine controlling strategy, wind power forecasts were realized by modeling the relationship between the corrected wind speed and power output using a censored GP. To validate the proposed approach, three real-world datasets were used for model training and testing. The empirical results were compared with several classical wind forecast models, and based on the mean absolute error (MAE), the proposed model provides around 9% to 14% improvement in forecasting accuracy compared to an artificial neural network (ANN) model, and nearly 17% improvement on a third dataset which is from a newly-built wind farm for which there is a limited amount of training data. © 2013 IEEE.

Mathematical Modeling for Studying Microbial Processes – Some Examples

Mathematical modeling may have different purposes in chemical and biochemical engineering sciences. One of them is to confirm or to reject kinetic models for certain processes, or to evaluate the importance of some transport phenomena on the net chemical or biochemical reaction rate. In the present paper different microbial processes are considered and modeled for evaluation of kinetic constants for batch and continuous processes accomplished by free and immobilized microbial cells. The practical examples are from the field of wastewater treatment and biosynthesis of products, like enzymes, lactic acid, gluconic acid, etc. By the aid of mathematical modeling the kinetics and the type of inhibition are specified for microbial wastewater denitrification and biodegradation of halogenated hydrocarbons. The importance of free and immobilized cells and their separate contribution to the overall microbial process is also evaluated for some fermentation processes: gluconic acid production, dichloroethane biodegradation, lactic acid fermentation and monochloroacetic acid biodegradation.

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.

Modeling Data for Complications in Diabetics Using Logistic Regression

2010 Mathematics Subject Classification: 62P10.

Three-dimensional brain fiber tracking modeling in diffusion tensor imaging

This dissertation establishes the foundation for a new 3-D visual interface integrating Magnetic Resonance Imaging (MRI) to Diffusion Tensor Imaging (DTI). The need for such an interface is critical for understanding brain dynamics, and for providing more accurate diagnosis of key brain dysfunctions in terms of neuronal connectivity. ^ This work involved two research fronts: (1) the development of new image processing and visualization techniques in order to accurately establish relational positioning of neuronal fiber tracts and key landmarks in 3-D brain atlases, and (2) the obligation to address the computational requirements such that the processing time is within the practical bounds of clinical settings. The system was evaluated using data from thirty patients and volunteers with the Brain Institute at Miami Children's Hospital. ^ Innovative visualization mechanisms allow for the first time white matter fiber tracts to be displayed alongside key anatomical structures within accurately registered 3-D semi-transparent images of the brain. ^ The segmentation algorithm is based on the calculation of mathematically-tuned thresholds and region-detection modules. The uniqueness of the algorithm is in its ability to perform fast and accurate segmentation of the ventricles. In contrast to the manual selection of the ventricles, which averaged over 12 minutes, the segmentation algorithm averaged less than 10 seconds in its execution. ^ The registration algorithm established searches and compares MR with DT images of the same subject, where derived correlation measures quantify the resulting accuracy. Overall, the images were 27% more correlated after registration, while an average of 1.5 seconds is all it took to execute the processes of registration, interpolation, and re-slicing of the images all at the same time and in all the given dimensions. ^ This interface was fully embedded into a fiber-tracking software system in order to establish an optimal research environment. This highly integrated 3-D visualization system reached a practical level that makes it ready for clinical deployment. ^

Computational modeling of intermediate temperature proton exchange membrane (PEM) fuel cells

A two-phase three-dimensional computational model of an intermediate temperature (120--190°C) proton exchange membrane (PEM) fuel cell is presented. This represents the first attempt to model PEM fuel cells employing intermediate temperature membranes, in this case, phosphoric acid doped polybenzimidazole (PBI). To date, mathematical modeling of PEM fuel cells has been restricted to low temperature operation, especially to those employing Nafion ® membranes; while research on PBI as an intermediate temperature membrane has been solely at the experimental level. This work is an advancement in the state of the art of both these fields of research. With a growing trend toward higher temperature operation of PEM fuel cells, mathematical modeling of such systems is necessary to help hasten the development of the technology and highlight areas where research should be focused.^ This mathematical model accounted for all the major transport and polarization processes occurring inside the fuel cell, including the two phase phenomenon of gas dissolution in the polymer electrolyte. Results were presented for polarization performance, flux distributions, concentration variations in both the gaseous and aqueous phases, and temperature variations for various heat management strategies. The model predictions matched well with published experimental data, and were self-consistent.^ The major finding of this research was that, due to the transport limitations imposed by the use of phosphoric acid as a doping agent, namely low solubility and diffusivity of dissolved gases and anion adsorption onto catalyst sites, the catalyst utilization is very low (∼1--2%). Significant cost savings were predicted with the use of advanced catalyst deposition techniques that would greatly reduce the eventual thickness of the catalyst layer, and subsequently improve catalyst utilization. The model also predicted that an increase in power output in the order of 50% is expected if alternative doping agents to phosphoric acid can be found, which afford better transport properties of dissolved gases, reduced anion adsorption onto catalyst sites, and which maintain stability and conductive properties at elevated temperatures.^

Quantifying the effects of temperature and concentration on variable-density flow in numerical modeling of groundwater systems: Implications for predictive uncertainty and data collection

Groundwater systems of different densities are often mathematically modeled to understand and predict environmental behavior such as seawater intrusion or submarine groundwater discharge. Additional data collection may be justified if it will cost-effectively aid in reducing the uncertainty of a model's prediction. The collection of salinity, as well as, temperature data could aid in reducing predictive uncertainty in a variable-density model. However, before numerical models can be created, rigorous testing of the modeling code needs to be completed. This research documents the benchmark testing of a new modeling code, SEAWAT Version 4. The benchmark problems include various combinations of density-dependent flow resulting from variations in concentration and temperature. The verified code, SEAWAT, was then applied to two different hydrological analyses to explore the capacity of a variable-density model to guide data collection. ^ The first analysis tested a linear method to guide data collection by quantifying the contribution of different data types and locations toward reducing predictive uncertainty in a nonlinear variable-density flow and transport model. The relative contributions of temperature and concentration measurements, at different locations within a simulated carbonate platform, for predicting movement of the saltwater interface were assessed. Results from the method showed that concentration data had greater worth than temperature data in reducing predictive uncertainty in this case. Results also indicated that a linear method could be used to quantify data worth in a nonlinear model. ^ The second hydrological analysis utilized a model to identify the transient response of the salinity, temperature, age, and amount of submarine groundwater discharge to changes in tidal ocean stage, seasonal temperature variations, and different types of geology. The model was compared to multiple kinds of data to (1) calibrate and verify the model, and (2) explore the potential for the model to be used to guide the collection of data using techniques such as electromagnetic resistivity, thermal imagery, and seepage meters. Results indicated that the model can be used to give insight to submarine groundwater discharge and be used to guide data collection. ^

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Tool cutting force modeling and wear estimation of micro -end-milling operations

The applications of micro-end-milling operations have increased recently. A Micro-End-Milling Operation Guide and Research Tool (MOGART) package has been developed for the study and monitoring of micro-end-milling operations. It includes an analytical cutting force model, neural network based data mapping and forecasting processes, and genetic algorithms based optimization routines. MOGART uses neural networks to estimate tool machinability and forecast tool wear from the experimental cutting force data, and genetic algorithms with the analytical model to monitor tool wear, breakage, run-out, cutting conditions from the cutting force profiles. ^ The performance of MOGART has been tested on the experimental data of over 800 experimental cases and very good agreement has been observed between the theoretical and experimental results. The MOGART package has been applied to the micro-end-milling operation study of Engineering Prototype Center of Radio Technology Division of Motorola Inc. ^

Comparing novice designer performance using a rule -based approach versus a pattern -based approach in conceptual data modeling tasks

Conceptual database design is an unusually difficult and error-prone task for novice designers. This study examined how two training approaches---rule-based and pattern-based---might improve performance on database design tasks. A rule-based approach prescribes a sequence of rules for modeling conceptual constructs, and the action to be taken at various stages while developing a conceptual model. A pattern-based approach presents data modeling structures that occur frequently in practice, and prescribes guidelines on how to recognize and use these structures. This study describes the conceptual framework, experimental design, and results of a laboratory experiment that employed novice designers to compare the effectiveness of the two training approaches (between-subjects) at three levels of task complexity (within subjects). Results indicate an interaction effect between treatment and task complexity. The rule-based approach was significantly better in the low-complexity and the high-complexity cases; there was no statistical difference in the medium-complexity case. Designer performance fell significantly as complexity increased. Overall, though the rule-based approach was not significantly superior to the pattern-based approach in all instances, it out-performed the pattern-based approach at two out of three complexity levels. The primary contributions of the study are (1) the operationalization of the complexity construct to a degree not addressed in previous studies; (2) the development of a pattern-based instructional approach to database design; and (3) the finding that the effectiveness of a particular training approach may depend on the complexity of the task.

Advanced methodologies in dynamic traffic assignment modeling of managed lanes

Managed lane strategies are innovative road operation schemes for addressing congestion problems. These strategies operate a lane (lanes) adjacent to a freeway that provides congestion-free trips to eligible users, such as transit or toll-payers. To ensure the successful implementation of managed lanes, the demand on these lanes need to be accurately estimated. Among different approaches for predicting this demand, the four-step demand forecasting process is most common. Managed lane demand is usually estimated at the assignment step. Therefore, the key to reliably estimating the demand is the utilization of effective assignment modeling processes. ^ Managed lanes are particularly effective when the road is functioning at near-capacity. Therefore, capturing variations in demand and network attributes and performance is crucial for their modeling, monitoring and operation. As a result, traditional modeling approaches, such as those used in static traffic assignment of demand forecasting models, fail to correctly predict the managed lane demand and the associated system performance. The present study demonstrates the power of the more advanced modeling approach of dynamic traffic assignment (DTA), as well as the shortcomings of conventional approaches, when used to model managed lanes in congested environments. In addition, the study develops processes to support an effective utilization of DTA to model managed lane operations. ^ Static and dynamic traffic assignments consist of demand, network, and route choice model components that need to be calibrated. These components interact with each other, and an iterative method for calibrating them is needed. In this study, an effective standalone framework that combines static demand estimation and dynamic traffic assignment has been developed to replicate real-world traffic conditions. ^ With advances in traffic surveillance technologies collecting, archiving, and analyzing traffic data is becoming more accessible and affordable. The present study shows how data from multiple sources can be integrated, validated, and best used in different stages of modeling and calibration of managed lanes. Extensive and careful processing of demand, traffic, and toll data, as well as proper definition of performance measures, result in a calibrated and stable model, which closely replicates real-world congestion patterns, and can reasonably respond to perturbations in network and demand properties.^

Intracellular Signaling and Trafficking in Cancer: Role of Rab5-GTPase in Migration and Invasion of Breast Cells

Metastasis is characterized pathologically by uncontrolled cell invasion, proliferation, migration and angiogenesis. Steroid hormones, such as estrogen, and growth factors, which include insulin growth factor I/II (IGF-1/IGF-2) therapy has been associated with most if not all of the features of metastasis. It has been determined that IGF-1 increases cell survival of cancer cells and potentiate the effect of E2 and other ligand growth factors on breast cancer cells. However not much information is available that comprehensively expounds on the roles of insulin growth factor receptor (IGFR) and Rab GTPases may play in breast cancer. The latter, Rab GTPases, are small signaling molecules and critical in the regulation of many cellular processes including cell migration, growth via the endocytic pathway. This research involves the role of Rab GTPases, specifically Rab5 and its guanine exchange factors (GEFs), in the promotion of cancer cell migration and invasion. Two important questions abound: Are IGFR stimulation and downstream effect involved the endocytic pathway in carcinogenesis? What role does Rab5 play in cell migration and invasion of cancer cells? The hypothesis is that growth factor signaling is dependent on Rab5 activity in mediating the aggressiveness of cancer cells. The goal is to demonstrate that IGF-1 signaling is dependent on Rab5 function in breast cancer progression. Here, the results thus far, have shown that while activation of Rab5 may mediate increased cell proliferation, migration and invasion in breast cancer cells, the Rab5 GEF, RIN1 interacts with the IGFR thereby facilitating migration and invasion activities in breast cells. Furthermore, endocytosis of the IGFR in breast cancer cells seems to be caveolin dependent as the data has shown. This taken together, the data shows that IGF-1 signaling in breast cancer cells relies on IGF-1R phosphorylation, caveolae internalization and sequestration to the early endosome RIN1 function and Rab5 activation.