Differential GPS as a monitoring tool on Volcano Santa Ana (Illamatepec) and the Coatepeque Caldera, El Salvador

We used differential GPS measurements from a 13 station GPS network spanning the Santa Ana Volcano and Coatepeque Caldera to characterize the inter-eruptive activity and tectonic movements near these two active and potentially hazardous features. Caldera-forming events occurred from 70-40 ka and at Santa Ana/Izalco volcanoes eruptive activity occurred as recently as 2005. Twelve differential stations were surveyed for 1 to 2 hours on a monthly basis from February through September 2009 and tied to a centrally located continuous GPS station, which serves as the reference site for this volcanic network. Repeatabilities of the averages from 20-minute sessions taken over 20 hours or longer range from 2-11 mm in the horizontal (north and east) components of the inter-station baselines, suggesting a lower detection limit for the horizontal components of any short-term tectonic or volcanic deformation. Repeatabilities of the vertical baseline component range from 12-34 mm. Analysis of the precipitable water vapor in the troposphere suggests that tropospheric decorrelation as a function of baseline lengths and variable site elevations are the most likely sources of vertical error. Differential motions of the 12 sites relative to the continuous reference site reveal inflation from February through July at several sites surrounding the caldera with vertical displacements that range from 61 mm to 139 mm followed by a lower magnitude deflation event on 1.8-7.4 km-long baselines. Uplift rates for the inflationary period reach 300 mm/yr with 1σ uncertainties of +/- 26 – 119 mm. Only one other station outside the caldera exhibits a similar deformation trend, suggesting a localized source. The results suggest that the use of differential GPS measurements from short duration occupations over short baselines can be a useful monitoring tool at sub-tropical volcanoes and calderas.

Geophysical and geological analysis of the Collingwood Member of the Trenton Formation

The Collingwood Member is a mid to late Ordovician self-sourced reservoir deposited across the northern Michigan Basin and parts of Ontario, Canada. Although it had been previously studied in Canada, there has been relatively little data available from the Michigan subsurface. Recent commercial interest in the Collingwood has resulted in the drilling and production of several wells in the state of Michigan. An analysis of core samples, measured laboratory data, and petrophysical logs has yielded both a quantitative and qualitative understanding of the formation in the Michigan Basin. The Collingwood is a low permeability and low porosity carbonate package that is very high in organic content. It is composed primarily of a uniformly fine grained carbonate matrix with lesser amounts of kerogen, silica, and clays. The kerogen content of the Collingwood is finely dispersed in the clay and carbonate mineral phases. Geochemical and production data show that both oil and gas phases are present based on regional thermal maturity. The deposit is richest in the north-central part of the basin with thickest deposition and highest organic content. The Collingwood is a fairly thin deposit and vertical fractures may very easily extend into the surrounding formations. Completion and treatment techniques should be designed around these parameters to enhance production.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Slope stability analysis of the Pacaya Volcano, Guatemala, using limit equilibrium and finite element method

The Pacaya volcanic complex is part of the Central American volcanic arc, which is associated with the subduction of the Cocos tectonic plate under the Caribbean plate. Located 30 km south of Guatemala City, Pacaya is situated on the southern rim of the Amatitlan Caldera. It is the largest post-caldera volcano, and has been one of Central America’s most active volcanoes over the last 500 years. Between 400 and 2000 years B.P, the Pacaya volcano had experienced a huge collapse, which resulted in the formation of horseshoe-shaped scarp that is still visible. In the recent years, several smaller collapses have been associated with the activity of the volcano (in 1961 and 2010) affecting its northwestern flanks, which are likely to be induced by the local and regional stress changes. The similar orientation of dry and volcanic fissures and the distribution of new vents would likely explain the reactivation of the pre-existing stress configuration responsible for the old-collapse. This paper presents the first stability analysis of the Pacaya volcanic flank. The inputs for the geological and geotechnical models were defined based on the stratigraphical, lithological, structural data, and material properties obtained from field survey and lab tests. According to the mechanical characteristics, three lithotechnical units were defined: Lava, Lava-Breccia and Breccia-Lava. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, and strength and deformation characteristics were computed in a specified stress range. Further, the stability of the volcano was evaluated by two-dimensional analysis performed by Limit Equilibrium (LEM, ROCSCIENCE) and Finite Element Method (FEM, PHASE 2 7.0). The stability analysis mainly focused on the modern Pacaya volcano built inside the collapse amphitheatre of “Old Pacaya”. The volcanic instability was assessed based on the variability of safety factor using deterministic, sensitivity, and probabilistic analysis considering the gravitational instability and the effects of external forces such as magma pressure and seismicity as potential triggering mechanisms of lateral collapse. The preliminary results from the analysis provide two insights: first, the least stable sector is on the south-western flank of the volcano; second, the lowest safety factor value suggests that the edifice is stable under gravity alone, and the external triggering mechanism can represent a likely destabilizing factor.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

Genetic association studies under the population stratification, family pedigree and application to genome-wide association studies

This dissertation has three separate parts: the first part deals with the general pedigree association testing incorporating continuous covariates; the second part deals with the association tests under population stratification using the conditional likelihood tests; the third part deals with the genome-wide association studies based on the real rheumatoid arthritis (RA) disease data sets from Genetic Analysis Workshop 16 (GAW16) problem 1. Many statistical tests are developed to test the linkage and association using either case-control status or phenotype covariates for family data structure, separately. Those univariate analyses might not use all the information coming from the family members in practical studies. On the other hand, the human complex disease do not have a clear inheritance pattern, there might exist the gene interactions or act independently. In part I, the new proposed approach MPDT is focused on how to use both the case control information as well as the phenotype covariates. This approach can be applied to detect multiple marker effects. Based on the two existing popular statistics in family studies for case-control and quantitative traits respectively, the new approach could be used in the simple family structure data set as well as general pedigree structure. The combined statistics are calculated using the two statistics; A permutation procedure is applied for assessing the p-value with adjustment from the Bonferroni for the multiple markers. We use simulation studies to evaluate the type I error rates and the powers of the proposed approach. Our results show that the combined test using both case-control information and phenotype covariates not only has the correct type I error rates but also is more powerful than the other existing methods. For multiple marker interactions, our proposed method is also very powerful. Selective genotyping is an economical strategy in detecting and mapping quantitative trait loci in the genetic dissection of complex disease. When the samples arise from different ethnic groups or an admixture population, all the existing selective genotyping methods may result in spurious association due to different ancestry distributions. The problem can be more serious when the sample size is large, a general requirement to obtain sufficient power to detect modest genetic effects for most complex traits. In part II, I describe a useful strategy in selective genotyping while population stratification is present. Our procedure used a principal component based approach to eliminate any effect of population stratification. The paper evaluates the performance of our procedure using both simulated data from an early study data sets and also the HapMap data sets in a variety of population admixture models generated from empirical data. There are one binary trait and two continuous traits in the rheumatoid arthritis dataset of Problem 1 in the Genetic Analysis Workshop 16 (GAW16): RA status, AntiCCP and IgM. To allow multiple traits, we suggest a set of SNP-level F statistics by the concept of multiple-correlation to measure the genetic association between multiple trait values and SNP-specific genotypic scores and obtain their null distributions. Hereby, we perform 6 genome-wide association analyses using the novel one- and two-stage approaches which are based on single, double and triple traits. Incorporating all these 6 analyses, we successfully validate the SNPs which have been identified to be responsible for rheumatoid arthritis in the literature and detect more disease susceptibility SNPs for follow-up studies in the future. Except for chromosome 13 and 18, each of the others is found to harbour susceptible genetic regions for rheumatoid arthritis or related diseases, i.e., lupus erythematosus. This topic is discussed in part III.

Development of record-breaking statistics for climatological time-series analysis

The number of record-breaking events expected to occur in a strictly stationary time-series depends only on the number of values in the time-series, regardless of distribution. This holds whether the events are record-breaking highs or lows and whether we count from past to present or present to past. However, these symmetries are broken in distinct ways by trends in the mean and variance. We define indices that capture this information and use them to detect weak trends from multiple time-series. Here, we use these methods to answer the following questions: (1) Is there a variability trend among globally distributed surface temperature time-series? We find a significant decreasing variability over the past century for the Global Historical Climatology Network (GHCN). This corresponds to about a 10% change in the standard deviation of inter-annual monthly mean temperature distributions. (2) How are record-breaking high and low surface temperatures in the United States affected by time period? We investigate the United States Historical Climatology Network (USHCN) and find that the ratio of record-breaking highs to lows in 2006 increases as the time-series extend further into the past. When we consider the ratio as it evolves with respect to a fixed start year, we find it is strongly correlated with the ensemble mean. We also compare the ratios for USHCN and GHCN (minus USHCN stations). We find the ratios grow monotonically in the GHCN data set, but not in the USHCN data set. (3) Do we detect either mean or variance trends in annual precipitation within the United States? We find that the total annual and monthly precipitation in the United States (USHCN) has increased over the past century. Evidence for a trend in variance is inconclusive.

Analysis of in-cylinder pressure transducer data quality utilizing a SIDI turbocharged engine

In-cylinder pressure transducers have been used for decades to record combustion pressure inside a running engine. However, due to the extreme operating environment, transducer design and installation must be considered in order to minimize measurement error. One such error is caused by thermal shock, where the pressure transducer experiences a high heat flux that can distort the pressure transducer diaphragm and also change the crystal sensitivity. This research focused on investigating the effects of thermal shock on in-cylinder pressure transducer data quality using a 2.0L, four-cylinder, spark-ignited, direct-injected, turbo-charged GM engine. Cylinder four was modified with five ports to accommodate pressure transducers of different manufacturers. They included an AVL GH14D, an AVL GH15D, a Kistler 6125C, and a Kistler 6054AR. The GH14D, GH15D, and 6054AR were M5 size transducers. The 6125C was a larger, 6.2mm transducer. Note that both of the AVL pressure transducers utilized a PH03 flame arrestor. Sweeps of ignition timing (spark sweep), engine speed, and engine load were performed to study the effects of thermal shock on each pressure transducer. The project consisted of two distinct phases which included experimental engine testing as well as simulation using a commercially available software package. A comparison was performed to characterize the quality of the data between the actual cylinder pressure and the simulated results. This comparison was valuable because the simulation results did not include thermal shock effects. All three sets of tests showed the peak cylinder pressure was basically unaffected by thermal shock. Comparison of the experimental data with the simulated results showed very good correlation. The spark sweep was performed at 1300 RPM and 3.3 bar NMEP and showed that the differences between the simulated results (no thermal shock) and the experimental data for the indicated mean effective pressure (IMEP) and the pumping mean effective pressure (PMEP) were significantly less than the published accuracies. All transducers had an IMEP percent difference less than 0.038% and less than 0.32% for PMEP. Kistler and AVL publish that the accuracy of their pressure transducers are within plus or minus 1% for the IMEP (AVL 2011; Kistler 2011). In addition, the difference in average exhaust absolute pressure between the simulated results and experimental data was the greatest for the two Kistler pressure transducers. The location and lack of flame arrestor are believed to be the cause of the increased error. For the engine speed sweep, the torque output was held constant at 203 Nm (150 ft-lbf) from 1500 to 4000 RPM. The difference in IMEP was less than 0.01% and the PMEP was less than 1%, except for the AVL GH14D which was 5% and the AVL GH15DK which was 2.25%. A noticeable error in PMEP appeared as the load increased during the engine speed sweeps, as expected. The load sweep was conducted at 2000 RPM over a range of NMEP from 1.1 to 14 bar. The difference in IMEP values were less 0.08% while the PMEP values were below 1% except for the AVL GH14D which was 1.8% and the AVL GH15DK which was at 1.25%. In-cylinder pressure transducer data quality was effectively analyzed using a combination of experimental data and simulation results. Several criteria can be used to investigate the impact of thermal shock on data quality as well as determine the best location and thermal protection for various transducers.

Systemic analysis of microarray data sets towards identifying genes regulating root development

Nitrogen and water are essential for plant growth and development. In this study, we designed experiments to produce gene expression data of poplar roots under nitrogen starvation and water deprivation conditions. We found low concentration of nitrogen led first to increased root elongation followed by lateral root proliferation and eventually increased root biomass. To identify genes regulating root growth and development under nitrogen starvation and water deprivation, we designed a series of data analysis procedures, through which, we have successfully identified biologically important genes. Differentially Expressed Genes (DEGs) analysis identified the genes that are differentially expressed under nitrogen starvation or drought. Protein domain enrichment analysis identified enriched themes (in same domains) that are highly interactive during the treatment. Gene Ontology (GO) enrichment analysis allowed us to identify biological process changed during nitrogen starvation. Based on the above analyses, we examined the local Gene Regulatory Network (GRN) and identified a number of transcription factors. After testing, one of them is a high hierarchically ranked transcription factor that affects root growth under nitrogen starvation. It is very tedious and time-consuming to analyze gene expression data. To avoid doing analysis manually, we attempt to automate a computational pipeline that now can be used for identification of DEGs and protein domain analysis in a single run. It is implemented in scripts of Perl and R.

HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.